Data-driven optimal binning for respiratory motion management in PET

Transcription

1 Data-driven optimal binning for respiratory motion management in PET Adam L. Kesner a) Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY, USA Joseph G. Meier Department of Imaging Physics, University of Texas MD Anderson Cancer Center, Houston, TX, USA Darrell D. Burckhardt Siemens Medical Solutions USA, Inc., Hoffman Estates, IL, USA Jazmin Schwartz Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY, USA David A. Lynch Department of Radiology, National Jewish Health, Denver, CO, USA (Received 17 May 217; revised 24 October 217; accepted for publication 24 October 217; published 2 November 217) Purpose: Respiratory gating has been used in PET imaging to reduce the amount of image blurring caused by patient motion. Optimal binning is an approach for using the motion-characterized data by binning it into a single, easy to understand/use, optimal bin. To date, optimal binning protocols have utilized externally driven motion characterization strategies that have been tuned with populationderived assumptions and parameters. In this work, we are proposing a new strategy with which to characterize motion directly from a patient s gated scan, and use that signal to create a patient/instance-specific optimal bin image. Methods: Two hundred and nineteen phase-gated FDG PET scans, acquired using data-driven gating as described previously, were used as the input for this study. For each scan, a phase-amplitude motion characterization was generated and normalized using principle component analysis. A patient-specific optimal bin window was derived using this characterization, via methods that mirror traditional optimal window binning strategies. The resulting optimal bin images were validated by correlating quantitative and qualitative measurements in the population of PET scans. Results: In 53% (n = 115) of the image population, the optimal bin was determined to include 1% of the image statistics. In the remaining images, the optimal binning windows averaged 6% of the statistics and ranged between 2% and 9%. Tuning the algorithm, through a single acceptance window parameter, allowed for adjustments of the algorithm s performance in the population toward conservation of motion or reduced noise enabling users to incorporate their definition of optimal. In the population of images that were deemed appropriate for segregation, average lesion SUV max were 7.9, 8.5, and 9. for nongated images, optimal bin, and gated images, respectively. The Pearson correlation of FWHM measurements between optimal bin images and gated images were better than with nongated images,.89 and.85, respectively. Generally, optimal bin images had better resolution than the nongated images and better noise characteristics than the gated images. Discussion: We extended the concept of optimal binning to a data-driven form, updating a traditionally one-size-fits-all approach to a conformal one that supports adaptive imaging. This automated strategy was implemented easily within a large population and encapsulated motion information in an easy to use 3D image. Its simplicity and practicality may make this, or similar approaches ideal for use in clinical settings. 217 American Association of Physicists in Medicine [ Key words: adaptive imaging, automatic binning, data driven, gated PET, optimal binning, personalized imaging 1. INTRODUCTION Positron Emission Tomography (PET) is an established imaging technology that has useful application across diverse areas of medicine. A limitation of PET is that it suffers from degradation caused by the patient respiratory motion, which in turn diminishes its diagnostic potential. Gating can be used to minimize the effects of motion, but at the expense of obtaining count-limited images. Developing robust methods for overcoming this issue, in a clinically efficacious manner, is fundamentally important to the goal of implementing respiratory motion correction of PET images in a clinical setting. 1 3 Our challenge has been well articulated in the title of a recent publication Respiratory Motion Handling Is Mandatory to Accomplish the High-Resolution PET Destiny. 1 While we have seen more than a decade of research and commercial solutions introduced into the field, respiratory motion solutions have not been adopted on a large scale. 4 We speculate that the 277 Med. Phys. 45 (1), January /218/45(1)/277/1 217 American Association of Physicists in Medicine 277

2 278 Kesner et al.: Data driven optimal binning 278 additional efforts associated with acquiring gated data, along with the uncertainties associated with using gated images, present the major hurdles preventing its acceptance and application. In this context, there remains room for the development of alternative strategies to generate motion-corrected images. 5 Data-driven strategies are enabled by modern computing technologies and offer new prospects for implementing practical motion correction in PET. 6 Data-driven gating has been presented as a solution to help with the practical acquisition of gated data. Data-driven gating can be used to acquire a motion characterization of a patient that is similar to one collected from hardware device, but is achieved in an operator independent, fully automated manner, and requires no changes to clinical protocols. 