Task-based assessment of binned and list-mode SPECT systems
TThis manuscript has been accepted to SPIE Medical Imaging, February 15-19, 2021. Please use the followingreference when citing the manuscript.Rahman, M. A. and Jha, A. K., “Task-based assessment of binned and list-mode SPECT systems," Proc. SPIEMedical Imaging, 2021. a r X i v : . [ phy s i c s . m e d - ph ] F e b ask-based assessment of binned and list-mode SPECTsystems Md Ashequr Rahman and Abhinav K. Jha
Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO,USA Mallinckrodt Institute of Radiology, Washington University in St. Louis, St. Louis, MO, USA
ABSTRACT
In SPECT, list-mode (LM) format allows storing data at higher precision compared to binned data. There issignificant interest in investigating whether this higher precision translates to improved performance on clinicaltasks. Towards this goal, in this study, we quantitatively investigated whether processing data in LM format,and in particular, the energy attribute of the detected photon, provides improved performance on the task ofabsolute quantification of region-of-interest (ROI) uptake in comparison to processing the data in binned for-mat. We conducted this evaluation study using a DaTscan brain SPECT acquisition protocol, conducted inthe context of imaging patients with Parkinson’s disease. This study was conducted with a synthetic phantom.A signal-known exactly/background-known-statistically (SKE/BKS) setup was considered. An ordered-subsetexpectation-maximization algorithm was used to reconstruct images from data acquired in LM format, includingthe scatter-window data, and including the energy attribute of each LM event. Using a realistic 2-D SPECTsystem simulation, quantification tasks were performed on the reconstructed images. The results demonstratedimproved quantification performance when LM data was used compared to binning the attributes in all the con-ducted evaluation studies. Overall, we observed that LM data, including the energy attribute, yielded improvedperformance on absolute quantification tasks compared to binned data.
Keywords:
List-mode, SPECT, binning, reconstruction, quantification, objective assessment of image quality
1. INTRODUCTION
Single photon emission computed tomography (SPECT) is a widely used clinical imaging modality with multipleclinical applications. In SPECT, using the detector measurements, for each detected photon, multiple attributesincluding the position of interaction in the detector, energy deposited in the detector and angle of acquisition canbe estimated and stored. Recording attributes for each detected photon results in list-mode (LM) data format. Traditional methods typically bin the attributes before reconstructing the image. Studies have shown that thisprocess of binning leads to information loss.
In particular, it was shown that a larger set of null functionsexist when binning is introduced.
3, 4, 6
The increase in null function results in bias on the task of quantification. Further, it has also been shown in a simplified SPECT system that the process of binning the angle of acquisitionattribute negatively impacts performance on the task of quantification. These findings motivate studying theimpact of binning on quantification performance for more realistic SPECT systems.One key attribute estimated by a SPECT system for each gamma-ray photon is the energy deposited bythe photon in the scintillation crystal. Studies are suggesting that this energy attribute contains information toperform tasks such as estimating the attenuation distribution.
5, 8–10
However, typically this attribute is binned,leading to different energy windows, and of these, the scatter-window data is typically discarded. More recentstudies are demonstrating that photons in the scatter-window data may contain information to estimate theactivity distribution.
5, 11
Thus, that leads to the question of whether processing these photons in LM formatwithout binning the energy attribute results in improved image quality. Our goal in this manuscript was to
Further author information: (Send correspondence to Abhinav K. Jha)Abhinav K. Jha: E-mail: [email protected]) (b)Figure 1. For synthetic phantom, (a) a realization of true activity distribution for signal-present case where mean SBR =2:1 and (b) true attenuation distribution. investigate this question. This would provide further insights on the impact of processing binned vs. LM dataon image quality in SPECT.Imaging systems and methods are developed for specific clinical tasks, such as detection, quantification,or a combination of both. Thus, a rigorous approach to image-quality evaluation should account for the clinicaltask performed on the acquired image. Objective assessment of image quality (OAIQ)-based studies providea mechanism for conducting such task-based evaluation quantitatively and by accounting for population vari-ability, imaging-system physics, the observer performing the task, and a figure of merit that quantifies thisperformance.
