osteoma with human clinical data

Transcription

1 Bone thermal modelling for magnetic resonance guided high intensity focused ultrasound therapy of osteoid osteoma with human clinical data by Alexander Chisholm A thesis submitted in conformity with the requirements for the degree of Masters of Applied Science Department of Mechanical and Industrial Engineering, Institute of Biomaterials and Biomedical Engineering University of Toronto c Copyright by Alexander Chisholm 2017

2 Bone thermal modelling for magnetic resonance guided high intensity focused ultrasound therapy of osteoid osteoma with human clinical data. Alexander Chisholm Masters of Applied Science Department of Mechanical and Industrial Engineering, Institute of Biomaterials and Biomedical Engineering. University of Toronto 2017 Abstract Introduction: MR-guided high intensity focused ultrasound (MRgHIFU) is used to treat osteoid osteomas (OOs). However, there is uncertainty about inadvertent injury. This uncertainty can be addressed by MRgHIFU heat transfer simulation within bone. The research goal is to develop a simulator that can accurately and efficiently predict the temperature after the treatment sonication time. Methods: A simulator was developed with three main components: automatic bone segmentation, an acoustic model, and a heat transfer model. The simulated data was compared with the clinical MRgHIFU sonication data. Results: With automatic segmentation, the average maximum temperature difference after sonication, with the clinical data was 2.1±9.5 C. The maximum simulation time was seconds. Conclusions: The results revealed that the simulator could accurately and efficiently predict the maximum temperature after 20 second sonications. A robust MRgHIFU bone thermal simulation platform has the potential to significantly improve the safety and efficiency of MRgHIFU treatment. ii

3 Acknowledgements I would like to thank my supervisor, Dr. James Drake for his guidance throughout my research. Under his direction, I learned how to produce impactful research. Also, going forward, Dr. Drake has motivated me to aspire towards success with medical research in my future career. I would like to thank Dr. Adam Waspe for his instrumental role throughout my thesis. He helped with the operation of medical devices and provided key input into conference abstracts, presentations, and thesis edits. His devotion for successful research was a primary motivation, and I cannot thank him enough. I would like to thank my co-supervisor, Dr. Dionne Aleman for her help and support throughout my research, and for her instrumental role in teaching me how to improve upon my essential scientific writing skills. I believe these writing skills will help me throughout my scientific research career. I would like to thank my committee member, Dr. Hai-Ling Cheng for her support and suggestions during important milestones throughout my degree. I would also like to thank Dr. Michael Temple, for providing the clinical data, which was the primary source of data for my thesis. I would like to thank Dr. Samuel Pichardo, for developing the initial CUDA code to solve acoustic simulations; for providing me with a better understanding of CUDA programming; and for his help with the acoustic simulation code. I would like to thank Dr. Charles Mougenot for sharing his knowledge of MRgHIFU and operating the Philips Sonalleve system. I would like to thank the current and previous members of the Center for Image Guided Innovation and Therapeutic Intervention (CITIGI) lab. I would like to thank Thomas Looi for his valuable input throughout my research. I would like to thank Thomas Hudson, who extended parts the HIFU simulation platform. His input helped me to better understand key components of the HIFU simulator allowing for the future development of the simulator. I would like to thank all of the other CITIGI members including: Karolina Piorkowska, iii

4 Jeremy Tan, Dr. Elodie Constanciel, Justin Wee, Karl Price, and Vivian Sin. The CITIGI lab members facilitated healthy academic discussions, as well as extra-curricular activities. The enjoyable, motivating, and accepting environment of the CITIGI lab provided me with an unforgettable lifelong experience. I would like to thank the funding sources: the Collaborative Health Research Program (CHIR-NSERC) grant, the Focused Ultrasound Foundation, and the Barbara and Frank Milligan Fellowship Award. Finally, I would like to thank my family and friends for their support and motivation throughout my studies. I could not have done it without them. iv

5 Contents 1 Introduction Acoustic propagation of HIFU HIFU image guidance modalities Literature review Segmentation Acoustic and thermal models Previous MRgHIFU simulations Segmentation Methods Results Discussion Acoustic model 38 5 Thermal simulations Methods Results Discussion Conclusions 67 Appendices 75 Appendix A Tissue Properties 75 v

6 List of Figures 1 CT Scan of an OO. The black arrow indicates the OO, and the white arrow indicates the cortical bone [24] Schematic diagram of HIFU treatment of liver Reflected and transmitted waves across different media [6] Longitudinal and transverse waves across liquid - solid - liquid media [6] Ultrasound image of a prostate [17] Image of clinical MRgHIFU treatment Philips Sonalleve MRgHIFU system. Source: com/prod/philips-healthcare/product html PRFS-based thermometry during sonication from a clinical treatment Acoustic transmission across a curved media interface. S is the curved surface of the radiator, θ 1 is the reflected angle, θ 2 is the transmitted angle, and r is the distance the radiated wave travels to the media interface [16] Simulated pressure distribution with (a) 10 7 emitted waves, (b) emitted waves, (c) 10 8 emitted waves, and (d) experimental hydrophone measurements [16] Simulated vs in vitro pressure distributions for a 1024 phased array transducer. The left column depicts the simulated distributions, the middle column depicts the measurements by the hydrophone, and the right column depicts the 50% contour overlay of the simulated and in vitro data. The top, middle, and bottom rows are different views of the pressure distributions in the different planes Simulated temperatures. (a) Temperature distribution of 6144 element transducer configuration 96-d, and (b) thermal dose distribution of 4 configurations 96-a - 96-d at a depth of 100 mm below tissue surface. The red line on the right figure is D240, the threshold to incur tissue necrosis [13] vi

7 13 Temperature comparison of (a) PRFS-based thermometry, and (b) vs simulated temperature [12] Temperature of the central thermocouple probe and the thermometry at varying depths below tissue surface [12] Simulated thermocouple probe data [12] in vivo experiment set up. [21] (a) Simulated temperatures, and (b) in vivo PRFS-based thermometry temperatures [21] Treated vs control in vivo bone histology results. (A) Normal cortical bone and sub-cortical marrow (SCM); (B) acute haemorrhage is depicted by the long arrows, and serous extravasation is defined by the short arrows; (C) vasodilation is defined by the arrows; (D) fat necrosis in the SCM is indicated by the arrows [21] D Slicer GUI MATLAB GUI segmentation window Axial slice of a patient s femur with OO (a) before sharpening, (b) after sharpening, (c) after ROI is defined, and (d) after segmentation The k-means algorithm [4] Image requiring the dilation/shrinking strategy. (a) Segmented cortical bone component with gap, (b) dilated cortical bone component, (c) shrunk cortical bone component, and (d) cortical bone component with gap connected Segmented images. (a) axial slice with cortical bone and marrow labelled separately; (b) segmented sagittal region after axial slices defining the ROI are concatenated Segmentation of images not requiring the dilation/shrinking strategy. (a) Unlabelled axial slice, (b) segmented axial slice, (c) and segmented sagittal slice vii

8 26 3D rotations [34] Clinical treatment setup Max temperature vs time of thermometry data for Patient 1, Sonication 9. The green circles indicate T20 and T40 for this sonication Max temperature vs time of simulated data for Patient 1, Sonication 9, with automatic segmentation (bolded, Table 7). Simulated temperature before median filter (dotted red line); after the weighted average and the median filter were applied (solid red line) Max temperature vs time with automatic segmentation of Patient 4, Sonication Max temperature vs time with automatic segmentation of Patient 5, Sonication Maximum temperature vs time for Patient 1, Sonication Maximum temperature vs time for Patient 1, Sonication Temperature and thermal dose distributions after 20 seconds of sonication for Patient 2a, Sonication Temperature and thermal dose distributions after 20 seconds of sonication for Patient 1, Sonication Temperature distributions after 20 seconds of sonication for Patient 1, Sonication List of Tables 1 Histology comparisons of treated vs control bone [21] Automatic and manual segmentation accuracy with theoretical phantom volume 33 3 Validation of automatic segmentation on clinical treatment bones Validation of automatic segmentation on volunteer bones viii

9 5 Clinical MR thermometry data after temporal interpolation in the sagittal plane. T20 and T40 are the maximum temperatures after 20 seconds of sonication and after 40 seconds of cooldown time, respectively; Z and Y are the distances from the ablation centroid to the sonication point on the the sagittal slice (Z and Y axes). If the ablation volume within the ROI was 0, the ablation centroid coordinates, Z and Y were undefined Philips Sonalleve QA standards [1] Simulated data with automatic (subscript a) and manual (subscript m) segmentation. All ratios are calculated as automatic over manual. Bolded values are results of particular interest, and are interpreted in Section Simulated data vs thermometry (automatic segmentation). All ratios are calculated as simulated over thermometry Simulation times for all sonications with automatic segmentation. The number of voxels along each axis for each MRI scan is indicated by (X, Y, and Z) Marrow properties Cortical bone properties Muscle properties Skin properties Blood properties Gel pad properties Oil properties Membrane properties ix

10 1 Introduction There is a significant incentive to pursue non-invasive treatments for bone tumours [27]. Two common bone tumours in paediatrics are osteoid osteoma (OO) and bone metastases, which can cause severe pain [28] and physical withdrawal [28]. Bone metastases are malignant tumours, comprising 10-13% of all cancerous tumours in the population aged 0-19 [15], while OO is a benign tumour commonly affecting the long bones in the body [19]. Approximately 80% of OOs are found in populations aged 5-24 [2], and account for 13.5% of all benign tumours [27]. A computed tomography (CT) scan of an OO near the hip is shown in Figure 1. The current standards for OO treatment are surgery, percutaneous radio-frequency ablation (RFA), and prescription drugs [29]. Surgery is highly invasive and can result in long recovery times [29]. In some cases, the symptoms of OO can be minimal, and the body may heal itself. In other cases, the severe pain can cause lack of sleep, and possibly a disturbance in bone growth [27]. If physical pain occurs, medical treatment is essential [27]. Prescription drugs, such as analgesics, and anti-inflammatory drugs, can provide temporary relief, however, they may cause side effects [29]. In addition, the OO symptoms can arise again after the medication is stopped [29]. Currently, the most popular treatment for OO is percutaneous RFA [29]. In RFA, a needle is placed at the core of the OO, called the nidus. An electric current is then applied to the tumour, and it is ablated by heat. RFA is 85-98% effective in relieving the symptoms of OO [29]. However, there is a risk of fracture, as a small hole must be drilled into the cortical bone of the patient [24]. Also, there is no real-time temperature feedback during treatment, leading to an increased possibility of damage to adjacent tissues surrounding the tumour [24]. High intensity focused ultrasound (HIFU) is a non-invasive alternative for OO treatment demonstrated to be effective in treating both bone and soft-tissue tumours [32, 43]. Highpowered acoustic waves are emitted from an ultrasound transducer, resulting in a small thermal lesion within the targeted tumour volume called the region of interest (ROI). In 1