7 Research is progressing in this field 8,9 and, since data-driven motion characterization requires nothing more than automated background processing, it is reasonable to envision a scenario in which motion characterization becomes ubiquitously available in clinical PET in the near future. In order to make such a situation reality, finding methods for using this information practically in clinical environments may be more relevant in coming years than it has been in the past, and is therefore gaining urgency. Many methods have been proposed for sorting motion-characterized PET data. 1,11 Motion correction in PET typically involves segregating raw data into bins, for each of which an image is reconstructed separately. The suitability of the sorting strategy is fundamentally important because it dictates the quality of the final images along with the risks of degrading the images diagnostic potential. Amplitude- or phase-based gating strategies are the most popular methods for dealing with motion-characterized PET data. These methods segregate data based on its relation to the amplitude or phase of the respiratory cycle. While the simplicity of these strategies is attractive, they are not ideal for use in the diagnostic clinic. First, data may be sorted into too many or too few bins. Patients have different tracer distributions and move to different extents, and the ideal number of gates is not fixed but rather unique to a patient/tracer/acquisition. In fact, a large portion of patients do not benefit at all from the gating effort 12,13 and their optimal image is nongated. Once 4D images are generated, physicians are asked to read motion-corrected image sets that are more numerous than the traditional nongated form, all of which have greater noise characteristics and may or may not be useful to a patient s diagnosis. Thus, physicians are weary of bringing motion correction technology, which comes with more work and more risk, into the clinic. An alternative strategy which has been presented for utilizing 4D data is optimal binning Optimal binning is a strategy aimed at using a subset of the originally acquired data to create a single, optimally binned, reduced motion image. Optimal binning has some practical advantages that make it appealing for clinical consideration and development: (1) Optimal binning is easy to understand: utilization of a subset of data (2) Optimal binning is easy to process: reconstruction of a subset of data (3) Optimal binning is easy to use clinically: output is a standard 3D image and works with any 3D image reading software (4) Optimal binning is practical to implement: processing is fully automated. (5) Optimal binning is easy to integrate in clinical procedures: presents an operator independent standardizable approach to handling motion The concept of optimal binning is that data are sorted such that the resultant image embodies a theoretical optimization between the resolution improvement and image statistics. Optimal binning has traditionally been implemented using all the data that are near the end expiration of the respiratory cycle, the quiescent period, as defined using an external hardware motion characterization device 17 such as a pressure belt or camera. The size of the optimal bin has in the past been determined from a population of respiratory traces; values of 35% 16 and 4% 15 of the total counts have been used. A problem with traditional optimal binning strategies is that they are based on theoretical optimization and not directly connected to specific images or acquisitions. Also they assume that the motion characterization is accurately associated with scan data. In this work, we introduce a new approach of applying data-driven principles to carry out an optimal binning strategy. This modification of an old strategy can potentially have significant implications because the optimization can now conform to the instance of data. The assumption that an external signal and internal motion correlate is no longer requisite. Also, by introducing an automated data-driven sorting algorithm, and combining it with data-driven gating, an entire datadriven motion correction workflow can be implemented and is exemplified in this work. The ease of a 1% fully automated software motion correction workflow option, as we present, could likely be integrated into clinics with ease. 18 In this work, we present data-driven optimal binning concepts, incorporated them into a data-driven motion correction workflow, and validated them in a population of scans to establish the proof of principle for automated adaptive motion correction in PET imaging. 2. MATERIALS AND METHODS Our methods for creating a data-driven optimally binned representation of a 4D data set consist of three main steps. A flowchart of the data-driven optimal binning workflow is shown in Fig A. Data driven optimal binning workflow Step 1 Generating a data-driven phase amplitude relationship characterization from a 4D phase-gated data set. A 4D phase-gated data set can be created from any PET acquisition that has (prospective or retrospectively collected) motion characterization associated with it by sorting image data

