Erlangung des Doktorgrades Dr.-Ing. Der Technischen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg. zur.

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1 Dynamic Interventional Perfusion Imaging: Reconstruction Algorithms and Clinical Evaluation Dynamische interventionelle Perfusionsbildgebung: Rekonstruktionsalgorithmen und klinische Evaluation Der Technischen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg zur Erlangung des Doktorgrades Dr.-Ing. vorgelegt von Michael Manhart aus Ingolstadt, Deutschland

2 Als Dissertation genehmigt von der Technischen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg Tag der mündlichen Prüfung: Vorsitzende des Promotionsorgans: Prof. Dr.-Ing. habil. M. Merklein Gutachter: Prof. Dr.-Ing. J. Hornegger Prof. Dr. G. Rose

3 Abstract Acute ischemic stroke is a major cause for death and disabilities with increasing prevalence in aging societies. Novel interventional stroke treatment procedures have the potential to improve the clinical outcome of certain stroke-affected patients. Certainly, prompt diagnosis and treatment are required. Brain perfusion imaging with computed tomography (CT) or magnetic resonance imaging (MRI) is a routine method for stroke diagnosis. However, in the interventional room usually only CT imaging with flat detector C-arm systems is available, which do not support dynamic perfusion imaging yet. Enabling flat detector CT perfusion (FD-CTP) imaging in clinical practice could support optimized stroke management. By stroke diagnosis in the interventional room precious time until the start of treatment could be saved. Recently, first promising clinical results for FD-CTP imaging under laboratory conditions have been presented. Based on this work, this dissertation introduces and evaluates novel technical contributions for noise reduction, artifact reduction and dynamic reconstruction in FD-CTP. Furthermore, the feasibility of FD-CTP imaging in clinical practice is demonstrated for the first time using data acquired during interventional stroke treatments. CT perfusion imaging requires measurement of dynamic contrast agent attenuation over time. The contrast agent signal in the brain tissue is very low and noise is a major problem. Thus a novel computationally fast noise reduction technique for perfusion data is introduced. Currently available C-arm systems have a comparably low rotation speed, which makes it challenging to reconstruct the dynamic change of contrast agent concentration over time. Therefore, a dynamic iterative reconstruction algorithm is proposed to utilize the high temporal resolution in the projection data for improved reconstruction of the contrast agent dynamics. Novel robotic C-arm systems (Artis zeego, Siemens Healthcare, Germany) provide a high speed rotation protocol (HSP) to improve the temporal acquisition of the contrast agent dynamics. However, the HSP suffers from angular under-sampling, which can lead to severe streak artifacts in the reconstructed perfusion maps. Thus a novel, computationally fast noise and streak artifact reduction approach for FD-CTP data is proposed. The feasibility of FD-CTP using the HSP is demonstrated with clinical data acquired during interventional treatment of two stroke cases. Furthermore, the design of a digital brain perfusion phantom for the thorough numerical evaluation of the proposed techniques is discussed. The quality of the perfusion maps acquired and reconstructed using the introduced novel approaches suggests that FD-CTP could be clinically available in the near future.

4 Kurzfassung Der akute ischämische Schlaganfall ist eine der Hauptursachen für Tod und Invalidität weltweit mit zunehmender Bedeutung in alternden Gesellschaften. Mit interventionellen Behandlungsmethoden ist es potentiell möglich, die gesundheitliche Folgeschäden von Schlaganfällen zu verringern. Dafür ist allerdings eine zeitnahe Diagnose und Behandlung des Schlaganfalls notwendig. Zur Schlaganfallsdiagnose wird als Routineverfahren die Hirnperfusionsbildgebung mit Hilfe der Computertomographie (CT) oder der Magnetresonanztomographie (MRI) verwendet. Üblicherweise ist im interventionellen Behandlungsraum nur CT Bildgebung mit Flachdetektor C-Bogen Systemen möglich, welche bisher die dynamische Perfusionsbildgebung nicht unterstützen. Flachdetektor CT Perfusionsmessung (FD-CTP) könnte zu einem verbesserten Schlaganfallsmanagement beitragen, wenn der Patient direkt im Interventionsraum untersucht und wertvolle Zeit bis zum Beginn der Behandlung gespart werden kann. Unlängst wurden erste vielversprechende klinische Ergebnisse von FD-CTP Messungen unter Laborbedingungen gezeigt. Aufbauend darauf werden in dieser Dissertation neue technische Verfahren zur Rauschreduktion, Artefaktreduktion und zur dynamischen Rekonstruktion für die FD-CTP vorgestellt und evaluiert. Des Weiteren wird zum ersten Mal die Durchführbarkeit von FD-CTP in der klinischen Praxis anhand von während interventioneller Schlaganfallbehandlungen aufgezeichneten Daten demonstriert, Bei der CT Perfusionsbildgebung wird die dynamischer Kontrastmittelschwächung über die Zeit gemessen. Dabei ist das Signal des Kontrastmittels im Hirngewebe sehr gering. Daher wurde eine neue recheneffiziente Rauschreduktionsmethode für Perfusionsdaten entwickelt. Aktuell verfügbare C-Bogen Systeme haben eine relativ langsame Rotationsgeschwindigkeit. Dies macht die Rekonstruktion der zeitlich dynamischen Kontrastmittelkonzentration zur Herausforderung. Für dieses Problem wurde ein dynamischer iterativer Rekonstruktionsalgorithmus entwickelt, der die hohe zeitliche Auflösung in den Projektionsdaten zur verbesserten Rekonstruktion der dynamischen Zeitkurven ausnutzt. Robotische C-Bogen Systeme (Artis zeego, Siemens Healthcare, Deutschland) verfügen über ein Aufnahmeprotokoll mit Hochgeschwindigkeitsrotation (HSP) zur verbesserten zeitlichen Aufnahme der Kontrastdynamik. Allerdings sind die HSP- Aufnahmen in der Winkelschrittweite unterabgetastet, was zu starken Streifenartefakten in den rekonstruierten Perfusionskarten führen kann. Deshalb wird ein neuer recheneffizienter Algorithmus zur Rausch- und Streifenartefaktreduktion in FD-CTP Daten vorgestellt. Die Durchführbarkeit der FD-CTP mit dem HSP in der klinischen Praxis wird anhand von Daten gezeigt, welche während der interventionellen Behandlung von zwei Schlaganfallsfällen aufgezeichnet wurden. Außerdem wird das Design eines digitalen Perfusionsphantoms zur numerischen Evaluierung der vorgestellten Techniken diskutiert. Die Qualität der mit den neuen Techniken rekonstruierten Perfusionskarten zeigt, dass FD-CTP in absehbarer Zeit klinisch verfügbar werden könnte.

5 Acknowledgment Research on such a challenging and interdisciplinary project is not possible without the support and advice from numerous people. Therefore, I want to express my gratitude to everyone who contributed to make this thesis possible. In particular, I would like to thank Prof. Dr.-Ing. Joachim Hornegger for providing the stimulating environment at the Pattern Recognition Lab and supervising my work with valuable feedback and advice. Prof. Dr. Georg Rose for reviewing my thesis and for the fruitful academic exchange with his research team from Magdeburg. Prof. Dr. Arnd Dörfler and PD Dr. Tobias Struffert for providing me essential feedback on the medical background as well as valuable clinical data. Dr.-Ing. Andreas Maier and all members of the medical image reconstruction group during my time at the Pattern Recognition Lab for fruitful discussions and a pleasant working atmosphere. Dipl.-Inf. Yu Deuerling-Zheng, M.Med., Dr.-Ing. Markus Kowarschik and Dr.-Ing. Andreas Fieselmann for many valuable feedback, inspiring teamwork and proofreading of my articles and thesis. Assoc. Prof. Rebecca Fahrig, Ph.D. and everybody at her research lab at Stanford University as well as Prof. Charles Strother, MD and his research team at the University of Wisconsin for providing valuable scientific advice and clinical data. Last but not least, I would like to thank all my family and friends for all the help and support they provided me during the last years. Erlangen, October 25th 2014 Michael Manhart

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7 Contents Chapter 1 Introduction Towards Interventional Brain Perfusion Imaging Clinical Background Acute Ischemic Stroke Diagnosis and Treatment Flat Detector CT Perfusion Flat Detector CT - Technical Background Flat Detector CT Perfusion - Technical Challenges Original Contributions Organization of the Thesis Chapter 2 Basics of Brain Perfusion Analysis and Related Work Brain Perfusion Analysis Introduction to Brain Perfusion Parameters Perfusion Parameter Computation Cerebral Blood Volume Measurement with Flat Detector CT Existing Techniques for Dynamic Flat Detector CT Perfusion Acquisition Protocol Interleaved Scanning Dynamic Iterative Reconstruction using Temporal Basis Functions Dynamic Iterative Reconstruction using a Gamma Variate Model Summary Chapter 3 Numerical Simulation of Flat Detector CT Perfusion Digital Brain Perfusion Phantom Brain Structure and Skull Generation Brain Perfusion Simulation Phantom MATLAB Toolbox Flat Detector CT Perfusion Projection Data Generation Dynamic Forward Projection Quantum Noise and Motion Simulation Quantitative Evaluation of Reconstructed Perfusion Maps Summary Chapter 4 Noise Reduction with Joint Bilateral Filtering Bilateral Filtering and Joint Bilateral Filtering Theoretical Background Computational Complexity and Parallelized Implementation Joint Bilateral Filter i

8 4.2 Joint Bilateral Filtering for Perfusion Imaging Guidance Volume Computation Related Perfusion Noise Reduction Methods Summary Chapter 5 Flat Detector CT Perfusion with Low Speed Acquisition Low Speed Acquisition Introduction Low Speed Acquisition Protocol Mathematical Formulation of Dynamic Iterative Reconstruction Modeling of Time-Contrast Curves Statistical Ray Weighting Landweber Iterations Vessel-Masked Backprojection Basis Functions Regularization by Joint Bilateral Filtering Implementation Details Initialization Dynamic Iterative Reconstruction Projection Pre-processing Complexity Analysis Evaluation Numerical Brain Phantom Study In Vivo Study Discussion and Conclusions Discussion Conclusions Practical Clinical Application Chapter 6 Flat Detector CT Perfusion with High Speed Acquisition High Speed Acquisition Introduction High Speed Acquisition Protocol Analytic Reconstruction with Denoising in Volume Space Feldkamp Reconstruction and Motion Compensation Denoising of Time-Contrast Curves Streak Removal from Guidance Image Complexity Analysis Alternative Methods for Noise and Artifact Reduction Analytic Reconstruction with Post-Processing Regularized Algebraic Reconstruction Evaluation Experimental Setup of Brain Phantom Simulation Study Experimental Setup of Patient Studies Results Brain Phantom Simulation Study Results Clinical Study: Patient Motion ii

9 6.4.5 Results Clinical Study: Pre- and Post-Treatment Acquisition Discussion and Conclusions Discussion Conclusions Chapter 7 Clinical Prototype Requirements and Design Implementation Chapter 8 Summary and Outlook Summary Outlook List of Symbols and Abbreviations 101 List of Figures 105 List of Tables 107 List of Algorithms 109 Bibliography 111 iii

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11 C H A P T E R 1 Introduction 1.1 Towards Interventional Brain Perfusion Imaging Clinical Background Flat Detector CT Perfusion Original Contributions Organization of the Thesis Towards Interventional Brain Perfusion Imaging Stroke is according to the World Health Organization (WHO) the number two cause of death in the world after ischemic heart disease and killed 6.2 million people in 2011, which accounts for 10.6 % of all deaths world wide [The 13]. Furthermore, stroke is the major cause of long-term physical, neurological and social disability of elderly people [Born 09] and thus a significant cost factor for the social insurance system. Therefore improvements in stroke prevention and treatment are an important field of research in the context of an aging society both in clinical and technical disciplines. Imaging of brain perfusion is a standard routine method in the emergency workup of patients suspected to suffer from stroke. It acquires hemodynamic information in the capillary level of the brain and provides information about the extent of the stroke. Thus it is an important technique in supporting the physician on deciding on the treatment. In recent years studies have revealed the potential of interventional stroke treatment procedures to improve the clinical outcome of certain stroke affected patients [Rha 07]. These procedures take place in the interventional room, where perfusion imaging is usually not available. If perfusion imaging in the interventional room would be possible, it could help to save time by directly referring stroke suspected patients to the interventional suite and allow intra-operative monitoring of the brain perfusion. Based on previous work [Fies 12a], this thesis introduces and evaluates novel technical approaches to make interventional perfusion imaging possible. Furthermore, first promising results from clinical patient studies are shown. The clinical background of stroke, the technical background of interventional imaging and the contributions and organization of this thesis are explained in this introductory chapter. 1

12 2 Introduction (a) robotic monoplane system (Artis zeego) (b) biplane system (Artis Q biplane) Figure 1.1: C-arm angiography systems (Siemens Healthcare, Germany) capable of CT-like imaging (images courtesy of Siemens Healthcare). 1.2 Clinical Background Acute Ischemic Stroke A stroke is a medical emergency caused by disturbance of the blood supply to the brain. The cause of the disturbed blood supply can be either an internal bleeding after a blood vessel rupture (hemorrhagic stroke) or the blockage (thrombosis) of a blood vessel (ischemic stroke). The focus of this work is on acute ischemic strokes (AIS), which account for more than 80 % of all strokes [Thri 01]. Due to the lack of blood supply the affected brain area cannot function, which leads to the typical symptoms of stroke. These symptoms include paralysis of the face or limbs on one side of the body, problems with understanding or formulating speech and impaired vision. In a brain of a patient experiencing a typical large vessel acute ischemic stroke, 1.9 million neurons, 14 billion synapses, and 12 km of myelinated fibers are destroyed in each minute [Save 06]. Thus patients showing typical symptoms of stroke urgently require prompt diagnosis and adequate therapy ( Time is brain ) Diagnosis and Treatment Since stroke can be caused by two entirely different incidents (ischemia and hemorrhage), it is essential to diagnose the actual cause before starting any treatment. The first imaging procedure applied to a patient suspect to have a stroke is usually a native cranial computed tomography (CT). The native CT images show hemorrhages, stroke mimics, e.g., tumors, and certain early signs of an ischemic infarct as possible causes for the stroke symptoms [Jans 11]. If hemorrhages and stroke mimics can be excluded as cause of the stroke symptoms, a CT perfusion (CTP) measurement is commonly conducted. CT perfusion allows quantitative measurement of hemodynamic information in the capillary level of the brain such as the cerebral blood flow (CBF) and the cerebral blood volume (CBV). The CTP images of patients affected

13 1.3 Flat Detector CT Perfusion 3 with AIS show brain regions with hypo-perfusion. Regions with reduced CBF and CBV delineate the infarct core, which is irreversibly destroyed. In contrast, regions with reduced CBF but preserved CBV depict hypo-perfused areas with potentially salvageable tissue ( Tissue at Risk ). Such areas are called penumbra. By showing the extend of the infarct core and the penumbra, the CTP images provide important support to the physician to decide on the right treatment [Jans 11]. Since all available stroke therapy procedures are associated with potentially dangerous side effects and complications, the physician has to make a well-balanced decision between possible benefits and risks. The goal of treating AIS is the recanalization of the occluded vessel, such that the blood flow to the hypo-perfused area is recovered and the tissue at risk can be saved. A meta analysis on stroke therapy articles [Rha 07] showed a strong relation of successful vessel recanalization to the final clinical outcome in AIS. If the stroke is diagnosed in a time window of up to 4.5 hours after onset, a common treatment is intravenous (IV) thrombolytic therapy [Hack 08]. A tissue plasminogen activator is injected intravenously to break down thrombolytic blood clots. The meta analysis by Rha and Saver [Rha 07] reported that the recanalization rate with IV thrombolytic therapy was approximately twice the spontaneous rate, but still less than half of all cases. Thus techniques to improve on this modest recanalization rate are desired. In recent years, interventional catheter-guided stroke therapy procedures were introduced to improve the recanalization rate and the treatment outcome. Interventional treatment procedures of AIS are intra-arterial (IA) thrombolytic therapy [Furl 99] and recanalization of occluded arteries using mechanical endovascular retrieval devices [Zaid 08]. For interventional stroke management the patient needs to be transported to an interventional room. The interventional room is equipped with a C-arm angiography system, which is a flexible X-ray imaging modality (Figure 1.1). One application area of C-arm systems is to help the physician to navigate the catheter through the patient s vessels. Recent generations of C-arm systems provide an option to acquire CT-like 3D images of the patient s body. This acquisition technique is called flat detector CT (FD-CT). The FD-CT images can be used for instance to detect hemorrhages in the brain [Stru 09] (Figure 1.3a). However, dynamic perfusion imaging with FD-CT not yet clinically available, since it is challenging due to hardware limitations. If FD-CT could provide equal information like conventional CT regarding the brain parenchyma, the vessel status and perfusion, then patients could be directly referred to the interventional suite saving time of moving the patient from a CT scanner room. Since stroke treatment is time-critical, perfusion imaging with flat detector CT (FD-CTP) has high potential benefit for therapy of AIS. Furthermore, FD-CTP would allow intra-operative monitoring of the brain perfusion and help the physician to assess the success of the treatment. 1.3 Flat Detector CT Perfusion Flat Detector CT - Technical Background Angiography C-arm systems are designed to provide X-ray projection images from flexible directions during interventional procedures. Figure 1.1 shows state-of-the-art

14 4 Introduction (a) C-arm projection image (b) DSA image Figure 1.2: C-arm X-ray projection images: (a) showing a human head and (b) showing a cerebral digital subtraction angiography (images courtesy of the Department of Neuroradiology, Universitätsklinikum Erlangen, Germany). (a) Bleeding (b) Cone beam artifact Figure 1.3: Flat detector CT reconstructions: (a) showing a bleeding in the right hemisphere and (b) a slice with cone beam artifacts (images courtesy of the Department of Neuroradiology, Universitätsklinikum Erlangen, Germany).

15 1.3 Flat Detector CT Perfusion 5 clinical systems. A X-ray tube and a flat panel detector are mounted on a C-shaped arm, which can rotate around the patient and allows to take X-ray images from different angles. An example projection image of a human head is shown in Figure 1.2a. Digital subtraction angiography (DSA) [Zwie 85] is a widely-used application area of C-arm systems, where a pre-contrast mask image is subtracted from later X-ray images with contrast agent filling to clearly visualize the contrast-enhanced blood vessels. Figure 1.2b shows an example DSA image of cerebral vascular structures. In recent years the C-arm systems became capable to provide CT-like soft-tissue images by FD-CT acquisitions [Stro 09]. Figure 1.3a shows an example FD-CT reconstruction of a human brain with a bleeding in the right hemisphere. For FD-CT the C-arm system performs a rotation around the patient, acquiring X-ray projection images from different directions in a range of typically 200 (short scan). To reconstruct a 3D volume from the 2D projection data, the projection data first needs to be pre-processed to compute the attenuation line integrals through the acquired object. The usual pre-processing steps include logarithmic processing, overexposure, scatter, and beam hardening correction [Stro 09]. For final reconstruction a dedicated C-arm reconstruction algorithm is used [Wies 00], which is based on the cone-beam reconstruction algorithm by Feldkamp, Davis and Kress (FDK) [Feld 84] in combination with Parker short scan weights [Park 82]. The short scan weighting is required to handle redundancy in the projection data, since certain X-rays are acquired twice in short scan acquisitions. The FDK algorithm is based on analytical filtered back projection (FBP) and provides computationally fast and robust cone beam reconstruction. However, the reconstruction is not exact for two reasons. First, the C-arm short scan acquisition does not fulfill Tuy s data sufficiency condition [Tuy 83], i.e., not all data to provide a mathematically correct cone beam reconstruction is acquired. Second, the Parker short scan weighting leads to an inaccurate handling of the acquired data outside the middle plane [Zeng 10]. The inexactness leads to artifacts in image slices reconstructed from data of higher cone beam angles, that is in slices with higher axial distance from the central slice. Figure 1.3b shows an example of such cone beam artifacts. A detailed introduction into the reconstruction of cone beam data can be found in the book by Zeng [Zeng 10] Flat Detector CT Perfusion - Technical Challenges Compared to classical CT imaging there are several technical limitations of FD- CT with C-arms, which make dynamic imaging like perfusion measurement more challenging. This thesis addresses the following technical challenges mainly related to perfusion imaging with FD-CT, but also to perfusion imaging in general: 1. Numerical Evaluation of Non-linear Reconstruction and Noise Reduction Techniques: Reconstruction algorithms with non-linear regularization and denoising techniques using non-linear filters have become popular field of research in recent years. They provide benefits like smoothing of homogenous regions, e.g., tissue, while preserving edges at high contrast structures, e.g., between bones and tissue. However, in contrast to linear methods their performance is dependent on the input data. Thus for a meaningful numerical

16 6 Introduction evaluation, it is essential to use simulation data with a similar structure and complexity as real clinical data. 2. Noise: To measure the brain perfusion, a time series of volumes is acquired to measure the contrast agent concentration over time in the brain tissue and vessels after injection of a contrast agent bolus. Since the contrast agent signal in the brain tissue is very low, one general challenge in perfusion imaging is noise. To compute the perfusion parameters reliably from the acquired time series, it is necessary to improve the contrast-to-noise ratio (CNR) in the tissue. Ideally, this is provided while preserving edges, e.g., at the highly contrasted vessels. 3. Slow Speed Acquisition: CTP acquires the time series of volumes in short temporal intervals of usually 1 s. Current clinical C-arm systems, however, need typically 4 5 s to acquire the projection data for one volume. This leads to temporal under-sampling of the dynamic contrast agent flow and can result in non-quantitative perfusion measurements. Furthermore, artifacts in the reconstructed volumes can arise, since the acquired volumes are not static and the projection data is inconsistent. 4. High Speed Acquisition: Novel robotic C-arm systems (Artis zeego, Siemens Healthcare, Germany, Figure 1.1a) support a high speed acquisition protocol (HSP) and can acquire projection data for one volume in less than 3 s. The HSP improves the temporal acquisition of contrast flow and reduces inconsistencies in the projection data. However, the number of projections which can be read from the detector during the HSP acquisition is limited. This leads to coarse angular sampling of the projection data and to streak artifacts in the reconstructed volumes because of aliasing. Indeed, FD-CTP has also advantages over perfusion imaging with a CT scanner in excess of its interventional applicability. In contrast to CT detectors, the flat panel detectors can acquire projection images capturing a full human head in isotropic resolution. Figure 1.2a shows a flat detector projection image of a human head. Thus, FD-CTP allows to reconstruct perfusion measurements with high resolution in the axial direction covering the complete head. CTP can acquire the full head with a shuttle mode, where the head is moved forward and backward in axial direction during the acquisition. However, the axial resolution is currently limited and the temporal sampling of the contrast agent flow is irregular between different slices. 1.4 Original Contributions Based on the technical challenges outlined in Section 1.3.2, an overview of the original contributions of this thesis along with the corresponding scientific publications is provided. 1. FD-CTP Simulation with a Dynamic Brain Phantom: Chapter 3 presents an elaborate way for numerical simulation of FD-CTP. Therefore a digital