11 Figure 1: CT Scan of an OO. The black arrow indicates the OO, and the white arrow indicates the cortical bone [24]. HIFU treatment, there is precise targeting of the lesion, with minimal damage done to the surrounding tissues. HIFU treatment is particularly effective when coupled with magnetic resonance imaging (MRI). The treatment is called magnetic resonance guided HIFU (MRgHIFU). There have been multiple MRgHIFU clinical trials for OO worldwide at specialized centers [28, 29]. However, HIFU treatment must be proven reliable and practical in order to be implemented in hospitals worldwide. The MRI visualizes the ROI and surrounding tissues, and the contrast in the images provides the ability to target the ROI with the HIFU transducer [6]. However, one of the main issues with HIFU ablation of bone tumours is the prediction of temperature within the target bone and bone marrow [41]. Lack of temperature signal increases the risk of inadvertent injury and makes it more difficult to estimate the optimal power to be applied to the target tumour area, while minimizing damage to the surrounding tissues. An MRgHIFU simulator was developed as a potential solution for overcoming these drawbacks. The specific research problem is to develop a simulator that can accurately predict the temperature during treatment in a clinically feasible amount of time. 2

12 Figure 2: Schematic diagram of HIFU treatment of liver Acoustic propagation of HIFU Ultrasonic waves are mechanical waves. The waves cause the molecules within the medium in which they travel to oscillate, resulting in a transfer of energy throughout the medium. In focused ultrasound, the acoustic waves are directed to a single focal point, ranging from 2-12 mm in diameter [22]. The focusing of the ultrasound is achieved with a multi-element spherical phased array transducer. The Philips Sonalleve MRgHIFU system uses a transducer with 256 elements, with a focal length of 12 cm. The effect of absorption from just one element will produce a negligible amount of absorbed heat. However, the acoustic waves from multiple transducer elements constructively interfere, resulting in a significant amount of absorbed energy at the focal point. The absorbed energy over time can reach temperatures hot enough to incur thermal ablation of biological tissue. The Philips Sonalleve system can focus ultrasound to within a 2 mm diameter cell. The sharp focus allows HIFU treatment to effectively ablate small lesions, while sustaining minimal damage to the surrounding tissues. Figure 2 portrays a schematic diagram of HIFU treatment of liver tissue, where HIFU is localized in the lesion within the liver, with no visible damage to the surrounding tissues. Ultrasonic waves will lose energy while travelling its medium. The dissipation of energy is referred to as attenuation. The attenuation coefficient of a medium is measured in terms of intensity loss over a distance, or Decibels per centimetre [6]. The first cause of attenuation 3

13 Figure 3: Reflected and transmitted waves across different media [6] is due to the absorption in the media in which the wave is travelling through, where the absorbed acoustic energy is converted to heat. The second cause of attenuation is by acoustic scattering. Acoustic scattering is the re-direction of acoustic waves due to interactions with particles smaller than the acoustic wavelength [6]. The third is due to reflection and refraction, as acoustic inhomogeneities within the media can cause the wave to divert from its path. The last is due to mode conversion. In solids, acoustic mode conversion can occur, where transverse transmitted waves travel perpendicular to the axis of propagation. Different media will have different acoustic properties, such as the speed of sound and density. When an ultrasonic wave crosses at an interface between media, it experiences both reflection and refraction. This process is shown in Figure 3. The incident, reflected, and transmitted ultrasonic waves are represented by φ i 1, φ r 1 and φ 2, respectively. The parameters ρ o1 and ρ o2 represent the densities of the two different media. The parameters c o1 and c o2 represent the speeds of sound of the two media, respectively, θ i is the incident angle, and θ t is the transmitted angle. When ultrasonic waves cross from a fluid into a solid, two different transmitted waves occur: longitudinal and transverse waves. Longitudinal waves travel in the direction parallel to the direction of propagation, and transverse waves travel in the direction perpendicular to the direction of propagation. This process is called mode conversion, and is depicted in Figure 4, where L and T represent the longitudinal and transverse waves, respectively. 4

14 Figure 4: Longitudinal and transverse waves across liquid - solid - liquid media [6] Cortical bone is solid due to its crystalline calcium phosphate matrix composition [46]. However, soft tissues, such as bone marrow, are considered semi-solid and produce negligible transverse propagation [6]. When acoustic waves transfer from a solid medium into a liquid medium, the incident waves can be both transverse and longitudinal. 1.2 HIFU image guidance modalities Image guidance is required to enable effective HIFU treatment. First, pre-operative treatment planning images are acquired to locate the ROI to be targeted for ablation. Second, intra-operative imaging is acquired to ensure the HIFU treatment is carried out effectively safely and. Finally, post-operative images are acquired to assess the success of the treatment. CT scans are a form of X-ray imaging. They consist of high energy electromagnetic waves [36]. CT provides superior contrast between bone and soft tissue in comparison to other imaging modalities, and provides good contrast between healthy and diseased tissues [24], observed in Figure 1. Therefore, CT scans can be used for pre-operative screening of HIFU bone tumour treatments. However, side effects from radiation may occur, and there is no real-time temperature feedback imaging sequence available [36]. Also, most HIFU transducers are made of piezeoceramic material and therefore radio opaque [36]. The x-ray projection will be obscured and many imaging artefacts will be created in the CT back projection algorithm [36]. 5

15 Figure 5: Ultrasound image of a prostate [17] Ultrasound is less expensive than other imaging modalities. It is portable, has a wide range of clinical applications, and is completely non-invasive. It also has the ability to produce observable images in real time [17]. It is an ideal intra-operative imaging guidance modality for treatment of moving organs, such as the heart [7]. In ultrasound guided focused ultrasound (USgFUS) applications, the ultrasound imaging device can be integrated with the HIFU transducer, however, the contrast is poor, and it may be more of a challenge to locate the tumour, (Figure 5). Ultrasound also provides poor contrast between bone tissues due to strong reflection artefacts [36]. Due to this poor contrast, ultrasound guidance is a poor choice to guide HIFU treatment of bone tumours. MR imaging provides good contrast for imaging soft tissues and can also provide contrast in bone tissues including OOs [36] (Figure 6). Another advantage of MRgHIFU is the ability to image and acquire temperature readings in real time [37, 38]. The real time MR sequence is called the T1-w spoiled gradient echo sequence (T1-FFE). This sequence is sensitive to the proton resonance frequency shift (PRFS) effect. Therefore, the sequence can be used to acquire real time temperature maps. The temperature feedback in PRFS-based thermometry allows for intra-operative observation during HIFU treatment. The interventional radiologist can observe if the heating location is within the ROI, and minimal heating is occurring in the surrounding tissues. Thus, MR provides the best imaging modality for HIFU guidance. Figure 7 depicts the Philips Sonalleve MRgHIFU system, with the MRI on the left and the HIFU bed on the right. Philips Sonalleve is used to conduct clinical MRgHIFU studies for OO. During treatment, the patient is positioned on top of the bed, such that the transducer 6

16 Figure 6: Image of clinical MRgHIFU treatment. Figure 7: Philips Sonalleve MRgHIFU system. Source: prod/philips-healthcare/product html in the bed is underneath the ROI. MRgHIFU treatment of OO has some drawbacks. First, there is almost a complete lack of MRI signal within bone in PRFS-based thermometry [28]. Second, there is a lack of computer assisted predictive treatment tools. The goal of PRFS is to provide real time temperature feedback intra-operatively during thermal ablation treatments to quantify how much tissue is destroyed. Temperatures during thermal ablation will typically range from degrees Celsius. Such high temperatures applied over a period of time cause protein denaturation, and thereby cause tissue necrosis [38]. Typically, thermal dose is measured in cumulative equivalent minutes of applied heat 7

17 at 43 degrees Celsius, or CEM43 [38]. 240 CEM43 is the accepted threshold to ensure tissue necrosis [38]. PRFS signal is acquired by the disruption of hydrogen bonds within water molecules. The hydrogen nucleus within a water molecule experiences nuclear shielding by electrons in the molecule. However, when there are multiple water molecules adjacent to each other, each molecule will experience hydrogen bonding. Opposite ends of the dipoles in the adjacent water molecules attract each other, establishing a hydrogen bond [5]. The pull of oxygen on hydrogen s electron decreases the shielding of the nucleus [38], and causes an increase in resonant frequency [38]. When the temperature of free water increases above body temperature, the water molecules become further apart from one another. Thus, the pull of oxygen becomes weaker, resulting a increase in the electron shielding of hydrogen, and a decrease in the resonant frequency of hydrogen [38]. The temperature increase associated with the resonant frequency shift is produced as a signal in real time [38]. Figure 8 represents a real time PRFS-based thermometry sequence acquired during a clinical OO treatment from a patient who was treated at the Hospital for Sick Children. This treatment was carried out using the Philips Sonalleve MRgHIFU system shown in Figure 7. The PRFS-based thermometry provides signal in the tissues surrounding the bone, however, there is a lack of signal within the bone. The lack of PRFS signal within bone is one of the key reasons for this research. Therefore, the motivation of this research is to better predict the temperature distribution within bone by using computer simulations. 8

18 Figure 8: PRFS-based thermometry during sonication from a clinical treatment 2 Literature review 2.1 Segmentation The purpose of medical image segmentation is to allow for computer assisted treatment planning [30]. Currently, manual segmentation is the accepted gold standard for segmentation of medical images [30]. However, manual segmentation is very time consuming and not practical in an intra-operative setting. Automatic medical image segmentation is a vast field of research, which attempts to segment medical images in a clinically feasible amount of time. Existing automatic segmentation techniques include thresholding, region growing, deformable mesh models, and clustering techniques. Thresholding techniques search for a threshold pixel intensity value and label pixels according to whether they lie above or below the defined threshold [30]. The values for the thresholds are often determined by inspection of the peaks within the pixel intensity histogram [30]. In binary segmentation, one threshold is defined to separate pixel intensities into two labels. If there are many different tissue types within the image, it is likely there will be multiple peaks in the histogram [30]. Therefore, a challenge with thresholding techniques is the selection of the number and range of thresholds to segment. In medical images with good image contrast, such as CT scans [36], simple thresholding techniques may be sufficient to segment tissues. Zhang et al. segmented bone and non-bone tissues of the spinal cord upon 9

