The Effects of PET Reconstruction Parameters on Radiotherapy Response Assessment. and an Investigation of SUV peak Sampling Parameters.

Transcription

1 The Effects of PET Reconstruction Parameters on Radiotherapy Response Assessment and an Investigation of SUV peak Sampling Parameters by Leith Rankine Graduate Program in Medical Physics Duke University Date: Approved: Shiva Das, Co Supervisor Timothy Turkington, Co Supervisor James Bowsher Bennett Chin Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Graduate Program in Medical Physics in the Graduate School of Duke University 2013

2 ABSTRACT The Effects of PET Reconstruction Parameters on Radiotherapy Response Assessment and an Investigation of SUV peak Sampling Parameters by Leith Rankine Graduate Program in Medical Physics Duke University Date: Approved: Shiva Das, Co Supervisor Timothy Turkington, Co Supervisor James Bowsher Bennett Chin An abstract of a thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Graduate Program in Medical Physics in the Graduate School of Duke University 2013

3 Copyright by Leith John Rankine 2013

4 Abstract Purpose: Our primary goal was to examine the effect of PET image reconstruction parameters on baseline and early treatment FDG PET/CT quantitative imaging. Early treatment changes in tumor metabolism in primary tumor and nodes can potentially determine if the patient is responding to therapy, but this assessment can change based on the reconstruction parameters. We investigated the effect of the following reconstruction parameters: number of Ordered Subset Expectation Maximization (OSEM) iterations, post reconstruction smoothing, and quantitative metrics (SUV max, SUV mean, SUV peak). A concurrent investigation explored in detail the sampling parameters of SUVpeak by way of a Monte Carlo digital phantom study. SUV peak was proposed as a compromise between SUV max and SUV mean, in hope to retain key attractive features of these two metrics (inter physician independence of SUV max, noise averaging of SUV mean) but reduce unwanted errors (noise dependence of SUV max, contourdependence of SUV mean). Sampling parameters have vaguely been defined, in particular, the scanning resolution (i.e. 1 voxel, 1/2 voxel, 1/4 voxel, etc.) of the SUV peak spherical ROI. We examined the role that partial voxel scanning plays in tumor SUV recovery in both noise free and realistic OS EM noise environments. iv

5 Materials and Methods: The response assessment investigation involved 19 patients on an IRB approved study who underwent 2 baseline PET scans (meanseparation = 11 days) prior to chemoradiotherapy (70 Gy, 2 Gy/fraction). An intratreatment PET scan was performed early in the course of therapy (10 20 Gy, mean = 14 Gy). The images were reconstructed with varying OS EM iterations (1 12) and Gaussian post smoothing (0 7 mm). Patients were analyzed in two separate groups, distinguished by the PET/CT scanner used to acquire data: (1) GE Discovery STE; and (2) Siemens Biograph mct. For each combination of iterations and smoothing, Bland Altman analysis was applied to quantitative metrics (SUV max, SUV mean, SUV peak) from the baseline scans to evaluate metabolic variability (repeatability, = 1.96 ). The number and extent of early treatment changes that were significant, i.e., exceeding repeatability, was assessed. An original SUV peak algorithm was developed, which measures SUV max and SUV peak for as small as 1/32 voxel scanning. Two rounds of digital phantoms were generated for the SUV peak investigation. First, 10,000 spherical tumors were generated at a random matrix location for each diameter 1 4 cm and smoothed with an isotropic Gaussian, FWHM = 0.8 cm, then evaluated using the SUV peak algorithm. Next, realistic body sized phantoms were generated with background activity, and 1,000 spherical tumors of activity 4 time the background for each diameter (1 4cm) were placed inside (8 tumors per phantom, location randomized within certain constraints). These images v

6 received realistic corrections in projection space for attenuation, spatial resolution, and noise, were reconstructed with an in house OS EM algorithm, and then assessed using the SUV peak algorithm. The mean recovered activity above background and its coefficient of variation were calculated for all metrics for each tumor size, for both simulations. For the realistic noise simulation, various levels of Gaussian smoothing was applied post reconstruction, the effects summarized in plots showing coefficient of variation vs. mean recovered activity above background a comparison of the effectiveness of SUV max and SUV peak. Results: For the GE Discovery STE 2D cases averaged over all metrics (SUV max, SUV mean, SUV peak) and structures (GTV, LN), repeatability,, improved with increasing smoothing and decreasing iterations. Individually, SUV mean repeatability was less affected by the number of iterations, but demonstrated the same relationship with smoothing. SUV mean outperformed SUV max and SUV peak with regards to the number of cases exceeding repeatability,. Considering,, and the sum of relative metric change outside repeatability, Ω, averaged over all metrics and all structures, and normalized, several combinations of reconstruction parameters produced five optimal combinations above set thresholds: 1 iteration with mm smoothing; and 2 iterations with mm smoothing. Current GE 2D reconstruction protocol for HN cases uses 2 iterations and 3.0 mm post smoothing, which lies on the edge, but within these recommendations. vi

7 The relationship between repeatability and number of iterations for the 3D cases was more complex; SUV max demonstrated the best repeatability with 2 iterations, with both SUV mean and SUV peak reaching the best repeatability with 4 iterations. The same dependence on smoothing was noted, i.e. increased smoothing gives lover (desirable) repeatability. SUV mean once again outperformed SUV max and SUV peak with regards to the number of cases exceeding repeatability,. The calculations of and Ω averaged over all metrics were limited severely by the low number of cases, damaging the statistical significance of the following recommendation. Three optimal combinations with averaged and normalized,, Ω, above a set threshold are recommended as most effective reconstruction parameter combinations: 4 iterations with mm smoothing. Current Siemens 3D reconstruction protocol for HN cases uses 4 iterations and 3.0 mm post smoothing, which lies within these recommended parameters. However, no statistically significant conclusions could be drawn from this analysis for this scanner, and performing similar data analysis on a larger patient pool is proposed. The minimum spherical tumor diameter required for full recovery was cm for SUV peak, and cm for SUV max. SUV max was found to overestimate the recovered value of tumors by up to 46% (vs. 10% for SUV peak); above the minimum diameter for full recovery, SUV peak values were significantly closer to actual tumor activity. Considering only the realistic noise tumors, the coefficient of variation for SUV vii