3 279 Kesner et al.: Data driven optimal binning 279 FIG. 1. Flow chart of data-driven optimal binning workflow. [Color figure can be viewed at wileyonlinelibrary.com] evenly across phases of the cycle. 19 The set of phase-gated images can then be analyzed to quantify motion content measures within each phase image to generate what we call a phase amplitude transfer function (PATF). This function serves to define an amplitude of motion measure for each phase of a patient s respiratory cycle. There are theoretically several ways to do this, including using center of mass measures or edge detection algorithms. In our work, we used principle component analysis. 2 Specifically, a phase amplitude relationship was described for each scan by plotting the first principle component (PC) weight array against phase. The first PC should adequately provide this characterization because it represents the greatest coherent signal variation in the field of view over the gated image cycle a measure which conveniently correlates with respiratory motion if it exists in the image. In this way, an amplitude of motion characterization can be derived from a phase-gated data set and used to define a patient-specific PATF. Example PATFs are shown in Fig. 2. Our strategy of associating phase and amplitude of motion in this step is in fact inspired by similar work; 21,22 the advancement of our work, however, is that we used an entirely internal, data-driven method for capturing the amplitude of motion signal from phase-gated data. The algorithm is compartmentalized such that the source of the motion characterization is immaterial. Step 2 Determining a scan-specific optimal binning window from phase amplitude motion characterization and using it to assign sorting of data. The PATF curve generated in step 1 is useful for describing patient motion over the cycle. Its units represent a measure of the total coherent changes in signal across a collection of image voxels over phase gates. We know in theory that we want to more aggressively subjugate data of patients who exhibit significant amounts of motion in their scans, while at the other end of the spectrum, we want to retain count statistics in patient scans that have no useful motion information in them. All images processed will be assigned some PATF by mathematical definition of principle component analysis, and we need to generate an understanding of its seemingly arbitrary magnitude to understand its significance. In order to gain perspective on the amplitude of the first PC curve, we compare it to the third PC curve, which is derived from the data in the same manner as the first PC. We do this because we assume that the first (and possibly second) PC components describe any true cycle respiratory motion. It is assumed that the third PC represents the amplitude of PC fluctuations that result from nonrespiratory motion, for example, noise, and we can use it to normalize the first PC curve. The magnitude of third PC fluctuations is used to create an amplitude-based acceptance window. Specifically we used the third PC curve to calibrate the magnitude of nonrespiratory fluctuations in our first PC signal, with the reasoning that this is the size of the window for random fluctuations and values within this window cannot confidently be labeled as dissimilar. More specifically, we defined our amplitude acceptance window as 3 standard deviations (SDs) of the third PC curve. This value was chosen using the assumption that the third PC represents Poisson noise and first PC curve variation changes outside 3 SDs are likely caused by nonnoise phenomena (e.g., motion). This single variable (width of acceptance window) can be adjusted in future works depending on the user s desire to be more or less conservative with respect to resolution and noise, and is considered further in the Results and Discussion. Once the amplitude acceptance window is defined, the PATF (first PC) is analyzed, and the portion of the curve that contains the most data points within the window s amplitude is chosen to define the optimal bin phase inclusion set. This is achieved by brute-force processing all permutations of bins are calculated and the window with maximum number of phases included in it is used. Examples of third PC-derived acceptance windows and phase inclusion selection are shown in Figs. 2(c) and 2(d). Step 3 Combining sorted data to obtain optimal image. A data-driven optimal bin image can be generated by combining data from accepted phases in a single, optimal bin. In this work, sorting was achieved by adding accepted phase image data together. 2.B. Clinical image analysis A population of 219 FDG PET scans were processed and reviewed. The images were acquired in a previous study 8 from a population of 112 individual patients undergoing single or dual time point clinically indicated PET/CT for radiologic evidence of pulmonary nodules measuring 6 2 mm, for whom PET/CT is clinically indicated. All scanning was performed on a BioGraph TruePoint PET/CT scanner (Siemens, Knoxville, TN, USA) having a single bed field of view of 22 cm. Injected radioactivity ranged between 5 and 73 MBq. Patients underwent standard whole-body PET/CT

4 28 Kesner et al.: Data driven optimal binning 28 Rela ve amplitude (normalized rel PCA weight) (a) Example PATF from image with useful mo on informa on Gate (phase gates) (b) Rela ve amplitude (normalized rel PCA weight) Example PATF from image with no useful mo on informa on Gate (phase gates) (c) Rela ve amplitude (normalized rel PCA weight) Example PATF from image with useful mo on informa on Gate (phase gates) (d) Rela ve amplitude (normalized rel PCA weight) Example PATF from image with no useful mo on informa on Gate (phase gates) Phase-mo on amplitude rela onship (1st PC) Non first principle component fluctua ons phase-mo on amplitude rela onship (3nd PC) Phased included in op mal window Acceptance window (= ± 3 * standard devia ons of non first principle component fluctua ons) FIG. 2. Illustration of phase amplitude transfer functions in two example patients. (a) A curve representing a patient with a significant amount of detectable motion. (b) A curve representing a patient with a