19 simple binary thresholding [48]. The image intensity histogram was separated into a mixture of two Gaussian distributions, and the threshold value was selected within the intersection of the distributions. Zhang et al. concluded that for a specific CT imaging system, an optimal threshold value can be experimentally determined to separate bone and non-bone tissue of the spinal cord [48]. However, more complex segmentation methods may be required to segment multiple tissues, or to segment tissues within other imaging modalities with worse contrast. Region growing segmentation requires two main steps. The first step is the selection of the initial seed points. The seed points can be selected based on simple thresholding of the image histogram, or by more complicated techniques such as the split and merge algorithm [30]. The seed points define regions of the image with similar pixel intensities. After the seed points are selected, adjacent pixels in a connected neighbourhood are then grown outwards. If all the pixels in the connected neighbourhood have the same intensity grouping as the seed point, they are labelled the same as that point, otherwise they are labelled differently [30]. One drawback of region growing segmentation is the selection of the initial seed points, in order to segment the individual regions [30]. If the image contains multiple connected regions with a wide range of intensities, the selection of initial seed points can be a difficult task [30]. Rundo et al. [39] used region growing techniques to perform a segmentation of MRI data from uterine fibroid patients after MRgHIFU treatment. After injection of a contrast die, the treated uterine fibroid(s) appeared darker in comparison to the surrounding tissues. Their method used the split and merge algorithm to determine the groups of seed points in order to separate regions of different intensities. They then implemented the region growing technique to grow the connected regions. A post image processing step then determined which connected regions corresponded to the uterine fibroids. This method is specialized for uterine fibroid segmentation, and may not be generalizable to segment ROIs with more tissues and more complex shapes. Also, the segmentations were performed on contrast-enhanced MRI images. Their method might not perform as well when attempting 10

20 to segment non-contrast enhanced images. In deformable mesh models, an initial mesh is selected within the ROI to be segmented. A mathematical model defines a set of rules applied to update the shape of the initial mesh [21]. The set of rules defines how the mesh will expand and conform to the tissue to be segmented within the ROI [21]. A converging criterion is established when there is minimal movement of the mesh [21]. There are two main disadvantages of deformable models. The first is the selection of the initial mesh within the ROI, and the second applies to deformable models that often experience poor convergence at concave boundaries [30]. Hudson [21] developed a deformable mesh based algorithm in an attempt to segment porcine femurs. The results of the deformable mesh algorithm showed significant disagreement with the gold standard, manual segmentation [21]. Data clustering is a branch of unsupervised machine learning [4]. Unsupervised machine learning algorithms take unlabelled data, such as a gray-scale MR image, and sort the data into groups or clusters [4]. It is often advantageous to use clustering techniques for segmentation when there are multiple groups of pixel intensities with complex shapes [30]. The k-means clustering technique involves four different steps [4]. The first step is the initialization, where k observations in the data are labelled as initial means. Data points closest to their corresponding mean are labelled the same. The second step is the cluster assignment, where k clusters are created by associating each data point with the closest mean. The third step is the calculation of the new mean, defined to be the centroid of the new clusters. The fourth step then defines new clusters based on the new means. These steps are iteratively repeated, until the algorithm converges. The disadvantage of the k- means technique is that it requires the user to estimate the number of clusters to segment [4]. However, the k-means algorithm may be advantageous if the ROI to be segmented in the image has a known number of tissues with distinct pixel intensities, in which case the choice of k may be intuitive [30]. Choosing an appropriate k value can lead to increased segmentation accuracy [30]. Another advantage of the k-means algorithm is that it is computationally 11

21 inexpensive [39]. Gaussian mixture models (GMM) are another clustering method, which can be used for medical image segmentation [4]. GMMs may perform well if the image intensities for each cluster follow distinct Gaussian distributions in the image histogram [4]. Zoroofi et al. implemented a combination of thresholding, region growing, and k-means clustering to segment patient femur data [50]. Their research examined patients with a condition called avascular necrosis of the femoral head (ANFH). Their research investigated the k-means algorithm, in combination with different image processing techniques, in order to automatically segment the ROI of the femur [50]. Segmentations were performed on the femur data of these patients with the assistance of a graphical user interface program called CBone, developed in Microsoft Windows. Automatic segmentation strategies were performed on a slice by slice basis in the GUI. The slices were then combined to create the segmented femur. Their method required a combination of multiple segmentation techniques, and may not be generalizable to other applications. The method is also not fully automatic, as the user must navigate slice by slice. 2.2 Acoustic and thermal models The Rayleigh integral (RI) models the ultrasonic velocity potential across a surface of a homogeneous media [16]. A simple calculation can then determine the velocity across the length of the medium. The first theoretical solutions of the RI were produced from a concave spherical radiator in 1949 [31]. Fan and Hynynen extended the model developed by O Neil [31] to include acoustic transmission across a curved surface between two media (Figure 9). The elements in a focused ultrasound transducer have a concave spherical curvature, which causes the waves to focus on the target. When ultrasonic waves cross a media interface, they experience both reflection and refraction. The transmitted angle is calculated by Snell s law [6]. There is no generalized solution to the RI across multiple media [16], therefore transmitted and reflected velocity coefficients must be calculated. The surface of the new medium acts as a new radiator, and the corresponding velocities emitted from this new 12

22 Figure 9: Acoustic transmission across a curved media interface. S is the curved surface of the radiator, θ 1 is the reflected angle, θ 2 is the transmitted angle, and r is the distance the radiated wave travels to the media interface [16]. radiator are then calculated [16]. After the velocity distribution in the new medium is determined, the velocity potential distribution can then be calculated [16]. The velocity potential distribution can then be converted into a pressure distribution, which can then be converted into a heat distribution. The drawback of the model developed by Fan and Hynynen [16] is that it only assumes a transmission between two fluid layers. In transmission from a solid into a fluid layer, or vice versa, acoustic mode conversion creates transverse waves [6]. In modelling acoustic propagation in solid substances, such as bone, transverse waves must also be considered [6]. Another method used to simulate acoustic HIFU propagation is the stochastic ray tracing technique [12, 25]. In stochastic ray tracing, stochastic integration is performed to calculate the numerical solution to the RI through each homogeneous media [25]. Stochastic integration means that there is an associated probability distribution for each emitted source element [25], as opposed to deterministic integration, where there is one path per source element, based on the input parameters [45]. Stochastic ray tracing is typically used to a create a coarse approximation in an efficient amount of time [25]. There are a number of disadvantages to the ray tracing technique [25]. First, it is challenging to model the effects of acoustic mode conversion at solid boundaries with complex shapes [25]. Second, the reflec- 13

23 tion and transmission coefficients are approximations based on a probability distribution of the transmitted rays, so there is a potential for inaccurately traced ray paths [25]. Third, it is a challenge to select an optimal amount of source elements to simulate, in order to create sufficient accuracy, while maintaining an efficient computation time [25]. Finally, due to the randomness of stochastic ray tracing, quantifying global accuracy is more difficult compared to deterministic methods [25]. The RI assumes material tissue properties such as the speed of sound, density, and thermal conductivity are constant [16]. In reality, they vary with temperature and pressure [6]. Kuznetsov, Zabolotskaya and Khokhlov developed a 3D acoustic propagation model to account for diffraction, absorption, and non-linearities, known as the KZK equation. The KZK equation accounts for these variable properties, however, numerical solutions to the KZK equation can be computationally expensive [6]. It is likely that the computation time to solve a non-linear model will not be feasible for intra-operative clinical applications. Also, non-linear viscosity properties of a medium are characteristic of fluids, but do not exist in solids such as bone [6]. Heat change can be modelled by a partial differential equation (PDE). Pennes originally developed the bio-heat transfer equation (BHTE) PDE in 1948 [33], which models how heat spreads in living tissue [33]. There are three main terms included in the BHTE. The first term is the conduction term, which represents the change in heat over time from the transfer in vibrational energy between neighbouring particles. The second term is the perfusion term, which models how heat is carried away by blood. The final term is the radiating heat source term applied over a certain length of time. In simulating acoustic propagation, the heat generated from the radiator can be modelled as the heat source term in the BHTE [21]. The net change in heat from radiation, perfusion, and conduction represents the total change in stored energy within a volume of tissue. It takes a certain amount of time for tissue necrosis to occur. For ablation to occur, an external heat source must be applied to the tissue for extended amounts of time [18]. The thermal dose can quantify the amount of ablated 14

24 tissue [40]. Based on solutions to the BHTE, the thermal dose can then be calculated. The thermal dose is measured in equivalent minutes of ablation at 43 C, meaning that it takes 240 minutes to destroy tissue at 43 C [40]. The tissue is ablated exponentially faster, the hotter the temperature is [40]. 2.3 Previous MRgHIFU simulations Koskela and Vahala conducted ex vivo MRgHIFU experiments on porcine thoracic and liver tissue using the Philips Sonalleve HIFU platform [25]. The purpose of their experiments was to replicate uterine fibroid MRgHIFU treatment. The acoustic pressure distribution at the ROI was measured by a hydrophone. The porcine tissues were manually segmented using the 3D Slicer program. Based on the segmented tissues, acoustic simulations were then performed using stochastic ray tracing. The simulated acoustic pressure distributions were normalized and visually compared to the experimental acoustic pressure distribution, (Figure 10). The stochastic ray tracing model developed by Koskela and Vahala [25] is a coarse and efficient model for simulating uterine fibroid MRgHIFU treatment. However, the model is subject to the disadvantages of stochastic ray tracing. Uterine fibroids range from 3 cm-12 cm [49], allowing a large margin of error for the transducer focus. A more precise simulation may be required for other clinical MRgHIFU applications with a narrow target [25]. Further investigation of this model with in vivo experiments and clinical data may help to establish its accuracy and applicability for computer assisted MRgHIFU treatment planning of uterine fibroid treatment. Ellens et al. investigated novel 1024-element and 6144-element phased array transducers, with different configurations of the elements [13]. These prototype transducers were built with the intention of improving MRgHIFU treatment of uterine fibroids. The purpose of the large amount of elements and different configurations allows for effective electronic steering of the transducer to minimize side lobes (high pressure areas away from the focus), and maximize the pressure at the focus. The large aperture of these novel transducers also allows the 15

25 Figure 10: Simulated pressure distribution with (a) 10 7 emitted waves, (b) emitted waves, (c) 10 8 emitted waves, and (d) experimental hydrophone measurements [16] transducer to focus at greater depths. Two 1024-element transducers were constructed, in order to conduct in vitro experiments. The resulting pressure distributions from sonications were measured by a hydrophone in a tank of degassed water. A MRgHIFU simulator was then developed in MATLAB to replicate the experimental results. A numerical, deterministic solution to the RI, was adopted from Fan and Hynynen [16]. For efficient computation time, the numerical solutions to the RI were calculated with parallel GPU computing, called: compute unified device architecture (CUDA). The pressure distributions of the simulated versus the in vitro data were determined to be comparable (Figure 11). In addition to pressure simulations, a thermal simulation model was also developed. A finite-difference time-domain (FDTD) method was implemented to produce a numerical solution to the BHTE. The solution to the BHTE was also calculated by the CUDA software. For the thermal simulations, a muscle layer was defined within a volume of water. The effect of reflection was neglected, and the transmission coefficient into the muscle layer was adopted from Fan and Hynynen [16]. Based on the temperature distributions of the simulated results, the thermal dose was calculated to assess the extent of thermal ablation at the focus. Figure 12 indicates temperature simulations of one transducer configuration (a), and thermal dose simulations of four 16