8 max ranged from %, whereas for SUV peak these values were lower, %. Partial voxel scanning did not substantially affect the coefficient of variation (<0.2%). Comparison of coefficient of variation vs. mean recovered value demonstrated that SUV max with additional Gaussian smoothing outperforms SUV peak by up to 0.8% for 1 cm tumors and 0.2% for 4 cm tumors. Other tumor sizes showed little difference between the two metrics. Conclusion: For patients scanned on the GE Discovery STE using the HN protocol (2D acquisition mode), images reconstructed for quantitative analysis may benefit from a low number of OS EM iterations ( 2). Some post reconstruction smoothing proved to be beneficial (1.0 mm FWHM 3.0 mm), however, oversmoothing for the sake of more qualitatively appealing images or improved image quality metric (e.g. SNR, CNR) may prove detrimental to quantitative response assessment analysis. Our results for the Siemens Biograph mct using the HN protocol (3D acquisition mode) demonstrated favor towards 4 iterations and limited range of smoothing (2.0 mm FWHM 4.0 mm). These results are statistically limited, further cases are necessary for any conclusive recommendations on reconstruction parameters. SUV peak was shown to reduce uncertainties associated with quantitative PET image analysis when compared directly to SUV max. Above the minimum tumor diameter required for full recovery, SUV peak also provides a better estimate of the actual tumor activity. However, initial comparisons of SUV peak and SUV max over viii

9 various levels of additional Gaussian smoothing found SUV max more favorable. Partial voxel scanning of SUV peak did not reduce the metric s coefficient of variation in images with realistic noise. Therefore, a phantom investigation is proposed to compare SUV peak and SUV max of real scanned images with various levels of post smoothing, which may conclusively eliminate the need for SUV peak. ix

10 Contents Abstract... iv List of Tables... xii List of Figures...xiv Acknowledgements...xvi 1. Introduction Quantitative PET Image Reconstruction SUV variability Metrics for quantitative PET analysis Radiotherapy response assessment Project Details Project One: Effect of PET reconstruction parameters on radiotherapy response assessment in head and neck cancer Project Two: Investigation of SUV peak sampling parameters Materials and Methods Project One Project Two SUV peak sphere precision of edge voxels Developing intra pixel search algorithm Monte Carlo investigation 1: SUV peak of randomly positioned digital tumors with spatial resolution effects x

11 3.2.4 Monte Carlo investigation 2: SUV peak of randomly positioned digital tumors with spatial resolution blurring and noise applied in projection space prior to OS EM reconstruction Results Project One Project Two Discussion Project One Patient data from GE 2D scanner Patient data from 3D scanner Project Two Scale up/scale down optimal SUF Noise free simulations, recovered activity and coefficient of variation Realistic OS EM reconstruction simulations Recovered activity and coefficient of variation for each SUV metric Comparison of SUV peak and SUV max with post smoothing Conclusions Appendix References xi

12 List of Tables Table 1: Repeatability values for each SUV metric vs. number of OS EM iterations and FWHM of post smoothing. Geometric average over structures, GE 2D cases only Table 2: Number of cases outside repeatability,, for each SUV metric vs. number of OS EM iterations and FWHM of post smoothing. Geometric average over structures, GE 2D cases only Table 3: Sum of relative metric change outside repeatability, Ω, for each SUV metric vs. number of OS EM iterations and FWHM of post smoothing. Geometric average over structures, GE 2D cases only Table 4: Repeatability values for each SUV metric vs. number of OS EM iterations and FWHM of post smoothing. Geometric average over structures, Siemens 3D cases only. 35 Table 5: Number of cases outside repeatability,, for each SUV metric vs. number of OS EM iterations and FWHM of post smoothing. Geometric average over structures, Siemens 3D cases only Table 6: Sum of relative metric change outside repeatability, Ω, for each SUV metric vs. number of OS EM iterations and FWHM of post smoothing. Geometric average over structures, Siemens 3D cases only Table 7: Summary table of GE 2D cases (arithmetic mean across metric, geometric mean across structure). Shows the effect of OS EM iterations and smoothing on: (a) repeatability, ; (b) number of cases exceeding repeatability, ; and (c) sum of relative metric change outside repeatability, Ω Table 8: Summary table of Siemens 3D cases (arithmetic mean across metric, geometric mean across structure). Shows the effect of OS EM iterations and smoothing on: (a) repeatability, ; (b) number of cases exceeding repeatability, ; and (c) sum of relative metric change outside repeatability, Ω Table 9: Overall effectiveness for GE 2D scanner, optimum combinations of iterations and smoothing. Normalized variable thresholds set to: 1/ = 0.85, = 0.95, Ω = Reconstruction parameter combinations given a value of 1 when all three variables (from Table 7) exceed thresholds xii

13 Table 10: Overall effectiveness for Siemens 3D scanner, showing optimum combinations of iterations and smoothing. Normalized variable thresholds set to: 1/ = 0.65, = 0.85, Ω = Reconstruction parameter combinations given a value of 1 when all three variables (from Table 8) exceed thresholds Table 11: Necessary SUF for scale up/scale down method to produce a sphere volume within 0.1% of known volume. Applicable for 1 cm sphere in (0.4 cm) 3 voxels xiii