nonsignificant amount of detectable motion. (c and d) Illustrations showing how the third principle component of a signal is used to define an amplitude acceptance window. The window, overlaid on the 1st principle component in the figure, is used to determine the phases that are accepted in the optimal bin, in a patient with a significant amount of detectable motion (c); and in a patient with a nonsignificant amount of detectable motion (d). Y axis shown scaled between and 1 for display. [Color figure can be viewed at wileyonlinelibrary.com] examinations, followed by a hardware-gated PET examination of the chest. Acquisition duration was 6 min, and acquisitions occurred 6 and/or 12 min after injection. Approximately 2% of the study sample had noticeable FDG uptake in lung lesions. Full accounting of acquisition criteria and scan settings can be found in the original reference. 8 4D respiratorygated PET data sets were generated using data-driven gating and phase-based binning (1 bins per cycle) 8 and used for primary analysis. Additional image sets generated using hardware gating system, and random gating triggers were also acquired and assessed for comparison. Hardware-driven respiratory gating was implemented using the Anzai pressure belt (Anzai Medical, Tokyo, Japan). All scans, including gated scans, were reconstructed using Siemens reconstruction software, with attenuation-weighted, ordered subsets expectation maximization reconstruction, two iterations, six subsets, 6-mm isotropic Gaussian post reconstruction filter, and delayed randoms correction. For each gated scan, a datadriven phase amplitude motion characterization was generated in the form of a PATF using methods described in this paper. To improve processing, the principle component analysis was processed using a truncated field of view five axial slices at each edge of the scan were cut to remove the low sensitivity/higher noise region. Three images were generated for each patient for the purpose of comparison: (a) nongated, (b) optimal bin, and (c) phase gated. Nongated images were defined as the sum of the gated images so as to reduce the variables specific to reconstruction. For quantitative analysis, we looked at noise and uptake measurements in the different images. Specifically, noise

5 281 Kesner et al.: Data driven optimal binning 281 was studied by quantifying the %SD in liver volumes of interest (VOIs), defined with a 71 cc spherical volume of interest (VOI) and placed on all images with obvious liver presentation in the field of view. Uptake measurements were taken by defining 8% maximum threshold VOIs on the subset of images that had obvious lesion uptake. Fullwidth half-maximum (FWHM) measurements were acquired from lesion superior inferior profiles taken at the VOI s center of mass, and reported for cases that had high enough signal to background ratios to make the measurement appropriate. For qualitative analysis, we compared observed motion with expected distribution of statistics in optimally binned images. In our previous study, 8 a qualitative assessment of motion was graded for each scan using three independent blinded readers. Two nuclear medicine physicians and one medical physicist, all with 1+ years experience and ABR certification, reviewed looping animations of phase-gated images, presented in random order on the screen. The animations consisted of coronal slice images with slice locations that had been preselected per scan for their proximity to either lung lesions or heart regions when there were no lesions present, determined through in-house 4D image navigation software, in an effort to present the slice that would most likely be affected by respiratory motion. The readers were asked to record whether or not (1 or ) they observed detectable motion in the looping image set. This qualitative assessment was performed independently of the present work, approximately 2 yr prior and with no knowledge it would be used in this study. 8 In this work, we look at the distribution of the number of gates included in the optimal bin across the population and compared them with the independent reader analysis. 3. RESULTS Two hundred and nineteen gated PET scans were processed and each binned into a single, optimal, 3D image. Given input sets of phase-gated images, processing only required approximately 5 s on a standard desktop PC. Given the default parameters: data-driven gating and an acceptance window of three standard deviations, in 53% (n = 115) of the scans, the optimal bin was determined to include 1% of the image statistics, that is, the patients did not noticeably benefit from the gating effort and the optimal bin was the nongated embodiment. For the remaining images, the optimal statistics binning windows contained an average of 6% of the statistics found in the nongated image and ranged between 2% and 9%. A histogram of the population data is shown in Fig. 3(a). Also shown in this figure are histogram statistics for alternative acceptance window settings (1 SD, 2 SD, 3 SD, and 4 SD) [Fig. 3(b)] and other source gating methods (hardware gating and random gating) [Fig. 3(c)]. The random gating method was included to show how the algorithm handles images that we know contain no useful motion information (motion should not be captured randomly). 