Thus, we conducted an OAIQ-based study to evaluate the impact of binning on performancein quantification tasks.A key enabler of our OAIQ-based study was a recently developed iterative method that uses LM data,including scatter-window data and containing the energy attribute, to reconstruct the activity distribution inSPECT. This method compensates for the relevant image-degrading processes in SPECT including scatter,attenuation, noise, and collimator-detector response. The method provides an avenue to investigate the impactof binning the LM event attributes, including the energy attribute, on performance in absolute quantificationtasks in SPECT. Our objective in this study was to investigate this impact using an OAIQ framework on thetask of absolute quantification in SPECT. For this purpose, we conducted OAIQ-based studies in the contextof quantiative dopamine transporter (DaT) SPECT. Quantitative uptakes in striatal regions in the brain, asextracted for DaT SPECT images, are being explored as biomarkers to measure severity of Parkinson’s disease.There is an important need for such biomarkers, given the exciting developments in developing disease-modifyingtherapies for this disease. However, for these quantitative uptakes to be applicable as biomarkers, they needto be reliably estimated from the images. We investigated whether using LM data would yield more reliablequantification of these uptake values.
2. METHOD
A simulation-based OAIQ study typically consists of five components: (a) a definition of the task, (b) objectmodel, (c) simulation of the imaging process, (d) process to extract the task-specific information and (e) figureof merit to measure task performance. In this section, we describe each of these components in our study. Asmentioned above, the study was conducted in the context of quantitative DaT-SPECT.
We evaluated the LM and binned systems on the task of quantifying activity within a pre-defined region ofinterest (ROI). In DaT-SPECT, the goal is to estimate the activity in the caudate and putamen regions. Theboundaries for these regions can be obtained by either segmenting these regions, or from other imagingmodalities, such as MRI. Thus, the ROI can be defined. We thus frame our task as estimating the activitywithin the known ROIs from the SPECT images. These SPECT images were acquired using a 2D acquisitionprotocol, as described in more detail in the next section.e conducted the quantitative analysis with a synthetic phantom that has similar properties as the brainphantom. Task performance was assessed over multiple realizations. The background was also varied in the dif-ferent realizations, while the signal properties were constant. Thus, this was a signal-known-exactly/background-known-statistically (SKE/BKS) study in the context of a quantification task except that the signal intensity wasnot known. The rationale behind conducting this study was to evaluate performance as the background variedon quantification tasks. Variation in background has been known to impact detection-task performance. To simulate an object similar to the brain, an elliptical shaped synthetic phantom (Fig. 1a) was considered wherethe background was simulated using a clustered lumpy background model. A circular region with 7 mm radiuslocated at an off-center position inside the phantom was considered as the known signal. To analyze the effectof varying signal/tumor-to-background ratio (SBR/TBR) on task performance, the mean SBR value was variedbetween 1.2:1, 1.5:1, 2:1 and 3:1. The attenuation distribution was considered to be non-uniform (Fig. 1b). Theattenuation coefficient was 21m − at the rim region of phantom which simulates a skull and 15m − at the innerregion simulating the soft tissue. We simulated a 2-D SPECT system with configuration similar to GE’s Optima 640 system and a low-energy highresolution (LEHR) parallel-hole collimator. We considered that the phantom has been injected with Ioflupane(I-123) radiotracer, which emits gamma-ray photon at 159 KeV energy. The detector position resolution was setto 4 mm. The detector energy resolution was set to 10% FWHM at 159 KeV and was assumed to be constantin the range of 80 KeV to 175 KeV. LM data, that falls into the energy range 70 KeV to 175 keV, was generatedusing Monte Carlo simulation and only contained events that went through up to first order of scatter. The datawas acquired in 120 fixed angular position over 360 ◦ . Approximately 8 × events were detected in a energywindow ranging from 80 KeV to 175 KeV, thus simulating a low-dose SPECT protocol.This LM data was reconstructed as such using the reconstruction algorithm described below. To study theimpact of binning on task performance, we binned the energy attribute of this data into multiple bins, namely 2bins and 3 bins. We set the first bin as same as the photo-peak energy window (143-175 KeV for DaT-SPECT).All the events inside this bin were assigned a fixed energy value, equal to the primary photon energy (159 KeV).Depending on the total number of bins, the scatter-window was then divided into equal-width windows. Allphotons within a given scatter-energy bin were assigned the energy value at the center of that bin. These binneddata were also reconstructed using the reconstruction algorithm described below. The measured projection data was reconstructed using the maximum-likelihood expectation-maximization-basedmethod as briefly described in Rahman et al. The method extends upon an approach originally proposedin
8, 27 and allows processing LM data acquired in any arbitrary-sized energy window and incorporate the energyattribute of detected photon. Further, the method compensates for attenuation, scatter, collimator-detectorresponse, and noise in SPECT. Here we briefly describe the technique.Consider a SPECT system that acquires LM data for a fixed scan time, T. The objective of the recon-struction method is to estimate the discrete activity distribution denoted by the N -dimensional vector λ over Q voxels. Let λ q denote the mean rate of emission from q th voxel. Denote the number of detected events by J .The detected events are stored in LM format where for each photon, the attributes of position of interaction ofdetected photon in the the scintillation crystal, energy deposited by the detected photon and time of detection arerecorded. We denote the true and measured attributes of j th detected event by vectors A j and ˆA j , respectively.We also denote P as the path traversed by an emitted photon and ˆ A as the full set of measured attributes where A = { ˆA j , j = 1 , , . . . J } . We can write the likelihood of the measured LM data aspr( ˆ A , J | λ ) = Pr( J | λ )pr( ˆ A| λ )= Pr( J | λ ) J Y j =1 pr( ˆA j | λ ) (1)= Pr( J | λ ) J Y j =1 X P pr( ˆA j | P )Pr( P | λ ) , (2)where, in the second step, we have used the fact that the LM events are all independent, while in the third step,we have decomposed pr( ˆA j | λ ) as a mixture model in terms of the probability that a photon takes a path andthe probability of that path. Here, we point that J is a Poisson distributed random variable. Let s eff ( P ) denotethe sensitivity of a path P and λ ( P ) denote the activity at the voxel where the path originates from. We canderive the form of pr( ˆA j | P ) using radiative transport equation as pr( P | λ ) = λ ( P ) s eff ( P ) P P λ ( P ) s eff ( P ) . (3)Thus we can write the log-likelihood of observed LM data as L ( λ | ˆ A , J ) = J X j =1 log X P pr( ˆA j | P ) λ ( P ) s eff ( P ) + J log( T ) − T X P λ ( P ) s eff ( P ) − log J ! . (4)To maximize this likelihood, an expectation-maximization algorithm is developed. For each event j and eachpossible path P , we denote a hidden variable z j, P where z j, P = ( j took the path P . . Let us denote the vector z j by accumulating all the hidden vectors of all possible path for this specific event j .The observed LM data and the hidden vectors form the complete data. We can derive the form of complete datalog-likelihood as: L C ( λ |{ ˆ A j , z j ; j = 1 , . . . J } , J )= J X j =1 "X P z j, P n log pr( ˆ A j | P ) + log λ ( P ) + log s eff ( P ) o + J log T − T X P λ ( P ) s eff ( P ) − log J ! . (5)Taking the expectation and maximization steps on this complete data log-likelihood leads to following iterativeupdate: ˆ λ ( t +1) q = P Jj =1 P P q ¯ z ( t +1) j, P q T P P q s eff ( P q ) , (6)where, P q denotes paths that start from voxel q , λ q denotes the activity rate at that starting voxel and ¯ z ( t +1) j, P = E h z j, P | ˆA j ; λ ( t ) i is the expected value of the hidden variable conditioned on observed LM data.However, the algorithm was still computationally intensive. Thus, in our OAIQ-based studies, we consid-ered only up to first-order scatter events. Further, to ensure that the number of scatter events in the forwardand inverse model match, we reconstructed the images using photons that scatter only once.From the