26 Figure 11: Simulated vs in vitro pressure distributions for a 1024 phased array transducer. The left column depicts the simulated distributions, the middle column depicts the measurements by the hydrophone, and the right column depicts the 50% contour overlay of the simulated and in vitro data. The top, middle, and bottom rows are different views of the pressure distributions in the different planes. different configurations (b). In 12(a), it can be observed that the temperature at the focus reaches 60 C. In 12(b), D240 represents a thermal dose of 240 equivalent minutes at 43 C, and is the threshold to ensure tissue necrosis. It is evident from 12(b), that the thermal dose at the focus for all transducer configurations is well above the D240 threshold. The novel transducers investigated by Ellens et al. [13] provide insight towards which kind of transducer to use for the most effective treatment of uterine fibroids. However, only in vitro and computer simulations were performed. Simulations of in vivo experiments and clinical data could provide further information to support the benefits of of these novel transducers. Eikelder et al. performed ex vivo experiments on a porcine femur section [12]. To avoid MRI segmentation, the cortical bone was shaped into a hollow cylinder (marrow removed), with known dimensions. The bone was then embedded into an agar gel, and three fibre optic thermocouple probes were inserted into the bone section closest to the transducer. MRgHIFU experiments were then conducted using the Philips Sonalleve platform. The 17

27 (a) Simulated temperature for transducer configuration 96-d (b) Simulated thermal dose for configurations 96-a - 96-d Figure 12: Simulated temperatures. (a) Temperature distribution of 6144 element transducer configuration 96-d, and (b) thermal dose distribution of 4 configurations 96-a - 96-d at a depth of 100 mm below tissue surface. The red line on the right figure is D240, the threshold to incur tissue necrosis [13]. temperature readings from the thermocouple probes and the PRFS-based thermometry data were collected during the experiments. An integrated MRgHIFU simulation platform was developed in MATLAB to perform the simulations, where acoustic propagation was modelled by stochastic ray tracing, and the temperature was modelled by a finite element solution to the BHTE. The effect of mode conversion between the gel-cortical bone and cortical bone-gel interfaces was included in this model. The simulated temperature provides an estimate of the temperature within the cortical bone, where thermometry signal is unavailable (Figure 13). The measured thermocouple temperature in Figure 14 confirms that there is a hot region within the cortical bone, which the thermometry does not measure. Figure 15 then compares the thermocouple measurements to the simulated temperatures. Eikelder et al. [12] confirmed that the temperatures measured by their simulations were in good agreement with the thermocouple probe measurements, and the simulation could be performed in a clinically feasible amount of time. This research provides significant progress towards modelling temperature within bone, for the application of improving MRgHIFU treatment of bone metastases and OOs. However, simulations were only performed in a simplified ex vivo 18

28 (a) PRFS thermometry (b) Simulated temperature Figure 13: Temperature comparison of (a) PRFS-based thermometry, and (b) vs simulated temperature [12]. experiment, and did not require segmentation prior to the simulations. Automatic MRI segmentation is required for intra-operative clinical simulations, and is a significant challenge. Also, the ray tracing technique is subject to the disadvantages discussed in Section 2.2. Hudson [21] conducted MRgHIFU in vivo experiments on porcine femurs using the Philips Sonalleve system, at the Hospital for Sick Children in Toronto. He collected real-time PRFSbased thermometry data for all the in vivo experiments. In addition to the the thermometry data, he collected thermocouple data from a fibre optic probe, which was inserted in the ROI (cortical bone) of two of the porcine femurs. He attempted to reproduce the heating distribution from the in vivo experiments, by simulating the experiments in an integrated computer platform coded into MATLAB computing software, developed by previous researchers. The simulator was comprised of a segmentation component, an acoustic simulation component, and a thermal simulation component. Hudson [21] manually segmented the porcine femurs. Then acoustic and thermal simulations were performed in an attempt to reproduce the heat distribution on the porcine femurs. His acoustic model was a deterministic numerical solution to the RI, adopted from Fan and Hynynen [16]. The calculations were performed in 19

29 Figure 14: Temperature of the central thermocouple probe and the thermometry at varying depths below tissue surface [12] Figure 15: Simulated thermocouple probe data [12]. 20

30 Figure 16: in vivo experiment set up. [21] CUDA. The homogeneous tissue layers can be observed in Figure 16. The simulations also included calculations of transmission and reflection across each media interface. The porcine cortical bone was considered solid, thus the effect of mode conversion was also included at the muscle-cortical bone and cortical bone-bone marrow tissue interfaces. A thermal simulation was performed by numerically solving the BHTE by the FDTD method. His simulated thermal results were then compared to real-time MR thermometry data, as well as the thermocouple data (Figure 17). After a comparison of simulated and thermometry data, Hudson concluded that the results were not accurate enough to implement in a clinical software platform. However, the maximum simulation time was 40 seconds, which was considered to be fast enough to be clinically feasible for intra-operative planning. Also, Hudson only considered simulations where the transducer was not angled. In clinical MRgHIFU treatments of OO, the transducer will often need to be angled in order to effectively focus the waves at the tumour location at normal incidence [14]. The treated porcine femurs from the in vivo experiments performed by Hudson [21] were extracted. Additional in vivo experiments under the same protocol were performed by other researchers at the Hospital for Sick Children. The femurs from these experiments were also 21

31 (a) PRFS-based thermometry (b) Simulated temperature Figure 17: (a) Simulated temperatures, and (b) in vivo PRFS-based thermometry temperatures [21]. extracted. After the bones were extracted, the bones were de-calcified, then slices were sectioned and prepared for histological analysis. Homatoxylin and eosin (H&E) staining was performed on the bones in order to identify tissue necrosis. Homatoxylin binds to negatively charged substances, and appears purple, while eosin binds to positively charged substances, and appears pink [21] (Figure 18). Histology was performed on a total of 20 treated porcine femurs and 12 control femurs. The histological comparisons of the pig bones treated with HIFU were compared to the control bones, and the results are summarized in Table 1. There were four different biological properties tested to confirm tissue necrosis: vasodilation (parametric), acute haemorrhage (parametric), serum extravasation (non-parametric) and fat necrosis (non-parametric). The null hypothesis is that the metrics defining necrosis were greater in the treated bone compared to the control. The Student s two-tailed t-test was performed to determine the statistical significance of the parametric results, and a Fisher s exact test was performed to test for the statistical significance of the non-parametric data. Statistical significance was defined to be p<0.05. Based on the results in Table 1, it was determined to be statistically significant that all metrics defining tissue necrosis were greater in the treated group, compared to the control group. Thus, the presence of necrosis was confirmed. 22

32 Table 1: Histology comparisons of treated vs control bone [21] Feature Control Group (n=12) Test Group (n=20) Significance Stat Test Vasodilatation (average) Student s 2-tailed t-test Acute haemorrhage (average) Student s 2-tailed t-test Serum extravasation (presence) 1 19 < Fisher exact test Fat necrosis (presence) 0 16 < Fisher exact test Figure 18: Treated vs control in vivo bone histology results. (A) Normal cortical bone and sub-cortical marrow (SCM); (B) acute haemorrhage is depicted by the long arrows, and serous extravasation is defined by the short arrows; (C) vasodilation is defined by the arrows; (D) fat necrosis in the SCM is indicated by the arrows [21]. 23

33 3 Segmentation 3.1 Methods An MRgHIFU clinical pilot study was conducted with six treatments on five OO patients from the Hospital for Sick Children and the Sunnybrook Health Sciences Center. The treatments were conducted using the Philips Sonalleve MRgHIFU system. The ROIs from the pre-operative MRI scans of the six treatments were manually segmented using the 3D Slicer program. Each manual segmentation was repeated three times. A snapshot of the 3D Slicer GUI is shown in Figure 19. An interactive MATLAB MRgHIFU simulation platform, including a graphical user interface (GUI) for automatic segmentation of the MRI data was developed by previous researchers (Figure 20). The segmentation GUI was extended, based on the previous version. The GUI window has three different view types. On the left is a coronal slice (anterior to posterior) of the femur, the center is an axial slice (knee to hip) of the femur, and on the right is a sagittal slice (right to left of thigh). The yellow triangle mask over the image represents the ultrasonic wave boundary as it penetrates towards the focus at the tumour. There is a secondary triangle, continuing past the focus, representing the a acoustic far-field boundary. The user can either manually select a sonication target on a slice in the segmentation GUI, or he/she can upload the coordinates from the file produced by the Phillips Sonalleve system after a patient treatment. This point is represented by the yellow dot within the triangle mask in the axial (center) image slice of Figure 20. The tumour appears as a dark area close to the yellow dot (Figure 20). The yellow and red lines represent the inner and outer curvatures of the patient s skin, respectively. There are multiple steps involved in the automatic segmentation process. Before the segmentation can occur, pre-image processing steps are required. First, image sharpening is applied, using the built-in MATLAB function imsharpen. The purpose of the image sharpening is to provide better contrast of edges in the image, such as the cortical bone section to allow the k-means algorithm to better define the cortical bone cluster of the image. 24

34 Figure 19: 3D Slicer GUI Figure 20: MATLAB GUI segmentation window 25

35 Figure 21(a) is an axial slice of a clinical MR dataset, and Figure 21(b) is the the image after a image sharpening has been applied. Next, the user defines a rectangular boundary around the ROI within the axial slice, defining the ROI to be segmented. Figure 21(c) is the sharpened MR image after a boundary has been defined around the ROI. MATLAB s built in k-means function kmeans was then used to segment the tissues within the ROI. The user inputs a number defining how many k clusters are needed to segment the patient s femur (this check box can be seen in Figure 20). However, determining the optimal number of clusters can be a challenge. In this research, k = 3 was selected to segment the clinical data, based on the number of tissue types within the ROI. All of the clinical MRI sequences segmented were T1 weighted. In T1 weighted MRI sequences, cortical bone has low intensity, muscle has medium intensity, and fatty tissues have high intensity [36]. Therefore, the k = 3 estimation was based on the following intensity categorization of the tissues prevalent in the ROI: fat (high intensity), fatty bone-marrow (high intensity), non-fatty marrow (medium intensity), muscle (medium intensity), and cortical bone (low intensity). A vectorized version of an axial slice of the image is provided to the k-means algorithm. The axial slice is now a vector of size n 1 of image pixel intensities (note that for an image of size i j, n = i j). A visualization of the algorithm with k = 2 can be observed in Figure 22. There are four steps involved in the k-means algorithm: 1. Initialization (Figure 22(a)): k observations in the data are labelled as initial means. The means are the red and blue X s, and the green circles are the data points. In the MATLAB k-means algorithm, the means are randomly initialized. 2. Assignment (Figure 22(b)): k clusters are created by associating each data point with the closest mean. In this research, the distance metric, is the squared Euclidean distance. Each colour (red and blue) represents the new labelled k clusters. 3. Calculation of a new mean (Figure 22(c)): The new mean is defined as the centroid of each new defined cluster. 26

36 (a) Axial MRI slice (b) Axial MRI slice after image sharpening (c) ROI of sharpened MR image (d) ROI of sharpened MR image Figure 21: Axial slice of a patient s femur with OO (a) before sharpening, (b) after sharpening, (c) after ROI is defined, and (d) after segmentation. 27