14 List of Figures Figure 1: Examples of the three types of coincidence events detected in PET scans [leftto right]: true (T), random (R), scattered (S) Figure 2: [left] PET digital phantom, 40cm 20cm, 8 tumors of 3cm diameter with 4 background activity; [center] PET image reconstruction without ACF; [right] PET image reconstruction with ACF. Window and level constant for all images Figure 3: The probability of e + decay from activity ai in the i th voxel resulting in a coincidence detection in the j th LOR is calculated/measured and recorded in the probability matrix Mij Figure 4: The effect of varying OSEM iterations (4 subsets) and post reconstruction smoothing. Reconstructions of PET digital phantom, 40cm 20cm, 8 tumors of 3cm diameter with 4 background activity. Iterations increase from left to right: 1, 2, 3, 4, 10, 20. FWHM of Gaussian smoothing from top to bottom: 0 mm, 4 mm, 8 mm. Window and level constant for all images Figure 5: Green voxels used to calculate SUV max [left], SUV mean [center], and SUVpeak [right]. Tumor contour (ROI) shown in red; Figure 7: Visual aid in the calculation of the sum of relative metric change outside repeatability, Ω. Baseline repeatability is shown by the blue dashed lines, and intratreatment PET change ( ) is shown as red circles. The individual elements in the sum, Ω, are physically represented by / Figure 8: Demonstration of scale up factors (SUF) on digital sphere approximation Figure 9: [top] Slices of SUV peak spherical ROI using binary definition. [bottom] Slices of same ROI using scale up method, SUF = 10. Windowed from 0 to Figure 10: [top row] Central slice of 3D digital spherical tumors of diameter (left toright) 1.0 cm, 1.5 cm, 2.0 cm, 2.5 cm, 3.0 cm, 3.5 cm, and 4.0 cm. [bottom row] Central slice of digital spherical tumors with 0.8 cm FWHM isotropic Gaussian smoothing Figure 11: Line profiles through tumors pre and post smoothing by a 0.8 cm FWHM Gaussian filter, representing extrinsic spatial resolution blurring. [left] Required tumor size for SUV max full recovery, 2.4 cm. [right] Hypothesized tumor size required for SUV peak full recovery, ( ) cm xiv

15 Figure 12: Digital phantoms, projections, addition of spatial resolution blurring, attenuation, and noise, followed by attenuation correction and OS EM reconstruction. 32 Figure 13: Mean tumor activity recovery by SUV max and SUV peak (1 1/32 voxel scanning) for various tumor sizes. Original spherical tumor s created with activity 1, followed by blurred by isotropic 0.8 cm FWHM Gaussian filter to simulate extrinsic spatial resolution effects. No statistical/reconstruction noise Figure 14: Coefficient of variation for SUV max and SUV peak (1 1/32 voxel scanning) for various tumor sizes. Original spherical tumor s created with activity 1, followed by blurred by isotropic 0.8 cm FWHM Gaussian filter to simulate extrinsic spatial resolution effects. No statistical/reconstruction noise Figure 15: Mean recovered tumor activity by SUV max and SUV peak (1 1/32 voxel scanning) for various tumor sizes from OS EM image ( = 2, = 20) with 6.0 mm post smoothing. Known tumor activity above background is Figure 16: Coefficient of variation of recovered tumor activity by SUV max and SUVpeak (1 1/32 voxel scanning) for various tumor sizes from OS EM image ( = 2, = 20) with 6.0 mm post smoothing. Known tumor activity above background is Figure 17: Coefficient of variation of recovered activity above background vs. mean recovered activity above background ( ) of SUV max and SUV peak for 1 cm tumor diameter. Each point represents different level of post smoothing (0 12 mm) Figure 18: Coefficient of variation of recovered activity above background vs. mean recovered activity above background ( ) of SUV max and SUV peak for 2 cm tumor diameter. Each point represents different level of post smoothing (0 12 mm) Figure 19: Coefficient of variation of recovered activity above background vs. mean recovered activity above background ( ) of SUV max and SUV peak for 3 cm tumor diameter. Each point represents different level of post smoothing (0 12 mm) Figure 20: Coefficient of variation of recovered activity above background vs. mean recovered activity above background ( ) of SUV max and SUV peak for 4 cm tumor diameter. Each point represents different level of post smoothing (0 12 mm) xv

16 Acknowledgements Thank you to Shiva Das and Timothy Turkington for always challenging me to do just a little bit more, and for the great support offered over the past two years. Thank you to Jim Bowsher for assisting with Siemens Biograph mct image reconstruction, and for providing the OS EM reconstruction software. Thank you to Josh Wilson for assisting with GE Discovery STE image reconstruction, and for always being willing to brainstorm an idea with me. archive DVDs. Thank you to Thomas Hawk for assisting with the retrieval of patient data from xvi

17 1. Introduction Positron Emission Tomography (PET) is an imaging technique capable of reconstructing three dimensional (3D) functional images of the human body. For images to be formed, a positron emitting radiotracer is first injected intravenously into the subject. The choice of radiotracer determines the distribution of radiotracer throughout the body as a function of time. For example, 2 deoxy 2 [ 18 F]fluoro D glucose (FDG) is commonly used to label metabolically active tissue [1]. Radiotracer decay emits a positron (e + ), which will annihilate in the vicinity of emission with a nearby electron (e ), producing two ~511 kev γ rays with approximately equal and opposite momentum. Images are formed when the patient is positioned inside a ring of γ ray detectors capable of detecting coincidence counts, i.e. two γ rays in different positions within a small timing window (τ). These coincidence counts occur along a line of response (LOR), the direct geometric path between detectors. The LOR defines the projection through the patient, and the count rate data for each LOR are used in collaboration with measured attenuation correction data from a computed tomography (CT) scan and several other corrections (section 1.1) to create a quantitatively meaningful 3D image of radiotracer concentration. This method of radiotracer injection and detection is known in nuclear medicine as functional imaging. The information from PET images can be used both qualitatively and quantitatively. A common example of using PET for qualitative purposes is when 1

18 nuclear medicine physicians use whole body FDG PET images to detect the presence of metastasized cancer sites or infected lymph nodes throughout the body, assisting with tumor staging. In fact, this makes up the majority of Medicare billing for PET scans in the USA [2]. An example of quantitative PET is examining the change in metabolic activity in a tumor between scans, i.e. to determine whether a tumor is responding to therapy. While qualitative imaging relies on visual patterns and relative intensity levels, the precision (uncertainty, variability) and accuracy (representative of truth) of the activity concentration are limiting factors in achieving reliable quantitative images. 1.1 Quantitative PET True quantitative imaging is only achieved through a series of scrupulous corrections and a quantitative reconstruction algorithm (section 1.2). The first step in achieving quantitatively accurate PET images is ensuring that the rate of coincident events determined by a detector pair (prompts, P) corresponds to the rate of actual coincidences. Therefore, detector dead time is used to directly correct P, and background coincidence count rates (b) are taken into account in the image reconstruction (section 1.3). The remaining prompts rate comes only from the γ rays coming from the patient, however, consideration must be paid to the fact that these events may be caused by one of three main scenarios [3], as demonstrated in Figure 1. Random events (R) occur when γ rays produced in separate annihilations interact with the detector ring simultaneously (within the timing window). The rate of random events 2