17 1.4 Original Contributions 7 brain perfusion phantom is combined with a dynamic forward projector. The brain phantom was build according to the phantom proposed by Riordan et al. [Rior 11] using segmentation of MR data from a human volunteer. Additionally, the phantom includes a cortical skull generated by classification of MR data. For FD-CTP projection data generation a dynamic forward projector with noise and motion simulation was developed. The phantom and projection data generation was presented at two international conferences [Manh 12a, Aich 13], is available online 1 and used for evaluation proposes in most other publications. 2. Noise Reduction and Regularization by Joint Bilateral Filtering: A novel technique to improve the CNR in the brain tissue of perfusion scans is discussed in Chapter 4. By iteratively applying a joint bilateral filter (JBF) [Pets 04] a strong noise reduction in the brain tissue can be achieved, while vessel edges are preserved. The noise reduction technique was first proposed at an international conference [Manh 12b] and is used in several other publications for regularization and denoising [Manh 13d, Manh 13b, Manh 13a, Manh 14]. 3. Dynamic Reconstruction Algorithm for Slow Speed Acquisition: Chapter 5 presents an algorithmic approach to improve temporal resolution and reduce artifacts in FD-CTP data acquired with slowly rotating C-arm scanners. A dynamic reconstruction technique is introduced, which describes the contrast agent flow by spline basis functions and uses JBF as regularization. The dynamic reconstruction approach is evaluated using numerical brain phantom data and real data from a canine stroke model. The dynamic reconstruction technique was presented at two international conferences [Manh 12b, Manh 13c] and in one journal article [Manh 13d]. 4. Streak Reduction Technique for High Speed Acquisition: In Chapter 6 the possibility of doing FD-CTP with the HSP of robotic C-arm systems is discussed. A novel algorithm for computationally fast noise and streak reduction is presented. The algorithm can handle streak artifacts arising due to the angular under-sampling of the projection data and patient motion. The HSP acquisition and the artifact and noise reduction techniques are evaluated with numerical brain phantom data and real clinical patient data. The FD- CTP with HSP, the denoising and the streak artifact reduction were presented at three international conferences [Manh 13b, Manh 13a, Roya 12] and in two journal articles [Manh 14, Roya 13]. 5. Development of a Clinical Prototype: Finally, Chapter 7 presents a clinical prototype. The clinical prototype integrates the denoising, streak reduction and perfusion parameter calculation techniques into clinical workstations with an easy-to-use interface. It will allow physicians to create perfusion measurements from FD-CTP data directly on the clinical workstations and is therefore an important component for further clinical studies. Furthermore, a journal article summarizing recent developments in FD-CTP was published [Fies 13]. 1 www5.cs.fau.de/data

18 8 Introduction 1.5 Organization of the Thesis This section explains the organization of the thesis and gives a short description of each chapter to provide a reading guide to this thesis. Chapter 1 - Introduction The introduction chapter summarizes the clinical background of the acute ischemic stroke and technical background of interventional flat detector CT necessary for the understanding of this thesis. Furthermore, the benefits and technical challenges of interventional perfusion imaging are discussed. Finally, an overview of the original contributions as well as the organization of this thesis is given. Chapter 2 - Basics of Brain Perfusion Analysis and Related Work This chapter gives an overview of previous related work, which serves as the basis of the conducted research. The common perfusion parameters and the basic principles of computing them from CTP acquisitions are discussed. Also a clinically available technique for interventional measurement of the static CBV perfusion parameter is described. Subsequently, an overview of existing techniques for dynamic FD-CTP addressing the limited acquisition speed is given. Chapter 3 - Numerical Simulation of Flat Detector CT Perfusion To provide a sound numerical evaluation of the non-linear reconstruction, noise and artifact reduction techniques, it is important to create realistic FD-CTP projection data with a similar complexity as real clinical data. This chapter discusses how the digital brain perfusion phantom is designed. Furthermore, the creation of the projection data with a dynamic forward projector including Poisson noise and motion is discussed. Chapter 4 - Noise Reduction with Joint Bilateral Filtering This chapter discusses the novel noise reduction and regularization technique based on joint bilateral filtering (JBF). First, the concept of the bilateral filter and its relation to other noise reduction techniques is summarized. Then its extension to the joint bilateral filter is described. Therefore a guidance image is included, which specifies the essential structures in the filtered data. Subsequently, the computation of the guidance image in perfusion imaging is discussed. Finally, the relation of JBF to other noise reduction methods developed for CTP is given. Chapter 5 - Flat Detector CT Perfusion with Low Speed Acquisition Chapter 5 presents a novel algorithmic approach for temporal resolution improvement and artifact reduction in FD-CTP data acquired with slowly rotating C-arm scanners. The novel approach combines dynamic iterative reconstruction (DIR) with regularization by JBF. The DIR describes the dynamic contrast flow by spline basis functions and uses an iterative Landweber scheme to reconstruct the spline weights

19 1.5 Organization of the Thesis 9 fitting best to the measured projection data. The JBF regularizer helps to handle noise and the under-determination of the reconstruction problem. The dynamic reconstruction approach is evaluated using numerical brain phantom data and real data from six canine stroke models. Finally, limitations of this approach in case of patient motion are discussed. Chapter 6 - Flat Detector CT Perfusion with High Speed Acquisition Chapter 6 describes denoising and artifact reduction techniques for FD-CTP data acquired with fast rotating robotic C-arm scanners. The temporal resolution is improved on hardware basis using a high speed acquisition protocol (HSP). However, the number of projections acquired in one C-arm rotation is limited in comparison to the slow rotation protocol. This angular under-sampling leads to streak artifacts in the reconstructed volumes, which can transfer to the perfusion maps. Therefore a novel streak artifact reduction method is introduced and combined with JBF. The streak artifact reduction method exploits information from the temporal dynamics of the contrast agent flow. The evaluation involves numerical brain phantom data and three clinical patient data sets from two different patients affected with AIS. It is shown that the novel method achieves improved results compared to other state-ofthe-art methods and similar results compared to an algebraic reconstruction method, but with considerably reduced the computation time. Chapter 7 - Clinical Prototype This chapter describes the design and the workflow of the clinical prototype. It integrates the denoising, streak reduction and perfusion parameter calculation techniques into clinical workstations for further clinical studies. Chapter 8 - Summary and Outlook The final chapter gives an overview of the conducted research and the progress achieved by the scientific work presented in this thesis. Also future research topics and directions to address the challenges of FD-CTP are discussed.

20 10 Introduction

21 C H A P T E R 2 Basics of Brain Perfusion Analysis and Related Work 2.1 Brain Perfusion Analysis Cerebral Blood Volume Measurement with Flat Detector CT Existing Techniques for Dynamic Flat Detector CT Perfusion Summary Brain Perfusion Analysis This section gives a brief introduction to the analysis of brain perfusion. The introduction is based on the review paper on deconvolution-based brain perfusion measurement by Fieselmann et al. [Fies 11b]. First, Section introduces the CTP acquisition workflow and the physical and clinical meaning of commonly used perfusion parameters. Subsequently, Section describes the algorithms to compute the perfusion parameters from a time series of bolus volumes with contrast agent enhancement. These algorithms are used to analyze the FD-CTP data and are implemented in the clinical FD-CTP prototype described in Chapter Introduction to Brain Perfusion Parameters To keep this introduction short and concise, the focus is on the analysis of brain CTP data for the diagnosis of AIS. However, perfusion measurement can also be conducted with magnetic resonance imaging (MRI), single photon emission computed tomography (SPECT), and positron emission tomography (PET) and is also used in oncology, e.g., to identify liver tumors [Pand 05], and in cardiology for myocardial perfusion measurement [Germ 95]. The CTP acquisition work flow starts with an IV injection of iodinated contrast agent with a volume of typically 50 ml. Approximately 10 s after the contrast agent injection, continuous scanning is performed for about 50 s acquiring a time series of volumes with a temporal sampling of typically 1 volume per second. After the acquisition, the CTP data is reconstructed and patient head motion is compensated by a registration of all acquired volumes onto the first temporal volume. Assuming that the contrast bolus has not yet arrived in the brain, the first temporal volume serves as a mask volume describing the anatomical struc- 11

22 12 Basics of Brain Perfusion Analysis and Related Work CBF in ml/100 g/min 0 CBV in ml/100 g MTT in s 0 TTP in s 0 Figure 2.1: CT perfusion parameter maps of cerebral blood flow (CBF), cerebral blood volume (CBV), mean transit time (MTT), and time-to-peak (TTP). The ischemic stroke lesion is marked with arrows (images are taken from [Fies 11b] and are courtesy of the Department of Neuroradiology, Universitätsklinikum Erlangen, Germany). Contrast attenuation [ HU] Time [s] 30 (a) Arterial input function (AIF) Contrast attenuation [ HU] Time [s] (b) Tissue TCC Figure 2.2: Time-contrast curves (TCCs) from human CTP data describing the contrast agent enhancement after subtraction of the mask image (a) in an artery and (b) inside a volume in the brain tissue.

23 2.1 Brain Perfusion Analysis 13 Full Name Physical Unit Formula CBV Cerebral blood volume ml/100 g (1/ρ voi ) k(τ) dτ 0 CBF Cerebral blood flow ml/100 g/min (1/ρ voi ) max k(t) MTT Mean transit time s k(τ) dτ/ max k(t) 0 TTP Time-to-peak s arg max t c voi (t) Table 2.1: Overview over commonly used perfusion parameters and the corresponding formulas to compute them from the flow-scaled residual function k(t) and the tissue TCC c voi (t). tures of the head without enhancement from the contrast agent. For noise reduction, also an average of the first several temporal volumes without contrast agent enhancement can be used as the mask volume. The mask volume is subtracted from all other volumes to extract a time series of volumes with the pure contrast agent enhancement. This time series of volumes describes the time-contrast curves (TCCs) of the contrast agent in the tissue and the vessels of the brain. Figure 2.2 shows example TCCs from the tissue and from an artery. After subtraction usually noise reduction is applied to increase the CNR in the low contrasted tissue TCCs [Brud 09]. In the next step, a TCC inside an artery needs to be selected as the arterial input function (AIF) either by user interaction or automatic detection. The AIF is required for the subsequent perfusion parameter computation, which is described in Section Finally, the resulting perfusion parameter maps are shown to the physician for diagnosis. Frequently used parameters are cerebral blood volume (CBV), cerebral blood flow (CBF), mean transit time (MTT) and time-to-peak (TTP). Figure 2.1 shows example slices of CTP parameter maps and Table 2.1 provides an overview of the perfusion parameters. The CBV parameter quantifies the blood volume normalized by the brain tissue mass and is usually measured in ml/100 g. Healthy brain tissue has typical CBV values of 2 ml/100 g for white matter and 4 ml/100 g for gray matter. As CBV is only related to the static blood volume, it is not a temporal dynamic parameter and can also be measured using static acquisition techniques. Section 2.2 describes a clinically available technique for measuring CBV with FD-CT. The CBF parameter describes transported CBV per minute and and is usually measured in ml/100 g/min. Typical CBF values for healthy brain tissue are 25 ml/100 g/min for white matter and 55 ml/100 g/min for gray matter [Park 04]. The MTT parameter specifies the average time a blood cell needs to pass through the capillary bed and is usually measured in seconds. The simplest parameter is TTP, which describes the time a TCC needs to reach its global maximum and is also usually measured in seconds. Tissue with reduced CBV mostly accounts for the unsaveable infarct core. In contrast, tissue with almost normal CBV but reduced CBF, increased MTT, or increased TTP accounts for the penumbra Perfusion Parameter Computation This section describes the implementation of the perfusion parameter calculation in the perfusion analysis framework. The framework is used for perfusion analysis in all experiments conducted in this thesis and in the clinical prototype. The formulas

24 14 Basics of Brain Perfusion Analysis and Related Work c art (t) arterial inlet c voi (t) V voi (a) Physiological model venous outlet r(t) Time [s] (b) Residual function r(t) Figure 2.3: (a) Physiological model of the tissue perfusion (image taken from [Fies 11b]). (b) Idealized residual function r(t) from a numerical simulation. and numerical methods to estimate the perfusion parameters are depicted to facilitate the reproducibility of the experiments. A descriptive and detailed derivation and discussion of these formulas and methods can be found in the review paper by Fieselmann et al. [Fies 11b]. The CBV, CBF and MTT parameters calculation is based on the indicatordilution theory [Oste 96]. The blood supply to the tissue is described by the physiological model shown in Figure 2.3a. Inside a volume of interest (VOI) V voi is the capillary bed, tissue fluid and the functional tissue of the organ (parenchyma). After contrast agent injection, the bolus enters V voi via the arterial inlet, is diluted into the capillary bed and leaves V voi via the venous outlet. The contrast agent flow in the arterial inlet is described by the TCC c art (t). In practice, c art (t) is approximated by the globally selected AIF. The mean contrast agent concentration in V voi is described by the TCC c voi (t). Due to the limited spatial resolution of the CT and FD-CT scanners, V voi will be in practice a voxel inside the brain tissue and contain numerous capillary beds as well as arterioles and venules. To work with the indicator-dilution theory, the residual function r(t) needs to be introduced. The residue function quantifies the relative amount of contrast agent that is left in V voi at time t after a contrast bolus shaped as a unit impulse has entered V voi at time t = 0. Figure 2.3b shows an idealized example of a residual function from a numerical simulation. The indicator-dilution theory provides the following relation between the TCCs, the residual function and the CBF c voi (t) = CBF ρ voi (c art r) (t), (2.1) where denotes the convolution operator and ρ voi the mean density in the capillary bed in V voi. To ease notation the flow-scaled residue function k(t) is introduced as k(t) = CBF ρ voi r(t), (2.2) which can be determined directly from the measured TCCs c voi (t) and c art (t) by deconvolution c voi (t) = (c art k) (t). (2.3) Since max (r(t)) = 1, CBF can be computed from k(t) as CBF= 1 ρ voi max (k(t)). (2.4)

25 2.2 Cerebral Blood Volume Measurement with Flat Detector CT (a) CTP CBV map. 15 (b) FD-CT CBV map. Figure 2.4: CBV maps from a clinical patient study acquired with (a) CTP and (b) a CBV acquisition protocol for FD-CT (images are courtesy of the Department of Neuroradiology, Universitätsklinikum Erlangen, Germany). The formulas to compute CBV and MTT from k(t) are shown in the overview in Table 2.1. In practice, the TCCs are sampled at discrete time points. Thus the deconvolution task to compute the flow-scaled residual function k(t) as stated in Equation 2.3 is represented as an algebraic problem and can be solved by singular value decomposition (SVD) [Golu 70]. As conducted in [Fies 11b], this deconvolution is an ill-posed problem. To obtain a numerically stable result, the SVD-based deconvolution is regularized by suppressing the influence of the small singular values. Therefore singular values with a value below 20 % of the maximal singular value are truncated. Finally, the CBV and CBF values are multiplied with a Hematocrit correction factor of The Hematocrit correction accounts for differences of the Hematocrit values between arteries and capillaries [Kons 09]. A higher Hematocrit value results in a smaller proportion of plasma in the blood. As the contrast agent is distributed in the plasma only, no Hematocrit correction results in a bias in the absolute quantification of CBV and CBF. The TTP parameter is defined by the time until the TCC in Vvoi reaches its peak and can be computed directly from cvoi (t) as TTP = arg max cvoi (t). t (2.5) For robust peak detection in noisy TCCs, the perfusion analysis framework applies a cubic Savitzky Golay filter [Savi 64] of size 25 samples on cvoi (t) prior to the peak search. 2.2 Cerebral Blood Volume Measurement with Flat Detector CT The CBV parameter does not necessarily require knowledge about the dynamic contrast agent change. Thus it is possible to measure CBV with FD-CT from acquisitions of a single mask volume and a single bolus volume (with contrast agent filling) as proposed by Ahmed et al. [Ahme 09]. Therefore a contrast agent injection protocol is

26 16 Basics of Brain Perfusion Analysis and Related Work used which produces a steady state of contrast medium in the brain parenchyma during the acquisition of the bolus volume. To generate the steady state of contrast agent a series of DSA acquisitions is initiated after IV injection of the contrast bolus. When the transverse sinus of the brain is opacified, it is assumed that the contrast medium is washed out into the capillary bed and the bolus volume acquisition is initiated. After acquisition, the mask and bolus volumes are reconstructed and subtracted. Air and bone structures are removed by segmentation and a spatial smoothing filter is applied to the subtracted volume for noise reduction. By automated histogram analysis of the vessel tree a steady state arterial input value is calculated. Finally, CBV maps are computed by scaling the subtracted volume accounting for the arterial input value and for other physiological values, e.g., Hematocrit correction. Figure 2.4 shows a clinical example for a FD-CT CBV map in comparison to a CBV map acquired with CTP. A high correlation of the CBV values and the CBV lesion volume of FD-CT CBV maps to CTP CBV maps was found in a series of clinical patient studies by Struffert et al. [Stru 10, Stru 11, Stru 12] pointing out that interventional CBV measurement is already feasible. However, CBV maps are limited to depict the infarct core but not the full extent of the ischemic tissue. Therefore the development of time-resolved perfusion flat detector imaging is highly desirable. 2.3 Existing Techniques for Dynamic Flat Detector CT Perfusion This section discusses existing techniques which have been proposed for dynamic perfusion measurement with FD-CT. First of all, Section introduces the FD- CT protocol which is used in this work for the dynamic acquisitions of a time series of volumes with a C-arm system. Accordingly, Section discusses a technique which improves the temporal resolution of FD-CT by properly combining a series of interleaved dynamic acquisitions. Finally, approaches to improve the temporal resolution in an algorithmic way by dynamic iterative reconstruction (DIR) using temporal basis functions (Section 2.3.3) and a Gamma variate model (Section 2.3.4) are discussed Acquisition Protocol Unlike traditional CT gantries current C-arm systems are not able to rotate continuously around the patient multiple times. Therefore a special acquisition protocol for dynamic FD-CT imaging is required to successively acquire a time series of volumes. First of all, before bolus injection the C-arm acquires projections from two rotations in forward and backward C-arm rotation to reconstruct the mask volumes with the static anatomical structures. Mask projections in both directions are acquired because the positions of X-ray source and detector are not exactly the same for the forward and backward rotations. Subsequently, the contrast agent is injected intravenously. Finally, when the contrast bolus reaches the brain, the C-arm rotates N rot times in a bi-directional manner in forward and backward direction to acquire the time series. In each rotation the

27 2.3 Existing Techniques for Dynamic Flat Detector CT Perfusion T p View angle λ [ ] T r Time t after starting acquisition [s] Figure 2.5: FD-CTP acquisition protocol: angular position λ of the C-arm rotating in a bi-directional manner in forward and backward direction to acquire a time series of volumes. T r denotes the time for one rotation and T p the pause time between rotations. (a) Interleaved scanning (b) Partial reconstruction interpolation Figure 2.6: Visualization of (a) the interleaved scanning (IS) protocol and (b) partial reconstruction interpolation (PRI) (images are taken from [Fies 12a]). C-arm acquires N proj projections equally distributed over an angular range of 200. Figure 2.5 shows a sketch of the angular C-arm position over time during the bolus volume acquisition. A typical time for a state-of-the-art clinical C-arm system (Artis zee, Siemens Healthcare, Germany) to acquire short scan projection data over 200 is T r = 4.3 s. Between the rotations the system stops for a pause of typically T p = 1.2 s Interleaved Scanning Recently a novel approach to increase the temporal resolution of FD-CTP by combining an interleaved acquisition protocol with a dedicated reconstruction technique was proposed by Fieselmann et al. [Fies 12a, Fies 12b]. This approach uses an interleaved scanning (IS) protocol, where a series of dynamic scanning sequences is acquired and the TCCs are computed from the IS data using partial reconstruction interpolation (PRI). Figure 2.6a illustrates the basic principle of interleaved scanning: several scanning sequences with different time delays between the contrast agent injection and the

28 18 Basics of Brain Perfusion Analysis and Related Work (a) CTP CBF map 0 (b) FD-CTP CBF map 0 Figure 2.7: CBF maps (units: ml/100 g/min) of a pig brain acquired (a) with CTP and (b) with FD-CTP with interleaved scanning using two sequences (images are taken from [Fies 12a]). start of the acquisition are acquired. For each sequence an identical contrast bolus injection is administrated and an identical contrast agent enhancement in the brain vessels and tissue is assumed. Typically two interleaved scanning sequences were acquired in animal studies [Fies 12b]. After IS acquisition, the TCCs are computed using the PRI approach illustrated in Figure 2.6b. The PRI processes the IS data by dividing the full angular range of one C-arm rotation (usually 200 ) into sub-intervals and reconstructing the projection data of each sub-interval separately using the FDK algorithm. In [Fies 12b] six intervals are suggested so that from each C-arm rotation six partial volumes are reconstructed, each from the projection data belonging to one sub-interval (e.g., projection data from 0-33, 33-66,...). To compute a volume with the samples of the TCCs at a certain time point t est, first the partial volumes sampled at t est are computed by interpolation between the temporally closest partial volumes. Then all interpolated partial volumes are summed up to generate the fully reconstructed volume with the TCCs sampled at t est. The combination of IS and PRI can help to increase the temporal resolution and to reduce artifacts arising from the inconsistencies in the projection data as shown in the numerical evaluation in [Fies 12b]. The IS-PRI approach was the first technique for FD-CTP showing clinical results. It was evaluated with data from a clinical pig study [Fies 12b, Gang 11]. Figure 2.7 shows CBF maps from the pig study acquired with CTP and FD-CTP using IS- PRI. The clinical evaluation showed a good correlation between CTP and FD-CTP perfusion maps and suggests that IS-PRI with two scan sequences can enable reliable tissue perfusion measurement. As required in clinical practice, the reconstruction with IS-PRI is computationally fast since it is based on the FDK algorithm. However, the requirement of multiple scanning sequences increases radiation and contrast agent dose to the patient. Furthermore, the assumption of the identical contrast agent enhancement in all scans might not always hold in practice, e.g., since blood circulation parameters might change. These limitations might restrict the application of this approach in practice. However, the problem of multiple contrast agent injections could be solved with a