98% of these scans were determined optimal with 1% of the statistics. To quantitatively asses the method, we looked at the effects of optimal binning on noise in the liver and on lesion quantification. In total, 12 images had well-defined liver in the FOV that would fit the 71 cc Spherical VOI. Since our method adapts to patient data and segregates data differently for each patient, it is not possible to characterize the noise implications of the algorithm in one single value. We found that noise, defined as SD/mean (%SD), correlated with statistics. When more statistics were included in an optimal bin, relative noise levels were lower. It is likely that noise is simply a function of statistics, which are clearly defined in our algorithm as a percentage of total. To test this hypothesis, we plotted theoretical Poisson noise defined as (sum SUV in VOI/sum SUV in image 9 # net trues)^ (1/2) vs. measured %SD (Fig. 4). The figure shows that counts (/theoretical noise) may be a predictor of measured noise, although the relationship is not purely Poisson as demonstrated in the nonunity slope. This divergence from theory is likely due to the fact that we are using iterative reconstruction with is known to be nonlinear. 23 Lesion VOIs were placed in 44 patient images that had definable lesions as described in methods. Generally speaking, the population average of the mean VOI measurement was highest in the gated images, when averaged over gates. However, we may expect this by definition as the gated images had the highest noise and smallest threshold VOI volumes. A summary of population lesion, VOI volume, and FWHM measurements is shown in Table I. To qualitatively asses the performance of the algorithm, we asked three observers to review animated phase-gated data (a central coronal slice looping through gates) throughout the population of scans and in random order. 89% of images assessed as not displaying motion, through agreement with three blind readers, were presented as optimal using 1% statistics qualitatively validating the tendency of the algorithm to leave scans without noticeable motion information in their nongated embodiment. Of the scans that were observed to have motion by all three readers, 78% of them were segregated into less than 1 bins, again illustrating the tendency of the algorithm to appropriately segregate scans with useful information. Visual inspection of the optimally binned images consistently showed better resolution when compared to the nongated images, and better noise characteristics than the original phase-gated images (which by definition were noisier because they contain less data). Example patient images are shown in Fig. 5 and online animations 1 and 2. An example lesion profile is shown in Fig DISCUSSION Optimal binning is a strategy for implementing motion correction in the clinic that is simple to understand and straightforward to use. In the work presented here, we extended the concept of optimal binning to a data-driven

6 282 Kesner et al.: Data driven optimal binning 282 (a) Number of images (b) Number of images (c) Number of images Histogram of op mal bin sta s cs in popula on Software gating, Acc window = 3 SD 1% 2% 3% 4% 5% 6% 7% 8% 9% 1% Por on of total sta s cs in op mal bin Histogram of op mal bin sta s cs in popula on Software gating, Acc window = 1 SD Software gating, Acc window = 3 SD Software gating, Acc window = 2 SD Software gating, Acc window = 4 SD 1% 2% 3% 4% 5% 6% 7% 8% 9% 1% Por on of total sta s cs in op mal bin Histogram of op mal bin sta s cs in popula on So ware ga ng, Acc window = 3 SD Random ga ng, Acc window = 3 SD Hardware ga ng, Acc window = 3 SD 1% 2% 3% 4% 5% 6% 7% 8% 9% 1% Por on of total sta s cs in op mal bin FIG. 3. Histogram of optimal bin statistics showing the number of images in the population that retain specified statistics in their optimal embodiment, as determined by our algorithm. (a) Histogram created using default parameters. (b) Comparison of algorithm behavior when using different acceptance windows. (c) Histogram showing behavior of algorithm when phase-gated input data come from different sources. [Color figure can be viewed at wileyonlinelibrary.com] form, in a way that supports adaptive optimization of image data. Our approach can be tuned and employed in an automated and standardized fashion. We have demonstrated (a) motion amplitude information can be derived from phasegated images, (b) optimal binning strategies can use this characterization to adapt data segregation to the instance of data in a way that correlates with independent, blinded reader analysis, (c) data-driven motion correction workflows, that span acquisition to reconstruction, can be applied in large populations with ease, and (d) adaptive motion correction algorithms are relevant because patients/scans contain varying capacities to support motion correction. In our quantitative analysis, the noise measurements exhibited behavior that we might expect. The greater the counts in our images, the lower the noise levels measured in uniform regions, as seen in Fig. 4. The lesion analysis was somewhat less conclusive. When averaged across the population, the SUV mean, SUV max, and lesion FWHM measurement in the optimal bin image were between the values for the gated and nongated embodiments, as could be expected. On closer analysis, specific changes varied among cases. In some instances, SUVs increased between gated and nongated image sets, while others decreased. This varying trend demonstrates the limitations of lesion analysis in differing noise environments. In our previous work, we have shown that the mere process of gating subjugating data into different bins can increase or decrease SUV measurements when studied in simulations. 