Collimator optimization for detection and quantitation tasks: application to gallium-67 imaging

Collimator and Energy Window Evaluation in Ga-67 Imaging by Monte Carlo Simulation

Objectives:

Gallium-67 (Ga-67) imaging is affected by collimator penetration and scatter components owing to the high-energy (HE) gamma-ray emissions. The characterization of penetration and scatter distribution is essential for the optimization of low-energy high-resolution (LEHR), medium energy (ME), and HE collimators and for the development of an effective correction technique. We compared the image quality that can be achieved by 3 collimators for different energy windows using the SIMIND Monte Carlo code.

Methods:

Simulation experiments were conducted for LEHR, ME, and HE collimators for Ga-67 point source placed at 12-cm distance from the detector surface using the Monte Carlo SIMIND simulation code. Their spectra point spread functions as well as the original, penetration, scattering, and X-rays curves were drawn and analyzed. The parameters full-width at half maximum and full-width at tenth maximum were also investigated.

Results:

The original, penetration, and scatter curves within 10% for LEHR were 34.46%, 33.52%, 17.29%, and 14.72%, respectively. Similarly, the original, penetration, scatter, and X-rays within 10% for ME and HE were 83.06%, 10.25%, 6.69%, and 0% and 81.44%, 11.51%, 7.05%, and 0%, respectively. The trade-off between spatial resolution and sensitivity was achieved by using the ME collimator at 185 photopeak of Ga-67.

Conclusion:

The Monte Carlo simulation outcomes can be applied for optimal collimator designing and for the development of new correction method in Ga-67 imaging.

Collimator optimization and collimator-detector response compensation in myocardial perfusion SPECT using the ideal observer with and without model mismatch and an anthropomorphic model observer

The collimator is the primary factor that determines the spatial resolution and noise tradeoff in myocardial perfusion SPECT images. In this paper, the goal was to find the collimator that optimizes the image quality in terms of a perfusion defect detection task. Since the optimal collimator could depend on the level of approximation of the collimator-detector response (CDR) compensation modeled in reconstruction, we performed this optimization for the cases of modeling the full CDR (including geometric, septal penetration and septal scatter responses), the geometric CDR, or no model of the CDR. We evaluated the performance on the detection task using three model observers. Two observers operated on data in the projection domain: the Ideal Observer (IO) and IO with Model-Mismatch (IO-MM). The third observer was an anthropomorphic Channelized Hotelling Observer (CHO), which operated on reconstructed images. The projection-domain observers have the advantage that they are computationally less intensive. The IO has perfect knowledge of the image formation process, i.e. it has a perfect model of the CDR. The IO-MM takes into account the mismatch between the true (complete and accurate) model and an approximate model, e.g. one that might be used in reconstruction. We evaluated the utility of these projection domain observers in optimizing instrumentation parameters. We investigated a family of 8 parallel-hole collimators, spanning a wide range of resolution and sensitivity tradeoffs, using a population of simulated projection (for the IO and IO-MM) and reconstructed (for the CHO) images that included background variability. We simulated anterolateral and inferior perfusion defects with variable extents and severities. The area under the ROC curve was estimated from the IO, IO-MM, and CHO test statistics and served as the figure-of-merit. The optimal collimator for the IO had a resolution of 9-11 mm FWHM at 10 cm, which is poorer resolution than typical collimators used for MPS. When the IO-MM and CHO used a geometric or no model of the CDR, the optimal collimator shifted toward higher resolution than that obtained using the IO and the CHO with full CDR modeling. With the optimal collimator, the IO-MM and CHO using geometric modeling gave similar performance to full CDR modeling. Collimators with poorer resolution were optimal when CDR modeling was used. The agreement of rankings between the IO-MM and CHO confirmed that the IO-MM is useful for optimization tasks when model mismatch is present due to its substantially reduced computational burden compared to the CHO.

Collimator optimization in myocardial perfusion SPECT using the ideal observer and realistic background variability for lesion detection and joint detection and localization tasks