29 2.3 Existing Techniques for Dynamic Flat Detector CT Perfusion Time [s] (a) Gaussian kernels Time [s] (b) Gamma variate function Figure 2.8: Models for dynamic reconstruction of TCCs: (a) basis set of Gaussian kernels and (b) Gamma variate function. bi-plane system which allows to acquire FD-CT projection data with both C-arms simultaneously. Though, such a system is currently not available Dynamic Iterative Reconstruction using Temporal Basis Functions The first approach to dynamically reconstruct TCCs from slowly rotating X-ray systems by estimating parameters of a TCC model was proposed by Neukirchen and Rose [Neuk 05]. Following an idea for reconstruction of dynamic SPECT data [Reut 00], the TCCs are described by a linear model as a weighted sum of temporal basis functions. Figure 2.8a shows a set of Gaussian kernel functions temporally distributed over the acquisition time as an example of a set of temporal basis functions. Serowy et al. [Sero 07] showed that the weights of the linear model can be computed from the acquired dynamic projection data using an iteration scheme which is similar to classical algebraic reconstruction techniques (ART) [Kak 88]. Solving the linear equation system by the ART-like scheme facilitates handling the extreme high dimensionality of the dynamic reconstruction problem, especially in case of the 3D cone beam data in FD-CT. The mathematical and technical details of this scheme are discussed in detail in Chapter 5. Neukirchen et al. [Neuk 10] uses the ART-like scheme in combination with bases formed by sets of temporally shifted Gaussian (Figure 2.8a) and Gamma variate functions (an example for a single Gamma variate function is shown in Figure 2.8b). Additionally, principal component analysis (PCA) is applied to the Gaussian and Gamma variate basis sets to generate basis sets with a maximum flexibility for a given number of basis functions. The reconstruction approach was evaluated using numerical projection data generated from a simple synthetic head phantom and from a clinical CTP data set. The results showed the potential of this approach to improve the temporal resolution and to generate clinically meaningful perfusion maps out of the reconstructed data. However, only numerical and no clinical data was used in the evaluation and a 2D parallel beam geometry instead of a 3D cone beam geometry

30 20 Basics of Brain Perfusion Analysis and Related Work was simulated. The noise is handled by early stopping of the iterations, which leads to smooth solutions resulting in lower noise but also spatial and temporal blurring of the TCCs [Hank 93]. Based on the work by Neukirchen et al. [Neuk 05, Neuk 10] and Serowy et al. [Sero 07] a novel dynamic iterative reconstruction technique for FD-CTP is developed in Chapter 5, which addresses the discussed limitations and is also evaluated with clinical data from canine stroke models Dynamic Iterative Reconstruction using a Gamma Variate Model A further approach to incorporate the dynamic information within the projection images was presented by Wagner et al. [Wagn 13]. Instead of using a set of temporal basis functions, each TCC is modeled by a Gamma variate function. The Gamma variate function is a common model for the dynamics of intravenously injected indicators in the bloodstream [Misc 08] and is defined as a (t d) b exp ( (t d) c) t > d c(t) = 0 t d, (2.6) where its shape is defined by the four parameters a 0 controlling the amplitude, b > 1 the initial rise, c > 0 the scaling, and d the temporal shift. Figure 2.8b shows an example of a Gamma variate function with a typical TCC shape. The Gamma variate functions model the TCCs with only four parameters. Thus it is less flexible than the basis function approach but reduces the dimensionality of the dynamic reconstruction problem even further. The algorithm by Wagner et al. extracts the parameters of the TCCs from the measured dynamic projection data using an ART-like algorithm. The Gamma variate model parameters are updated during the ART iterations using the Levenberg algorithm [Leve 44]. To handle noise, the algorithm uses a non-linear regularization similar to rank filtering [Jaeh 05]. The algorithm is evaluated with numerical FD- CTP data created from clinical CTP data sets and a real clinical FD-CTP data set from a canine stroke model. The results showed improvements in correlation and absolute quantification of the resulting perfusion maps for the dynamic reconstruction using the Gamma variate model in combination with the non-linear regularization compared to an approach based on FDK reconstruction. The benefit of the Gamma variate compared to the temporal basis functions is the further reduced dimensionality. However, its reduced flexibility might limit the robustness in practical application if the measured data does not suit the model (e.g., a second pass of contrast agent in the projection data can currently not be modeled). The comparison of the different approaches proposed by different research groups is so far an open issue.

31 2.4 Summary Summary Section 2.1 gives a concise review of deconvolution-based analysis methods for perfusion quantification using data acquired with CT or MRI. The analysis methods are used for computation of the perfusion parameter maps in this work. Section 2.2 discusses an existing approach for measuring the non-dynamic cerebral blood volume parameter with FD-CT. In Section 2.3 several existing approaches for dynamic FD-CTP are discussed, which are based on special interleaved acquisition protocols or dynamic reconstruction algorithms. The dynamic reconstruction approach using basis function modeling serves as basis of the novel approach presented in Chapter 5.

32 22 Basics of Brain Perfusion Analysis and Related Work

33 C H A P T E R 3 Numerical Simulation of Flat Detector CT Perfusion 3.1 Digital Brain Perfusion Phantom Flat Detector CT Perfusion Projection Data Generation Summary Digital Brain Perfusion Phantom Non-linear methods are a popular field of research in CT imaging. They are commonly used for regularization in ART algorithms, e.g., to handle artifacts arising from angular under-sampling [Sidk 08], or as adaptive filters in a volume post processing step, e.g., for edge-preserving noise reduction [Brud 11]. Also in perfusion imaging dedicated non-linear noise reduction methods have been proposed [Mend 11, Sait 08]. The non-linear techniques enable to smooth out unwanted image fractions like noise or streaking artifacts, while preserving desired structures as edges between tissue and bones. However, they are also much more difficult to analyze than linear methods, since their behavior depends on the input data. Many non-linear methods rely on the assumption that the reconstructed or filtered object is mostly homogenous. For example, the ASD-POCS reconstruction method by Sidky and Pan [Sidk 08] applies constrained total variation (TV) [Rudi 92] minimization assuming an object with sparse gradient magnitude. Classical images for testing reconstruction algorithms such as the Shepp Logan phantom [Shep 74] are usually constructed from simple mathematical shapes like ellipsoids and have a much higher homogeneity than clinical data. Thus they favor the homogeneity assumption and do not allow the realistic evaluation of the non-linear methods. This section describes the design of a realistic digital phantom to simulate brain perfusion. The design is based on the dynamic brain perfusion phantom introduced by Riordan et al. [Rior 11]. Section describes how the brain structure and the skull of the head are generated from MR data. Subsequently, Section describes how the TCCs are simulated inside the brain structure. Finally, Section introduces a MATLAB toolbox for annotating stroke-affected areas in the phantom and generating a time series of volumes simulating the contrast agent flow in a brain perfusion 23

34 24 Numerical Simulation of Flat Detector CT Perfusion (a) ToF image (b) T1 image (c) Brain segmentation Figure 3.1: MR acquisitions to create brain phantom structure: (a) time-of-flight (ToF) acquisition showing the arteries with high contrast, (b) T1-weighted acquisitions showing brain tissue with high contrast, and (c) brain segmentation created from MR scans (segmentation legend: white: white matter, gray: gray matter, magenta: arteries, green: cerebrospinal fluid). acquisition. The toolbox with the phantom data is available online 1. The phantom has a similar complexity and dynamic behavior as clinical patient perfusion data and thus allows for a realistic evaluation of non-linear brain perfusion reconstruction and noise reduction methods [Manh 13d, Manh 14] Brain Structure and Skull Generation To enable the realistic evaluation of non-linear methods in the context of brain perfusion imaging, a brain perfusion phantom with a similar structural complexity and dynamic behavior as a real human brain is required. Therefore the structure of the phantom was created from clinical acquisitions of a real human brain. MR scans of the head of a 27 year old male volunteer were acquired for this work using a Magnetom Verio 3T MR scanner (Siemens Healthcare, Germany). Brain Structure Generation The basic brain structure persisting of white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF), was created from volumetric T1-weighted MR data showing the brain tissue in high contrast. As suggested in [Rior 11], the volumetric segmentation of the MR acquisition into WM, GM and CSF was performed with the Freesurfer image analysis suite 2 [Dale 99, Fisc 01]. Furthermore, arteries were included into the phantom to simulate the arterial inflow of the contrast agent. They were generated by segmentation of a volumetric time-of-flight (ToF) MR angiography acquisition by thresholding and manual post-processing. Figure 3.1 shows example slices from the ToF acquisition, the T1-weighted MR data, and the final segmentation, which serves as the structural basis of the dynamic brain phantom. 1 www5.cs.fau.de/data 2

35 3.1 Digital Brain Perfusion Phantom 25 (a) First echo UTE- TE1 image (b) Second echo UTE- TE2 image (c) Attenuation estimation Figure 3.2: Attenuation estimation of the skull from a volunteer MR acquisition: (a) first echo UTE-TE1 image, (b) second echo UTE-TE2 image and (c) MR-predicted attenuation image (images are taken from [Aich 13]). Skull Estimation To complete the basic brain phantom structure, the cortical bone of a human skull is included into the phantom. The bone structures are particularly important for simulating reconstructions from projection data with coarse angular sampling. The angular under-sampling results in streak artifacts, if high frequency structures like bones are present in the acquired object. The skull for the phantom was created from an MR acquisition of the human volunteer using a MR cortical bone estimation technique in combination with dedicated MR scanning sequences. Generally, cortical bones are difficult to detect from conventional MR sequences due to the similarity between air and cortical bone intensities. Recently, the introduction of PET/MR hybrid imaging has encouraged the development of novel methods on the estimation of bones from MR images. The knowledge of attenuation maps, which are dominated by the bone structures, is important for quantitative PET reconstruction. Navalpakkam et al. [Nava 13] introduced a novel method to estimate the cortical bone based on dedicated MR sequences. Therefore an ultra-short echo time (UTE) sequence is acquired to image the cortical bone. On images reconstructed from the two UTE echoes TE1 (0.07 ms) and TE2 (2.46 ms), cortical bone appears on UTE-TE1 images but is absent on UTE-TE2 images as shown in Figure 3.2. Furthermore a 3D Dixon-VIBE (volume interpolated breath hold examination) MR scan was performed. A continuous valued attenuation map is created from the acquired UTE and Dixon-VIBE MR data by using support vector regression [Smol 04]. The support vector regression was trained by data from five patients with MR and CT head acquisitions. The generated attenuation map is shown in Figure 3.2c. The skull structure was extracted from attenuation map and added to the brain perfusion phantom structure Brain Perfusion Simulation The generated brain structure serves as the basis for the simulation of TCCs. As suggested in [Rior 11], TCCs of different tissue classes are simulated according to

36 26 Numerical Simulation of Flat Detector CT Perfusion Healthy Reduced Severely Reduced Tissue Blood Flow Blood Flow WM GM WM GM WM GM CBF 25 ± ± ± ± ± ± 1.4 [ml/100 g/min] CBV 1.9 ± ± ± ± ± ± 0.12 [ml/100 g] MTT [s] 4.6 ± ± ± ± ± 1 8 ± 1 Table 3.1: Perfusion parameters for digital brain phantom (WM = white matter, GM = gray matter) chosen in the range of the average perfusion values measured by Parkes et al. [Park 04]. Contrast attenuation [ HU] Arterial input function Healthy tissue 10 Diseased tissue 10 (a) Maximum intensity projection Time [s] (b) TCCs simulated in the brain phantom Figure 3.3: (a) Maximum intensity projection of the digital brain phantom and (b) simulated TCCs in the arteries, in healthy tissue and in diseased tissue. Tissue TCCs are scaled by a factor of 10. The location of the shown TCCs is marked in (a). the brain tissue segmentation and the user-defined annotation of stroke-affected areas. The user can define areas with healthy tissue, with reduced perfusion and with severely reduced perfusion. According to the segmentation in white matter and gray matter, different perfusion values are assigned to the annotated areas. Table 3.1 shows an overview of the tissue classes and the assigned perfusion values. The perfusion values were chosen in the range of the average perfusion values measured by Parkes et al. [Park 04]. After assigning the perfusion values to the voxels in the phantom, the indicatordilution theory is used to generate the corresponding TCCs similar to Equation 2.1. For the AIF c art (t) the corresponding TCC shown in [Rior 11] is used, which was created by averaging AIFs from several clinical CTP acquisitions. The tissue TCCs c voi (t) are computed from the assigned CBF and MTT values by convolution of the AIF c art (t) with the residual function r(t) scaled by the CBF, c voi (t) = CBF ρ voi (c art r) (t),

37 3.1 Digital Brain Perfusion Phantom 27 (a) Annotation image (b) CBV map (c) CBF map (d) MTT map (e) TTP map Figure 3.4: (a) Perfusion phantom with segmented brain structures and annotation of stroke-affected areas (white: white matter, gray: gray matter, magenta: vessels, yellow: areas with reduced blood flow (penumbra), red: areas with severely reduced blood flow and blood volume (infarct core)), (b-d) perfusion maps created from phantom annotation. where the residual function r(t) is defined as exp ( (t MTT)) t MTT r(t) = 1 t < MTT. (3.1) The tissue density is assumed to be ρ voi = 1 g/ml. An example of r(t) is shown in Figure 2.3b. Figure 3.3b shows the AIF and two examples of tissue TCCs in healthy and stroke-affected tissue. After simulation of the contrast dynamics, appropriate constant HU values were added to the TCCs to incorporate the anatomic tissue structures into the phantom. Similar to what is suggested in [Rior 11], contrast attenuation values in the following intervals were added: gray tissue 35 ± 3 HU, white tissue 29 ± 3 HU, vessels 40 ± 3 HU, and CSF 12 ± 3 HU. To further reduce the homogeneity of the phantom, the perfusion parameters and the HU values of the anatomic structures were varied inside the indicated intervals. The variation is created by association of each brain phantom tissue voxel with a normalized value of the corresponding voxel in the T1-weighted MR volume. The MR values are normalized to the unit interval [ 1, 1] in each slice by first computing the mean and the standard deviation σ of all MR values inside the slice associated to a segmented tissue voxel. Then the mean is subtracted from the MR values, the values are clamped to [ 2σ, +2σ] and divided by 2σ. The perfusion parameters and the attenuation of the anatomic structures in each tissue voxel are varied by PV (x) = P (x) + NMR(x) DP(x), (3.2) where P V (x) denotes the varied parameter of the voxel at volume index x N 3, P (x) the default parameter, NMR(x) the normalized MR value, and DP (x) the maximal deviation of the parameter. Figure 3.4 shows an example of a brain phantom annotation with stroke-affected areas and the corresponding perfusion parameter maps.

38 28 Numerical Simulation of Flat Detector CT Perfusion Figure 3.5: Screenshot of MATLAB tool for annotation of stroke affected areas in the digital brain perfusion phantom Phantom MATLAB Toolbox The brain perfusion phantom data and corresponding tools are available online in a framework to provide a publicly available basis for realistic and reproducible evaluation of perfusion reconstruction, denoising and parameter analysis algorithms. The brain phantom data includes the brain and skull segmentation and the T1-weighted MRI data for parameter variation. The framework provides tools to annotate strokeaffected areas in the segmented brain and to create the dynamic 3D+t perfusion simulation according to the annotation. The tools are implemented in the MATLAB (MathWorks, Natick, MA, USA) numerical computing environment. Figure 3.5 shows a screenshot of the framework tool which provides a graphical user interface (GUI) for annotating areas with reduced and severely reduced perfusion. The user can define the stroke-affected areas by drawing 2D or 3D ellipsoids or by freehand drawing and view the annotation in axial, coronal and sagittal directions. Subsequently, the user can save the annotation and use the phantom creation tool to generate the dynamic phantom data. The phantom creation tool simulates the TCCs according to the annotation as described in Section and adds the anatomical attenuation values from the skull and the brain tissue. The resulting 3D+t phantom data is stored using a temporal sampling distance defined by the user as a time series of volumes together with a mask volume describing the anatomical structures and the ground truth perfusion maps. The detailed procedure to create brain perfusion phantom data is described in the framework documentation.

39 3.2 Flat Detector CT Perfusion Projection Data Generation 29 (a) Full phantom projection (b) Contrast agent projection (c) Contrast agent projection with noise Figure 3.6: FD-CT projection images created from the dynamic brain phantom: (a) full phantom projection, (b) contrast agent projection after subtraction of skull and tissue structures and (c) contrast agent projection with noise. 3.2 Flat Detector CT Perfusion Projection Data Generation The evaluation of reconstruction and denoising techniques for FD-CTP requires dynamic projection data, which simulates a FD-CTP acquisition conducted with the acquisition protocol described in Section Therefore the time series of volumes of the digital brain perfusion phantom needs to be forward projected to a virtual detector according to the acquisition geometry of the C-arm system. Section describes how the numerical FD-CTP projection data is computed by dynamic forward projection. Furthermore, quantum noise in the projection data and rigid motion of the acquired head can be simulated as described in Section Finally, Section shows how reconstructed perfusion maps can be evaluated quantitatively Dynamic Forward Projection The simulation of FD-CTP acquisitions according to the protocol described in Section is conducted using a dynamic forward projection technique. The projection images for the mask and bolus acquisitions are computed by ray-casting of the volumetric brain perfusion phantom data. According to the FD-CTP acquisition protocol, first the mask acquisitions in forward and backward rotation directions are computed by forward projection of the anatomical structures of the brain phantom. Subsequently, the time series of volumes with the TCCs added to the anatomical structures is forward projected with respect to the dynamic C-arm acquisition protocol visualized in Figure 2.5. For each rendered projection image, the contrast agent enhancement corresponding to the acquisition time point of the projection image is estimated from the phantom time series by linear interpolation between the two closest temporal volumes. Thus the simulated projection data incorporates the dynamic change of the contrast attenuation during a single C-arm rotation.

40 30 Numerical Simulation of Flat Detector CT Perfusion Each projection image is rendered with respect to a real C-arm geometry (Artis zeego, Siemens Healthcare, Germany). The projection-acquisition geometry of C- arm systems is commonly specified by 3 4 projection matrices, which describe the extrinsic (e.g., X-ray source position) and intrinsic (e.g., detector discretization) parameters of the X-ray imaging system. They are generally used for the backward projection step in an implementation of the FDK algorithm, which is robust to the irregular geometry of the C-arm systems [Wies 00]. Galigekere et al. [Gali 03] have shown how to render projection images with respect to the geometric information in a projection matrix without decomposing it into its single parameters. Based on these results, Keck et al. [Keck 09] developed a forward projector implementation for the common unified device architecture (CUDA) (NVIDIA, USA), which calculates the computationally most expensive steps on graphics processing units (GPUs). The forward projector determines the attenuation value of a certain pixel on the detector plane by tracing a ray which points from the X-ray source towards the detector pixel position. The attenuation values inside the forward projected volume are sampled equidistantly along the ray, with a selected sampling distance of half of the isotropic voxel size. Therefore trilinear interpolation is applied between the nearest neighbor voxels of the sampled spatial location on the ray. The sum of the sampled attenuation values on the ray results in the simulated attenuation measured at the corresponding detector pixel. The forward projection is easy to parallelize, since all simulated rays on one projection image can be computed independently. Thus general-purpose computation on GPUs, which enables the use of GPU hardware for general computation tasks traditionally handled by the central processing unit (CPU), provides a possibility to create forward projections in short computation time by massive parallelization without using expensive high performance computer systems. Furthermore, the computationally expensive trilinear interpolation can be calculated on recent GPUs with hardware accelerated texture access. The forward projection is parallelized by tracing each ray in one individual thread. The details of the ray tracing implementation are described in the work by Keck et al. [Keck 09]. Figure 3.6a shows an example of a simulated C-arm projection image created by forward projection of the brain perfusion phantom. An example of a projection image of the pure dynamic contrast agent enhancement neglecting the anatomic structures is shown in Figure 3.6b Quantum Noise and Motion Simulation The contrast agent attenuation in the brain tissue is very small and the peaks of the tissue TCCs are typically in a range of 5 30 HU (Figure 3.3b). Thus the reconstruction from projection data corrupted by noise is a major challenge in perfusion imaging. For a realistic FD-CTP simulation it is essential to include a physically correct model of the noise statistics. Following recent studies [Abou 10], physicians tend to avoid the general anesthesia of stroke-affected patients during endovascular therapy. Thus the patient might move the head during the acquisition, which constitutes a further challenge in FD-CTP imaging.

41 3.2 Flat Detector CT Perfusion Projection Data Generation 31 Noise Noise in tomographic X-ray imaging is arising from two classes of noise sources: quantum noise and electronic noise. Quantum noise originates from the statistic processes appearing in generation, attenuation and detection of X-ray radiation and is related to the amount of emitted X-ray radiation during the acquisition (dose). In contrast, electronic noise is related to the utilized detector technology [Buzu 08]. With the advancing of detector technology, the amount of electronic noise is reduced more and more, and quantum noise is becoming the dominating part of the noise corruption in the projection images. Thus quantum noise is modeled and the electronic noise is neglected in the simulations conducted in this thesis. As X-ray radiation consists of X-ray quanta (photons), its statistic properties are modeled by discrete random processes. As discussed in [Buzu 08], the statistical chain of photon generation in the X-ray tube, the interaction of photons with the irradiated matter, and the measurement by the X-ray detector is described by a cascaded Poisson process. Hence, the number of measured photons at a detector pixel is described according to the Poisson distribution, which specifies the probability P N (n) of measuring n photons in case of an expected number of N photons arriving at the detector pixel by P N (n) = N n exp ( N). (3.3) n! The number of expected photons N is given by the law of Lambert-Beer [Lamb 60, Beer 52] from the measured attenuation line integral µ and the expected number of arriving phantoms in the unattenuated case N 0 by N = N 0 exp ( µ). (3.4) The simulation of quantum noise is controlled by the definition of N 0 and the attenuation line integral µ. As the brain phantom data is given in Hounsfield units (HU), the HU values need to be transformed to attenuation values. In this work a monochromatic photon energy of 60 kev is simulated. Thus the HU values are scaled to attenuation values using the definition of HU CT values [Buzu 08] with a corresponding attenuation value for water of µ w = [Hubb 95]. To simulate mm the Poisson random process in the forward projector implementation, the rejection algorithm after Atkinson is used [Atki 79]. Figure 3.6c shows an example of a brain phantom projection image after anatomic mask subtraction assuming an expected number of N 0 = arriving photons per mm 2 at the detector in the unattenuated case. Rigid Head Motion To simulate head motion the forward projector implementation provides the possibility to move the head phantom in a rigid way during the projection data generation. For the numerical experiments incorporating motion, a slight movement of the head between the acquisition of the mask volumes and the bolus volumes is simulated. Therefore the bolus volumes are rotated around the axial axis by 2 with respect to the mask volume. It is likely that the patient moves during this part of the acquisition procedure, because there is a pause of 10 s between mask and bolus scans.