24 In our further work, using this same study population, we found that SUV mean and SUV max measurements will increase in the population 13% 8 and 4% 8, respectively, from the segregation of data and with no incorporation of motion information. 8 Patients have different uptake patterns, have different extents of breathing motion, have varying counts in their images, and different centers use different scanners reconstruction protocols. The specific number of gates used for sorting data also affects measurement outcomes. Gating will affect lesion SUV measurement in different patients differently and therefore should be used cautiously when assessing the success of a method. Our qualitative analysis was performed by comparing the amount of data in optimal bins in the population and with blinded reader assessment of the images and their motion content. The fact that we did not find absolute agreement between the readers and the algorithm likely illustrates this assessment had limitations. The blind review was limited by the assessment of only a single slice rather than the whole volume, and the optimal binning algorithm was calibrated at a specific sensitivity which we expect would not necessarily match that of the reviewers. Despite these limitations, the correlations we found between observed motion in the images and the data segregation produced by the algorithm across the population indicate that the algorithm is largely performing as predicted and far from random or incorrect. Further qualitative improvements are demonstrated in the images provided. In Fig. 5(a), we can see that the lesion is better defined (smaller) and greater small structure detail in the optimal bin image than the nongated image. At the same time, the noise in the liver is favorable in the optimal bin image as compared to the gated image. More examples of these improvements are demonstrated in online Figs. 1 and 2. Within the data-driven optimal binning algorithm, there is a question which arises as to how best define the acceptance

7 283 Kesner et al.: Data driven optimal binning 283 3% Measured vs theore cal noise in liver Gated Nongated Op mal Bin Linear fit (Gated) Linear fit (Nongated) Linear fit (Op man Bin) 25% Measured % SD 2% 15% y =.363x +.12 R² = % 5% y =.1688x +.49 R² =.91 y =.841x R² =.462 % % 5% 1% 15% 2% 25% 3% Theore cal % SD (Poisson noise) FIG. 4. Measured vs. theoretical Poisson noise in the liver for different reconstructions. Linear best fit lines, with equations and R 2 values, shown on chart. [Color figure can be viewed at wileyonlinelibrary.com] TABLE I. Summary of lesion measurements, averaged across population. N Nongated Optimally binned Average gated value Best gated value Worst gated value SUV mean SUV max Volume (cc) (8% max thresh) FWHM a FWHM Pearson correlation between.85 optimally binned and nongated FWHM Pearson correlation between optimally.89 binned and gated a Average FWHM derived from scans that had appropriate profiles, scans not amiable to FWHM characterization were not included. window for separating noise and motion [visualized by the gray stripe in Figs. 2(c) and 2(d)]. We used a window of 3 standard deviations of the assumed noise magnitude for much of our analysis. However, we also tested other window sizes ranging from 1 4 SDs, as shown in Fig. 3b, and found that the window size affected the results as theory predicts. It is likely that this parameter should be calibrated for the desired sensitivity. If limiting noise in output images outweighs concerns of recovering resolution, a wider window could be used so to include more signal, but less motion information. The opposite is true as well; that is, a narrower window could be used to ensure that more detailed motion information is preserved, but at the cost of introducing a greater amount of noise in the optimal bin data. It is important to clarify that when working with optimal binning, or any 4D signal utilization strategy, there is no absolute true or correct way to segregate data. The goal of optimal binning is to find an optimal trade-off, and its definition will likely depend on the desired use of the data. What we know for sure, however, is what we want from the conceptual extremes. Data sets that do not benefit from data segregation should be left in their nongated embodiment, and those with useful information in them should incorporate segregation. Our application of adaptive optimal binning was successful in that it spanned this spectrum in a conformal manner, and in a way that correlated with reader observation. Optimal binning is a well-established concept. To our knowledge, all optimal binning strategies published to date use a fixed width window for segregating data, applied uniformly across a population. Modifying the method to be data driven, as we did, has several benefits: it is automated, straightforward to use and, perhaps most importantly, it conforms to the capacity of data in each image instance, making maximal use of the information available for the given patient s PET scan. The process results in an amplitude-based optimally binned 3D image. The method is unique in that it is scan-specific and can be used to optimize any instance of a gated image, irrespective of how it was created (gating method, reconstruction, etc.). Our strategy for optimal binning is based on a data-driven approach. It can be compartmentalized and implemented with standard hardware gating systems, as we did for the secondary measurement as shown in Fig. 3(c), or it can be integrated with data-driven gating to enable an entire data-driven motion correction workflow, 6 as demonstrated in this work. Full data-driven workflows are a new concept in the field that