In SPECT imaging, collimators are a major factor limiting image quality and largely determine the noise and resolution of SPECT images. In this paper, we seek the collimator with the optimal tradeoff between image noise and resolution with respect to performance on two tasks related to myocardial perfusion SPECT: perfusion defect detection and joint detection and localization. We used the Ideal Observer (IO) operating on realistic background-known-statistically (BKS) and signal-known-exactly (SKE) data. The areas under the receiver operating characteristic (ROC) and localization ROC (LROC) curves (AUCd, AUCd+l), respectively, were used as the figures of merit for both tasks. We used a previously developed population of 54 phantoms based on the eXtended Cardiac Torso Phantom (XCAT) that included variations in gender, body size, heart size and subcutaneous adipose tissue level. For each phantom, organ uptakes were varied randomly based on distributions observed in patient data. We simulated perfusion defects at six different locations with extents and severities of 10% and 25%, respectively, which represented challenging but clinically relevant defects. The extent and severity are, respectively, the perfusion defect's fraction of the myocardial volume and reduction of uptake relative to the normal myocardium. Projection data were generated using an analytical projector that modeled attenuation, scatter, and collimator-detector response effects, a 9% energy resolution at 140 keV, and a 4 mm full-width at half maximum (FWHM) intrinsic spatial resolution. We investigated a family of eight parallel-hole collimators that spanned a large range of sensitivity-resolution tradeoffs. For each collimator and defect location, the IO test statistics were computed using a Markov Chain Monte Carlo (MCMC) method for an ensemble of 540 pairs of defect-present and -absent images that included the aforementioned anatomical and uptake variability. Sets of test statistics were computed for both tasks and analyzed using ROC and LROC analysis methodologies. The results of this study suggest that collimators with somewhat poorer resolution and higher sensitivity than those of a typical low-energy high-resolution (LEHR) collimator were optimal for both defect detection and joint detection and localization tasks in myocardial perfusion SPECT for the range of defect sizes investigated. This study also indicates that optimizing instrumentation for a detection task may provide near-optimal performance on the more challenging detection-localization task.

PETSTEP: Generation of synthetic PET lesions for fast evaluation of segmentation methods

Purpose

This work describes PETSTEP (PET Simulator of Tracers via Emission Projection): a faster and more accessible alternative to Monte Carlo (MC) simulation generating realistic PET images, for studies assessing image features and segmentation techniques.

Methods

PETSTEP was implemented within Matlab as open source software. It allows generating three-dimensional PET images from PET/CT data or synthetic CT and PET maps, with user-drawn lesions and user-set acquisition and reconstruction parameters. PETSTEP was used to reproduce images of the NEMA body phantom acquired on a GE Discovery 690 PET/CT scanner, and simulated with MC for the GE Discovery LS scanner, and to generate realistic Head and Neck scans. Finally the sensitivity (S) and Positive Predictive Value (PPV) of three automatic segmentation methods were compared when applied to the scanner-acquired and PETSTEP-simulated NEMA images.

Results

PETSTEP produced 3D phantom and clinical images within 4 and 6 min respectively on a single core 2.7 GHz computer. PETSTEP images of the NEMA phantom had mean intensities within 2% of the scanner-acquired image for both background and largest insert, and 16% larger background Full Width at Half Maximum. Similar results were obtained when comparing PETSTEP images to MC simulated data. The S and PPV obtained with simulated phantom images were statistically significantly lower than for the original images, but led to the same conclusions with respect to the evaluated segmentation methods.

Conclusions

PETSTEP allows fast simulation of synthetic images reproducing scanner-acquired PET data and shows great promise for the evaluation of PET segmentation methods.

Review of SPECT collimator selection, optimization, and fabrication for clinical and preclinical imaging

In single photon emission computed tomography, the choice of the collimator has a major impact on the sensitivity and resolution of the system. Traditional parallel-hole and fan-beam collimators used in clinical practice, for example, have a relatively poor sensitivity and subcentimeter spatial resolution, while in small-animal imaging, pinhole collimators are used to obtain submillimeter resolution and multiple pinholes are often combined to increase sensitivity. This paper reviews methods for production, sensitivity maximization, and task-based optimization of collimation for both clinical and preclinical imaging applications. New opportunities for improved collimation are now arising primarily because of (i) new collimator-production techniques and (ii) detectors with improved intrinsic spatial resolution that have recently become available. These new technologies are expected to impact the design of collimators in the future. The authors also discuss concepts like septal penetration, high-resolution applications, multiplexing, sampling completeness, and adaptive systems, and the authors conclude with an example of an optimization study for a parallel-hole, fan-beam, cone-beam, and multiple-pinhole collimator for different applications.

Collimator performance evaluation for In-111 SPECT using a detection/localization task

In SPECT, the collimator is a crucial element in controlling image quality. We take a task performance approach to collimator performance evaluation in which an ideal observer is applied to the raw camera data without regard to the subsequent reconstruction stage. The clinical context of our collimator study is one of searching for and detecting neuroendocrine tumor metastases in the liver as seen in In-111 Octreotide SPECT. Our task involves detection and localization of a signal and thus differs from the conventionally used detection-only task. The scalar task performance metric is ALROC, the area under the localization receiver operating characteristic curve. Since In-111 emits photons at both 171 and 245 keV, the higher energy emissions can contribute significant septal scatter and penetration. Our collimator evaluations address a question previously considered by Mähler et al (2012 IEEE Trans. Nucl. Sci. 59 47–53) who used a different methodology: does allowing a limited amount of septal scatter and penetration yield improved task performance? We used simulation methods to evaluate five parallel-hole collimators. The collimators had roughly equal geometric sensitivity and resolution but a range of contributions from septal effects leading to variations in total sensitivity and resolution. We found that the best performance was obtained with a collimator that allowed a moderate amount of septal scatter and penetration.