42 32 Numerical Simulation of Flat Detector CT Perfusion (a) Mask volume (b) Subtracted volume w/o motion (c) Subtracted volume w/ motion Figure 3.7: (a) Mask volume reconstructed from digital brain phantom data, (b) subtracted volume generated without simulated motion and (c) subtracted volume with simulated motion. During the pause the contrast medium is injected intravenously and transported to the intracranial arteries. This simulated motion constitutes a further challenge for non-linear denoising techniques in case of angular under-sampling of the projection data. The FD-CTP acquisition protocols typically suffer from angular under-sampling, as the C-arms needs to rotate fast to acquire the dynamic projection data and the detector readout rate is limited. Figure 3.7a shows a brain phantom volume reconstructed from an acquisition with only 133 projections. Streak artifacts appear due to the angular under-sampling and the high frequencies introduced by the high-contrast bone structures of the skull. If no motion occurs, the volumes generated from subtraction of the mask volume from a bolus volume do not contain streak artifacts and are only corrupted by noise. An example slice of such a volume is shown in Figure 3.7b. As the streaks are introduced by the skull and reproduced in the mask and the bolus volumes, they subtract out. If motion occurs, it can be compensated by rigid registration of the mask and bolus volumes. However, the streaks are not fully eliminated by the subtraction and show up in the subtracted volumes as illustrated in Figure 3.7c. This is a challenge for non-linear noise reduction methods, which are commonly designed to preserve edges and therefore also preserve or even enhance streak artifacts. In this work only motion between acquisitions is simulated. Motion during the acquisition of a single volume might also occur and can be simulated with the forward projector implementation. This leads to additional challenges and makes the forward projection implementation for the dynamic brain phantom data an interesting tool for creating numerical data for future research work on FD-CTP Quantitative Evaluation of Reconstructed Perfusion Maps The generated numerical FD-CTP projection data is used for the evaluation of the reconstruction and noise reduction algorithms in this work. Perfusion maps are computed from TCCs reconstructed by the evaluated techniques using the perfusion analysis technique discussed in Section For the quantitative evaluation

43 3.3 Summary 33 of the resulting perfusion maps, the Pearson correlation (PC) and root mean square error (RMSE) between the reconstructed and the reference perfusion maps are calculated. Therefore an automated region of interest (ROI) analysis with vascular pixel elimination [Fies 12b] is applied. Air, bone and vessel structures are excluded from the perfusion maps according to the brain segmentation. A rectangular grid with a certain line spacing (e.g., 8 8 mm 2 ) is used to subdivide each slice of the perfusion map into square ROIs. For each ROI, the mean perfusion value is calculated for the reference and the reconstructed FD-CTP map. ROIs including voxels not belonging to brain tissue according to the segmentation are ignored. The PC and RMSE between the mean values of all valid ROIs in all slices are computed. The automated ROI analysis does not require manual selection of ROIs and is therefore user-independent. The RMSE and PC are computed from the N reconstructed samples x and the N reference samples x by RMSE (x, x ) = 1 N N (x i x i) 2, (3.5) i=1 PC (x, x ) = Ni=1 (x i x) (x i x ) with x = 1 N N x i. (3.6) i=1 (x i x) 2 (x i x ) 2 N i=1 3.3 Summary This chapter is concerned with the numerical simulation of FD-CTP for a meaningful evaluation of non-linear techniques for noise and artifact reduction. Non-linear methods are a popular field in medical imaging as they usually show superior results compared to linear approaches by exploiting prior known characteristics of the reconstructed object (e.g., homogeneity). As they are also dependent on the input data, numerical data with a similar structure and complexity as real data is required. Therefore a numerical brain phantom based on MR data acquired from a real human head was built. Section 3.1 describes the design of the phantom structure based on MR acquisition of a human brain and the numerical perfusion simulation. The phantom design is based on the work by Riordan et al. [Rior 11], which is extended by varying the perfusion parameters for further homogeneity reduction and including a high-resolution human skull. Furthermore, MATLAB software for easy-to-use phantom data creation is presented and made available online. In Section 3.2, the creation of numerical FD-CTP data by dynamic forward projection of the digital brain phantom is described including quantum noise and motion simulation. Finally, an automated ROI analysis technique for the quantitative evaluation of the reconstructed perfusion maps is described.

44 34 Numerical Simulation of Flat Detector CT Perfusion

45 C H A P T E R 4 Noise Reduction with Joint Bilateral Filtering 4.1 Bilateral Filtering and Joint Bilateral Filtering Joint Bilateral Filtering for Perfusion Imaging Summary Bilateral Filtering and Joint Bilateral Filtering Noise reduction in images by smoothing in homogenous areas while preserving the edges represents a main field of research in image processing. In perfusion imaging, denoising in the brain tissue areas is mandatory before perfusion parameter computation due to the low contrast agent signal in the tissue. At the same time, edges at highly contrasted vessels and between differently perfused areas in the brain tissue should be preserved. The bilateral filter is a popular tool for edge-preserving noise reduction as it shares many properties with other state-of-the art techniques, but has an intuitive formulation and is easy to implement. Section introduces the definition of the bilateral filter in the framework of neighborhood filters and discusses its relationship to other noise reduction methods including techniques emerging from the Bayesian framework for maximum a-posteriori (MAP) estimation. Subsequently, Section describes the parallelized implementation of the bilateral filter used in this work and discusses its computational complexity. Finally, Section introduces the joint bilateral filter (JBF) as an extension to the bilateral filter for performing improved edge-preserving noise reduction if additional knowledge from a guidance image is available Theoretical Background The bilateral filter (BF) is a non-linear image filter from the class of neighborhood filters (NF). Neighborhood filters [Buad 06] are designed to take average of the values of pixels which are both close in gray level value (range similarity) and spatial distance (spatial similarity). Let I : S R be a gray value image with arbitrary dimensions defined on the continuous support S such that I (p) is the gray value of the image at spatial location p S. Furthermore, let w σr : R + 0 R + 0 be a function to enforce range similarity and w σs : R + 0 R + 0 a function to enforce spatial similarity. The 35

46 36 Noise Reduction with Joint Bilateral Filtering parameter σ R R + controls the scope of the range similarity and the parameter σ S R + the scope of the spatial similarity, respectively. The general neighborhood filter on image I is defined as [Buad 06] NF(I(p)) = 1 ˆ w σr ( I (q) I (p) ) w σs ( q p W (p) 2 ) I (q) dq, (4.1) S were denotes the absolute value, 2 the Euclidean distance, and W (p) is a normalization factor ˆ W (p) = w σr ( I (q) I (p) ) w σs ( q p 2 ) dq. (4.2) S Common choices for the similarity functions w σd and w σr are the indicator function 1 t σ w σ (t) = (4.3) 0 t > σ, or the Gaussian kernel function w σ (t) = exp ( t 2 /σ 2) with standard deviation σ. (4.4) The classical linear Gauss filter can be recovered from the NF by ignoring the range similarity (w σr 1) and using the Gauss kernel for w σs. However, for edge-preserving filtering the range similarity must be considered in the weighting of the computed averages. Therefore w σr must not be constant. Then the NF becomes dependent on the input image and thereby spatial variant and non-linear. The first edge-preserving neighborhood filter known to the author was proposed by Lee [Lee 83] in 1983 as the sigma filter. The sigma filter uses the indicator function (Equation 4.3) for range and spatial 1 similarity determination. In 1985 Yaroslavsky proposed in his book on digital picture processing [Yaro 85] a NF using the Gauss kernel for range similarity and the indicator function for spatial similarity. The today s most common variant of the neighborhood filter is the bilateral filter, which uses Gaussian kernels both for range and spatial similarity weighting. The bilateral filter was first described in a PhD thesis by Weule [Weul 94] published in 1994 and a conference article by Aurich and Weule [Auri 95] published in Smith and Brady rediscovered the bilateral filter as part of the SUSAN image processing framework [Smit 97]. In 1998 the bilateral filter was proposed again independently of the previous work by Tomasi and Manduchi [Toma 98] and it finally became a popular tool for many image processing applications. The review article by Paris et al. [Pari 07] gives a broad overview of its properties, manifold applications and efficient implementation. The bilateral filter is popular, as it has a simple, intuitive formulation based on only two parameters (spatial and range similarity) and produces similar and possibly better results than more complex and less intuitive techniques for edge-preserving smoothing. In [Pari 07] the relationship of the bilateral filter to other common nonlinear denoising methods is discussed. It is shown that bilateral filtering is equivalent 1 Indeed, the filter proposed by Lee uses a box shaped neighborhood for averaging. Thus the Euclidean norm in the spatial similarity function in Equation 4.1 needs to be replaced by the maximum norm.

47 4.1 Bilateral Filtering and Joint Bilateral Filtering 37 to local mode filtering [Weij 01]. Furthermore, Durand and Dorsey [Dura 02] pointed out that the bilateral filter is a robust filter in the sense of robust statistics [Hamp 05]. The range weight introduces a robust metric, which differentiates between inliers and outliers. This assures that pixels that are unrelated to each other (i.e., that have different intensities) have little influence on each other in the weighted average. Further mathematical links of the bilateral filter to existing robust estimation techniques for image noise reduction were discussed by Elad [Elad 02], Barash and Comaniciu [Bara 04], and Buades et al. [Buad 06]. To elaborate this link, Elad [Elad 02] introduced a penalized least squares (PLS) functional, which penalizes image gradients in homogenous image regions, but allows high gradients at image edges. This PLS functional is similar to previous approaches [Lage 88], but makes use of several scales of image gradients. The minimization of such a PLS functional emerges from the Bayesian framework and corresponds to MAP estimation [Jain 89]. Correspondingly, Elad showed that one iteration of the bilateral filter is equivalent to one iteration of the Jacobi algorithm [Luen 03] to optimize the introduced PLS functional. Thus the result of bilateral filtering an image corrupted by additive white Gaussian noise represents a Bayesian MAP estimate using an edge-preserving prior. Barash and Comaniciu [Bara 04] established the relationship of the bilateral filter to mean shift filtering [Coma 02]. Buades et al. [Buad 06] proved that for continuously defined images iterating the Yaroslavsky filter is asymptotically equivalent to the evolution of the anisotropic diffusion equation introduced by Perona and Malik [Pero 90]. An interesting alternative to the bilateral filter is the non-local means (NLM) noise reduction technique proposed by Buades et al. [Buad 05]. The NLM filter reduces the noise by computing a weighted average of all pixels in the whole image with a similar neighborhood as the processed pixel. Thus the NLM filter makes use of redundant structures in the whole image, where the neighborhood filters only account for spatially close structures. However, this comes for the price of a significantly higher computational effort. Furthermore, the non-locality makes the filter less intuitive and predictable than the neighborhood filters Computational Complexity and Parallelized Implementation As the bilateral filter is an intuitive tool, which is simple to implement but nevertheless has very similar properties as other state-of-the-art methods, it serves as the basis of the noise reduction techniques introduced in this work. Below the parallelized implementation of the bilateral filter is discussed. All volumes processed in this work are considered as a discrete 3D volume defined on a voxel grid with isotropic spacing v S. The volume has a size of N x, N y, N z N in x, y and z direction, respectively, and a total number of S V = N x N y N z voxels. The voxels in the grid are addressed by index i K with K {i = (i x, i y, i z ) 0 i x < N x ; 0 i y < N y ; 0 i z < N z } N 3 0. (4.5) The volume function V (i) : K R maps the voxel index to the measurement value (usually HUs) of the corresponding voxel.

48 38 Noise Reduction with Joint Bilateral Filtering The bilaterally filtered value at voxel i results from the weighted average of the voxel values in the neighborhood N i defined by the discrete version of Equation BF (V (i)) = w σr ( V (j) V (i) ) w σs ( j i W (i) 2 /v S ) I (j), (4.6) j N i W (i) = w σr ( V (j) V (i) ) w σs ( j i 2 /v S ). (4.7) j N i The distance functions w σr and w σs correspond to the Gaussian kernel function defined in Equation 4.4. The spatial similarity w σs is scaled by the isotropic voxel size v S to keep the spatial smoothing kernel independent from the actual voxel size. The neighborhood N i is defined by a 3D cube centered around voxel i. The side length of the cube is usually set to 4 σ S /v S voxels if 4 σ S /v S is odd and 4 σ S /v S + 1 if 4 σ S /v S is even. This ensures that the support of the kernel is large enough to cover most of the energy of the spatial kernel and the computational complexity is reduced to the minimum. If a voxel inside the neighborhood N i lies outside the support of the volume, the value of the spatial closest voxel inside the support is assigned (clamping). Each voxel in the bilateral filter Equation 4.6 can be processed independently. Thus bilateral filtering is easy to parallelize for multiprocessor computing systems. Like the forward projector described in Section 3.2.1, the bilateral filter was implemented using the CUDA programming language for massively parallel computation on GPUs. The bilateral filter is parallelized by computing the bilaterally filtered values of each column in each volume slice in one individual thread. The evaluation of Equation 4.6 requires the computation of the weighted sum inside the neighborhood of each voxel. As the side length of the cubic neighborhood depends on σ S, the computational complexity for bilateral filtering with a brute force implementation as conducted in this work is O (S V σs). 3 Thus the computational load rapidly becomes tremendous with increasing bandwidth of the spatial kernel. Several approaches for reducing the computational complexity have been proposed. Weiss [Weis 06] presented a histogram-based approach to approximate bilateral filtering with a computational complexity of O (S V log σ S ). Yang et al. [Yang 09] introduced an algorithm for photo images with a computational complexity of O (S V ), which is independent of the spatial kernel support by splitting the bilateral filter into linear Gaussian filter responses. However, these approaches require integral images which are discretized in the range domain. The bolus volumes in perfusion imaging have like other volumes reconstructed from CT projection data a much higher dynamic range than usual gray scale photo images. Therefore the range of CT volumes is usually quantized in 16 bit in contrast to the 8 bit images used in the work by Yang et al. [Yang 09]. As the size of the range domain influences the computation speed and memory consumption of the proposed algorithms, it is not clear if they perform practically faster than the brute force method when applied to CT data. To keep the computational complexity moderate, voxel grids with an isotropic voxel side length of v S 1 mm are used in this work. This allows to cover the human brain inside a volume with of size N x = N y = N z = 256 voxels. For a typical spatial smoothing parameter σ S = 1.5 mm a kernel size of voxel is sufficient.

49 4.1 Bilateral Filtering and Joint Bilateral Filtering Joint Bilateral Filter The joint bilateral filter is a variant of the bilateral filter which incorporates additional information from a guidance image to improve the edge preservation. It was proposed simultaneously in 2004 by Petschnigg et al. [Pets 04] and by Eisemann and Durand [Eise 04], who named it cross bilateral filter. The equation for the joint bilateral filter can be derived from the bilateral filter Equation 4.6 by using a guidance image G for computing the range similarity in the kernel function w σr 1 JBF (V (i)) = w σr ( G (j) G (i) ) w σs ( j i W (i) 2 /v S ) I (i), (4.8) j N i W (i) = w σr ( G (j) G (i) ) w σs ( j i 2 /v S ). (4.9) j N i The guidance image G needs to have the same size as the filtered image V. The initial idea of joint bilateral filtering was to improve no-flash photograph pictures taken in low-light conditions by combining the no-flash image with a flash picture taken from the same scene. The non-flash image of a low-light scene (e.g., with candle light) has a pleasing and natural illumination. In low-light environments the exposure time of the camera is usually increased to avoid visible image noise. However, the longer exposure time increases the risk of motion blur due to camera shake or scene motion. An additional flash image of the same scene describes the details of the scene with a much higher signal-to-noise ratio. The joint bilateral filter allows to use the details from the low-noise flash image for edge preserving noise reduction in the pleasing no-flash picture by filtering the no-flash image guided by the flash image. Thus prolonged exposure times can be avoided and a non-flash image with low noise, sharp details and pleasant light atmosphere can be computed. By now further applications and extensions of the joint bilateral filter have been proposed, e.g., the joint bilateral up-sampling method [Kopf 07] or the dual bilateral filter [Benn 07]. The dual bilateral filter is used for noise reduction in a combined RGB and infra-red video stream by computing the range similarity with respect to both the guidance image and the filtered image itself. Apparently the joint bilateral filter has the same computational complexity as the bilateral filter and can be implemented for parallel GPU computing in a very similar way. Yang et al. [Yang 09] showed how to extend their O (S V ) implementation of the bilateral filter to joint bilateral filtering. He et al. [He 13] introduced a novel filter for guided image filtering with O (S V ) complexity. This filter also applies smoothing by weighted averaging in neighborhoods, but computes the weights from the guidance image by a local linear regression model. The computation speed and memory consumption of this guided filter is not dependent on the size of the range domain. Therefore an adaption of this filter for 3D noise reduction in perfusion imaging might be an interesting option for computation speed increase.

50 40 Noise Reduction with Joint Bilateral Filtering 4.2 Joint Bilateral Filtering for Perfusion Imaging Subsequent to the introduction of the joint bilateral filter and its application for noise reduction in general image processing, Section describes how joint bilateral filtering can be applied for noise reduction in perfusion imaging and shows examples of its beneficial application. Finally, Section discusses the relation to existing noise reduction techniques for perfusion imaging Guidance Volume Computation To apply the joint bilateral filter in perfusion imaging, a suitable guidance image is required. In this work, the temporal maximum intensity projection (MIP) of the reconstructed time series of bolus volumes after mask subtraction is used as guidance volume (the subtracted bolus volumes describe the contrast agent enhancement over time). The beneficial properties of the MIP as guidance volume to preserve the relevant structures in the bolus volumes, especially the edges at the vessels, are discussed below. The MIP M (i) : K R is formed by computing the peak attenuation for every voxel i K from all N rot acquired bolus volumes V t (i) : K R, t = 1... N rot M (i) = max {V t (i) t = 1... N rot }. (4.10) Figure 4.1a shows a slice of the MIP volume computed from a time series of bolus volumes, which were reconstructed from simulated projection data created with the digital brain perfusion phantom described in Chapter 3 without adding Poisson noise. A FD-CTP acquisition with N rot = 10 bolus rotations and N proj = 133 projections per rotation was simulated assuming a rotation time of T r = 2.6 s and a pause time between rotations of T p = 1 s. As the focus of this chapter is on noise reduction, no head motion was simulated. Figure 4.1b shows the resulting MIP created from projection data with Poisson noise assuming an emitted X-ray density of photons per mm 2 at the detector and a monochromatic photon energy of 60 kev. The bolus volumes were reconstructed using the FDK algorithm with a non-smoothing filter kernel to avoid blurring of edges at the vessels. However, due to the low contrast agent signal in the brain tissue, the tissue areas in the MIP are very noisy and the tissue contrast agent enhancement is barely visible. Thus the MIP needs to be denoised before it can serve as a guidance volume for noise reduction in the bolus volumes. Figure 4.1c shows the MIP after applying a 3D Gauss filter with a standard deviation of σ S = 1.5 mm. The noise in the tissue is clearly reduced, but the edges at vessels are blurred leading to a partial volume effect, which can be seen in the line profiles through a vessel shown in Figure 4.2. The peak of the vessel in the Gauss-filtered MIP is reduced from to 430 HU to 180 HU. Figure 4.1d shows the resulting slice after bilateral filtering according to Equation 4.6 with a spatial bandwidth of σ S = 1.5 mm and a range bandwidth of σ R = 80 HU. The σ R parameter is adapted to the estimated noise level according to the relation σ R = 1.95σ n suggested by Liu et al. [Liu 06]. The noise level σ n is estimated by measuring the standard deviation in a homogenous area inside the CSF of the phantom. In the bilaterally filtered slice the noise in the tissue is still clearly reduced, but the edges at the vessels are much better preserved. The line profiles

51 4.2 Joint Bilateral Filtering for Perfusion Imaging 41 (a) Original MIP (b) Noisy MIP (c) Gauss filtered MIP (d) Bilateral filtered MIP (e) MIP after joint bilateral filtering Figure 4.1: Slices of the maximum intensity projection (MIP): (a) slice reconstructed from noiseless data, (b) slice reconstructed from noisy data, (c) MIP after filtering with a Gauss kernel, (d) MIP after filtering with bilateral filter, and (e) MIP recomputed after joint bilateral filtering of the time series of volumes (window: (a) and (e) [0 40] HU; (b), (c) and (d) [0 100] HU). The red arrow in (a) and (e) indicates a region with reduced perfusion. Contrast attenuation [ HU] Reference Noisy Gauss Filter Bilateral Filter Joint Bilateral Filter x [Pixel] Figure 4.2: Line profile through tissue and a vessel after Gauss filtering and bilateral filtering of the MIP and in the MIP recomputed after joint bilateral filtering of the time series of volumes.