8 284 Kesner et al.: Data driven optimal binning 284 (a) Phase gated, bin 1 stats: 1% Op mal bin stats: 5% Nongated stats: 1% (b) Phase gated, bin 1 stats: 1% Op mal bin stats: 1% Nongated stats: 1% FIG. 5. Example coronal phase-gated, optimal bin, and nongated image reconstructions for a patient who had a significant amount of detectable motion (a), and a patient who did not have a significant amount of detectable motion (b). The stats statistic shows the fraction of nongated data used in the reconstruction. The figure illustrates how the optimal bin image can conform to the capacity of the data. The images in this figure correspond to the patient data used in Fig. 2. [Color figure can be viewed at wileyonlinelibrary.com] Voxel ac vity (SUV) Example Lesion Profile Rela ve loca on (mm) single gate (FWHM = 7.9 mm) op mal bin (FWHM = 8.2 mm) average bin (FWHM = 1. mm) FIG. 6. Example lesion profile [Coronal images shown in Fig. 4(a)]. [Color figure can be viewed at wileyonlinelibrary.com] may have significant practical benefits because they can be introduced to clinical environments with ease. Data-driven gating allows us to characterize motion and create phasegated images from PET scans with no extra effort and no changes to clinical protocols, and in a standardized way. 8 Data-driven 4D signal utilization, the topic of this paper, allows us to create patient-specific solutions that conform to the information contained in the patient scans. The two methods go together elegantly: count limited data will not have useful respiratory signal and not benefit from gating, and our algorithm will detect this and revert the image back to its nongated embodiment, whereas traditional hardware-based/ population-calibrated methods would deliver a less useful image. This may be a key feature of our algorithm. If we want to address the problem of motion in diagnostic PET, we need solutions that do not degrade the subpopulation of images that do not benefit from the gating process. A limitation of this work may be in the assumption that we can characterize patient motion and the PATF using the first PC weight array and relative noise using the 3rd. Theory tells us that cyclic motion, and noise, should be represented in the measured first PC signal, when the data represent a single cycle scan (e.g., a respiratory-gated PET scan). The third PC likely contains little motion information and is thus a similar measure of noise. These are first-order assumptions and are variables that can be studied, and possibly improved upon in future work. Integrating motion correction in PET imaging can help with diagnosis, 25 localization, 26 and quantification, 27 and aid with radiotherapy planning. 28 The scope of this work has been to establish proof of principle for a new strategy of motion correction that addresses practical motion correction. Ideally, fully automated motion correction may in effect extend the dimensional imaging capacity of PET to inherently include respiratory motion. Specifically, it could support protocols where the complimentary motion-corrected images are generated alongside standard PET images, for all acquisitions with no changes to procedures, using methods similar to those presented here. Alternatively, data-driven motion correction workflows can be integrated with extended acquisitions to get higher count/higher quality motioncorrected images. The problem of motion is a well-articulated problem in PET imaging. In our work here, we developed an algorithm that addresses the drawbacks of traditional one-size-fits-all optimal binning solutions as well as the need for clinically

9 285 Kesner et al.: Data driven optimal binning 285 practical protocols. It is reasonable to expect that it can be improved upon with further methodological developments. A possible opportunity for improvement may be to incorporate the data segregation with reconstruction. In this work, the reconstructed phased-gated images that fell within the reference window were averaged together. Future work can also assess the benefit of resorting data prior to reconstruction, which should benefit the final images because iterative reconstruction, used in PET, is non-linear. Further improvement may be found by forcing the optimal bin to align with the corresponding attenuation map, to reduce the occurrence of artifacts stemming from attenuation mismatch. Ultimately, the goal is to use these methods to improve clinical use of PET. For that to happen, clinical utility of these methods must be assessed. 5. CONCLUSION We have presented a proof-of-principle study showing that it is possible to derive an amplitude characterization of motion from a phase-gated data set using data-driven strategies. We have also shown that we can use that characterization to generate adaptive optimal bin images. When applied to a population of FDG PET images, we found large variations in optimal bin characteristics of different patients, indicating a need and an appropriateness of developing personalized imaging approaches. Future work will include assessing these strategies in clinical operations, quantifying their benefit, and extending these methods to other modalities (SPECT, CT, MR) and other types of motion including cardiac motion. ACKNOWLEDGMENTS We would like to acknowledge the support of Siemens (Hoffman Estates, IL, USA), who provided grant support for study recruitment and image analysis. We would also like to thank specifically Ramya Rajaram and James Hamill of Siemens for their help in the acquisition/processing of study data. We would also like to thank Dr. Phillip Koo and Dr. Jennifer Kwak for their aid in the analysis as blinded readers. CONFLICTS OF INTEREST The authors have no relevant conflicts of interest to disclose. a) Author to whom correspondence should be addressed. Electronic mail: kesnera@mskcc.org; Telephone: REFERENCES 1. Daou D. Respiratory motion handling is mandatory to accomplish the high-resolution PET destiny. Eur J Nucl Med Mol Imaging. 