37 (a) Step 1, initialization (b) Step 2, assignment (c) Step 3, calculation of a new mean (d) Step 4, iterative process Figure 22: The k-means algorithm [4] 4. Iterative process (Figure 22(d)): Steps 2 and 3 are repeated until the algorithm converges. The convergence criterion is when moving any point within a defined cluster to a different cluster, results in an increase in the total sum of distances of all points to their respective means. After the algorithm converges, a ternary image is created, with labels 1 (low intensity), 2 (medium intensity), and 3 (high intensity). To extract just the cortical bone (low intensity) component from this image, the medium and high intensity labels were both re-labelled as 0 (Figure 21(d)). The cortical bone region appears as a ring-like connected component, and will be the largest connected component in the ROI. All the smaller connected components of the segmented image (not part of the cortical bone) were removed by the built-in MATLAB image processing function bwareaopen. The result after this image processing step is a 28

38 single connected component defining the cortical bone region (Figure 23(a)). However, it is noticeable from Figure 21(d), that there are gaps in the apparent cortical bone connected component, and a section of the cortical bone component was removed (Figure 23(a)). The axial MRI slice in Figure 21(a) is near the hip region, and the cortical bone component can be as thin as one pixel. Imaging artefacts can make it difficult to identify regions of the cortical bone that are very thin. The following strategy was developed to interpolate the missing pixels in the cortical bone region, for the patients with apparent cortical bone thickness of one pixel or less. First, the cortical bone component is dilated, using the built-in MATLAB function imdilate (Figure 23(b)). Next, the dilated image is shrunk to one pixel thick, by the same factor that it was dilated, using the built-in MATLAB function bwmorph (Figure 23(c)). Finally, the shrunk cortical region outline is overlayed on top of the original image (Figure 23(d)). The cortical bone region is now a closed ring structure, and the inside of the ring is labelled separately as bone marrow. Figure 24(a) is Figure 23(d), after the inside of the cortical bone region is labelled as marrow, and corresponds to the current navigated slice on the segmentation GUI (Figure 20). Before the segmentation occurs, the user must navigate, slice by slice on the GUI and count how many slices are necessary in order to segment out the entire ROI. The number of slices can vary depending on the patient. The segmentation is repeated by the defined amount of slices before and after the first segmented slice. The segmented slices are then concatenated to create a 3D segmented bone around the ROI (Figure 24(b)). Figure 25 shows the segmentation process for a patient that did not require the dilation/shrinking strategy. After the bone is segmented from the image, the simulator requires a user input to segment the patient s skin. A cursor can be placed over the skin location on the MR image. A spherical mesh is then created by manually approximating the inner and outer radii of the skin, as well as the center point. The approximation is based on visual conformation to the patient s skin in the MATLAB segmentation GUI. The patient s skin is assumed to conform to the shape of the membrane of the HIFU transducer (yellow and red lines in Figure 20). 29

39 (a) Cortical bone connected component (b) Dilated cortical bone component (c) Shrunk cortical bone component (d) Connected cortical bone component Figure 23: Image requiring the dilation/shrinking strategy. (a) Segmented cortical bone component with gap, (b) dilated cortical bone component, (c) shrunk cortical bone component, and (d) cortical bone component with gap connected. 30

40 (a) Axial Segmented Image (b) Sagittal Segmented Image Figure 24: Segmented images. (a) axial slice with cortical bone and marrow labelled separately; (b) segmented sagittal region after axial slices defining the ROI are concatenated. The skin mesh area is then converted into a separate tissue label. All other regions within the skin boundary which are not bone or skin are then labelled as muscle. An axial slice of the segmented skin, bone, and muscle can be observed in the bottom right corner of the GUI in Figure Results A plastic bone phantom was created to compare the volume estimation accuracies of the developed k-means based segmentation versus the gold standard, manual segmentation. A template was made for the phantom in the SOLIDWORKS software program. The output file from SOLIDWORKS was used as a template, and printed by a 3D printer with ABS plastic. To imitate bone marrow, butter was then melted and poured into the hollow part of the phantom. The phantom was then embedded in agar gel, and the phantom was then imaged by the Philips MR system. The phantom was then manually and automatically segmented. The automatic segmentations were performed in the developed GUI (Figure 20). The manual 31

41 (a) MRI axial slice (b) Segmented axial slice (c) Segmented sagittal slice Figure 25: Segmentation of images not requiring the dilation/shrinking strategy. (a) Unlabelled axial slice, (b) segmented axial slice, (c) and segmented sagittal slice. 32

42 Table 2: Automatic and manual segmentation accuracy with theoretical phantom volume Phantom Number V t (cm 3 ) V a (cm 3 ) V m (cm 3 ) VE a (%) VE m (%) segmentations were performed in 3D Slicer by a volunteer to eliminate bias. VE a and VE m are the volume errors of automatic and manual segmentation, respectively: VE a = V a V t V t (1) VE m = V m V t V t (2) where V t is the theoretical volume calculated by SOLIDWORKS, V a is the automatically segmented volume, and V m is the manually segmented volume. V t was assumed to be more accurate than the manual and automatic segmentation techniques, however, it is still subject to a print volume error. The automatic segmentation error of 3.80% was less than the manual segmentation error of 7.11% when comparing it against the theoretical volume calculated by SOLIDWORKS (Table 2). Repeated tests will be needed in order to make a significant conclusion about the accuracy of the segmentation methods. However, these results suggest that it is possible for an automatic segmentation to be more accurate than manual segmentation. Automatic and manual segmentations were performed on the six clinical MRI data sets. To validate the accuracy of the automatic segmentation, validation metrics were calculated to compare the manually segmented, and automatically segmented bones according to previous litterature [8]. VE is the volume error, AVE is the absolute volume error, V o is the volume overlap error, and S is the sensitivity: VE = V a V m V m (3) 33

43 AVE = VE (4) V o = 1 FP + FN V m (5) S = TP V m (6) where FP is the number of false positive isotropic voxels, FN is the number of false negative isotropic voxels, and TP is the number of true positive isotropic voxels. On average for all data, the AVE was 0.84±1.25(%), V o was 91.0±4.56%, and S was 95.6±2.01% (Table 3). The segmentations for Patients 3 and 5 did not perform as well as the other patients. In these cases, the patients had very thin cortical bone as well as a poor contrast between the cortical bone and adjacent muscle. The algorithm classified some of the pixels in the muscle tissue as cortical bone. Another notable result, is the difference in V o between the two treatments of Patient 2 (93.1 % vs 97.2%, respectively). Very similar ROIs were segmented for each treatment, as it was the same patient in each case. Damaged tissues from the first treatment of Patient 2 may still have been present within the ROI during the second treatment. If damaged tissues from the first treatment were present, it could could lead to a different range of voxel intensities within the MR scans, thus explaining the differences in both manual and automatic segmentations. If thermal simulations are performed on both the automatically and manually segmented data, and the thermal results compare well with the PRFS-based thermometry data, it can be concluded that the automatically segmented bones compare well to the manually segmented bones. In addition to the clinical data, MRI data was obtained from four volunteers, and the same validation metrics were performed. On average, AVE was 2.30±1.78%, V o was 91.3±1.71%, and S was 94.4±0.93% (Table 4). On average, the AVE had a higher discrepancy compared to the clinical data. A notable difference between the two data sets is that the clinical data 34

44 Table 3: Validation of automatic segmentation on clinical treatment bones. Patient number VE (%) AVE (%) V o (%) S (%) V a (mm 3 ) V m (mm 3 ) a b Mean Std was taken from children, and the volunteer data was taken from adults. The average VE of (Table 4) means that the manual segmentations are estimating a higher volume in comparison to the automatic segmentation. It is possible that a greater volume error is occurring within the manual segmentations. The user manually segmenting the bones may have tended to overestimate the volume of segmentation, due to the superior contrast around the edges of the cortical bone within the adult volunteers. Conversely, the user may have also tended to underestimate the volume in the manual segmentations of the clinical cases (children), due to the inferior contrast around the edges. The sensitivity, volume errors, and volume overlap were comparable between the volunteers and the clinical data. The sample size of clinical cases was only 6, and the sample size for volunteers was only 4. A larger sample size would be needed to make a statistical conclusion about these segmentation validation metrics. 3.3 Discussion MRI segmentation is required for MRgHIFU simulation within the integrated platform. However, manual MRI segmentation can be a very time consuming process. Manual segmentation would likely take a prohibitively long time if performed in an intra-operative setting. Therefore, an automatic segmentation strategy using the k-means clustering technique was developed. However, the automatic segmentation strategy must be proven reliable 35

45 Table 4: Validation of automatic segmentation on volunteer bones Volunteer Number VE (%) AVE (%) V o (%) S (%) V a (mm 3 ) V m (mm 3 ) Mean Std and robust in order to be implemented within a clinical setting. To assess the accuracy of both the automatic and manual segmentation strategies, a bone phantom with known dimensions was built. The phantom was then scanned with the same MRI sequence as the clinical treatments. After the phantom was scanned, it was manually and automatically segmented. Upon comparison of the manually and automatically segmented volumes with the theoretical volume from the 3D printer, it was determined that the automatically segmented volume was closer. The closer comparison of the automatic segmentation suggests that even though manual segmentation is considered the gold standard, it is possible for automatic segmentation to be more accurate. However, the comparison of segmentation techniques was only performed on a sample size of one. A comparison of the segmentation technique accuracies on a much larger sample size would be required in order to make a statistically relevant conclusion. For validation of the automatic segmentation developed, the six clinical MRI data sets and the four volunteer MRI data sets were manually, and automatically segmented. There were notable differences in the results when the segmentation of the OO patients was compared to the segmentation of the volunteers who were adults. The segmentation of the OO patients performed slightly better in comparison to the segmentation of the volunteers. In general, adults have thicker cortical bone in comparison to children. Overall, the contrast of the volunteer bones appeared to be better than the OO patients. The fact that segmentation 36

46 of the OO patients performed better seems unintuitive. It is possible that the automatic segmentation was performing better than the manual segmentation. Another explanation for this finding could be due to the small sample size of OO patient and volunteer data. The segmentation validation metrics were adopted from Cool et al. [8]. Cool et al. assessed the accuracy of a semi-automatic deformable mesh segmentation algorithm for segmentation of the prostate. Based on the defined validation metrics, the segmentation comparison of the OO patients and volunteers was in better agreement in comparison to the segmentations made by Cool et al. [8]. However, Cool et al. [8] segmented ultrasound images, which are known to have significantly worse contrast in comparison to MR images. Hudson developed a deformable mesh based segmentation algorithm to segment MRI scans of porcine femurs. Hudson also manually segmented these femurs using 3D slicer, and compared the segmentation results with the same validation metrics. However, based on the segmentation validation metrics, he concluded that the automatic segmentation algorithm he developed was not accurate enough in comparison to the manual segmentation. The validation metrics comparing the segmented data of the OO patients to that of volunteers were in significantly better agreement in comparison to the porcine femurs segmented by Hudson [21]. There were some subjects in which the manual segmentation did not compare as well to the manual segmentation. It is possible that minor differences in segmentation may result in large differences in the simulated results. Therefore, a very close comparison of automatically segmented data with manually segmented data may be required to ensure its reliability for thermal simulation in an intra-operative setting. To improve the accuracy of automatic segmentation, different avenues for future research can be pursued. First, further research towards optimizing the performance of the k-means algorithm would improve segmentation accuracy. The distance metric used for the k-means algorithm was the Euclidean distance metric. There are different variations of the k-means algorithm which use different distance metrics, such as the Mahalanobis distance, which is the distance between a point and a distribution [4]. It is possible that using a different distance metric for the k-means algorithm 37