52 42 Noise Reduction with Joint Bilateral Filtering (a) Bolus slice from noiseless data (b) Bolus slice from noisy data (c) Bilaterally filtered bolus slice (d) Joint bilaterally filtered bolus slice Figure 4.3: Slices of a bolus volume: (a) slice reconstructed from noiseless data, (b) slice reconstructed from noisy data, (c) bolus slice after bilateral filtering and (d) bolus slice after joint bilateral filtering with MIP as guidance image (window: [0 20] HU). in Figure 4.2 show that the peak in the vessel remains almost unchanged. However, the area with reduced perfusion visible in the noiseless reference image (Figure 4.1a, indicated by the red arrow) is not perceptible. Thus the generation of a further improved guidance volume is desired. The bilaterally filtered MIP serves as a guidance volume for a first joint bilateral filtering iteration for noise reduction in the bolus volumes. Each volume in the bolus time series V t, t = 1... N rot is denoised using the joint bilateral filter according to Equation 4.8 with a spatial bandwidth of σ S = 1.5 mm and a range bandwidth of σ R = 32 HU. Figure 4.3 shows the results of noise reduction in the second bolus volume, which has a low contrast enhancement in vessels ( 50 HU) and no contrast enhancement in tissue yet. In Figure 4.3b the bolus volume slice reconstructed from noisy data is shown. The contrast in the vessels is low compared to the noise level. Thus if a bilateral filter (σ S = 1.5 mm/σ R = 80 HU) is used, the edges at vessels are blurred and the contrast agent enhancement is underestimated as shown in Figure 4.3c and in the line profile in Figure 4.4. In contrast, the joint bilateral filtering result shown in Figure 4.3d uses the strong edge information from the MIP. Thus the edges at the vessels are preserved and no partial volume effect arises. The peak of

53 4.2 Joint Bilateral Filtering for Perfusion Imaging 43 Contrast attenuation [ HU] Reference Noisy Bilateral Filter Joint Bilateral Filter x [Pixel] Figure 4.4: Line profile through tissue and vessel structures in a bolus slice after bilateral filtering and joint bilateral filtering with MIP as guidance image. the vessel in the line profile (Figure 4.4) is very close to the reference. Furthermore, the guidance volume assures that all bolus volumes are filtered with same spatially variant filter kernels. From the denoised bolus time series the temporal MIP can be recomputed according to Equation Figure 4.1e shows the updated MIP, where the hypo-perfused area (indicated by the red arrow) becomes visible again. These results suggest that iterating the joint bilateral filter with recomputation of the MIP as guidance volume is useful. In Section 6.2, the iterative noise reduction with JBF is discussed in detail Related Perfusion Noise Reduction Methods The benefits of non-linear noise reduction in perfusion imaging were discussed already by Murase et al. [Mura 01] in They compare slice-wise 2D spatial filtering using the linear Gauss filter, the median filter [Aria 09] and the anisotropic diffusion technique [Pero 90] for noise reduction in dynamic susceptibility contrastenhanced MR (DSC-MR) CBF imaging. The evaluation using simulation and clinical data sets shows that the anisotropic diffusion technique outperforms Gauss and median filtering as it preserves quantitative accuracy while efficiently removing noise. Similarly, Saito et al. [Sait 08] proposed to use a 2-D nonlinear diffusion scheme [Weic 98] for CTP denoising. Kosior et al. [Kosi 07] introduced spatio-temporal 4D bilateral filtering to DSC-MR perfusion imaging and showed its superior performance in comparison to 4D linear Gauss filtering using simulation and clinical data. However, the 4D bilateral filter has a considerably high computational complexity (O (S V σs) 4 per temporal volume). Furthermore, it does not allow to handle the temporal and spatial domain separately, despite that the temporal behavior of the TCCs is different to the spatial structures. The CTP noise reduction by Bruder at al. [Brud 11] avoids these limitations by splitting the spatio-temporal filtering into 3D spatial bilateral filtering of all temporal volumes followed by 1D temporal bilateral filtering of the TCCs. However, as discussed in Section the 3D spatial bilateral filter leads to blurring of vessels in volumes with low contrast agent enhancement in

54 44 Noise Reduction with Joint Bilateral Filtering the beginning and end of the time series. Furthermore, in FD-CTP the TCCs are temporally coarsely sampled and no further temporal smoothing is desired. Another interesting technique for CTP noise reduction is the time-intensity profile similarity (TIPS) bilateral filter presented by Mendrik et al. [Mend 11]. As the JBF, it is a 3D spatial bilateral filter applied to each volume in the time series separately. In contrast to JBF, TIPS considers not only the peak values but the Euclidean distance of the whole TCCs to compute the range similarity function. The TIPS filter is a variant of the neighborhood filter defined in Equation 4.1, where the spatial similarity is controlled by a Gaussian kernel with variance σ 2 S and the range similarity between a voxel pair (i, j) is defined by w σtips (i, j) = exp 1 ( 1 N rot 2 N rot t=1 ) 2 (V t (i) V t (j)) 2 /σ TIPS. (4.11) The TIPS filter parameter σ TIPS controls the range similarity. The JBF and the TIPS filter share the advantages of avoiding temporal smoothing, filtering all volumes with the same filter kernels and preserve edges also in volumes with low contrast agent enhancement. The TIPS filter is computationally more expensive compared to JBF, as the TIPS has to be computed for every compared voxel pair (i, j). If all volumes are filtered simultaneously, the TIPS needs to be computed only once per voxel pair and the computational overhead compared to JBF is limited. However, TIPS is more challenging to implement for fast parallel GPU computation. Using the TIPS filter simultaneously on all volumes requires access to the data in the neighborhoods around the filtered voxel in all acquired volumes. This requires more GPU memory, in which all temporal volumes need to be stored, and makes it more difficult to find coalesced memory access patterns, which are required for efficient GPU computations [CUDA 11]. Furthermore, the JBF is easier and more intuitive to analyze and to extend (e.g with the streak artifact reduction method discussed in Section 6.2), as it is controlled by the guidance volume. Thus it is used for noise reduction in this work. Fang et al. [Fang 13] introduced an approach for low dose CTP, which combines perfusion parameter analysis by deconvolution (see Section 2.1.2) with a sparse representation of the perfusion maps by patches. An online dictionary learning technique [Mair 09] is used to learn the patches from training perfusion maps acquired with higher dose. As this approach is an extension of the perfusion analysis step, it can be combined with the neighborhood filter noise reduction techniques. However, it requires the existence of a suitable database of training volumes, which is currently not available for FD-CTP. CTP training data might limit the advantages of FD-CTP, like high resolution in axial direction. 4.3 Summary This chapter presents a novel method for noise reduction in perfusion imaging using joint bilateral filtering. Section 4.1 introduces the bilateral filter based on the concept of the edge-preserving neighborhood filters. Its relation to other non-linear noise reduction techniques and its computational complexity is discussed. Subsequently,

55 4.3 Summary 45 the joint bilateral filter is introduced, which is a variant of the bilateral filter using a guidance image. Section 4.2 shows how the joint bilateral filter can be beneficially applied for noise reduction in perfusion data by iteratively filtering the time series of bolus volumes guided by the temporal maximum intensity projection. Finally, the relation of the joint bilateral filter to other existing perfusion noise reduction techniques like the TIPS filter [Mend 11] is elaborated.

56 46 Noise Reduction with Joint Bilateral Filtering

57 C H A P T E R 5 Flat Detector CT Perfusion with Low Speed Acquisition 5.1 Low Speed Acquisition Mathematical Formulation of Dynamic Iterative Reconstruction Implementation Details Evaluation Discussion and Conclusions This chapter is based on Dynamic Iterative Reconstruction for Interventional 4-D C-Arm CT Perfusion Imaging, by M. Manhart, M. Kowarschik, A. Fieselmann, Y. Deuerling-Zheng, K. Royalty, A. Maier, and J. Hornegger. IEEE Transactions on Medical Imaging, Vol. 32, No. 7, pp , July Low Speed Acquisition Introduction One challenge in FD-CTP imaging with classical C-arm angiography systems is the slow rotation speed of the C-arm gantry, which leads to a coarse temporal sampling of the acquired contrast agent enhancement if static reconstruction algorithms are used. This chapter discusses a novel approach to improve the temporal sampling with a dynamic algebraic reconstruction technique. The novel approach combines a spline basis model to describe the TCCs with statistical ray weighting and a regularization based on joint bilateral filtering to handle noise and data insufficiency. Dynamic iterative reconstruction (DIR) is used to find the parameters of the spline basis model. The algorithm is evaluated with digital dynamic brain phantom data and with clinical data from six canine stroke models. Section introduces the slow speed FD-CTP acquisition protocol, which is used for generating numerical data and the acquisition of the animal data. Section 5.2 discusses the basic concept and mathematical formulation of the DIR algorithm. On this basis Section 5.3 presents the detailed implementation using GPU computing. Subsequently, the new algorithm is evaluated in Section 5.4 using simulated data and in vivo data. In Section 5.5, the benefits of the novel technique compared to existing approaches and its current limitations in practical clinical use are discussed. 47

58 48 Flat Detector CT Perfusion with Low Speed Acquisition view-angle increment 0.8 number of views per rotation (N proj ) 248 angular range per rotation time per rotation (T r ) 4.3 s pause time (T p ) 1.2 s number of rotations (N rot ) 7 total scanning time (T scan ) 37.3 s source-to-detector distance 1200 mm detector pixel size mm 2 number of detector pixels (S P ) after 4 4 re-binning total detector size mm 2 tube peak voltage 70 kvp system dose 1.2 µgy / projection Table 5.1: Low speed acquisition parameters Low Speed Acquisition Protocol The FD-CTP slow speed acquisition protocol is based on the protocol described in Section with the following parameters: each rotation takes T r = 4.3 s, with a pause of T p = 1.2 s between two successive rotations. Thus, direct reconstruction of the rotations would allow a temporal sampling of TCCs with period T r + T p = 5.5 s during the total scan time T scan = N rot T r + (N rot 1) T p = 37.3 s. In each rotation N proj = 248 projections along an angular range of are acquired. After contrast agent injection, the C-arm is rotated N rot = 7 times in bi-directional manner as illustrated in Figure 2.5. The measured photon counts (X-ray intensities) of all N rot bolus rotations are denoted by vector k B N S P N P (B: bolus), where SP denotes the number of detector pixels and N P = N rot N proj the total number of projections for N rot rotations. The mask photon counts are denoted by the vector k M N S P N P (M: mask). Each entry in vector k M is given by the intensity value of the mask projection, which corresponds to the intensity value of the respective bolus projection in vector k B (i.e., with the same source position and ray direction). By logarithmic pre-processing of k M and k B, the X-ray attenuation line integrals denoted by the vectors p M and p B are computed p M/B i = ln ks i k M/B i, i = 1... S P N P, (5.1) where ki S denotes the number of emitted photons for ray i. The mask projections are subtracted from the bolus projections to generate the projection data vector p = p B p M = [ p T 1,..., p T N P ] T, p R N P S P, containing the line integrals describing the pure contrast agent dynamics and noise. Furthermore, the vector t P = [ t P 1,..., t P N P ] T describes the acquisition time point of every projection in p. Table 5.1 shows an overview of all acquisition parameters.

59 5.2 Mathematical Formulation of Dynamic Iterative Reconstruction Mathematical Formulation of Dynamic Iterative Reconstruction Modeling of Time-Contrast Curves There is a continuous contrast agent flow during the acquisition, so the observed volume is different for each of the N P projection images. For an exact solution, the 3D+t volume vector x = [ x T 1,..., x T N P ] T would have to be reconstructed, consisting of N P 3D volumes X i R Nx Ny Nz represented as column vectors x i R S V with S V = N x N y N z and i = 1... N P. To describe the mapping of the 3D+t volume to the projection data, the system matrix A is defined. A is assembled from the matrices A i, which map the 3D volumes to the projection images according to the acquisition geometry, such that p i = A i x i and p = Ax A A 2 0 A = A NP (5.2) with A i R S P S V and A R (N P S P ) (N P S V ). Directly solving p = Ax for the exact solution x is not possible since the equation system is heavily under-determined. Therefore each of the TCCs described by x is constrained to be inside a subspace spanned by a set of N w N P basis functions b j (t), j = 1... N w, such that the vector x i, which approximates the contrast agent attenuation in the volume at time point t P i, is computed by a linear combination of basis functions with weight vectors w j N w ( ) x i = b j t P i wj, w j R S V. (5.3) j=1 The interpolation of the 3D+t volume vector x from all basis weights w w = [ w T 1,..., w T N w ] T (5.4) is a linear operation denoted by the matrix B R (N P S V ) (N w S V ) such that x = Bw. Using basis functions to describe the TCCs reduces the degrees of freedom of the reconstruction problem from S V N P to S V N w. The reconstruction problem to obtain the basis weights w from the measured projection data p can be expressed as a least-squares problem, which minimizes the Euclidean distance between the measured projection data p and the forward projected estimated 3D+t volume w = 1 2 arg min w ABw p 2 2. (5.5) In this optimization problem the weight vector w and the interpolation matrix B describe the temporal dynamics of the contrast agent flow and the matrix A describes the projection geometry of the C-arm system.

60 50 Flat Detector CT Perfusion with Low Speed Acquisition Statistical Ray Weighting In the next step, a statistical noise model is included into Equation 5.5 to transform this equation into the maximum likelihood (ML) estimate of the weights ˇw from projection data corrupted by quantum noise. To account for quantum noise, the numbers of measured photons can be described by independent Poisson random processes [Buzu 08]. First, it is discussed how to model the noise in the projection data p, which is generated by logarithmic pre-processing of k M and k B followed by subtraction. Let ˆk P ( µ = k ) be a Poisson random variable describing a photon measurement with mean k corresponding to the unknown number of ideally measured arriving photons. In tomographic brain imaging a large number of counts can be assumed, i.e., k > For such large counts, a Gaussian process is an excellent approximation of the Poisson process [John 05] ˆk N ( µ = k; σ 2 = k ). (5.6) By taking the logarithm of ˆk according to Equation 5.1 the random variable ˆp is obtained, which describes the corresponding line integral. The distribution of ˆp can be approximated by [Hsie 98] ˆp N ( µ = p = ln ( k S / k ) ; σ 2 = 1/ k ), (5.7) where k S denotes the number of emitted photons. If ˆp B and ˆp M denote bolus and corresponding mask measurements, respectively, which are two independent Gaussian random variables, their difference ˆp S = ˆp B ˆp M, which represents the pure contrast agent enhancement, is also a Gaussian random variable ˆp S N ( µ = p B p M ; σ 2 = 1/ k B + 1/ k M). (5.8) Thus the noise in the subtracted projection data p can be modeled by additive Gaussian noise, where the variance is related to the number of photon counts measured in mask and bolus acquisitions. Since the contrast agent attenuation is very small compared to the attenuation of the anatomic structures, the variance σi 2 of each entry p i in p is approximated by the number of photons measured in the corresponding mask acquisition σi 2 1/ki B + 1/ki M 2/ki M. (5.9) The maximum likelihood estimation of the weights ˇw from projection data with Gaussian noise is provided by the weighted least squares function (WLS) D (w) [Zeng 10], which combines Equation 5.5 with the diagonal weighting matrix D ˇw = arg min w D (w), (5.10) D (w) = 1 2 (ABw p)t D (ABw p), (5.11) where D = diag { k M 1 /2,, k M S P N P /2 }.

61 5.2 Mathematical Formulation of Dynamic Iterative Reconstruction 51 (a) w/o vessel masking (b) w/ vessel masking (c) projection mask Figure 5.1: Temporal maximum intensity projection (MIP) of numerical projection data from the digital brain phantom reconstructed without and with vessel-masked back projection (window: [0 50] HU) Landweber Iterations It is practically infeasible to solve Equation 5.10 directly, because the data dimensions are huge and the system matrix of image reconstruction problems is typically ill-conditioned [Jian 03]. Thus this large scale problem is solved as described in [Neuk 10] by a gradient-based iterative procedure using the Landweber iteration scheme [Land 51] w new = w old + β B T A T D ( p ABw old). (5.12) The parameter β controls the step size of the weights update in each iteration. The matrix product AB describes the calculation of the 3D+t volume x by interpolation using the basis functions followed by the forward projection using the system matrix A. The diagonal matrix D weights each entry of the error image p ABp old according to its statistical uncertainty resulting in the weighted error vector e = D ( p ABw old). The matrix product B T A T is a back projection of e into the weight vector w old, where B T introduces an additional weighting of the back projected errors. To describe the effect of the transposed interpolation matrix B T, the weighted error vector e is split into parts e i, i = 1... N P, where e i corresponds to projection image p i. The update of the weight vector w j belonging to basis function b j (t) is defined by w new j = wj old N P + β i= Vessel-Masked Backprojection b j ( t P i ) A T i e k i. (5.13) Figure 5.1a shows a slice of the temporal MIP volume reconstructed from digital brain phantom data after 30 iterations of the Landweber scheme according to Equation 5.12 (with D chosen as unity matrix since data without noise was used). Severe streak artifacts around the vessels show up. To avoid these artifacts, an empirical modification of the weight update step in Equation 5.12 is applied by using a vessel-masked

62 52 Flat Detector CT Perfusion with Low Speed Acquisition Time [s] 30 (a) Linear asymmetric splines Time [s] 30 (b) Linear splines, T scale = 2 s Time [s] 30 (c) Cubic splines, T scale = 2 s Figure 5.2: Basis functions used to describe the reconstructed TCCs. Red and green solid curves: basis functions. Blue dashed curves: relative angular C-arm position. back projection. The back projection step is modified such that rays intersecting with high contrast vessel structures are only used for updating voxels containing vessels. Therefore a first reconstruction of the projection data p is done using FDK reconstruction to initialize the weights w. Then the temporal MIP volume M is computed and a binary vessel mask v V {0, 1} S V in volume space is created by thresholding M. By forward projection of v V a vessel mask in projection space v P {0, 1} S P N P is calculated (Figure 5.1c). The complete error image e is only back projected into vessel voxels indicated by v V. Into the remaining voxels (indicated by v V ) only the rays without any vessel intersection (indicated by v P ) are back projected ( describes element-wise multiplication and describes element-wise negation), i.e., w new = w old + β B T w V, (5.14) w V = v V A T e + v V A T ( v P e ). (5.15) With the modified back projection step, no streak artifacts arise as shown in the MIP slice in Figure 5.1b. Details on the initialization and the vessel mask creation are given in Section 5.3.

63 5.2 Mathematical Formulation of Dynamic Iterative Reconstruction Basis Functions The performance of different sets of basis functions to model the TCCs is evaluated. Basis functions with compact support are used, such that in the interpolation step (Equation 5.3) and in the update step (Equation 5.13) only the addends with non-zero basis function values have to be evaluated. This reduces the computational effort. Three different classes of basis functions are investigated in this work: asymmetric linear splines, symmetric linear splines, and cubic splines. The first class is given by asymmetric linear functions shown in Figure 5.2a. The TCCs are described by N w = 2 N rot weight vectors w j. The knots of the basis functions are placed at the time points t w = [ t w 1,..., t w N w ] T, where t w j = j 1 j 1 2 (T 2 stop + T rot ) T rot j odd (Tstop + T rot ) T rot j even. The TCCs are described by linear interpolation between the knots, which have nonuniform distance to each other. Therefore two different functions to describe the basis are defined. If the knot index j is odd then b ALO j (t) is used and if j is even then b ALE j (t) is used. These basis functions are defined with T 1 = T rot /2, T 2 = T rot /2 + T stop, and t = t t w j as 1 + t /T 2 T 2 t < 0 b ALO j (t) = 1 t /T 1 0 t T 1 0 else, b ALE j (t) = 1 + t /T 1 T 1 t < 0 1 t /T 2 0 t T 2 0 else. Exceptions need to be defined for the beginning and for the end of the acquisition. For j = 1, T 2 = T rot /4 is used, since it is assumed that the TCCs rise from 0 HU in the beginning. For t > t w N w, a constant basis function is used. This reflects the assumption that a steady-state plateau phase of residual contrast is expected in the end. This type of basis functions avoids to place spline knots in the pauses between the acquisitions. The second class of basis functions is given by linear spline functions with uniformly distributed knots placed in distance T scale, which are shown in Figure 5.2b. In this work, basis functions with T scale = 1 s and T scale = 2 s are used. With the total scan time T scan, the total number of splines used is N w = T scan /T scale and the places of the spline knots are t w j = j T scale, j = 1... N w. The linear basis functions are defined as b LS j (t) = 0 t 1 1 t t < 1, (5.16) with t = t t w j /Tscale. Again a constant basis function for t > t w N w is used. The third class of basis functions is given by cubic spline functions with uniformly distributed knots, which are shown in Figure 5.2c. The knots are placed like the

64 54 Flat Detector CT Perfusion with Low Speed Acquisition linear spline knots. The cubic spline basis functions are defined by the closed-form representation of the cubic B-spline as [Unse 99] b CS j (t) = 0 t 2 (2 t ) 3 /6 2 > t 1 2 ( 3 t t ) t < 1, (5.17) with t = t t w j /Tscale Regularization by Joint Bilateral Filtering To allow reliable reconstruction of TCCs under noisy conditions, the ML estimate of Equation 5.10 is combined with joint bilateral filtering as described in Section 4.2. Additionally a physically correct solution is enforced by allowing only nonnegative spline weights. As discussed in Section 4.1, the bilateral filter is related to Bayesian noise removal. The JBF is similar to bilateral filtering, just the weights in the penalty term are defined by the guidance volume. Thus the combination of the ML reconstruction of the weights with joint bilateral filtering results in a maximum a-posteriori (MAP) estimation. The MAP estimation is denoted as the DIR-MAP technique and can be expressed as a penalized weighted least squares (PWLS) problem. The constrained formulation of the PWLS problem in combination with a JBF penalty function R JBF (w) is w = arg min w RJBF (w) s.t. D (w) ε and w 0. (5.18) It searches for the non-negative spline weights w, which have the lowest JBF penalty at a data inconsistency D (w) of not more than ε R +. The data inconsistency parameter results from the sum of the minimally achievable inconsistency ε min > 0 and an additional tolerance ε t 0: ε = ε min +ε t. The minimal inconsistency ε min will always be positive since noise, physical effects such as beam hardening, discretization, and the approximation of the TCCs by the splines will not allow to find a solution with perfect data consistency in practical applications. The tolerance ε t is a parameter to control smoothness and noise level in the brain tissue. For example, a higher ε t achieves a solution with lower data consistency and lower JBF penalty, which means less noise but more blurring in the tissue. In this work, Equation 5.18 is not solved directly. Instead, a solution matching the goals of data consistency, edge-preserving smoothness, and positivity is found using the empirical approach discussed in the next section. 5.3 Implementation Details This section describes the details of the DIR-MAP implementation, which finds an empirical approximation of the MAP estimate w according to Equation A flow chart of the complete algorithm is shown in Figure 5.3 and a detailed overview of the single steps is shown in Algorithm 5.1. These steps are discussed below.