19 can be measured or calculated using equation (1), where RA and RB are the singles (not coincidence) count rates of detectors A and B, and τ is the timing window [4]. 2 (1) Scattered events (S) arise when the direction of a γ ray is altered due to Compton scattering. The rate of scattered events can be estimated by measuring the scatter fraction, the ratio of scattered to true and scattered events, /, measured using standardized techniques [5]. True events (T) arise when two γ rays from the same e + /e annihilation reach the detector ring, without scattering; true events are proportional to the radiotracer concentration along the LOR, and are therefore the only desirable events in creating PET images. To ensure quantitative accuracy, T must be separated from R and S using equation (2). Finally, a measured normalization correction is applied for each LOR, correcting for variations in detector sensitivity. (2) Figure 1: Examples of the three types of coincidence events detected in PET scans [left to right]: true (T), random (R), scattered (S). 3

20 After LOR true count rates T have been correctly determined, one must consider the physical interactions of a γ ray traveling through a dense body; the attenuation of γ rays will alter the true count rate at the detectors. When radiotracer positrons decay inside the body, a portion of γ rays emitted from the e + /e annihilations are attenuated before reaching the PET detector ring. For each LOR the attenuation correction factor (ACF) is given by line integral in equation (3), where μ(r,e) is the linear attenuation coefficient for photons of energy E = 511 kev at location r in the body. ACF exp, (3) An example of digital phantom reconstructions with and without including ACFs is shown in Figure 2. A major innovation in clinical quantitative PET was the introduction of combined PET/CT systems [6,7], allowing for ACFs to be calculated from E = kev attenuation data provided by a CT scan. Figure 2: [left] PET digital phantom, 40cm 20cm, 8 tumors of 3cm diameter with 4 background activity; [center] PET image reconstruction without ACF; [right] PET image reconstruction with ACF. Window and level constant for all images. 4

21 After the above corrections have been made, the relative intensities of image voxels have been fully corrected are accurate relative to each other this is enough to generate qualitatively useful images. However, detectors in a PET scanner simply count the number of coincidence events, which is then divided by scan time to devise the count rate along each LOR. A 3D reconstruction (section 1.2) of these data will only produce voxels with units of relative activity concentration. The final correction necessary for quantitative PET imaging is known as the Well Counter Calibration (WCC). This requires a physical PET scan of a large phantom with known activity concentration, which is reconstructed using all of the above corrections. The known activity concentration is compared to the reconstructed relative activity concentration to create a conversion factor into meaningful units (kbq/ml). Quantitative images produced in absolute units of kbq/ml are physically meaningful, but not physiologically meaningful. For example, in oncology, physicians want to know the relative metabolic uptake (FDG radiotracer) of tumors compared to that of healthy tissue. For this reason, the final step in creating physiologically meaningful quantitative PET images is to define units of Standardized Uptake Value (SUV) [8], which considers the activity concentration, injected activity, and patient s body mass. SUV is a near dimensionless quantity, defined in units of g/ml, i.e. dimensionless for tissue with density ρ = 1.0 g/ml. 5

22 SUV Activity Concentration / Injected Activity / Body Mass (4) One additional point to consider is that close attention must be paid to the kinetics of the radiotracer when interpreting SUV as true functional imaging. That is, an accurate model of how the radiotracer moves within the body from time of injection to time of scan must be applied. For FDG PET, which is the most common clinical PET radiotracer and the focus of this thesis, the combination of half life of 18 F (T1/2 = 110 min) and kinetic properties of 2 deoxy 2 fluoro D glucose have led to patients being scanned approximately hr post injection, so the acquired images have a much larger component of accumulated activity compared to vascular flow activity. Increased tumor contrast has been demonstrated with longer scan times (up to 3 4 hr [9,10]), but this longer post injection wait time would mean approximately 2 injected dose to the patient be necessary to maintain equivalent imaging statistics. Therefore, the common hr is a compromise between radiotracer distribution and radiotracer decay. 1.2 Image Reconstruction The corrections required for producing quantitative PET images with accurate SUV values have been outlined in detail. However, one of the key aspects to this type of imaging is the algorithm used for image reconstruction. Such an algorithm must be quantitatively accurate and consistent (reproducible results). In the early history of PET imaging, filtered back projection (FBP) was used due to its speed and mathematical linearity; for this second reason, it is still used to as the standard in determining the 6

23 spatial resolution of a PET scanner [11]. However, modern commercial PET scanners have moved towards using Ordered Subset Expectation Maximization (OS EM) [12], a computationally efficient modification of the well established Maximum Likelihood Expectation Maximization (ML EM) method [13]. These EM algorithms can compensate for physical corrections (section 1.1) within the algorithm and does not require a complete projection set to reconstruct accurately. FBP does not retain quantitative accuracy if the projection set is incomplete, due to interpolation [14]. In addition, any physical corrections must be applied to the sinogram before FBP reconstruction, thereby artificially amplifying noise in some cases, e.g. multiplying sinogram by ACFs. A detailed outline of the mathematical theory behind ML EM is beyond the scope of this introduction, but is well described by Shepp and Vardi [13] or Lange and Carson [15]. The foundational principle of ML EM, as described by Cherry, Sorenson and Phelps [16], involves using statistics to compute the most probable distribution of source activity (a) that would have created the observed intensity of true counts (p) on each LOR. The image region is divided into a matrix of i voxels, the dimensions of which are defined to provide sufficient sampling according to the system spatial resolution 1. We can define a probability matrix M such that Mij is the probability that a radioactive 1 According to the Nyquist sampling theorem, 1/pixel size should be at least 2 the highest spatial frequency, e.g. a system with 8 mm FWHM resolution will have approximately 1/8 mm 1 maximum spatial frequency, therefore the required sampling frequency is 1/pixel size is 2/8 mm 1 = 1/4 mm 1 and reconstruction pixel size should be no larger than 4 mm. 7