28;35: Chi A, Nguyen NP. 4D PET/CT as a strategy to reduce respiratory motion artifacts in FDG-PET/CT. Front Oncol. 214;4: Lamare F, Ledesma Carbayo MJ, Cresson T, et al. List-mode-based reconstruction for respiratory motion correction in PET using non-rigid body transformations. Phys Med Biol. 27;52: Weber WA, Gatsonis CA, Mozley PD, et al. Repeatability of 18F-FDG PET/CT in advanced non-small cell lung cancer: prospective assessment in two multicenter trials. J Nucl Med. 215;56: Rahmim A, Rousset O, Zaidi H. Strategies for motion tracking and correction in PET. PET Clin. 27;2: Kesner A, Schleyer P, Buther F, Walter M, Schafers K, Koo P. On transcending the impasse of respiratory motion correction applications in routine clinical imaging - a consideration of a fully automated data driven motion control framework. EJNMMI Phys. 214;1:8. 7. Kesner AL, Kuntner C. A new fast and fully automated software based algorithm for extracting respiratory signal from raw PET data and its comparison to other methods. Med Phys. 21;37: Kesner AL, Chung JH, Lind KE, et al. Validation of software gating: a practical technology for respiratory motion correction in PET. Radiology. 216;281: Buther F, Vehren T, Schafers KP, Schafers M. Impact of data-driven respiratory gating in clinical PET. Radiology. 216;281: Dawood M, B uther F, Lang N, Schober O, Sch afers KP. Respiratory gating in positron emission tomography: a quantitative comparison of different gating schemes. Med Phys. 27;34: Pepin A, Daouk J, Bailly P, Hapdey S, Meyer ME. Management of respiratory motion in PET/computed tomography: the state of the art. Nucl Med Commun. 214;35: Guerra L, De Ponti E, Elisei F, et al. Respiratory gated PET/CT in a European multicentre retrospective study: added diagnostic value in detection and characterization of lung lesions. Eur J Nucl Med Mol Imaging. 212;39: Liu C, Pierce LA 2nd, Alessio AM, Kinahan PE. The impact of respiratory motion on tumor quantification and delineation in static PET/CT imaging. Phys Med Biol. 29;54: Van Der Gucht A, Serrano B, Hugonnet F, Paulmier B, Garnier N, Faraggi M. Impact of a new respiratory amplitude-based gating technique in evaluation of upper abdominal PET lesions. Eur J Radiol. 214;83: Liu C, Alessio A, Pierce L, et al. Quiescent period respiratory gating for PET/CT. Med Phys. 21;37: van Elmpt W, Hamill J, Jones J, De Ruysscher D, Lambin P, Ollers M. Optimal gating compared to 3D and 4D PET reconstruction for characterization of lung tumours. Eur J Nucl Med Mol Imaging. 211;38: Daouk J, Fin L, Bailly P, Meyer ME. Improved attenuation correction via appropriate selection of respiratory-correlated PET data. Comput Methods Programs Biomed. 28;92: Kesner AL. The relevance of data driven motion correction in diagnostic PET. Eur J Nucl Med Mol Imaging. 217;44: Nehmeh SA, Erdi YE, Ling CC, et al. Effect of respiratory gating on reducing lung motion artifacts in PET imaging of lung cancer. Med Phys. 22;29: Smith LI. A tutorial on Principal Components Analysis; pdf Accessed 4/2/ Liu C, Alessio AM, Kinahan PE. Respiratory motion correction for quantitative PET/CT using all detected events with internal-external motion correlation. Med Phys. 211;38: Silin R, Xiao J, Chung C, et al. Data-driven event-by-event respiratory motion correction using TOF PET list-mode centroid of distribution. Phys Med Biol. 217;62: Schmidtlein CR, Beattie BJ, Bailey DL, et al. Using an external gating signal to estimate noise in PET with an emphasis on tracer avid tumors. Phys Med Biol. 21;55: Kesner AL. A Simulation of Noise Effects on SUV Measurements in Gated/Ungated Data - A Story of Apples and Oranges European Association on Nuclear Medicine Annual Conference; 21; Vienna, Austria 25. van der Vos CS, Koopman D, Rijnsdorp S, et al. Quantification, improvement, and harmonization of small lesion detection with state-ofthe-art PET. Eur J Nucl Med Mol Imaging. 217;44: Polycarpou I, Tsoumpas C, King AP, Marsden PK. Impact of respiratory motion correction and spatial resolution on lesion detection in PET: a

10 286 Kesner et al.: Data driven optimal binning 286 simulation study based on real MR dynamic data. Phys Med Biol. 214;59: Lupi A, Zaroccolo M, Salgarello M, Malfatti V, Zanco P. The effect of 18F-FDG-PET/CT respiratory gating on detected metabolic activity in lung lesions. Ann Nucl Med. 29;23: Bettinardi V, Picchio M, Di Muzio N, Gianolli L, Gilardi MC, Messa C. Detection and compensation of organ/lesion motion using 4D-PET/CT respiratory gated acquisition techniques. Radiother Oncol. 21;96: SUPPORTING INFORMATION Additional Supporting Information may be found online in the supporting information tab for this article. Fig. S1. Sample coronal slices from population of patient PET scans showing nongated, optimally binned, and gated (1 gates) images side by side. Gates are looped in animation so that motion can be observed on the gated images. Fig. S2. Sample coronal slices, zoomed in over lesion, from population of patient PET scans showing nongated, optimally binned, and gated (1 gates) images side by side. Gates are looped in animation so that motion can be observed on the gated images.