65 5.3 Implementation Details 55 Algorithm 5.1: DIR-MAP reconstruction algorithm Data: Raw mask projection data k M and bolus projection data k B Result: DIR-MAP reconstruction of basis weights w /* The symbol describes element-wise multiplication, the symbol describes element-wise negation and max describes element-wise maximum selection. */ 1 Compute p by pre-processing and subtraction of k M and k B 2 FDK reconstructions of each rotation: x i = FDK {p i }, i = 1... N rot 3 Create MIP M and volume vessel mask v V : M = max {x i i = 1... N rot }, v V = (M > τ MIP ), v V {0, 1} S V 4 Create projection vessel mask: v P i = ( A i v V > 0 ), v P i {0, 1} S P, i = 1... N P 5 Initialize basis weights w from FDK reconstructions 6 Apply bilateral filter on M with σ R0 and σ S 7 Apply N JBF iterations of JBF on w with σ R and σ S 8 for k = 1... N it do 9 for o = 1... N rot do 10 for p = 1... N sub do 11 Initialize temporary weights: w j = 0, j = 1... N w, w j R S V 12 for q S o,p do 13 Interpolate dynamic volume x at t P q : x = j S J b j ( t P q ) wj, S J = { j b j ( t P q ) > 0 } 14 Compute error image via forward projection: e = D q (p q A q x) 15 Vessel-masked back projection of error image: ( w = v V A T q e + v V A T q v P q e ) 16 Update temporary weight vectors: w j = w j + β b j ( t P q ) w, j S J 17 end 18 Update weight vectors: w j = w j + w j, j = 1... N w 19 Assure non-negativity: w = max {w, 0} 20 end 21 end 22 if (k mod 3 == 0) then 23 Apply JBF on w with σ R and σ S : w = JBF {w} 24 end 25 end 26 Output result: w = w

66 56 Flat Detector CT Perfusion with Low Speed Acquisition Figure 5.3: DIR-MAP algorithm flow chart Initialization In Step 1, the projection data p with pure contrast agent enhancement is computed by subtraction of the mask from the bolus projection images. In case of real data, additional pre-processing is required, particularly to compensate for small motion of objects inside the field of view. These pre-processing steps are described in Section In Step 2, all rotations are reconstructed using the short-scan FDK reconstruction method described in Section with a non-smoothing filter kernel. In Step 3, the temporal MIP M is computed and the binary vessel mask volume v V is created by thresholding M with the vessel threshold τ MIP. To remove single voxels with MIP value above τ MIP due to the heavy noise, v V is processed by a 3D erosion and dilation operation. Accordingly, in Step 4 vessel masks in projection space vi P are computed for all i = 1... N P projections by a maximum intensity forward projection of v V. Note that the acquisition geometry is the same for each forward and for each backward rotation, respectively. Thus practically only vessel masks for 2 N proj projection images have to be computed. In Step 5, the weights w are initialized by the attenuation values from the initial FDK reconstructions. Therefore initial TCCs are interpolated from the FDK reconstructions. The spline weights w are matched by least squares fitting of the TCCs described by w to the initial TCCs using singular value decomposition [Golu 70]. In Step 6, the MIP M is denoised using bilateral filtering with range variance σr0 2 and domain variance σs. 2 Accordingly, the initial weights w are denoised using N JBF iterations of JBF with range variance σr 2 and domain variance σs 2 (Step 7). After each application of the JBF on all weight volumes, the guidance image M is recomputed from the filtered weights.

67 5.3 Implementation Details Dynamic Iterative Reconstruction After the initialization steps, the algorithm iterates N it times (Step 8). In each iteration, all rotations are processed subsequently (Step 9). To improve convergence speed, the projections of one rotation are processed using an ordered subset (OS) [Huds 94] approach. The projections of each rotation are partitioned into N sub = 10 subsets S o,p, o = 1... N rot, p = 1... N sub, maximizing the difference of the projection acquisition angles in each subset. The subsets belonging to one rotation are processed subsequently (Step 10). In Step 11, temporary weight vectors w j R S V, j = 1... Nw are initialized to store the weight update values from one processed subset. Then, the algorithm iterates through the projection images belonging to the current subset S o,p (Step 12). For each projection image, the estimated contrast agent attenuation values x R S V for the projection acquisition time point t P q are computed by GPU-based interpolation (Step 13). In the interpolation step, only the weight vectors associated with basis functions which are non-zero at t P q have to be considered. The interpolated volume x is forward projected to compute the error image e, which is weighted with the statistical ray weights D q (Step 14). The forward projection is computed using the ray-casting technique discussed in Section In step 15, vessel-masked back projection of the error image onto a temporary weight volume w is applied using a voxel-driven back projector. Note that in the practical implementation, only one back projection is required and the two operators A T q are only shown to ease notation. The back projection is implemented GPU-based as described in [Keck 09]. In Step 16, the temporary weights are updated with the back projected error weights. The update vector w is weighted by the step size parameter β and the basis function value b j ( t P q ). Again only the weight vectors associated with non-zero basis functions have to be considered. After processing one subset, the weight vectors are updated from the temporary weight vectors in Step 18 and non-negativity of all weights is enforced in Step 19. In Step 23, the reconstructed weights are regularized by applying JBF every three full iterations with range variance σ 2 R and domain variance σ 2 S. After each application of the JBF on all weight volumes, the guidance image M is recomputed from the filtered weights Projection Pre-processing To reconstruct clinical data, the projections acquired with the C-arm system need to be pre-processed. To compensate for small movements of the acquired head (or other objects in the acquired scene) between the mask and the bolus acquisitions, a nonrigid 2D-2D motion correction [Deue 06] is applied before the subtraction. However, this correction is not exact, since correction of 3D motion in 2D projection space is ambiguous. To avoid artifacts in the reconstructed volumes due to false attenuation values in the subtracted data caused by motion, a correction step for invalid pixels in the subtracted projection images is applied. First, a volume vessel mask v V similar to Step 2 of Algorithm 5.1 is created. Then, all N rot rotations are processed subsequently as follows: first, the volume ˆx is reconstructed from the subtracted projections of the rotation using the FDK algorithm. In the next step, all voxels in the reconstructed volume ˆx which do not belong to a vessel structure (as indicated by v V ) are set to

68 58 Flat Detector CT Perfusion with Low Speed Acquisition no correction with correction Figure 5.4: Invalid pixel correction. Upper left image: subtracted projection image with invalid pixel values (marked with red circles), which are too high due to a plastic tube, which has moved between the mask and the bolus acquisitions. Upper right image: corrected subtracted projection image. Lower left image: CBF map reconstructed from uncorrected projections. Lower right image: CBF map reconstructed from corrected projections. zero, such that only the vessels remain and the tissue attenuation and especially the artifacts are suppressed. Afterwards all projections p i belonging to the rotation are corrected by detecting and replacing invalid pixel values. To detect invalid values, the vessel projection image ˆp i is created by forward projecting ˆx. Let p i,k = p i (k), k = 1... S P, denote the value of pixel k in projection i and ˆp i,k = ˆp i (k) the corresponding value in the vessel projection image. If ˆp i,k = 0, the pixel does not belong to a vessel and is compared to the thresholds τl C R and τh C R + defining reasonable upper and lower bounds of values for line integrals not intersecting with high contrast vessels. If p i,k < τl C or p i,k > τh C, then p i,k is marked as an invalid pixel. If τl C < p i,k < 0, it is assumed that the pixel value is invalid not because of motion, but only due to noise and p i,k is set to zero. If ˆp i,k > 0, the pixel belongs to a vessel and is marked as invalid if p i,k ˆp i,k > τv C or p i,k < 0. The threshold τv C defines a reasonable range of variation in contrast attenuation for pixels belonging to rays intersecting with vessels. The variation stems from the changing attenuation of the vessels during the acquisition and the tissue attenuation, which are both not considered in the static volume ˆx. After the invalid pixels on the projection image are marked, they are replaced by row-wise 1D linear interpolation between the closest valid pixels. In this work, the following thresholds are used: τl C = 0.08, τh C = 0.8, and τv C = Figure 5.4 shows an example of how the invalid pixel correction can help to improve the reconstructed maps. Due to motion of a plastic tube between the mask and bolus projections, there are invalid pixels with too high and too low attenuation values in some of the subtracted projections. This leads to streak artifacts in the resulting CBF map. Using the invalid pixel correction, the streak artifacts can be avoided.

69 5.4 Evaluation Complexity Analysis In this section, the computational complexity of the DIR-MAP algorithm (Algorithm 5.1) is investigated. The DIR-MAP algorithm is composed from the initialization (Steps 1-7) and the iterative part (Steps 8-25). The computational complexity of the single steps in the initialization part and the iterative part are discussed below to finally obtain the complexity of the complete algorithm. The initialization part starts with the projection pre-processing in Step 1. For the complexity analysis, it is assumed that no additional motion artifact correction is applied and the pre-processing corresponds to a constant operation on each measured ray and thus has a complexity of O (N P S P ). In Step 2, the FDK algorithm is used to reconstruct all acquired rotations. The most complex part of the FDK algorithm is the back projection operation, where all acquired N P projections are back projected on the reconstructed S V voxels [Neop 07]. Thus this step has a complexity of O (N P S V ). The subsequent MIP computation, initialization and filtering of the weights in Steps 3, 5, 6, and 7 have a complexity of O (N w S V ) (assuming a constant kernel size for the bilateral filters). In Step 4, the segmented MIP is forward projected to generate the projection vessel masks. The complexity of one forward projection step is O (S V S P ) as it is computed by tracing one ray for each of the S P detector pixels and less than 2 S V samples are evaluated on the traced ray, because the ray is sampled with a distance of half of the voxel size (see Section 3.2.1). Thus, the complexity of the vessel mask computation for all 2 N proj projections is O (N proj S V S P ). As the number of spline weights N w and the number of acquired projections N P can be assumed to be smaller than the number of detector pixels S P and the number of voxels S V, the complexity of the initialization part is given with N w, N P S P, S V by the complexity of the projection vessel mask generation O (N proj S V S P ). (5.19) In the iterative part of the algorithm, the initialization (Step 11), the interpolation (Step 13), the back projection (Step 15), the weight vector updates (Steps 16 & 18), the non-negativity enforcement (Step 19) and the JBF (Step 23) have an individual complexity of at most O (N w S V ) each. The forward projection to compute the error image in Step 14 has a complexity of O (S V S P ). As N w < S P can be assumed, the most complex individual step is again the forward projection. As this step is also part of the innermost loop, which is computed N it N P times, the complexity of the iterative part of the DIR-MAP algorithm is finally given by O (N it N P S V S P ). (5.20) This is also the complexity of the complete algorithm since N proj < N P. 5.4 Evaluation In the evaluation, pure FDK reconstruction is compared with FDK reconstruction followed by JBF (FDK-JBF) and the DIR-MAP approach using different basis functions. The FDK-JBF method corresponds to the initialization part of the DIR-MAP

70 60 Flat Detector CT Perfusion with Low Speed Acquisition Parameter Value Parameter Value N it 12 τ MIP 55 HU β 2.4/N proj σ R σ S 1.5 mm σ R N JBF 3 Table 5.2: Parameters of the DIR-MAP algorithm. approach (DIR-MAP with N it = 0 and linear asymmetric basis functions). Simulation data created from the realistic digital brain phantom described in Chapter 3 and data from clinical canine stroke model studies is used Numerical Brain Phantom Study Brain Phantom Data Creation Dynamic FD-CTP projection data was created by forward projecting the 3D+t brain phantom according to the slow speed acquisition protocol described in Section 5.1. Poisson-distributed noise was added to the projection data as described in Section assuming an emitted X-ray density of photons per mm 2 at the detector and a monochromatic photon energy of 60 kev. No skull and no motion was simulated. The emitted X-ray density was adjusted to simulate a realistic noise level corresponding to real C-arm acquisitions. Therefore a real C-arm CT scan of a water cylinder phantom with the acquisition parameters shown in Table 5.1 was performed, but with a system dose of 0.36 µgy / projection. In the numerical studies the noise level of a lower system dose was simulated to investigate a potential dose reduction for future patient studies compared to the animal study. The water cylinder projection data was reconstructed using the FDK algorithm and the standard deviation inside the homogenous water region was measured. Then projection data from a static version of the brain phantom containing only homogenous tissue structures was created. Poisson noise for a specific emitted photon density was added to the projection data and the data was reconstructed. The standard deviation inside the reconstructed homogenous brain phantom was measured and compared to the standard deviation measured in the water cylinder phantom. The emitted photon density was adapted until a similar standard deviation was measured. Investigations The brain phantom projection data was reconstructed with the DIR-MAP approach using linear asymmetric splines, linear splines with T scale = 1 s and T scale = 2 s, and cubic splines with T scale = 1 s and T scale = 2 s as basis functions and also with the FDK-JBF and the FDK algorithm. For DIR-MAP and FDK-JBF reconstruction, the parameters shown in Table 5.2 were used (with N it = 0 for FDK-JBF). The pure FDK reconstruction was done with smooth filter kernel (Shepp-Logan kernel multiplied with a Gaussian with a standard deviation of σ K = 1.25 pixel). After reconstruction of the TCCs, the perfusion parameters were calculated with the perfusion analysis

71 5.4 Evaluation 61 Algorithm FDK FDK-JBF DIR-MAP Basis Functions lin. lin. lin. cub. cub. T scale asym. 2 s 1 s 2 s 1 s RMSE AIF [ HU] RMSE Tissue [ HU] PC CBF RMSE CBF [ml/100 g/min] PC CBV RMSE CBV [ml/100 g] PC MTT RMSE MTT [s] PC TTP RMSE TTP [s] Table 5.3: Quantitative results digital brain phantom (PC: Pearson correlation, RMSE: root mean square error). Best result in each category is written in bold numbers. technique described in Section Reference perfusion maps were created with this technique from the ground truth TCCs. For quantitative evaluation, the RMSE over time between the reconstructed and the reference TCCs was computed for the arterial input function (AIF) and the TCCs of the brain tissue. Furthermore, the Pearson correlation (PC) and the RMSE between the reconstructed and the reference perfusion maps were calculated (CBF, CBV, MTT, and TTP). RMSE and PC are defined in Equation 3.5 and 3.6. The automated ROI analysis described in Section was applied. A rectangular grid using a line spacing of 8 8 mm 2 was used and the perfusion map slices containing the annotated stroke-affected areas inside a sub-volume of size were considered. In addition, a qualitative comparison of artifacts around the arteries in DIR-MAP and FDK-JBF reconstructed CBF maps was done. These artifacts arise due to the high contrast dynamics in the arteries [Fies 11a]. Results Figure 5.6 shows the AIFs from DIR-MAP, FDK-JBF, and FDK reconstructions used to calculate the perfusion parameters compared to the reference curve. The quantitative results comparing the DIR-MAP, FDK-JBF, and FDK reconstructions are shown in Table 5.3. The CBF, CBV, MTT, and TTP perfusion maps from the three reconstruction algorithms compared to the reference maps are shown in Figure 5.7 and Figure 5.8. Figure 5.5 compares artifacts around the arteries in CBF maps reconstructed with DIR-MAP and FDK-JBF.

72 62 Flat Detector CT Perfusion with Low Speed Acquisition Reference DIR-MAP FDK-JBF Figure 5.5: Artifacts in CBF maps (units: ml/100 g/min) comparing DIR-MAP and FDK-JBF reconstructions to the reference for two different slices. In the second row, zoomed views of the CBF maps shown in Figure 5.7 are provided as indicated by the rectangular regions in the lower left image. [ HU] Reference FDK FDK JBF DIR MAP Time [s] Figure 5.6: AIFs reconstructed from the digital brain phantom data with DIR-MAP (with linear asymmetric basis functions), FDK-JBF and FDK approach compared to the reference curve.

73 5.4 Evaluation 63 Reference 70 DIR-MAP CBF 0 FDK-JBF FDK Reference 0 6 DIR-MAP CBV 0 FDK-JBF 6 FDK Figure 5.7: CBF (units: ml/100 g/min) and CBV (units: ml/100 g) perfusion maps from digital brain perfusion phantom data reconstructed with DIR-MAP (with linear asymmetric basis functions), FDK-JBF, and FDK algorithm.

74 64 Flat Detector CT Perfusion with Low Speed Acquisition Reference DIR-MAP MTT 0 FDK-JBF Reference TTP 14 FDK-JBF FDK DIR-MAP FDK Figure 5.8: MTT (units: s) and TTP (units: s) perfusion maps from digital brain perfusion phantom data reconstructed with DIR-MAP (with linear asymmetric basis functions), FDK-JBF, and FDK algorithm.

75 5.4 Evaluation 65 contrast medium injection type injection rate total contrast volume total saline chase volume X-ray delay 370 mgi/ml intravenous 2.0 ml/s 16 ml 10 ml 5 s Table 5.4: Canine study IV injection protocol In Vivo Study Materials & Methods To validate the DIR-MAP algorithm under realistic conditions, an in vivo brain perfusion study with canine ischemic stroke models was conducted, where CTP was used as reference for the validation. The ischemic stroke was induced in the healthy canines using the procedure discussed in [Yasu 12]. Four hours after stroke creation, CTP was acquired and immediately followed by a FD-CTP acquisition. The contrast agent injection parameters were the same for both modalities and are summarized in Table 5.4. The FD-CTP data was acquired with a clinical C-arm angiography system (Artis zeego, Siemens Healthcare, Germany) using the acquisition protocol described in Section 5.1. The CTP was performed using a clinical 64-section volume CT scanner (GE Healthcare, USA) with continuous scanning for 50 s, 1 s per rotation, 80 kv tube voltage and 200 ma tube current. The reconstructed data from the CTP exam covered 8 slices with a voxel size of mm 3 and was sampled in a temporal interval of 0.5 s. The CTP data was denoised using the TIPS filter [Mend 11] described in Section with a spatial similarity kernel of bandwidth σ D = 1.5 mm and and a TIPS kernel of bandwidth σ R = 55 HU. The FD-CTP data was pre-processed as described in Section and reconstructed using DIR-MAP and FDK-JBF with linear asymmetric basis functions and the parameters shown in Table 5.2, but with τ MIP = 155 HU and σ R = (and N it = 0 for FDK-JBF). The perfusion parameters were calculated with the perfusion analysis technique described in Section 2.1.2, where a TCC inside the basilar artery was selected as AIF. For quantitative evaluation, the PC and the RMSE between the FD-CTP perfusion maps reconstructed with the DIR-MAP and the FDK-JBF approaches and the CTP were computed. Therefore the slice thickness of the FD-CTP volumes was aligned to the CTP slice thickness by applying a moving average filter (kernel size 5 mm) in axial direction. Then the FD-CTP volumes were registered to the CTP volumes using rigid 3D-3D registration [Viol 97]. The registration matrix was computed between mask volumes of the FD-CTP and CTP acquisitions. The PC and the RMSE were computed using the automated ROI analysis described in Section Since there is no ground truth segmentation for the canine brains, the air and bone structures were found by thresholding the mask volume. Then remaining tissue not belonging to the brain was removed manually. The vascular structures were removed

76 66 Flat Detector CT Perfusion with Low Speed Acquisition DIR MAP FDK JBF CTP [ HU] Time [s] Figure 5.9: Examples of the arterial input function obtained from a canine (canine C in Table 5.5) reconstructed with DIR-MAP and FDK-JBF. Also, the CTP curve is shown. by excluding voxels with CBV values higher than 8 ml/100 g in the CBV CTP map. The ROI size was set to 2 2 mm 2. Results Figure 5.9 shows examples of AIFs from the FD-CTP acquisition of a canine reconstructed with DIR-MAP and FDK-JBF and from the CTP acquisition for comparison. In Figure 5.10, co-registered perfusion maps from FD-CTP acquisition reconstructed with DIR-MAP and FDK-JBF and from CTP acquisition are shown. The quantitative results measuring the PC and the RMSE between the maps are given in Table 5.5. Figure 5.11 illustrates 3D perfusion maps reconstructed with DIR-MAP in different viewing directions. The reconstructions were performed on a laptop computer with an Intel i7 M GHz CPU, 8 GB RAM, and an Nvidia Quadro FX 880M graphics chip set. The reconstruction of a typical 3D+t volume of size voxels with linear asymmetric basis functions took about 36 min using a non-optimized DIR- MAP implementation and about 4.5 min using the FDK-JBF approach, where the projection pre-processing and perfusion parameter computations are not included. 5.5 Discussion and Conclusions Discussion The results of the digital brain phantom study show the potential of the dynamic DIR-MAP algorithm to improve FD-CTP compared to pure FDK reconstruction and

77 5.5 Discussion and Conclusions 67 CBF 60 CBV CTP with TIPS noise reduction FD-CTP with DIR-MAP reconstruction FD-CTP with FDK-JBF reconstruction MTT TTP CTP with TIPS noise reduction FD-CTP with DIR-MAP reconstruction FD-CTP with FDK-JBF reconstruction Figure 5.10: CBF (units: ml/100 g/min), CBV (units: ml/100 g), MTT (units: s), and TTP (units: s) maps of canine C with an induced ischemic stroke obtained with CTP and FD-CTP. The FD-CTP maps were reconstructed with the DIR-MAP and the FDK-JBF techniques and registered to the CTP maps.

78 68 Flat Detector CT Perfusion with Low Speed Acquisition XY XZ YZ CBV CBF MTT TTP 5 Figure 5.11: CBV (units: ml/100 g), CBF (units: ml/100 g/min), MTT (units: s), and TTP (units: s) maps in XY, XZ and YZ viewing directions of canine C obtained with FD-CTP. The maps were reconstructed with the DIR-MAP technique and an isotropic voxel size of mm 3.