24 decay in image voxel i will be counted as a true coincidence in the LOR j (Figure 3). Thus, the expected number of true counts for each LOR is given by pj in equation (5). (5) By this definition, some of the section 1.1 corrections (attenuation correction, background, scattered counts) and other physical effects (e.g. finite detector resolution, known patient boundaries, etc.) can be added into the Mij probability matrix. Accounting for these corrections by altering Mij will result in a less noisy image compared to a direct modification of the sinogram before reconstruction. Figure 3: The probability of e + decay from activity ai in the i th voxel resulting in a coincidence detection in the j th LOR is calculated/measured and recorded in the probability matrix Mij. Computing the activity image a via ML EM reconstruction is an iterative process, defined in equation (6), which maximizes the log of the product of Poisson probabilities 8

25 of counts collected in the detectors from voxels in the body. Here the image a k+1 is the activity in the (k+1) th iteration, which is formed by modifying the k th iteration image, a k. (6) Each iteration involves varying each voxel activity ai towards the most likely solution for equation (5). After an infinite number of iterations, the measured projection (LOR) data pj will be equal to the calculated Σi Mij ai for all j, and a k+1 = a k. In reality, after a large finite number of iterations (nitr) the approximation a k+1 a k is valid and further iterations do not noticeable alter the image. ML EM is quantitatively accurate, able to reconstruct images from limited projection data, and can account for physical corrections within Mij. However, the required computational power is a limiting factor in clinical applicability. OS EM was introduced to combat the computational intensive nature of ML EM. The underlying principles (pj, ai, Mij) are identical, the only difference being that the LORs (pj) are broken up into nsub subsets. The image a is updated after a subset of projection data has been processed using equation (6). The process of binning of pj into subsets depends on the scanner geometry, therefore on commercial scanners there are usually limited predefined choices for nsub which can be selected by the user. Each subset must be processed an equal number of times to ensure coherence with ML EM. When reconstructing identical data, the number of ML EM iterations (nitr) required to achieve the same signal to noise ratio (SNR) and contrast to noise ratio (CNR) is approximately 9

26 equal to the number of OS EM iterations (nitr) multiplied by the number of subsets (nsub) [17]. This results in a computational speed up of a factor of nsub when using OS EM. Increasing the number of OS EM iterations will increase the signal of high activity regions (tumors) and increase the contrast compared to background. However, image noise increases with the number of iterations, nitr [17]. For this reason, to achieve optimal SNR and CNR, most clinical reconstruction protocols include several iterations of OS EM followed by post reconstruction smoothing with a Gaussian filter to suppress noise. An example of the effects of iterations and smoothing is shown in Figure 4, where various iterations of an OS EM (nsub = 4) reconstruction is combined with various levels of smoothing. The choice of nitr and Gaussian full width half maximum (FWHM) smoothing affects quantitative analysis of PET images [18]. Figure 4: The effect of varying OSEM iterations (4 subsets) and post reconstruction smoothing. Reconstructions of PET digital phantom, 40cm 20cm, 8 tumors of 3cm diameter with 4 background activity. Iterations increase from left to right: 1, 2, 3, 4, 10, 20. FWHM of Gaussian smoothing from top to bottom: 0 mm, 4 mm, 8 mm. Window and level constant for all images. 10

27 There is an additional noise consideration for quantitative PET concerning areas of high activity (e.g. tumors). Incorporation of Poisson statistics into the OS EM algorithm results in greater importance being placed on those pj with high count rates. However, this results in the highest activity voxels being more affected by noise than the rest of the image, unlike with FBP where the noise level is uniform throughout the image [19]. This is one of many causes for SUV variability (section 1.3), and must be considered when developing clinical quantitative PET reconstruction protocols, as will be discussed in section SUV variability Due to the complexity of human physiology, several biological factors can cause inter scan temporal variability in SUV [18]. Patient weight composition, i.e. percentage body fat, may alter SUV values due to body fat having less FDG uptake than muscle. Heavier patients with high percentage body fat have demonstrated higher SUV values (up to 2 ) in blood [20]. The body mass term in the denominator of equation (4) may change during the course of treatment due to patient weight loss, which is particularly prevalent during radiation therapy. Certain corrections, such as using body surface area or lean body mass, have been shown to remove weight dependence of SUV [21]. In addition, the patient s blood glucose level at time of FDG injection influences FDG uptake and can affect SUV values. One study showed a high glucose diet immediately prior to injection caused some SUVs to decrease by more than 50% [22]. Physical activity 11

28 prior to or post injection will affect the uptake of active muscles, possibly affecting the SUV calculation [23]. The time allotted post injection for FDG uptake before scanning (1 1.5 hr between injection and scan) may also cause variability in SUV values. As mentioned earlier, the kinetic model of FDG radiotracer is simplified by assuming an equilibrium point is established approximately hours post injection. Normal tissue cells clear FDG more rapidly than malignant tissue [18]; a longer post injection uptake time may result in higher SUVs for high grade tumors [24]. Finally, necessary respiratory motion during a PET scan may cause differences between true γ ray attenuation and the ACFs calculated from the CT scan during a breath hold, particularly for lung scans [25]. Several technical factors relating to both hardware and software also affect SUV values. Variability between commercial scanners up to 20% has been documented and attributed to crystal type and dimensions, bore diameter, randoms correction method, and 2D (septa) or 3D mode [26]. Reconstruction algorithms, particularly the choice of parameters, also bring about variability in SUV values. Reconstructions of identical data sets (sinograms) with different field of view (FOV) and/or transaxial pixel size have shown variation in SUV values due to partial volume effects [18]. Specifically for OS EM reconstruction, other variable parameters include the number of iterations 2 nitr, which 2 More specifically, product of iterations and subsets, nitr nsub ; however if subsets are held constant, dependence of SUV values of iterations can be quantified as described in section

29 has been shown to affect SUV max more than SUV mean [27], and the FWHM of Gaussian post reconstruction smoothing. Due to variability in individual voxel SUV values, several metrics have been defined to quantitatively assess a region of interest (ROI) in PET imaging. 1.4 Metrics for quantitative PET analysis In radiation oncology, the contouring (outlining of the boundaries) of tumors and organs at risk (OAR) is performed on a high resolution planning CT image. An advantage of PET/CT scanners is that the spatial coordinates of a CT contour can be directly 3 translated over to the corresponding PET image as a region of interest (ROI). The SUV values of voxels inside an ROI are commonly reduced to a single numeric value that is used to aid in clinical diagnosis or assessment. Three evaluation metrics have been defined for this purpose: SUV max, SUV mean, and SUV peak (Figure 5). Figure 5: Green voxels used to calculate SUV max [left], SUV mean [center], and SUVpeak [right]. Tumor contour (ROI) shown in red; 3 Digital Imaging and Communications in Medicine (DICOM) spatial registration exists between two imaging modalities performed on the same scanner. < 13