47 will enhance its performance. Second, developing a strategy using an appropriate combination of the automatic segmentation methods, such as the methods discussed in Section 2.1 may improve the accuracy of segmentation. Finally, extending the segmentation GUI with user input options to manually correct apparent errors in segmentation after the algorithm has run, can also improve the accuracy of segmentation. Though the initial results of the proposed automatic segmentation strategy are positive, validation with manual segmentation within a larger sample size would be necessary in order to show statistical significance. In addition to segmentation validation metrics, the accuracy of segmentation can be assessed by analysis of the thermal results. If the thermal simulation results with automatic segmentation prove to be comparable to results with manual segmentation, with statistical significance, it would indicate that the segmented volumes are close enough to produce an insignificant difference in the thermal results. Also, if the simulations with automatic segmentation are comparable to the clinical PRFS-based thermometry with statistical significance, it would indicate that the automatic segmentation is sufficiently accurate. To show statistical significance, it would require data from a large sample size of clinical treatments. The continuation of the clinical pilot study in this research, as well as the data collaboration between MRgHIFU research centers worldwide, may establish a large enough sample size of OO patient data to segment and establish a statistically valid segmentation technique. 4 Acoustic model After the ROI has been segmented, the user defines the sonication region and HIFU transducer angulation on the MR image. The angle and sonication region can either be manually input into the simulator, or imported from the file that is produced by the Philips Sonalleve MRgHIFU system after patient treatment. As discussed in Section 2.3, Hudson performed in vivo MRgHIFU simulations on porcine femur data with the HIFU transducer typically 38

48 angled normal to the porcine femur (90 ) [21]. In clinical treatments, the transducer should be angled optimally in order to effectively ablate the tumour without causing damage to the surrounding tissues. A mathematical transformation matrix has been coded into the simulator to allow for 3D rotations, in order for the HIFU simulator to account for the transducer angulations in each of the three image planes (axial, sagittal, and coronal). The transformations were applied using three sequential rotations in 3D space, where x, y, and z represent the coordinate systems (Figure 26). The angles: α, β, and γ are the corresponding rotations about the x, y, and z axes, respectively; and are referred to as Euler angles (Figure 26) [34]. R x (α), R y (β), and R z (γ) are the rotations about the x, y, and z axes, respectively: R x (α) = 0 cos(α) sin(α) 0 sin(α) sin(α) cos(β) 0 sin(β) R y (β) = sin(β) 0 cos(β) cos(γ) sin(γ) 0 R z (γ) = sin(γ) cos(γ) (7) (8) (9) There are a total of 27 different permutations of rotation sequences possible in the 3D plane. R xyz corresponds to the sequence of rotations R x (α) R y (β) R z (γ), and is calculated 39

49 Figure 26: 3D rotations [34] by the matrix multiplication R x (α)r y (β)r z (γ): cos(β) cos(γ) cos(β) sin(γ) sin(β) R xyz = sin(α) sin(β) cos(γ) cos(α) sin(γ) sin(α) sin(β) sin(γ) + cos(α) cos(γ) sin(α) cos(β) cos(α) sin(β)cos(γ) + sin(α) sin(γ) cos(α) sin(β) sin(γ) sin(α) cos(γ) cos(α) cos(β) (10) In the Philips Sonalleve MRgHIFU system, Equation 10 describes the sequential rotations of the HIFU transducer about its focal point, where the coordinate system is in reference to the HIFU transducer. Equation 10 was coded into the MRgHIFU simulator to account for transducer angulations from the clinical treatments. The bright yellow dot from Figure 20 defines the sonication target, and the angle transformations rotate about this point. The acoustic boundary (yellow mask in Figure 20) was defined from the physical specifications of the Philips Sonalleve HIFU transducer. Once the sonication point, acoustic propagation boundary, and transducer angulation are defined, the acoustic field calculations are performed. The RI was used to model acoustic propagation through each homogeneous tissue [16], providing the velocity potential: φ(r, t) = 1 2π ue S1 ikr ds 1 (11) r 40

50 where S 1 is the surface of the HIFU transducer, r is the distance to a point in the acoustic field, k is the complex wave number, u is the transmitted velocity from the transducer surface, and t is time. A discretized numerical solution to the RI was adopted from Fan and Hynynen [16]. The solution provides the velocity potentials, φ 1n emitted from each transducer surface element, n: φ 1n (r, t) = 1 2π N u n e ikrn n=1 r n S 1n (12) Once the velocity potentials were calculated at the surface of the first medium, the corresponding velocities across the acoustic field, v 1n, were calculated: v 1n = φ 1 n r n = ik 2π N n=1 u n e ikrn r n (1 i 1 kr n )S 1n (13) After the velocities across the first media were calculated, the transmitted angles, θ 2m were calculated using Snell s law: θ 2m = arcsin c 2 sin θ 1m c 1 (14) where m is the number of transmitted waves, θ 1m are the incident angles, c 1 is the speed of sound in the incident medium, and c 2 is the speed of sound in the transmitted medium [6]. The surface of the new medium acts as a new radiator, and the effective transmitted velocities emitted from this new radiator, v 2m, were calculated: v 2m = T m v 1m cos θ 2m (15) where T m is the transmission coefficient. For transmission between two liquid media, T m was calculated by T m = 2ρ 1 c 1 cos θ 1m 2ρ 2 c 2 cos θ 1m + 2ρ 1 c 1 cos θ 2m (16) where ρ 1 and ρ 2 are the densities of the first and second media, respectively [6]. The reflected velocities across two liquid boundaries were calculated similarly, where the reflection coeffi- 41

51 cient, R was calculated by the relationship R = T 1 [6]. After the velocities across the new medium were calculated, the velocity potentials in the new medium, φ 2m were calculated: φ 2m (r, t) = 1 2π M v 2m e ikrm m=1 r m S 1m (17) Soft tissues, such as muscle, are considered semi-solid, and produce negligible transverse propagation [6], however, cortical bone is solid due to its crystalline calcium phosphate matrix composition [46]. Snell s law can be extended to include transmission between solidliquid and liquid-solid boundaries. The transverse and longitudinal transmitted angles: θ T and θ L can be calculated by the extension of Snell s law: sin θ 1 c 1 = sin θ L c L = sin θ T c T (18) where c T and c L represent the speeds of sounds in the transverse medium and the longitudinal medium, respectively [6]. The longitudinal and transverse transmission coefficients, T L and T T, respectively, were calculated: T L = (2ρ 1 /ρ 2 ) cos 2θ T Z L cos 2 2θ T + Z T sin 2 2θ T + Z (19) T T = ( 2ρ 1 /ρ 2 ) cos 2θ T Z T cos 2 2θ T + Z T sin 2 2θ T + Z (20) where Z = ρ 1c 1 cos θ 1 is the acoustic impedance of the orignal medium, Z L = ρ 2c L cos θ T impedance of the longitudinal wave medium, and Z T = ρ 2c T cos θ T is the impedance of the transverse wave medium [6]. The reflection coeficent was also calculated: is the acoutic R = Z L cos 2 2θ T + Z T sin 2 2θ T Z Z L cos 2 2θ T + Z T sin 2 2θ T + Z (21) When acoustic waves transfer from a solid medium into a liquid medium, the incident waves 42

52 can be both transverse and longitudinal. All combinations of the transmission and reflection coefficients were calculated: T LL = (1 R LL) tan(θ 2 ) cot(θ L ) cos(2θ T ) (22) T T L = 2(1 + R T T ) tan(θ 2 ) cos(2θ T ) sin 2 (2θ T ) (23) R LL = Z + Z T sin 2 (2θ T ) Z L cos 2 (2θ T ) Z + Z T sin 2 (2θ T ) + Z L cos 2 (2θ T ) (24) R T T = Z + Z L cos 2 (2θ T ) Z T sin 2 (2θ T ) Z + Z L cos 2 (2θ T ) + Z T sin 2 (2θ T ) (25) R LT = 2(1 R LL) cot(θ L ) sin 2 (2θ T ) cos(2θ T ) (26) R T L = 2(1 R T T ) tan(θ L ) cos(2θ T ) sin 2 (2θ T ) (27) where θ 2 is the transmitted angle in the new liquid medium, and the order of subscripts T and L correspond to the modes of the initial and final waves, respectively [6]. The velocity potentials and the transmission coefficients were calculated across the following media interfaces: Oil tank - Membrane - Skin - Muscle - Cortical bone - Bone marrow (Figure 27). To save computation time, all computations were calculated by CUDA parallel computing software. The computations were performed on a computer with 18GB RAM, 2.53GHz Intel Xeon processor, and an NVIDIA GTX670 card with 4GB VRAM. There are limitations to the developed acoustic model. First, there was subcutaneous fat within the acoustic field, however, it was not segmented in the model. Fat tissue has a lower acoustic impedance compared to muscle [20]. The presence of a fat layer creates an extra medium 43

53 Figure 27: Clinical treatment setup. layer in the acoustic field simulation, changing the propagation pattern. Second, the model assumes linear propagation within homogeneous tissue. In reality, non-linear acoustic effects such as non-homogeneous tissue properties and scattering are present [6]. Models such as the KZK equation take non-linearities into account, and allow for a more accurate acoustic simulation [26, 47]. However, even with modern day computers, such non-linear simulation takes prohibitively long for an intra-operative setting. A future avenue of research could examine simulation with the KZK equation for a pre-operative MRgHIFU application, such as patient screening and pre-treatment planning. After the velocity potential was calculated at the ROI, the pressure distribution was calculated: P = iωρφ (28) where ω is the angular frequency [16]. The pressure distribution was then converted into a heat distribution Q: P 2 Q = abs ρc (29) where abs is the absorption coefficient of the medium [16]. Once the heat source term, Q was calculated, it was then sent for thermal simulation. All parameters involved in the acoustic 44