79 5.5 Discussion and Conclusions 69 CBF CBV MTT TTP DIR-MAP FDK-JBF DIR-MAP FDK-JBF DIR-MAP FDK-JBF DIR-MAP FDK-JBF A B C D E F Mean ± SD PC ± 0.08 RMSE ± 1.5 PC ± 0.08 RMSE ± 3.7 PC ± 0.10 RMSE ± 0.33 PC ± 0.09 RMSE ± 0.23 PC ± 0.09 RMSE ± 0.84 PC ± 0.18 RMSE ± 2.90 PC ± 0.22 RMSE ± 0.97 PC ± 0.16 RMSE ± 1.16 Table 5.5: PC and RMSE between perfusion parameters measured with CTP and FD-CTP in six canines with induced stroke (labeled from A to F) reconstructed with DIR-MAP and FDK-JBF (SD: standard deviation). The total number of ROI samples used to measure PC and RMSE is n = Best mean result for each perfusion parameter is written in bold numbers. also to FDK-JBF reconstruction. Comparing the AIFs shown in Figure 5.6, the AIF reconstructed with the DIR-MAP approach is the best approximation of the reference AIF with the lowest underestimation of the peak. Pure FDK reconstruction with a smooth filter kernel results in a severe underestimation of the AIF. The underestimation caused by the smooth filter kernel can be avoided by using a non-smoothing reconstruction kernel followed by denoising with JBF. However, the dynamic DIR- MAP approach can still perceptibly improve the AIF estimation. Also PC and RMSE of all reconstructed maps are the best for DIR-MAP (Table 5.3), e.g., for the linear asymmetric basis functions the CBF PC increases from 0.85 (FDK) to 0.87 (FDK- JBF) and to 0.92 (DIR-MAP), and the RMSE error decreases from 8.4 to 4.6 to 3.7 ml/100 g/min, respectively. Furthermore, the results in Table 5.3 also show that the simple linear asymmetric basis functions are able to provide sufficiently accurate perfusion maps, and more complex basis functions such as cubic splines do not improve them perceptibly. The perfusion maps reconstructed with DIR-MAP and FDK-JBF compared to the FDK maps (Figure 5.7 and Figure 5.8) are smoother, the stroke-affected areas are better separated from the healthy tissue and the vascular structures, which are visible as the red structures in the CBF and CBV maps, are not blurred into the brain tissue. Comparing the DIR-MAP with the FDK-JBF maps, the DIR-MAP approach avoids the artifacts around the arteries, which appear in filtered back projection algorithms such as FDK around structures with high contrast dynamics (for a detailed analysis of such artifact see [Fies 11a]). Figure 5.5 shows these artifacts in more details.

80 70 Flat Detector CT Perfusion with Low Speed Acquisition Also, there is less overestimation of the perfusion parameters in the DIR-MAP CBF and CBV maps, which corresponds to the improved RMSE shown in Table 5.3. The improved RMSE can be attributed to the higher peak in the AIF estimation compared to the FDK-JBF result, since the algorithm used to calculate the perfusion parameters uses the AIF to normalize the perfusion data. The results of the canine study confirm the results of the simulation study that the dynamic DIR-MAP approach can improve FD-CTP compared to the static FDK- JBF technique. The mean and variance of PC and RMSE between the CTP and FD-CTP acquisitions are improved for all perfusion parameters, except the mean PC for CBV. However, CBV is not a dynamic perfusion parameter and can also be measured using steady-state acquisitions [Ahme 09]. Thus, improvements from a dynamic approach are not necessarily expected. The higher peak in the DIR-MAP AIF estimation (see Figure 5.9) improves the RMSE of the CBF and CBV maps. The canine perfusion maps presented in Figure 5.10 also confirm the simulation results. The artifacts arising from the big vessels in the upper middle of the maps are reduced considerably by the DIR-MAP approach. Furthermore, the CBF and CBV values are less overestimated in DIR-MAP than in FDK-JBF FD-CTP maps when comparing to the CTP maps. Figure 5.11 shows the 3D perfusion maps of a FD-CTP acquisition reconstructed with DIR-MAP from different viewing directions. This highlights another advantage of FD-CTP compared to CTP: the possibility to reconstruct 3D perfusion maps with high resolution in axial direction covering the full brain. Since this is not possible with CTP, no reference maps can be provided. However, the extend of the stroke in the CBF, MTT, and TTP maps looks very similar. These parameters are computed in a very different way from the reconstructed TCCs: CBF and MTT are computed using a deconvolution-based approach and TTP simply corresponds to the temporal position of the peak of the tissue TCC. Therefore the similarity of both maps can be considered as an indication for the correctness of the FD-CTP acquisition and reconstruction method. The DIR-MAP algorithm is an empirical technique, which alternately maximizes data consistency and minimizes the Bayesian regularization term by bilateral filtering. It is not known if and how this approach converges and finds an solution of Equation 5.18 at a certain data inconsistency ε. For static reconstruction with TV regularization, algorithms have been proposed seeking for a minimal TV solution at certain ε by adapting the TV step size to the data consistency [Sidk 08, Rits 11]. For bilateral filtering, such algorithms are not known to the author. Bilateral filtering is used as it is a very intuitive tool and the effect of its parameters on the filtered image are predictable. Furthermore, it provides an apparent possibility to use a guidance image. The evaluation shows the potential of the empirical approach to enhance the reconstructed perfusion maps. An algorithm directly seeking an optimal solution of Equation 5.18 might help to further improve the results. However, even when directly solving Equation 5.18, the selection of an appropriate data inconsistency tolerance ε t is still an empirical problem.

81 5.5 Discussion and Conclusions Conclusions In Section the IS-PRI approach [Fies 12b] for FD-CTP is discussed, which combines interleaved scanning with partial volume reconstruction. The IS-PRI approach increases the X-ray and contrast agent dose and is based on the assumption that the contrast TCCs are reproducible in subsequent FD-CTP acquisitions. This is not assured in clinical practice, since for example blood circulation parameters may change. Therefore the DIR-MAP reconstruction approach was developed in this work with the potential to compensate the low C-arm rotation speed without repeated scanning. The algorithm is based on the iterative parameter estimation technique described by Neukirchen et al. [Neuk 10]. In contrast to [Neuk 10], the algorithm is developed for a real 3D C-arm cone beam geometry instead of a 2D parallel beam geometry and uses an acquisition protocol available in state-of-the art clinical C-arm systems, including pauses between the acquisitions. Spline basis functions with compact support are used to describe the TCCs, which reduces the computational effort compared to the non-compact basis functions used in [Neuk 10]. The back projection step was modified to avoid streaking artifacts around high contrast vessel structures in the cone beam reconstructions. To handle noise and the underdetermination of the dynamic reconstruction problem, a non-linear regularization based on joint bilateral filtering and statistical ray weighting is applied. To handle the high computational effort of dynamic iterative reconstruction, the most computationally expensive steps are implemented using general purpose GPU computing. The novel algorithm is evaluated numerically with the digital brain phantom and data from an in vivo study with canine stroke models. Both evaluations showed that the DIR-MAP algorithm consistently outperforms static FDK reconstruction, even if the FDK data is also processed with the JBF denoising. The results from the animal study are particularly promising: similar average Pearson correlation of the FD-CTP maps and the reference CTP maps in the canine study were received as by Fieselmann et al. [Fies 12b] in a pig study. However, in [Fies 12b] the IS-PRI approach with the need for repeated contrast agent injections and scanning sequences is applied. For instance, the DIR-MAP approach achieved an average PC for CBF of 0.73 in the canine study (Table 5.5). The IS-PRI approach required three interleaved scans to reach this PC value in the pig study [Fies 12b]. The savings in radiation and contrast agent dose come at the price of an increased computational complexity of the iterative reconstruction method. Thus, further code optimization and the use of high end hardware would be required for interventional use Practical Clinical Application While the DIR-MAP algorithm applied to data from the canine animal study showed expedient results, its application on real clinical patient data turns out to be challenging. Following recent studies, many physicians avoid sedation of the patient during stroke treatment [Abou 10]. Thus motion of the patient head during the projection data acquisition can arise. The dynamic iterative reconstruction approaches rely on the subtraction of mask projection images from the bolus projection images before reconstruction. If the patient head moves, there will be residual anatomic structures in the subtracted images. Since the contrast agent enhancement especially in the

82 72 Flat Detector CT Perfusion with Low Speed Acquisition Figure 5.12: Subtracted projection images of a contrast agent enhanced acquisition in a clinical patient study. The right projection image is the successive angular projection to the left image. Red square ROI in brain tissue: the mean of the measured attenuation changes from in the left image to in the right image. Yellow ROI in left image: subtraction artifact due to patient head motion between mask and bolus acquisition. (Images courtesy of the Department of Neuroradiology, University of Erlangen-Nuremberg, Germany). tissue is very low compared to the anatomical attenuation, the anatomical attenuation will dominate the projection images in case of even slight motion. Figure 5.12 show two successively acquired subtracted images. Since the patient moved slightly between mask and bolus acquisition, artifacts arise and the contrast agent attenuation is suppressed by the residual anatomical structures. Furthermore, the measured accumulated X-ray attenuation inside a ROI changes rapidly between the angular adjacent projection images. The subtracted image correction algorithm discussed in Section will not recover the correct attenuation values, since it is only suitable for correction of small movements of externals objects. Thus for future application of dynamic iterative approaches in clinical practice, additional work for compensation of the subtraction error due to motion will be required.

83 C H A P T E R 6 Flat Detector CT Perfusion with High Speed Acquisition 6.1 High Speed Acquisition Analytic Reconstruction with Denoising in Volume Space Alternative Methods for Noise and Artifact Reduction Evaluation Discussion and Conclusions This chapter is based on Denoising and Artefact Reduction in Dynamic Flat Detector CT Perfusion Imaging using High Speed Acquisition: First Experimental and Clinical Results, by M. Manhart, A. Aichert, T. Struffert, Y. Deuerling-Zheng, M. Kowarschik, A. Maier, J. Hornegger and A. Doerfler. Physics in Medicine and Biology. Vol. 59, No. 16, pp , August High Speed Acquisition Introduction As discussed in Chapter 5, the practical clinical application of the dynamic algebraic reconstruction approaches might be limited due to the increased computational effort and the sensitivity to patient motion. Another novel possibility to obtain TCCs with improved temporal resolution are robotic C-arm systems like the Artis zeego system (Siemens Healthcare, Germany) shown in Figure 1.1a. The Artis zeego system provides a high speed protocol (HSP) with increased C-arm rotation speed of up to 100 /s. The HSP enables the acquisition of projection data for one brain volume in less than 3 s. Royalty et al. [Roya 13] evaluated the HSP in an experimental study measuring the brain perfusion of canines with induced focal ischemic regions. A strong correlation of FD-CTP maps to CTP maps as gold standard was reported. However, the results showed only a fair intra-observer performance in ischemic lesion mismatch detection and a consistent overestimation of CBF and CBV values in FD- CTP. The CBF and CBV overestimation resulted from the underestimation of the AIF mostly caused by a partial volume effect, which was introduced by the smooth filter kernel in the FDK reconstruction. 73

84 74 Flat Detector CT Perfusion with High Speed Acquisition In this chapter a reconstruction scheme based on Feldkamp reconstruction followed by iterative noise reduction in volume space using joint bilateral filtering is presented. The noise reduction technique is combined with a novel approach to handle streak artifacts caused by motion of the patient s head and angular under-sampling of the projection data. It is likely that the patient moves during the acquisition procedure, especially because there is a pause of 10 s between the acquisition of the mask projection images and the bolus projection images (with contrast agent enhancement). During the pause the contrast medium is injected intra-venously and transported to the intracranial arteries. This motion can cause severe artifacts in the perfusion maps. Due to limitations in the detector read-out rate, the angular sampling of the projection data in high speed scanning is coarse. This leads to streak artifacts in the reconstructed volumes. Mask volumes with static anatomical structures are subtracted from the volumes with contrast agent enhancement to compute volumes with pure contrast agent enhancement (bolus volumes). The streaks vanish in the bolus volumes since they are mainly caused by the patient s skull and are similar in the mask volumes and the volumes with contrast agent enhancement. If patient motion occurs between the C-arm rotations, it can be compensated by rigid registration. However, the streaks will not cancel out during subtraction in case of even slight errors in registration due to their high frequency structure. Therefore a novel technique for FD-CTP streak removal (SR) is presented and evaluated using digital brain phantom data and clinical patient data. Below the HSP acquisition process and the protocols are detailed. Subsequently, the novel reconstruction and filtering algorithm is described in detail in Section 6.2. Section 6.3 discusses alternative techniques, in particular the TIPS filter [Mend 11] and an algebraic reconstruction approach applying total variation (TV) regularization. In Section 6.4, the novel approach is evaluated using digital brain phantom data and data from clinical patient studies. Finally, the chapter is summarized and the benefits and current limitations of the novel approach are discussed in Section High Speed Acquisition Protocol The HSP for robotic C-arm systems is based on the FD-CTP acquisition protocol introduced in Section Each rotation acquires 133 projections over a 198 angular range and requires T r [2.6, 2.8] s for data acquisition with a pause of T p [1, 1.2] s between any two successive rotations. Thus, TCCs can be reconstructed with a temporal sampling of T s = T r +T p [3.6, 4] s. First, two rotations acquire projections to reconstruct two mask volumes in forward and backward C-arm rotation before bolus injection. Subsequently, the contrast agent is injected intravenously. Finally, when the contrast bolus reaches the brain, the time series of bolus volumes is acquired in N rot = 7 or N rot = 10 consecutive rotations. Due to changes in prototype C-arm control software between the studies, the protocol parameters differ slightly for the different experiments.

85 6.2 Analytic Reconstruction with Denoising in Volume Space 75 Reconstruction & Motion compensation 1. FDK reconstruction 2. Rigid motion compensation 3. Mask subtraction 8. Segment brain Identify streaks 12. Smooth out streaks Streak removal Initial denoising Create guidance volume 6. Joint bilateral filtering 7. Update guidance volume 13. For i = 1 N it 14. Joint bilateral filtering 15. Update guidance volume Final denoising Figure 6.1: FDK-SR-JBF algorithm flow chart. 6.2 Analytic Reconstruction with Denoising in Volume Space This section introduces the FDK-JBF algorithm, which combines FDK reconstruction with noise reduction by joint bilateral filtering, and the FDK-SR-JBF algorithm, which extends the FDK-JBF with a streak artifact reduction method. Figure 6.1 shows an overview of the FDK-SR-JBF algorithm, the single steps are detailed in Algorithm 6.1. The FDK-SR-JBF algorithm constitutes reconstruction with motion compensation and mask volume subtraction (Steps 1-3), JBF denoising (Steps 4-7 and 13-15), as well as streak artifact detection and removal (Steps 8-12). The algorithm is optimized for several criteria: 1. Tissue regions with the low-contrast perfusion information must be denoised. 2. Blood vessels may not be blurred into the tissue, because that would lead to an over-estimation of contrast agent in the tissue and an under-estimation of contrast agent in the vessels. This in turn would cause an overall overestimation of blood flow and blood volume in the perfusion maps. 3. The algorithm needs to be resilient to streak artifacts. The single steps of the algorithm are discussed in detail in the following sections Feldkamp Reconstruction and Motion Compensation In Step 1 of Algorithm 6.1, all mask and bolus acquisitions are reconstructed using the C-arm reconstruction method detailed in Section 1.3.1, which is based on the FDK algorithm [Feld 84]. This results in two mask volumes and 7 or 10 bolus volumes.

86 76 Flat Detector CT Perfusion with High Speed Acquisition Algorithm 6.1: FDK-SR-JBF reconstruction algorithm Data: Pre-processed mask and bolus projection data Result: Bolus volumes with reduced noise and streak artifacts 1 FDK reconstruction of mask and bolus acquisitions 2 Motion compensation by rigid 3D-3D registration 3 Compute bolus volumes by mask volume subtraction 4 Compute temporal maximum intensity projection M 5 Bilateral filtering of M with parameters σ S and σ R0 6 Initial joint bilateral filtering of bolus volumes with guidance image M and parameters σ S and σ R (Result only used for streak detection) 7 Re-compute M from filtered volumes 8 Segment brain tissue by thresholding mask volume (Thresholds: τ Air and τ Bone ) 9 Identify vessels and streaks by thresholding M (Thresholds: τ M_min and τ M_max ) and time curve analysis (Parameters: ν local and ν global ) 10 Identify additional streaks by thresholding TV (M) (Threshold: τ TV ) 11 Combine streak and vessel masks 12 Remove streaks in M by smoothing 13 for k = 1... N it do 14 Joint bilateral filtering of bolus volumes with guidance image M and parameters σ S and σ R 15 Re-compute M from filtered volumes 16 end A non-smoothing Shepp-Logan filter kernel [Shep 74] is used to preserve the edges around the high contrast vessels. All reconstructed volumes are registered to the forward mask volume in Step 2 using 3D-3D rigid registration [Viol 97] to compensate for possible patient head motion during the s acquisition time. In Step 3, the mask volumes are subtracted from the contrast agent enhanced volumes. Any misalignment between mask and bolus volumes leads to incorrect attenuation values and dominates the slight contrast changes in tissue. In the ideal case, the subtraction removes the patient anatomy (i.e., bones, tissue) and reconstruction artifacts, leaving nothing but the contrasted agent enhancement and noise. Streak artifacts due to the low angular sampling are identical in the mask and bolus volumes, because they depend on the acquisition geometry and the location of high contrast structures, i.e., the skull. However, when the patient moves and the registration step compensates for that motion, these artifacts will not cancel out Denoising of Time-Contrast Curves The Shepp-Logan filter kernel from Step 1 yields sharp vessel edges, but a high noise level in the contrast agent enhancement of the tissue. Thus, noise reduction based on JBF technique described in Section 4.2 is conducted. Therefore the guidance volume M is computed in Step 4 by finding the maximum attenuation in temporal direction. The temporal MIP contains sharp edges for vessels, but is very noisy and streaky in

87 6.2 Analytic Reconstruction with Denoising in Volume Space 77 (a) Original temporal MIP (b) Guidance volume M after bilateral filtering (c) Segmentation of bilaterally filtered M (d) Guidance volume M after streak removal; red circle: blurred vessel (e) Final guidance image M after JBF iterations Figure 6.2: Slice from temporal MIP M (a) before bilateral filtering, (b) after bilateral filtering, (c) segmentation of bilateral filtered M, (d) M after streak removal, and (e) M after all JBF iterations. Segmentation legend: orange: streaks, light green: vessels, dark green: tissue, black: bone, blue: air. Window: [0 50] HU. the tissue regions (Figure 6.2a). Therefore M is denoised by bilateral filtering with range variance σr0 2 and domain variance σs 2 in Step 5. Figure 6.2b shows an example of M after bilateral filtering. In addition to the vessels, the guidance volume M can contain edges due to streak artifacts. These false edges need to be detected and removed, otherwise they will translate to the filtered bolus volumes Streak Removal from Guidance Image For streak detection, first a series of denoised bolus volumes is created by joint bilateral filtering of each bolus volume with range variance σ 2 R and domain variance σ 2 D in Step 6. Afterwards the guidance volume M is updated from the denoised series in Step 7. This series is only used for the streak detection described below, where denoised data is required for the TCC analysis. Voxels in M that are affected by streaks are identified based on their contrast intensity and the shape of the TCC at the voxel position. Initially, the forward mask volume is segmented into air, bone, and tissue by thresholding in Step 8. Voxels with a radiodensity below τ Air are classified as air, voxels with a radiodensity above τ Bone

88 78 Flat Detector CT Perfusion with High Speed Acquisition are classified as bone, and the remaining voxels are classified as brain tissue. To avoid misclassification by noise and artifacts, the mask volume is filtered by a 3D Gaussian kernel with domain variance σ 2 S before thresholding. Subsequently, streaks and vessels inside the segmented tissue are identified in Step 9. Therefore a tissue voxel in M is classified as streak, if its intensity is below τ M_min 0. No negative radiodensity values are expected, except slightly negative values due to noise, registration errors or artifacts. If a tissue voxel in M has a large intensity above a threshold τ M_max, it can belong to either a vessel or a streak. To differentiate between vessels and streaks, the TCCs are analyzed. Vessels have typical TCCs with monotonic increase up to a clear contrast peak and possibly a second smaller peak due to second pass, while streaks produce irregular TCCs. Figure 6.3 shows a typical arterial TCC compared to a TCC observed at a streak. The difference between the peak value and the value from which the monotonic increase to the peak starts is denoted as uptake µ. Figure 6.3 shows the uptake of the dominant peak of an arterial TCC. To differentiate streaks and vessels, a voxel is heuristically identified as vessel if its corresponding TCC has 1. a single global peak with an uptake µ global of at least ν global = 70 % of the peak value itself, 2. no further peak with an uptake µ local of more than ν local = 30 % of the global peak uptake µ global. Otherwise, this voxel is classified as streak. Step 10 classifies tissue voxels of all other intensities as streaks if they have a total variation (TV) above τ TV. The TV is defined in Equation 6.3. The final brain segmentation is generated in Step 11 by combining the detected streaks and vessels. First a slice wise dilation operation on the segmented vessels using a 2D rectangular element of size 3 3 voxels is applied. The dilation of the vessels ensures that the vessel edges are preserved in the streak removal step. Then a slice wise erosion (1 2 element) followed by dilation (2 2 element) operation is applied to the streak mask to remove single outliers and close gaps in the detected streak areas. Finally, the brain segmentation is created by combining the vessel and streak masks with the initial brain tissue segmentation. If a voxel is identified as streak and vessel after dilation, it is classified as vessel. An example segmentation result is shown in Figure 6.2c. In Step 12, the identified streaks are removed by smoothing with a truncated 3D Gaussian kernel with domain variance σ 2 D averaging over spatial close tissue voxels which are not classified as vessels. Figure 6.2d shows M after the streak reduction was applied. The most pronounced streaks are removed, while the edges of all vessel structures except one smaller vessel are preserved. However, also some less dominant streak structures are still preserved. Finally, N JBF = 3 JBF denoising iterations are applied on the original bolus data in Steps The streak-reduced M is used as the initial guidance image. To handle the remaining artifacts, M updated in each iteration by recomputing the temporal MIP. Figure 6.2e shows the final MIP after the last JBF iteration with smooth tissue regions and sharp edges at the vessels.

89 6.2 Analytic Reconstruction with Denoising in Volume Space 79 Contrast Attenuation [ HU] Uptake µ global Time [s] Arterial TCC Streak TCC Figure 6.3: time-contrast curves in an artery and in streak-affected brain tissue. Parameter Value Parameter Value JBF kernel size voxels τ M_min -5 HU σ S 1.5 voxels τ M_max 150 HU σ R 20 HU (clinical data) τ TV 20 HU 10 HU (simulation data) σ R0 120 HU ν global 70 % τ Air HU ν local 30 % τ Bone 350 HU σ G 2 mm N it 3 Table 6.1: FDK-SR-JBF algorithm parameters.