30 SUV max is simply defined as the maximum SUV value of all voxels within the ROI (Figure 5, left). This simple metric minimizes inter physician differences in quantitative assessment that arise due to contouring differences not every physician draws the same contour on a CT scan, but they will generally all encompass SUV max. The downside of this metric is that, as previously described, areas of high activity, i.e. SUV max, are the noisiest part of OS EM reconstructed images. As a result, SUV max comes with a high variability and a general over estimation of the relative activity concentration inside the ROI. The average SUV over all voxels within an ROI is termed SUV mean (Figure 5 center). By taking the mean across noisy voxels, SUV mean is less affected by image noise than SUV max. However, SUV mean is prone to poor consistency because of physician dependent differences in contour definition [28]. In a recent attempt to develop a consistent framework for quantitative PET, Wahl et al proposed a draft of the PET Response Criteria in Solid Tumors (PERCIST) [29]. Due to the previously discussed pros and cons associated with SUV max and SUV mean, a compromising metric was proposed. SUV peak is defined as the local average within a sphere of diameter d = 1.2 cm (Figure 5), however other diameter spheres have been proposed [30]. Essentially lying somewhere between SUV max and SUV mean, the sphere is moved throughout all locations in the ROI until a maximum is found and recorded. Some uncertainty is associated with the proposed definition, in particular the 14

31 treatment of voxels at the edge of the 1.2 cm sphere (binary or partial voxel averaging) and the allowed location of the sphere center (freely moving or voxel centers only). By its very definition, SUV peak should show decreased reconstruction noise variability (compared to SUV max), and remain relatively unaffected by inter physician inconsistency (compared to SUV mean). This research further investigates SUV peak, as discussed in section 2.2. When drawing conclusions from a quantitative analysis using one of the three metrics presented here (Figure 5), the strengths and weaknesses of each metric must be clearly understood and considered. Despite these technical considerations of variability (noise) and inter physician consistency, for physiological reasons, some evaluation metrics have been shown to provide a better indication of biological response to therapy, depending on the type of disease [31]. For this reason, all metrics are used for quantitative assessment in this research (section 2.1). 1.5 Radiotherapy response assessment Interest in quantitative FDG PET has recently increased in the field of response assessment in radiation oncology [32]. Patients receive a baseline FDG PET scan prior to therapy, which is quantitatively analyzed using one the previously described metrics. A second FDG PET scan at a certain timepoint, either early into treatment (early response) or post treatment, may reveal a change in the SUV metric, which may be an indication of response to therapy. Promising results have been shown in the assessment of tumor 15

32 response of various diseases to radiotherapy [33,34], as well as chemoradiotherapy [35 38] and neoadjuvant chemo or radiotherapy [39 41]. As discussed in section 1.3, SUV variability caused by biological and technical factors is detrimental to response assessment. For example, if the inherent variation in baseline scan is ±15%, then the timepoint scan must be lower or higher by at least this amount to be considered indicative of response; an even greater change is required to increase statistical certainty. This issue of SUV variability provides the basis for Project 1, introduced in section

33 2. Project Details 2.1 Project One: Effect of PET reconstruction parameters on radiotherapy response assessment in head-and-neck cancer FDG PET has demonstrated strong potential in quantitative detection of early response to radiotherapy in head and neck (HN) cancer [31]. Intra treatment quantitative assessment of CT contoured primary tumor (GTV) and lymph node (LN) metabolic response provides beneficial information on whether or not the patient is responding to treatment, allowing for the therapy to be appropriately modified. Currently, quantitative PET assessment by comparing pre treatment PET imaging to intra treatment PET imaging is hampered by the inherent variability in SUV values of reconstructed images, due to both biological and technical factors [18]. Biological variability stems from the inherent temporal fluctuations in tumor metabolism. Technical factors, e.g. image reconstruction parameters, affect the reconstructed images and hence their interpretation. Current recommendations [18] for reducing technical variability is to use the same PET/CT scanner, scan protocol, and reconstruction parameters for successive scans of each individual patient. In this work, we attempt to account for biological variability by acquiring two baseline PET scans pre radiotherapy. We study the effect of technical factors on variability between the baseline scans by varying the number of OS EM iterations and amount of post reconstruction smoothing. We study the effect of varying the technical factors on the interpretation of intra treatment change that is greater than baseline 17

34 variability. These results provide a basis for selecting optimum reconstruction parameters for quantitative imaging. This study is particularly innovative because it quantifies the impact of FDG PET reconstruction parameters on intra radiotherapy PET treatment response assessment while taking into account inherent temporal metabolic variability (between 2 baseline PET scans). Reconstruction parameter optimization accounting for biological variability is truly novel. The outcome is invaluable for optimizing PET protocols for specifically quantitative imaging purposes. 2.2 Project Two: Investigation of SUV-peak sampling parameters The PERCIST review article [29] suggested that SUV max has become the most widely used metric for quantitative tumor analysis in PET/CT clinics, due to the ease of use (precise tumor ROI not required) and simple implementation for scanner/software manufacturers. However, this single voxel approach is greatly affected by statistical reconstruction noise [42] and pixel size, i.e. partial volume effects [43]. The use of SUVpeak in quantitative assessment of PET images may demonstrate reduced variability compared to SUV max for tumors in patient scans with realistic, clinical noise levels [44]. The original proposal of SUV peak [29] was not a precise definition, but more of a suggested method to possibly reduce variability in quantitative PET. For this reason the sampling parameters, such as diameter, treatment of partial voxels on the edge of the sphere, and location of sphere center, were not clearly defined. SUV peak measurements 18