reconstructed images, we estimated the mean activity uptake inside the known region of interestROI). Let the N -dimensional vector χ k denote the binary mask that denotes the ROI for the k th region. Letˆ a k denote the estimated activity in that region using this procedure. Then, mathematically,ˆ a k = P Qq =1 λ q χ qk P Qq =1 χ qk . (7) The performance of the list-mode and binned-based estimation approaches on the task of activity estimationwas quantified on the basis of accuracy and precision of the estimated uptake using the metrics of normalizedbias and variance. Further, the overall reliability of the estimated uptake was quantified using the metric ofnormalized root mean squared error (NRMSE). This is a summary figure of merit that quantifies the effect ofboth bias and variance, and thus indicates the overall reliability on the quantification task. Let a k and ˆ a k denotethe true and estimated activities within the k th ROIs. Let P denote the number of noise realizations. Then, theNRMSE for the k th ROI was defined as:
N RM SE = 1 a k s P Pi =1 ( a k − ˆ a ki ) P . (8)
3. RESULTS
Fig. 2a shows that processing the energy attribute in LM format led to a lower bias for SBR values greater than1.5 in comparison to binning this attribute. Binning the list-mode attributes leads to increase in null space,
3, 4 and as shown in another study, this causes a bias in quantification performance. Our results are consistent withthat study and show that binning the energy attribute leads to an increase in bias.At the same time, we observe that the standard deviation when using the LM data is higher comparedto when using the binned format (Fig. 2b). However, in case of the NRMSE, which is a combination of the biasand variance, it is observed that LM data yields a lower NRMSE compared to the binned format (Fig. 2c). Thissuggest that the improvement in bias is more significant compared to the impact on increasing variance whenusing list-mode data
4. DISCUSSIONS
In this manuscript we evaluated the effect of binning the energy attributes of the LM data on the task ofquantifying uptake within a pre-defined ROI in a 2-D DaT-SPECT system. We consistently observed thatprocessing data in LM format yielded improved quantification performance. As mentioned above, LM formatallows storing the data at higher precision compared to binned format. Our results show that this increase inprecision very much translates into a tangible improved performance on quantification tasks.In our quantification study, we did not perform any partial volume compensation (PVC). Previous stud-ies have demonstrated that compensating for PVEs results in improved quantification performance. Thus,integrating this LM-based reconstruction approach with a PVC approach may lead to even more reliable quan-tification, and is an important area of future research.The current study has some limitations. We evaluated the performance of LM and binned data basedon a 2-D SPECT system. We considered only up to single-order of scatter in forward model and reconstructionframework. Our promising results motivate extension of this study to 3-D setup and modeling multiple scatterevents. .5 2 2.5 3 SBR -0.200.20.40.6 N o r m . b i a s i n R O I up t a k e (a) SBR V a r i an c e i n R O I up t a k e (b) SBR NR M SE i n R O I up t a k e (c)Figure 2. For different binning configuration, (a) normalized bias, (b) variance and (c) NRMSE between the estimatedactivity uptake inside signal region and true mean activity uptake as a function of mean SBR in a SKE/BKS setup.
5. CONCLUSIONS
Our objective-assessment-of-image-quality-based analysis provides evidence that processing SPECT-emissiondata in list-mode format provides improved performance compared to binned format for the task of estimat-ing activity within a known region of interest, as evaluated in clinically relevant applications conducted in thecontext of quantitaitve dopamine transporter SPECT. This analysis motivates large-scale 3D simulation andphysical-phantom studies to further validate this finding. Improved performance with list-mode data in thesestudies would provide evidence to process the energy attribute in list-mode format as opposed to binning datain energy windows.
ACKNOWLEDGMENTS
This work was financially supported by NIH R21 EB024647 (Trailblazer award) and by an NVIDIA GPU grant.The authors thank Richard Laforest, PhD for helpful discussions.
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