90 80 Flat Detector CT Perfusion with High Speed Acquisition Complexity Analysis The computational complexity of the FDK-SR-JBF algorithm (Algorithm 6.1) is investigated in this section. As described in Section 5.3.4, the FDK reconstruction in Step 1 has a complexity of O (N P S V ), where N P = N rot N proj denotes the total number of acquired projections from all rotations and S V the number of voxels in each reconstructed volume. The motion compensation in Step 2 has a complexity of O (N rot S V ), since the rigid registration of each volume using a stochastic maximization algorithm [Viol 97] has constant complexity and the subsequent transformation has a complexity of O (N rot S V ). It is easy to see that steps 3 11 have complexity of either O (S V ) or O (N rot S V ) and the final JBF iteration a complexity of O (N it N rot S V ) (in all cases a constant kernel size for the bilateral filters is assumed). As N it < N proj can be assumed, the complexity of the FDK-SR-JBF algorithm is given by the FDK reconstruction step O (N P S V ). (6.1) 6.3 Alternative Methods for Noise and Artifact Reduction The FDK-SR-JBF approach is compared with the FDK-JBF approach (leaving out the streak removal steps) and other basic and state of the art approaches. The approaches are based on the framework shown in Figure 6.1 with the modifications described below Analytic Reconstruction with Post-Processing Smooth FDK Filter Kernel (FDK-SMOOTH) The denoising and streak removal parts are omitted. Noise is reduced by applying the FDK algorithm with a smooth filter kernel (Shepp-Logan kernel multiplied with a Gaussian kernel with σ = 1.25 pixel). 3D Gauss Filter (FDK-GAUSS) The streak removal parts are omitted and noise reduction is provided by a single iteration of 3D Gauss filtering (σ S = 1.25 mm) of all bolus volumes. TIPS Filter (FDK-TIPS-1/FDK-TIPS-3) The streak removal parts are omitted. For noise reduction the time-intensity profile similarity (TIPS) filter [Mend 11] described in Section is applied. One single application of the TIPS filter is denoted by FDK-TIPS-1. Similar as the JBF filter, the TIPS filter was also iterated N TIPS = 3 times due to the high noise and artifact level of the FD-CTP data. This approach is denoted as FDK-TIPS-3. The selection of the TIPS parameter for the simulation study was done similarly to [Mend 11] by measuring the average sum of squared differences (SSD) of the TCCs

91 6.3 Alternative Methods for Noise and Artifact Reduction 81 in the cerebral spinal fluid (CSF) located in the ventricles of the digital brain phantom. For the initial noise reduction, a TIPS parameter of σ TIPS0 = 3119 HU was determined. For the further iterations, a TIPS parameter of σ TIPS = 615 HU was used, which was determined by the average SSD in the CSF after the initial TIPS denoising. Similarly to the JBF range parameter, the TIPS parameter is doubled to σ TIPS = 1230 HU for the clinical data Regularized Algebraic Reconstruction Algorithm 6.2: OS-TV algebraic reconstruction algorithm Data: Pre-processing projection data m Result: Reconstructed volume y /* max describes element-wise maximum selection */ 1 y 0 = 0 2 for k = 1... N it do 3 Data consistency: ŷ k = OS-ART ( y k 1) (3 iterations) 4 Regularization by itv-type minimization: ỹ k = itv ( ŷ k) 5 Assure positivity: y k = max ( 0, ỹ k) 6 end 7 y = y N it The FDK-SR-JBF algorithm is compared to a fully algebraic reconstruction technique implying TV regularization denoted as OS-TV algorithm. The denoising and streak removal parts are omitted and the FDK reconstruction is replaced by a TVbased algebraic reconstruction approach with ordered subsets. The ART-based method reconstructs a 3D volume represented as a column vector y using the pre-processed projection data m from a single rotation (mask or bolus). Therefore the following constrained minimization problem is approximately solved arg min y y TV s.t. Fy m 2 ε and y 0. (6.2) The system matrix F describes the cone-beam acquisition geometry of the reconstructed rotation and y TV is a TV penalty term incorporating prior knowledge about volume smoothness. The data consistency parameter ε defines the maximal allowed deviation of the reconstructed volume y from the measured projection data and controls the influence of the TV penalty. The total variation penalty term y TV is defined as y TV = N x,n y,n z x,y,z=2 (y x,y,z y x 1,y,z ) 2 + (y x,y,z y x,y 1,z ) 2 + (y x,y,z y x,y,z 1 ) 2, (6.3) where y x,y,z denotes the value in y assigned to the voxel with index (x, y, z) in a volume of size N x N y N z.

92 82 Flat Detector CT Perfusion with High Speed Acquisition Equation 6.2 is solved using Algorithm 6.2 by alternately minimizing the data consistency term Fy m 2 and the TV regularization term y TV for a fixed number of full iterations N it = 8. In Step 3 of Algorithm 6.2, the data consistency is enforced by applying three iterations of the GPU-based Ordered Subsets-ART (OS- ART) method presented by Keck et al. [Keck 09]. Ordered subsets are used for the data consistency update to improve the convergence speed [Huds 94]. Therefore the projection images are partitioned into 10 disjoint subsets. In Step 4, prior knowledge about the reconstructed volume is incorporated by applying a TV regularization with automatic adaption of the TV gradient step size as proposed in the itv algorithm [Rits 11]. The automatic adaption assures improved data consistency after each iteration. The non-negativity constraint is enforced in Step 5 by setting negative values to zero, which corresponds to a projection over convex sets approach [Sidk 08]. 6.4 Evaluation Table 6.1 shows the parameters of the reconstruction algorithm used in the evaluation. The range variance of the JBF filter σ 2 R was reduced to 10 HU in the simulation studies, since a range variance of 20 HU had already smoothed out many of the streaks in the simulation data. The patient study has been approved by the ethics commission of the Medical Faculty at Friedrich-Alexander Universität Erlangen-Nürnberg, Germany, Ethik-No on December, 14th Experimental Setup of Brain Phantom Simulation Study Dynamic FD-CTP projection data was created by forward projection of the 3D+t brain phantom described in Chapter 2 according to the high speed acquisition protocol described in Section Patient motion was simulated by rotation of the bolus volumes by 2 relative to the mask volume around the z axis before generating the projection data. The dynamic C-arm projection data was created by forward projection of the 4D brain phantom according to the high speed protocol with 10 rotations after contrast agent injection, 133 projections per rotation, rotation time T r = 2.8 s, and a pause time of T p = 1.2 s. Afterwards, Poisson-distributed noise was added to the projection data as described in Section simulating an emitted X-ray density of photons per mm 2 at the detector and a monochromatic photon energy of 60 kev. For quantitative evaluation of the reconstructed perfusion maps, the Pearson correlation (PC) (Equation 3.6) and the root mean square error (RMSE) (Equation 3.5) were calculated between the reconstructed and the ground truth maps by applying the automated region of interest (ROI) analysis (see Section 3.2.3). The slices of the perfusion maps with stroke annotation were partitioned into quadratic areas of 4 4 pixels. All slices with stroke annotation were used for the PC calculation (altogether 50 slices and samples). The computation time for reconstruction and denoising of the simulation data was measured on a workstation with 8 Intel(R) Xeon(R) W3565 CPUs with 3.20 GHz, 12 GB RAM, and an NVIDIA Quadro FX 5800 display adapter. The algorithms were implemented in the C++ and CUDA programming languages, with the most

93 6.4 Evaluation 83 Pearson Correlation RMSE FDK-SR-JBF OS-TV FDK-SR-JBF OS-TV CBF [ml/100 g/min] CBV [ml/100 g] MTT [s] TTP [s] Computation Time [s] Table 6.2: Quantitative results of brain phantom study. Pearson correlation (PC) and root mean square error (RMSE) of CBF, CBV, MTT and TTP perfusion maps reconstructed with FDK-SR-JBF and OS-TV approaches to reference volumes. Best result for category is written in bold numbers. computationally expensive steps (forward projection, backward projection, and JBF) being computed on the GPU Experimental Setup of Patient Studies The clinical data sets include 3 different FD-CTP acquisitions from 2 patients. The patients were both suffering from AIS and were treated by interventional intra-arterial recanalization with self-expanding stents. The first patient (69 year old male) was admitted due to an acute occlusion of the middle cerebral artery on the left. Corresponding to the side of occlusion the patient was suffering from hemiplegia of the right side of the body. A HSP FD-CTP acquisition was performed after successful recanalization with 7 rotations after contrast agent injection, 133 projections per rotation, rotation time T r = 2.8 s, and a pause of T p = 1 s. The second patient (72 year old female) was admitted due to an occlusion of the vertebral artery on the left, including the posterior inferior cerebellar artery. Correspondingly, this patient presented clinical dizziness. Two HSP FD-CTP acquisitions were performed before and after successful recanalization with 10 rotations after contrast injection, 133 projections per rotation, rotation time T r = 2.6 s, and a pause of T p = 1 s Results Brain Phantom Simulation Study Figure 6.4 shows axial slices of reconstructed CBF maps compared to the ground truth map. The maps were reconstructed with the FDK-SMOOTH, FDK-GAUSS, FDK- JBF, FDK-TIPS-1 and FDK-TIPS-3 methods, respectively. Figure 6.5 shows axial slices from CBF, CBV, MTT, and TTP maps reconstructed with the FDK-SR-JBF and OS-TV algorithms and compared to the ground truth maps. The quantitative results are shown in Table 6.2. They compare the PC and RMSE of the reconstructed maps to the reference maps and the computation time for reconstruction and denoising on the workstation for the FDK-SR-JBF and OS-TV algorithms.

94 84 Flat Detector CT Perfusion with High Speed Acquisition (a) Reference map (b) FDK-SMOOTH (c) FDK-GAUSS (d) FDK-JBF (e) FDK-TIPS (f) FDK-TIPS Figure 6.4: Axial slices of CBF maps created from numerical brain perfusion phantom FD-CTP data compared to the ground truth map (a) (units ml/100 g/min). Maps created from reconstructions with (b) FDK-SMOOTH, (c) FDK-GAUSS, (d) FDK- JBF, (e) FDK-TIPS-1, (f) FDK-TIPS-3. Axial position of the slices relative to central slice is 26 mm.

95 6.4 Evaluation 85 CBF CBV MTT TTP Reference FDK-SR-JBF OS-TV X Y Figure 6.5: Axial slices of CBF, CBV, MTT and TTP maps reconstructed from brain perfusion phantom data with FDK-SR-JBF and OS-TV approaches compared to the ground truth. Map windows: CBF [X = 0, Y = 80] ml/100 g/min; CBV [0, 6] ml/100 g; MTT [0, 15] s, and TTP [13, 23] s. Axial position of the slices relative to central slice is 26 mm.

96 86 Flat Detector CT Perfusion with High Speed Acquisition (a) FDK-GAUSS (b) FDK-JBF (c) FDK-TIPS Figure 6.6: CBF maps created from clinical patient data with head motion using the FDK-GAUSS, FDK-JBF, and FDK-TIPS-3 approaches (units ml/100 g/min). Axial position of the slices relative to central slice is 56 mm Results Clinical Study: Patient Motion Figure 6.6 shows axial slices of CBF maps reconstructed from HSP FD-CTP data of the first patient using the FDK-GAUSS, FDK-JBF, and FDK-TIPS-3 algorithms. Figure 6.7 shows slices of the CBF, CBV, MTT, and TTP perfusion maps in axial and coronal viewing directions. These maps were reconstructed with the FDK-SR-JBF and the OS-TV algorithms Results Clinical Study: Pre- and Post-Treatment Acquisition Figure 6.8 shows slices of CBF and CBV maps from HSP FD-CTP data acquired from the second patient. All maps were reconstructed with the FDK-SR-JBF approach. Maps displaying the brain perfusion before (pre) and and after (post) successful recanalization are shown in axial and sagittal directions. The pre- and post-treatment perfusion maps where registered to each other using rigid registration. Axial slices from the cerebellum and the occipital lobes are shown. The cerebellum slices show stroke-affected tissue before and after successful treatment and the occipital lobe slices show healthy tissue and visualize the reproducibility of the HSP FD-CTP acquisition and reconstruction. Figure 6.9 shows the corresponding MTT and TTP maps. 6.5 Discussion and Conclusions Discussion The evaluated FDK-SR-JBF algorithm applies FDK reconstruction followed by guided noise reduction with JBF. The JBF guidance volume is computed from the temporal maximum intensity projection of the bolus volumes time series. To handle streak artifacts in the JBF guidance volume, a streak removal method is applied. Therefore the brain is segmented into tissue, vessels, and streaks using information from the time-contrast curves and total variation calculation. Subsequently, the streaks are

97 6.5 Discussion and Conclusions 87 axial coronal FDK-SR-JBF OS-TV FDK-SR-JBF OS-TV CBF CBV MTT TTP X Y Figure 6.7: Axial and coronal slices of perfusion maps created from clinical patient data with head motion reconstructed with FDK-SR-JBF and OS-TV approaches. Windows: CBF [X = 0, Y = 80] ml/100 g/min; CBV [0, 8] ml/100 g; MTT [0, 12] s; TTP [12, 22] s. Axial position of the slices relative to central slice: (axial) -56 mm; (coronal) -60 to +60 mm.

98 88 Flat Detector CT Perfusion with High Speed Acquisition CBF CBV Pre Post Pre Post (ax,cb) (ax,ol) (sa) X Y Figure 6.8: Axial (ax) and sagittal (sa) slices of CBF and CBV maps from a patient study with pre- and post-treatment acquisitions. Axial slices from cerebellum (cb) and occipital lobes (ol). Map windows pre-treatment acquisition: CBF [X = 0, Y = 80] ml/100 g/min; CBV [0, 8] ml/100 g. Map windows post-treatment acquisition: CBF [0, 60] ml/100 g/min; CBV [0, 6] ml/100 g. Axial position of the slices relative to central slice: (ax,cb) 70 mm; (ax,ol) 22 mm; (sa) -72 to +72 mm.

99 6.5 Discussion and Conclusions 89 MTT TTP Pre Post Pre Post (ax,cb) (ax,ol) (sa) X Y Figure 6.9: Axial (ax) and sagittal (sa) slices of MTT and TTP maps from a patient study with pre- and post-treatment acquisitions. Axial slices from cerebellum (cb) and occipital lobes (ol). Map windows pre-treatment acquisition: MTT [X = 0, Y = 16] s; TTP [10, 22] s (ax,ol slice) and [14, 28] s (ax,cb and sa slice). Map windows post-treatment acquisition: MTT [0, 20] s; TTP [11, 25] s. Axial position of the slices relative to central slice: (ax,cb) 70 mm; (ax,ol) 22 mm; (sa) -72 to +72 mm.

100 90 Flat Detector CT Perfusion with High Speed Acquisition removed by smoothing the identified areas in the JBF guidance image. Finally, noise and artifacts are reduced in the bolus volumes by iteratively applying JBF using the streak-reduced guidance volume. The axial CBF slices reconstructed from the numerical phantom data shown in Figure 6.4 demonstrate that the alternative post-processing methods do not provide sufficient image quality. The perfusion maps created by FDK-SMOOTH and FDK- GAUSS are noisy and the edges at the high contrast vessels are blurred into the tissue. Furthermore, especially the 3D Gauss filtering causes a partial volume effect (i.e., an underestimation of the contrast agent enhancement in the vessels), which leads to an overestimation of the CBF values. The JBF and TIPS methods avoid the blurring of the vessels, but also preserve the edges caused by streak artifacts. The streaks are visible in the CBF maps and impede the visibility of the stroke affected area. These results are confirmed by the CBF maps created from the FD-CTP data of the first patient shown in Figure 6.6. Sufficient noise and artifact reduction in combination with preserved edges at vessels is achieved by the FDK-SR-JBF and OS-TV approaches in the numerical perfusion maps shown in Figure 6.5 and the clinical perfusion maps shown in Figure 6.7. Both approaches provide similar visual quality. Also the quantitative results in Table 6.2 show similar PC and RMSE distance to the ground truth. However, the computation time of OS-TV is with 26 min 50 s by a factor of more than 23 higher than the computation time of FDK-SR-JBF with 1 min 9 s. In the TTP and MTT brain phantom maps (Figure 6.5) the differentiation of the infarct core to the penumbra is lost. The contrast agent enhancement in the infarct core is very low (peak 5 HU) and therefore the contrast-to-noise ratio is accordingly small. This affects the MTT and TTP parameters. As MTT = CBV/CBF, MTT gets numerically unstable if CBF very small (as in the infarct core). TTP relies on the detection of the TCC peak, which is difficult in case of very low CNR. However, the infarct core can still be depicted from the penumbra by the physician by comparing the CBV map showing the infarct core to the CBF, MTT, and TTP maps showing the full infarct area. The pre- and post-treatment perfusion maps of the second patient in Figures 6.8 and 6.9 provide physiological meaningful results. The pre-treatment maps clearly show a reduction of CBF and CBV and an increase of MTT and TTP in the left hemisphere of the cerebellum, which corresponds to the stroke-affected area. After successful recanalization of the cerebellum, the post-treatment maps show increased CBF and CBV and decreased MTT and TTP in the stroke-affected area. This corresponds to hyper-perfusion, which is a common finding after recanalization in stroke. Furthermore, the perfusion maps of the occipital lobes of the brain, which were not affected by stroke and not subject to treatment, look very similar in the pre- and post-treatment maps. This supports the reproducibility of the proposed acquisition and reconstruction technique. The FDK-SR-JBF approach produced clinically useful results in first simulation and real data studies. The perfusion maps allow the physician to determine the infarct area with the infarct core and the penumbra. Furthermore, the computation speed of FDK-SR-JBF is sufficiently fast for interventional use on clinical workstations. Therefore it could be a promising approach for interventional FD-CTP. However,

101 6.5 Discussion and Conclusions 91 this heuristic approach can likely fail to discern streaks and vessels at some voxels and some streak artifacts could be preserved or small vessels blurred (e.g., see Figure 6.2d). Such limitations affect the image quality of the perfusion maps, but do not strongly impede the clinical value of the perfusion maps Conclusions The simulation and patient studies show the potential of the FDK-SR-JBF approach for providing FD-CTP maps with decent artifact and noise level. The FDK-SR- JBF approach produced perfusion maps with a quality comparable to an algebraic reconstruction technique based on total variation minimization, but the computation time is reduced by factor of more than 23 on a clinical workstation. The evaluation using the pre- and post-treatment acquisitions shows that interventional FD-CTP acquisition is feasible with FDK-SR-JBF reconstruction. However, further validation of the clinical applicability and robustness is required by a thorough quantitative comparison of C-arm perfusion maps to CT perfusion and MR perfusion and will be carried out in the future. One limitation of the evaluated noise and artifact reduction techniques for FD- CTP is that they can only handle the head motion which occurs between the acquisitions. Motion during one rotation of the C-arm will cause additional artifacts and might make the acquired volume unusable for the perfusion computation. Thus including online motion correction techniques [Debb 13, Wick 12] represents an important direction for future research. Furthermore, the usage of exact analytical reconstruction algorithms [Kats 03, Defr 94] could help to improve the image quality in higher cone beam angles as they avoid the inexact handling of the cone beam projection data by the Feldkamp short scan algorithm.

102 92 Flat Detector CT Perfusion with High Speed Acquisition

103 C H A P T E R 7 Clinical Prototype 7.1 Requirements and Design Implementation Requirements and Design To enable reliable stroke diagnosis with interventional perfusion imaging, the extensive validation of the physiological significance and reproducibility of FD-CTP is required. Thus an essential direction for future research is the evaluation of FD-CTP in clinical practice. Therefore software is required, which can be intuitively used by clinical users (e.g., physicians) and is integrated directly into the clinical workstations. In previous work [Fies 12a] a first prototype for FD-CTP was developed, which was designed as an external software and required extensive manual export and import operations for processing the acquired data. This chapter introduces the novel FD-CTP software developed in this work, which avoids the data import and export overhead and is integrated directly into Siemens clinical workstation software. Furthermore, it provides the novel noise and streak reduction techniques introduced in this thesis. The requirements on the novel prototype and its design and workflow are shown in this section. The single steps of the implementation are discussed in Section 7.2. For an efficient and intuitive use in clinical practice, the prototype software is designed to comply with the following requirements: 1. The perfusion map computation is robust to noise and patient motion. 2. The computation time is in a viable range below 15 min to provide an efficient processing of the acquired data. However, a fully optimized code is not required yet since the perfusion maps are not used for interventional diagnosis but in a retrospective evaluation. 3. All clinical acquisition protocols are supported and detected automatically without additional user interaction. Acquisition protocols differing in the number of acquired rotations and projections and in the rotation and pause time are supported (high speed and slow speed acquisition). 4. The software can be used intuitively by users versed in the clinical workstation software. The required user interaction and parameter adjustment is minimized. 93

104 94 Clinical Prototype (a) Reconstruction (b) AIF selection (c) Perfusion maps Figure 7.1: Screenshots of clinical prototype for FD-CTP.

105 7.2 Implementation 95 Figure 7.2: Time volume from dynamic angiography series. To comply with the requirements 1 and 2 the reconstruction of the TCCs is based on the FDK-SR-JBF algorithm discussed in Chapter 6, which is computationally fast and can handle noise and motion artifacts. To fulfill requirements 3 and 4 the prototype detects the acquisition protocol and selects the corresponding reconstruction parameters automatically. The user interaction during the reconstruction is thereby limited to the selection of the position and the temporal starting point of the AIF. The workflow to reconstruct brain perfusion maps from the acquired data consists of the following steps: first the user selects the acquired perfusion projection data in the workstation and starts reconstruction by selecting the prototype plug-in in the reconstruction menu. The prototype also supports projection data, where the mask and bolus acquisitions are stored in separated data sets. Then the data is reconstructed and subsequently the noise and streak artifact reduction and the TCC interpolation is carried out automatically. The progress of the reconstruction is displayed in an additional status bar to the user. Figure 7.1a shows a screenshot of the workstation during the reconstruction process. Subsequently, the position and temporal starting point of the AIF need to be defined by the user (Figure 7.1b). Finally, the perfusion maps are calculated and exported into the workstation database and the perfusion maps can be viewed with the workstation software (Figure 7.1c). The prototype also provides an option to export the interpolated time series of volumes into the workstation database. This allows to visualize a dynamic angiography describing contrast flow over time in the vessels. Figure 7.2 shows one temporal volume of a dynamic angiography series. 7.2 Implementation Step 1: Projection Pre-processing and Reconstruction Native software on the workstation is used for pre-processing [Stro 09] and reconstruction of the acquired data using a Feldkamp-type [Feld 84] algorithm as described in Section The back projection step is computed using GPU acceleration.