35 with various sphere diameters have been explored [30], and the suggested diameter of d = 1.2 cm was used for this research. However, a comprehensive investigation into the location of the SUV peak sphere center has not yet been published in the literature. In the first part of this work, we investigate the effects of allowing free movement of the SUV peak sphere, rather than restricting movement to locations where the sphere center is at the center of a voxel. This effect is termed partial voxel scanning with the SUV peak sphere. We present results from a Monte Carlo (MC) based digital phantom study in which we evaluate the coefficient of variation in SUV recovery of various size tumors. The MC approach randomizes tumor location, accounting for partial volume effects, for which it was hypothesized that said partial voxel scanning may help to recover. These simulations included spatial resolution losses typical of a commercially available PET scanner. The second round of MC simulations once again tested partial voxel scanning, but this time both spatial resolution and noise were added to image projections (sinograms), which were then reconstructed using an in house OS EM algorithm. Here we compare the robustness of SUV max and SUV peak in evaluating images with realistic clinical noise and resolution effects. We add various levels of Gaussian postreconstruction smoothing and record the changes in coefficient of variation of SUV max and SUV peak. 19

36 If SUV peak were to simply be fixed on center voxel location, this metric can simply be thought of as the maximum voxel resulting from the convolution of a uniformly weighted sphere with the original image. Thus, this second investigation looks to compare SUV peak to the more common SUV max + Gaussian smoothing. Smoothing performed with a uniformly weighted sphere (a jinc function in k space) may favor certain spatial frequencies and disregards others. Therefore, our hypothesis is that applying additional Gaussian smoothing and recording SUV max will outperform recording SUV peak alone. 20

37 3. Materials and Methods 3.1 Project One Nineteen patients enrolled on an IRB approved study received 2 pre treatment baseline PET scans (, ), separated by an average of 11 days, prior to chemoradiotherapy (70 Gy, 2 Gy/fraction). Subjects also received 1 intra treatment PET scan ( ) early into the course of therapy (after Gy). Of the 19 patients, 11 scans were performed on a GE Discovery STE PET/CT in 2D mode (septa), non time of flight (NTOF), with acquisition time of 6 min per bed position. The remaining 8 patient scans were performed on a Siemens Biograph mct in 3D mode, with TOF, 8 min per bed position. These 2D and 3D data were analyzed separately. This investigation does not compare response assessment of 2D vs. 3D, but this difference in scanning technique furthered the need for separation of patient groups, and was found to be a convenient naming convention. Each PET image was reconstructed with 1, 2, 4, and 12 iterations of either GE s (20 subsets) or Seimens (21 subsets) onboard OS EM algorithm. No advanced reconstruction algorithms were used (e.g. Siemens TrueX) and no onboard smoothing was applied. Post reconstruction smoothing was manually applied to the images, using an isotropic Gaussian filter. For each combination of iterations and smoothing, both primary tumor (GTV) and lymph node (LN) structures in baseline and intra treatment images were quantitatively analyzed using the metrics SUV max, SUVmean, and SUV peak. 21

38 Bland Altman analysis [45] was applied to the baseline data for these metrics for all subjects, after applying the Fourth Spread (FS) method to remove outliers from the baseline scans. The Bland Altman method assesses variability by a quantity termed repeatability, defined as 1.96 (7) where is the standard deviation of the difference between the baseline values for a particular metric (SUV max, SUV mean, or SUV peak). A smaller repeatability for some combination of reconstruction parameters is considered desirable. The intra treatment PET change ( ) is considered significant only if it is greater in magnitude than the repeatability. For each combination, the total number of cases ( ) with intra treatment metric values outside repeatability, and the total sum (Ω) of the relative metric change outside repeatability (equation (8)) were calculated (Figure 6). Ω (8) Reconstruction parameters that yield larger values of and Ω are desirable, since they result in greater separation between the baseline and intra treatment images. Tables of,, and Ω were generated to show the dependence of these values on and smoothing FWHM. These tables were generated for each patient set (GE 2D and Siemens 3D), each metric (SUV max, SUV mean, and SUV peak), and each structure (GTV and LN). The geometric mean was then taken over structures GTV and LN. The geometric 22

39 mean was used because it yields a lower value than the arithmetic mean for cases where the / /Ω value is high for one structure but low for the other structure, i.e. it is biased towards the lower of the two values. Tables of,, and Ω are shown for each patient set and metric (Table 1 Table 6). Summary tables was then created, which were produced by normalizing the original values, taking the arithmetic mean over all three SUV metrics, followed by the geometric mean across structures, then normalizing to unity. The resulting tables of 1/,, and Ω are displayed for each patient data set to provide an overview of the effects of PET reconstruction parameters on response assessment. Figure 6: Visual aid in the calculation of the sum of relative metric change outside repeatability,. Baseline repeatability is shown by the blue dashed lines, and intratreatment PET change ( ) is shown as red circles. The individual elements in the sum,, are physically represented by /. 23

40 3.2 Project Two SUV-peak sphere precision of edge voxels SUV peak is defined as the local average over a spherical ROI, however the treatment of the ROI s edge voxels is open to interpretation. In the simplest form, SUVpeak could wholly include voxels of which the central coordinates are within the sphere diameter. A slightly more complex approach that better represents an actual spherical average is to assign voxel weights based on their partial volume within the ROI. Calculating the partial volume of edge voxels is analytically complex, but a close approximation can be achieved by scaling the sphere up by a scale up factor (SUF), then creating the ROI (setting voxels inside sphere to 1, outside to 0), and finally scaling the ROI back down to the required dimensions. Voxels are combined during the scale down process by taking an average, which results in edge voxels with a number between 0 and 1 that represents the partial volume that was inside the SUV peak sphere. Figure 7: Demonstration of scale up factors (SUF) on digital sphere approximation. 24

41 The goal of our initial investigation was to determine the magnitude of this scaleup factor required to accurately represent the volume of a true sphere to within 1%. Spherical ROIs of 1 cm diameter on a grid of (0.4 cm) 3 voxels were created with scale up factors of 4, 8, 16, 32, and 64, and the resulting volumes compared to the known volume of a sphere, given in equation (9). 4 3 (9) Several example slices of SUV peak ROIs created with and without the scale up/scaledown process are shown in Figure 8. By comparing this ROI volume to the known volume of a sphere, we determined the necessary SUF to reach <0.1% accuracy (Table 11). This SUF was then used in the development of the SUV peak algorithm. Figure 8: [top] Slices of SUV peak spherical ROI using binary definition. [bottom] Slices of same ROI using scale up method, SUF = 10. Windowed from 0 to 1. 25