54 model were obtained from the literature values (Appendix A). 5 Thermal simulations After the automatic clinical MRI segmentation strategy and the acoustic model were developed, a thermal model was developed to predict where and how much heat is spreading at The ROI. The thermal model requires the heat source distribution, Q at the ROI, calculated from the numerical solution to the RI in the acoustic model. After the thermal model was developed, MRgHIFU simulations were performed. In the simulations, both temperature and thermal dose distributions were modelled at the ROI. 5.1 Methods The thermal simulations were modelled by the BHTE [33]: ρc p T t = (κ T ) w bc b (T b T ) + Q (30) There are three terms on the right side of Equation 30. The first, (κ T ), is the volumetric heat spread by conduction (transfer in the vibrational energy between neighbouring particles), where κ is the thermal conductivity; the second, w b c b (T b T ), is the dissipation of energy based on the perfusion on blood, where w b is the perfusion rate of blood, c b is the specific heat of blood, and T b is the temperature of the blood entering the tissue; and the third, Q, is the effective volumetric spread of heat by convection from the applied transducer T pulse. The term on the left of Equation 30, ρc p, is the change in stored energy in a volume t of tissue based on the density (ρ) and heat capacity (c p ) of the tissue. A discretized solution to Equation 30 was calculated in CUDA, using the finite difference time domain (FDTD) method [23]. The forward time temporal discritization of the temperature was calculated: T t = T n+1 i,j,k T i,j,k n t (31) 45

55 where Ti,j,k n is the temperature at the voxel location (i, j, k), n is the time step, and t is the temporal resolution [23]. The central difference spatial discretization was also calculated: 2 T = T n i+1,j,k 2T n i,j,k + T n i 1,j,k h 2 + T n i,j+1,k 2T n i,j,k + T n i,j 1,k h 2 + T n i,j,k+1 2T n i,j,k + T n i,j,k 1 h 2 (32) where h is the spatial resolution [23]. When the BHTE (Equation 30) is discretized, T is replaced by Ti,j,k n, and Q is replaced by Qn i,j,k. The heat pulse was evenly distributed between n time steps. The temporal resolution, t, was chosen to enforce the Courant-Friedrichs- Lewy (CFL) condition: κ ρc p t h 1 (33) If the CFL condition does not hold true, the model is not guaranteed to produce a stable solution [9]. It takes a certain amount of time for tissue necrosis to occur. For ablation to occur, an external heat source must be applied to the tissue for extended amounts of time [18]. The thermal dose, D quantifies the amount of ablated tissue: D = 0.25 T (t) < 43 C R 43 T (t) dt R = t T (t) 43 C tn (34) where t 1 is the time step when the heat source was applied, and t n is the time step when the heat source was removed. Thermal dose is measured in cumulative equivalent minutes of ablation at 43 C (CEM43), and it takes 240 minutes to destroy tissue at 43 C [40]. The tissue is ablated exponentially faster the hotter the temperature is, and the exponential coefficient, R, increases from 0.25 to 0.50 above 43 C. Based on solutions to the BHTE, a disctretized solution to the thermal dose equation was calculated in CUDA: D n i,j,k = R43 T n i,j,k R 43 T 1 i,j,k t 1 t n t n t 1 ln(r) (35) 46

56 where Di,j,k n corresponds to the thermal dose at the voxel location (i,j,k) during the elapsed pulse time from t 1 to t n. 5.2 Results During the clinical OO treatments, PRFS-based thermometry signals were dynamically acquired on the three different orthogonal planes (axial, sagittal, and coronal), with each plane centred about the sonication point. During treatment, lower-powered sonications were used as test sonications to ensure the HIFU beam was focusing well before treatment. The test sonications were neglected in the results. The sagittal plane PRFS-based thermometry data was acquired for analysis for all treatment sonications of the six clinical OO treatments. MR thermometry sequences often take longer than one second to acquire a dynamic temperature signal. In the case of Patient 1, Sonication 9 (bolded in Table 5), the dynamic acquisition time for acquiring signals was seconds. Temporal interpolation, using the built-in MATLAB function, imresize, was applied to all of the thermometry data in order to create transformed data with 1-second time intervals, over the 20 seconds of sonication and 40 seconds of cooldown time. After the temporal interpolation was applied to the the raw thermometry data, a median filter was performed on the thermometry data, using the built-in MATLAB function, medfilt2. In image processing, median filters have been shown to smooth images and reduce noise [42]. The median filter works by changing each pixel to the median of the nearest 2 2 neighbourhood, and the pixels on the boundary of the image stay the same. After the median filter was applied, the maximum thermometry temperatures were recorded at each second for the 60-second period. The maximum temperatures were recorded within a mm ROI, centered about the sonication point, in the sagittal plane. The maximum temperatures after 20 seconds of sonication (T20) and the maximum temperatures after 40 seconds of cooldown time (T40) were recorded for all sonications. Figure 28 provides a visualization of the maximum temperature over time in the ROI for the raw thermometry data (blue stars), interpolated data (blue line), and median filtered data (green 47

57 Figure 28: Max temperature vs time of thermometry data for Patient 1, Sonication 9. The green circles indicate T20 and T40 for this sonication. line), for the case of Patient 1, Sonication 9 (bolded in Table 5). T20 and T40 for Patient 1, Sonication 9 were 62.4 C and 49.2 C, respectively (bolded in Table 5). Based on the temperature distributions, the thermal dose calculations were calculated by Equation 35 at each voxel for each time step. If the thermal dose was above the CEM240 ablation threshold, the voxel was labelled as necrosed tissue. The dynamically acquired PRFS-based thermometry slices have a corresponding slice thickness and resolution. The volume of necrosed tissue at the ROI was calculated by the sum of the necrosed tissue voxels, multiplied by the image resolution. The volume of necrosed tissue at the ROI and the coordinates of the ablation centroid (Z,Y ), were calculated for all sonications. The volume of necrosed tissue for Patient 1, Sonication 9 was 17.4 mm 3 (bolded, Table 5). The Philips Sonalleve MRgHIFU system provides quality assurance (QA) standards for temperature measurements. The temperature measurement QA standard is to be within ±5 C compared to a known reference temperature in a thermally sensitive gel (Table 6) [1]. The treatment positioning accuracy QA standard is to be within 3 mm of the defined sonication point (Table 6) [1]. After the thermometry data was processed, MRgHIFU simulations were performed, then the temperature and thermal dose maps were calculated. Simulations were run on the sonications from the six clinical treatments of five patients, with both the automatic and the 48

58 Table 5: Clinical MR thermometry data after temporal interpolation in the sagittal plane. T20 and T40 are the maximum temperatures after 20 seconds of sonication and after 40 seconds of cooldown time, respectively; Z and Y are the distances from the ablation centroid to the sonication point on the the sagittal slice (Z and Y axes). If the ablation volume within the ROI was 0, the ablation centroid coordinates, Z and Y were undefined. Patient Sonication Power Ablated volume T20 T40 Z Y (W) (mm 3 ) ( C) ( C) (mm) (mm) 1 2a 2b

59 Table 6: Philips Sonalleve QA standards [1]. Feature Specification Temperature change measurement accuracy ±5 C Treatment point positioning accuracy 3 mm or better manually segmented data. After the final temperature map at the ROI was calculated, there was further data processing. First, the temperature data output was manipulated to imitate the partial volume effect of the thermometry data. Todd et al. determined that for a threedimensional isotropic voxel, the adjacent voxels affect the PRFS-based thermometry signal due to the partial volume effect, and the fact that the dynamically acquired voxel signal is a weighted average of the signals throughout the whole volume. Todd et al. [44] found that the signal of a voxel is affected by a weight of 64% of the side voxel signals, 41% of the edge voxel signals, and 25% of the corner voxel signals. They concluded that the partial volume effect quickly drops off at the more distant pixels. Therefore, to imitate the partial volume effect of the PRFS-based thermometry, the simulated temperature output data was transformed based on the weighted average of the directly adjacent voxels, as described by Todd et al. [44]. For consistency with thermometry data, the same median filter was also applied to the thermal simulation results (Figure 29). Simulations were run using both automatically and manually segmented data. The same metrics were calculated for the simulated data that were calculated for the thermometry data. All simulations were performed using literature parameter values from Appendix A (Tables 10-16). After all of the simulations were run using both automatically segmented and manually segmented data, simulation results using the different segmentation techniques were compared, using T20 difference, T40 difference, ablation volume ratio, centroid distance, and Z coordinate distance. The average T20 difference for all sonications was 1.2±5.7 C (bolded in Table 7). These temperature comparisons are within 5 C of each other, which satisfies the Philp s Sonalleve QA standard for temperature accuracy (Table 6). However, there were some notable discrepancies. On average, the T20 difference was 3.2 ± 9.0 C for Patient 2b 50

60 Figure 29: Max temperature vs time of simulated data for Patient 1, Sonication 9, with automatic segmentation (bolded, Table 7). Simulated temperature before median filter (dotted red line); after the weighted average and the median filter were applied (solid red line). and 0.5 ± 8.7 C for Patient 5 (bolded in Table 7). The standard deviations of 9.0 and 8.7 suggests that there is significant fluctuation in the differences between T20 for simulations with automatic segmentation and simulations with manual segmentation. For Patient 5, the volume overlap was 84.9% between segmentations, which was below the average (Table 3). The larger discrepancy in segmented volumes may have caused significantly different thermal results, resulting in a high standard deviation for the T20 difference. However, for Patient 2b, the volume overlap of 97.2% was more comparable (Table 3), indicating that a small difference in segmentation can significantly alter the thermal result. It is possible that the angles of incidence of the HIFU waves at the ROI differed significantly as a result of small differences in segmentation. If only a small chunk of bone was misclassified in either segmentation strategy, the segmented volumes could still be very similar. However, if the misclassified region is near the sonication focus, a higher incident angle may occur, leading to an underestimation of T20. The average T40 difference was 0.5 ± 1.5 C, and was within 5 C for every sonication (bolded in Table 7). The close T40 difference suggests that the predicted temperatures tend to decay towards the trivial equilibrium (37 C) at similar rates. The T20 and T40 differences for Patient 4, Sonication 8 were both 0 (bolded in Table 7), 51

61 Figure 30: Max temperature vs time with automatic segmentation of Patient 4, Sonication 8 indicating that the shapes of the segmented bone surfaces were nearly identical at this sonication point. The maximum temperatures over 60 seconds for these simulations are nearly identical (Figure 30). However, the T20 and T40 differences for Patient 5, Sonication 10 were C and -4.9 C, respectively (bolded in Table 7). The large discrepancy between the maximum temperature vs time plots of these simulations is apparent (Figure 31). The average ablation ratio for all sonications was 0.9±0.8 (bolded in Table 7). If the angle of incidence at the ROI was over-predicted, the temperature at the ROI was underestimated. If the temperature was under-predicted too much, it resulted in a prediction of no ablated tissue volume. If the ablated tissue volume prediction with manual segmentation was 0, the ratio was infinite or undefined. These ratios were not calculated in the average ablation ratio, and left blank (Table 7). There were also instances of simulations with automatic segmentation predicting 0 ablated volume, creating a higher standard deviation of 0.8. The average centroid distance and Z coordinate distance were 0.6 ± 0.4 mm and 0.2 ± 0.6 mm, respectively. These distances are within the Philips QA standard for sonication positioning of 3 mm, indicating that the simulations accurately predict the location of ablation, regardless of segmentation choice. In the instances where the ablation ratio was either 0 or 52