42 3.2.2 Developing intra-pixel search algorithm An SUV peak finding program was developed using the C programing language. The program requires inputs of the image data, dimensions, pixel size, SUVpeak sphere diameter, and the coordinates of a rectangular prism ROI over which the algorithm will restrict the search. The algorithm works in the following way: 1. An SUV peak ROI is generated, centered over the voxel center, using scaleup/scale down method, SUF = A convolution is performed over input ROI, moving the peak ROI by steps of 1 voxel. The maximum of this convolution (SUV peak) and its coordinates are recorded. 3. Convolution step size is reduced by a factor of 2. A convolution is performed in the vicinity (±3 step size in all directions) of the previous maximum with this new reduced step size. Technically, new SUV peak ROI spheres are created at each convolution point, but some symmetry is exploited. The new maximum SUV peak value and location are recorded. 4. Step 3 is repeated until step size has reached a desired stopping point, e.g. stepsize of 1/32 voxels. The program source code is shown in the Appendix. 26

43 3.2.3 Monte Carlo investigation 1: SUV-peak of randomly positioned digital tumors with spatial resolution effects Digital spherical tumors of diameters cm were created using the scaleup/scale down method with SUF = 16 (Figure 9). The voxel size of tumor images was cm 3 to simulate the clinical reconstruction matrices of the GE Discovery STE and Discovery 690 PET/CTs. The location of each tumor relative to the voxel matrix was chosen randomly to simulate the occurrence of partial volume effects. For each tumor size, 10,000 tumors were created and smoothed with a 3D Gaussian filter of 0.8 cm FWHM to simulate typical PET extrinsic spatial resolution effects. These images were evaluated using the in house algorithm (section 3.2.2), from which SUV max and SUVpeak were recorded, in addition to SUV peak with 1/2, 1/4, 1/8, 1/16, and 1/32 partialvoxel scanning. Figure 9: [top row] Central slice of 3D digital spherical tumors of diameter (left toright) 1.0 cm, 1.5 cm, 2.0 cm, 2.5 cm, 3.0 cm, 3.5 cm, and 4.0 cm. [bottom row] Central slice of digital spherical tumors with 0.8 cm FWHM isotropic Gaussian smoothing. 27

44 These results were analyzed by calculating the coefficient of variation for each metric for each tumor size, where standard deviation and mean were calculated over the 10,000 samples. For the same tumor, less variation in a quantitative metric is desirable (Figure 13). Each metric was also assessed based on the minimum tumor size required for full activity recovery (Figure 12), which could play a role in selecting an appropriate metric if the tumor size is known. The minimum tumor diameter for full SUV max recovery is estimated as 3 FWHM of extrinsic spatial resolution (example in Figure 10). We hypothesize that the minimum tumor diameter for full SUV peak recovery will be given by 3 FWHM. (10) Figure 10: Line profiles through tumors pre and post smoothing by a 0.8 cm FWHM Gaussian filter, representing extrinsic spatial resolution blurring. [left] Required tumor size for SUV max full recovery, 2.4 cm. [right] Hypothesized tumor size required for SUV peak full recovery, ( ) cm. 28

45 3.2.4 Monte Carlo investigation 2: SUV-peak of randomly positioned digital tumors with spatial resolution blurring and noise applied in projection space prior to OS-EM reconstruction. In this Monte Carlo simulation study, digital spherical tumors with 4 background activity were generated with SUF = 16 and placed inside a 40 cm 20 cm body of background activity. For each tumor diameter (1 cm, 2 cm, 3 cm, and 4 cm), 125 phantoms were generated, each phantom containing 8 tumors, giving a total of 1,000 samples (Figure 11a). Activity projections were taken through each slice every 1 with cm detector elements to form activity sinograms (Figure 11b). Spatial resolution effects were simulated by applying 0.8 cm FWHM Gaussian smoothing to the sinograms along the r (detector) and z (slice) directions (Figure 11c). Attenuation was simulated by calculating attenuation projections ( ) through the body for each r and θ, where μ = cm 1 for tissue equivalence. Each element in the smoothed sinogram was multiplied by the respective attenuation factor (Figure 11d). At this stage, we estimated that, during a clinical scan time, approximately 10 6 true counts would be collected from a background only slice. This information was used to scale the sinogram, after which each sinogram value was replaced with a random number from a Poisson distribution with a mean equal to the original value this simulated real counting statistical noise (Figure 11e). Attenuation correction involved multiplying this noisy sinogram by attenuation correction factors (or dividing by attenuation factors), reversing the earlier process (Figure 11f). This process of attenuation, noise, then attenuation correction, 29

46 simulates realistic noise experienced in PET imaging, where image noise is more severe at depth. After the activity projection sinograms had been altered to include the effects of spatial resolution losses, attenuation, and statistical noise, the reconstruction was performed with an in house OS EM 2D reconstruction algorithm (see Acknowledgements). Reconstructions were performed with 2 iterations and 20 subsets (Figure 11g). Various levels of post smoothing were applied, to test the hypothesis that SUV max and Gaussian smoothing is equal or better in functionality than SUV peak. Gaussian isotropic smoothing was applied to reconstructed images with FWHM of 3 mm, 6 mm, 9 mm, and 12 mm. The images were analyzed for SUV max and SUV peak (including partial voxel scanning from 1/2 1/32 voxels). Analysis proceeded by first examining the mean recovered activity and its coefficient of variation for SUV max and each of the SUV peak partial voxel scanning metrics (Figure 14 and Figure 15, respectively). The images with 6.0 mm post smoothing were used for this analysis, because post smoothing of this magnitude on a 2 iteration, 20 subset reconstruction is typical in clinical reconstruction protocols. After the least variable scanning method was established, plots of the coefficient of variation vs. mean recovered activity were generated for both SUV max and the optimal SUV peak for various levels of post smoothing (Figure 16 Figure 19). Here, if the coefficient of variation for SUV max falls below that of SUV peak when smoothing is applied, then 30

47 the need for the new SUV peak metric may be replaced by additional image smoothing as part of the quantitation process. 31

48 Figure 11: Digital phantoms, projections, addition of spatial resolution blurring, attenuation, and noise, followed by attenuation correction and OS EM reconstruction. 32