62 Table 7: Simulated data with automatic (subscript a) and manual (subscript m) segmentation. All ratios are calculated as automatic over manual. Bolded values are results of particular interest, and are interpreted in Section 5.2. Patient Sonication Power V a V m Ablation T20 a T20 m T20 T40 a T40 m T40 Z a Y a Z m Y m Ablation Z (mm 3 ) (mm 3 ) volume ( C) ( C) difference ( C) ( C) difference (mm) (mm) (mm) (mm) centroid distance ratio ( C) ( C) distance (mm) (mm) Average Std a Average Std b Average Std Average Std Average Std Average Std Total average Total std

63 Figure 31: Max temperature vs time with automatic segmentation of Patient 5, Sonication 10 infinite, the ablation centroid was non-existent, thus the Ablation centroid distance and Z distance were undefined (Table 7). These blank entries were not calculated in the averages and standard deviations. To assess the accuracy and robustness of the simulations with automatic segmentation, the simulated results were compared to the processed thermometry data. The thermometry data was considered to be the gold standard of comparison. If the simulation can robustly meet the QA standard values in comparison to the thermometry data, it is considered sufficiently reliable for an intra-operative setting. The average T20 difference for all sonications was 2.1 ± 9.5 C (bolded in Table 8). The average is within the Philips QA standard of of 5 C. However, the high standard deviation of 9.5 C indicates that the temperature is commonly predicted outside of 5 C. There are multiple potential explanations for the large variation in the T20 difference. First, when the simulated temperature predicts a temperature greater than the thermometry, there could be a lack of thermometry signal within the bone. A higher temperature prediction could be due to an overestimation of the angle of incidence at the ROI due to errors in the segmentation or the acoustic model. Second, there could be ambiguous thermal parameters within the necrosed tissue. The average T20 differ- 54

64 ences for Patient 2a and Patient 2b were 2.7 ± 2.7 C and 4.7 ± 6.6 C, respectively (bolded in Table 8). Since the two treatments were performed on the same patient, with a similar treatment plan in both treatments; it is expected that the thermal results will be comparable. The T20 difference could potentially be due to segmentation error. Alternatively, the difference could be explained by other factors such as the potential for ambiguous thermal parameters that may exist due to the presence of necrosed tissue. For Patient 1, Sonication 11, the T20 difference was 2.0 C (bolded in Table 8), while the maximum simulated temperature remains close to the thermometry temperature for this sonication (Figure 32). For Patient 1, Sonication 7, the T20 difference was C (bolded in Table 8), and it is apparent that there is a large discrepancy between the maximum simulated and thermometry temperatures for this sonication (Figure 33). A likely explanation for the large discrepancy is due to an over-estimation of the incident angles at the ROI due to segmentation error, leading to increased reflection and a lack of focus. On average for all sonications, the T40 difference was 6.2±4.8 C (bolded Table 8), indicating that the simulations are consistently underestimating the temperature during the cooldown period. Again, this discrepancy could potentially be explained due to the presence of necrosed tissue with different thermal properties. If the specific heat of the necrosed tissue is actually higher in comparison to the surrounding cortical bone, this difference could explain why the thermometry temperature remains higher during the cooldown period. Incorporating a different specific heat for necrosed tissue in the thermal model may result in a higher temperature prediction during the cooldown period, and a better comparison with the thermometry as a result. The average ablation ratio was 0.8 ± 0.8 on average for all sonications (bolded in Table 7). Due to a lack of temperature signal within bone, the thermometry predicts very minimal necrosed volume in the cortical bone region. For Patient 2a, Sonication 11, the temperature distributions for the simulation and thermometry both appear to centred close to the origin along the Y axis (Figure 34(c)). However, the distributions along the Z axis (Figure 34(d)) are significantly shifted, due to the lack of temperature signal in the thermometry. Due to 55

65 Table 8: Simulated data vs thermometry (automatic segmentation). All ratios are calculated as simulated over thermometry. Patient Sonication Power Ablation T20 T40 Ablation centroid Z (W) volume ratio difference ( C) difference ( C) distance (mm) distance (mm) Average Std a Average Std b Average Std Average Std Average Std Average Std Total average Total std

66 Figure 32: Maximum temperature vs time for Patient 1, Sonication 11 Figure 33: Maximum temperature vs time for Patient 1, Sonication 7 57

67 the lack of signal, the ablation centroid calculation in the thermometry would be shifted away from its true location. Therefore, in the calculation for the ablation volume ratio, only the necrosed volume within muscle and the boundary voxels along the cortical bone were calculated. There were some cases in which there was a much higher necrosed tissue volume in the simulation, such as Patient 5, Sonication 6, where the ratio was 2.9 (bolded in Table 7). In other cases, there was no ablated tissue volume predicted by the simulation (Table 7). The large fluctuations in ablation volume could explain the higher standard deviation. The average ablation ratio for Patient 2a was 0.2 ± 0.2 (bolded in Table 8). The lower predicted volume of necrosed tissue in the simulation for Patient 2 could indicate that the thermometry over-predicted the volume of tissue destroyed, when in fact minimal tissue was destroyed. For Patient 2a, Sonication 11, It is evident that the heating pattern is much more diffuse along the Y axis in the thermometry (Figure 34(a)), compared to the simulation (Figure 34(b)), thus there is a much greater volume of necrosed tissue predicted in the thermometry (Figure 34(e)) compared to the simulation (Figure 34(f)). The average predicted ablation volume from the simulation was 0.5 ± 0.1 in Patient 2b (bolded Table 8), higher in comparison to Patient 2a. Patient 2 had indicated significantly reduced pain after the second treatment, and the higher ablation ratio predicts that more tumour tissue was destroyed. However, this patient was not fully responsive to the treatment. The ablation ratio for Patient 2b was still significantly less than 1, and could potentially explain why Patient 2 was not fully responsive to the treatment. On average for all sonications, the ablation centroid distance was 4.2 ± 2.7 mm (bolded in Table 8), which is outside of the Philips QA standard for sonication positioning of 3 mm. The Z distance was 3.0 ± 3.0 mm on average (bolded in Table 8), indicating that most of the distance discrepancy was in the Z axis. The Z axis is parallel to the axis of HIFU propagation. The true focus of the HIFU waves are skewed towards the transducer because cortical bone is a highly attenuating tissue [6]. The sonication point is at the origin, so the more negative the Z coordinate is, the further away the centroid is from the sonication point, 58

68 (a) Sagittal slice, thermometry temperature distribution (b) Sagittal slice, simulated temperature distribution (c) Maximum temperatures along the Y axis (d) Maximum temperatures along the Z axis (e) Sagittal slice, thermometry thermal dose distribution (f) Sagittal slice, simulated thermal dose distribution Figure 34: Temperature and thermal dose distributions after 20 seconds of sonication for Patient 2a, Sonication 11 59

69 hence why the Z coordinate is consistently negative in both the thermometry data (Table 5) and the simulated data (Table 8). For Patient 2a, Sonication 11, the simulated ablation centroid appears roughly 10 mm to the left of the origin (Figure 34(f)). The necrosed tissue appears far away from the dark area on the MR scan defining the tumour (34(f)), potentially explaining why this patient did not have a fully successful treatment. The Z distance was more negative on average in the simulations. The more negative Z distance could be the result of an over-estimation in acoustic impedance of cortical bone, or an over-estimation of thermal conductivity in the muscle. Over-estimations in these parameters would skew the temperature distribution towards the muscle tissue, thus skewing the ablation centroid in the negative Z direction. For Patient 1, Sonication 11, there is a lack of thermometry temperature signal beyond the cortical bone boundary (Figure 35(a)), where a temperature distribution can be observed within the cortical bone in the simulation (Figure 35(b)). The peak temperatures are close to the location of the sonication point. The temperature distributions appear to follow a similar distribution along the Y axis, with a slightly wider peak in the simulated temperature (Figure 35(c)). However, the narrow thermometry temperature peak, skewed to the right of the origin along the Z axis, confirms the lack of signal within the cortical bone region (Figure 35(d)). Also, the simulated temperature distribution appears to be consistently higher than the thermometry further away from the origin along Z axis, beyond the cortical bone boundary (Figure 35(d)). The wider radius of the simulated temperature indicates a more diffuse heating pattern. The corresponding thermometry and simulated thermal dose distributions were also calculated (Figures 35(e) and 35(f)). The ablation volume ratio for this sonication was 1.3 (bolded in Table 8). The ablation volume ratio only included the simulated ablated voxels containing the cortical bone boundary and muscle tissue. Therefore, the similar, but slightly wider simulated temperature peak along the Y axis, agrees with the slightly larger simulated ablated tissue volume. For Patient 1, Sonication 7, there was zero predicted ablated volume in the simulation. For this sonication, there was also a lack of thermometry signal within the cortical bone region in the thermom- 60

70 Table 9: Simulation times for all sonications with automatic segmentation. The number of voxels along each axis for each MRI scan is indicated by (X, Y, and Z). Patient X Y Z t Total number of voxels Min sim time (s) Max sim time (s) E a E b E E E E Max Min etry (Figure 36(a)). In comparison to the simulated temperature distribution for Patient 1, Sonication 11 (Figure 35(b)), the simulated temperature for Patient 1, Sonication 7 resulted in a wider distribution, with a lower temperature peak, and a majority of the heating in the muscle region (Figure 36(b)). It is evident that the temperature distribution is significantly shifted away from the origin along the Z axis, with a significantly lower temperature peak compared to the thermometry (Figure 36(c)). The skewed temperature distribution away from the origin provides supporting evidence that there was an over-estimation of the incident angle resulting in more reflected waves away from the sonication focus. The maximum and minimum simulation times for all sonications were seconds and 33.0 seconds, respectively (Table 9). The MRI sequence that was used for pre-operative imaging in each clinical treatment, was the T1 volume isotropic turbo spin echo acquisition (VISTA), by Philips Medical Systems. This image acquisition time is in the neighbourhood of five minutes. On average, the combined user input and k-means segmentation adds up to roughly 2 minutes. Therefore, the combined simulation and segmentation time can fit within one pre-operative image acquisition time. 5.3 Discussion A thermal model based on a numerical solution to the BHTE was developed and integrated into the simulation platform. Using manual segmentation as a benchmark, the average 61

71 (a) Sagittal slice, thermometry temperature distribution (b) Sagittal slice, simulated temperature distribution (c) Maximum temperatures along the Y axis (d) Maximum temperatures along the Z axis (e) Sagittal slice, dose distribution thermometry thermal (f) Sagittal slice, simulated thermal dose distribution Figure 35: Temperature and thermal dose distributions after 20 seconds of sonication for Patient 1, Sonication 11 62

72 (a) Sagittal slice, thermometry temperature distribution (b) Sagittal slice, simulated temperature distribution (c) Maximum temperatures along the Z axis Figure 36: Temperature distributions after 20 seconds of sonication for Patient 1, Sonication 7 63