Optimization of convergent collimators for pixelated SPECT systems

PURPOSE

The optimization of the collimator design is essential to obtain the best possible sensitivity in single photon emission computed tomography imaging. The aim of this work is to present a methodology for maximizing the sensitivity of convergent collimators, specifically designed to match the pitch of pixelated detectors, for a fixed spatial resolution value and to present some initial results using this approach.

METHODS

Given the matched constraint, the optimal collimator design cannot be simply found by allowing the highest level of septal penetration and spatial resolution consistent with the imposed restrictions, as it is done for the optimization of conventional collimators. Therefore, an algorithm that interactively calculates the collimator dimensions, with the maximum sensitivity, which respect the imposed restrictions was developed and used to optimize cone and fan beam collimators with tapered square-shaped holes for low (60-300 keV) and high energy radiation (300-511 keV). The optimal collimator dimensions were locally calculated based on the premise that each hole and septa of the convergent collimator should locally resemble an appropriate optimal matched parallel collimator.

RESULTS

The optimal collimator dimensions, calculated for subcentimeter resolutions (3 and 7.5 mm), common pixel sizes (1.6, 2.1, and 2.5 mm), and acceptable septal penetration at 140 keV, were approximately constant throughout the collimator, despite their different hole incidence angles. By using these input parameters and a less strict septal penetration value of 5%, the optimal collimator dimensions and the corresponding mass per detector area were calculated for 511 keV. It is shown that a low value of focal distance leads to improvements in the average sensitivity at a fixed source-collimator distance and resolution. The optimal cone beam performance outperformed that of other optimal collimation geometries (fan and parallel beam) in imaging objects close to the collimator surface.

CONCLUSIONS

These results demonstrate the potential of this kind of optimal convergent collimators for the use in small field of view imaging applications.

A collimator optimization method for quantitative imaging: application to Y-90 bremsstrahlung SPECT

PURPOSE

Post-therapy quantitative 90Y bremsstrahlung single photon emission computed tomography (SPECT) has shown great potential to provide reliable activity estimates, which are essential for dose verification. Typically 90Y imaging is performed with high- or medium-energy collimators. However, the energy spectrum of 90Y bremsstrahlung photons is substantially different than typical for these collimators. In addition, dosimetry requires quantitative images, and collimators are not typically optimized for such tasks. Optimizing a collimator for 90Y imaging is both novel and potentially important. Conventional optimization methods are not appropriate for 90Y bremsstrahlung photons, which have a continuous and broad energy distribution. In this work, the authors developed a parallel-hole collimator optimization method for quantitative tasks that is particularly applicable to radionuclides with complex emission energy spectra. The authors applied the proposed method to develop an optimal collimator for quantitative 90Y bremsstrahlung SPECT in the context of microsphere radioembolization.

METHODS

To account for the effects of the collimator on both the bias and the variance of the activity estimates, the authors used the root mean squared error (RMSE) of the volume of interest activity estimates as the figure of merit (FOM). In the FOM, the bias due to the null space of the image formation process was taken in account. The RMSE was weighted by the inverse mass to reflect the application to dosimetry; for a different application, more relevant weighting could easily be adopted. The authors proposed a parameterization for the collimator that facilitates the incorporation of the important factors (geometric sensitivity, geometric resolution, and septal penetration fraction) determining collimator performance, while keeping the number of free parameters describing the collimator small (i.e., two parameters). To make the optimization results for quantitative 90Y bremsstrahlung SPECT more general, the authors simulated multiple tumors of various sizes in the liver. The authors realistically simulated human anatomy using a digital phantom and the image formation process using a previously validated and computationally efficient method for modeling the image-degrading effects including object scatter, attenuation, and the full collimator-detector response (CDR). The scatter kernels and CDR function tables used in the modeling method were generated using a previously validated Monte Carlo simulation code.

RESULTS

The hole length, hole diameter, and septal thickness of the obtained optimal collimator were 84, 3.5, and 1.4 mm, respectively. Compared to a commercial high-energy general-purpose collimator, the optimal collimator improved the resolution and FOM by 27% and 18%, respectively.

CONCLUSIONS

The proposed collimator optimization method may be useful for improving quantitative SPECT imaging for radionuclides with complex energy spectra. The obtained optimal collimator provided a substantial improvement in quantitative performance for the microsphere radioembolization task considered.

Joint optimization of collimator and reconstruction parameters in SPECT imaging for lesion quantification

Obtaining the best possible task performance using reconstructed SPECT images requires optimization of both the collimator and reconstruction parameters. The goal of this study is to determine how to perform this optimization, namely whether the collimator parameters can be optimized solely from projection data, or whether reconstruction parameters should also be considered. In order to answer this question, and to determine the optimal collimation, a digital phantom representing a human torso with 16 mm diameter hot lesions (activity ratio 8:1) was generated and used to simulate clinical SPECT studies with parallel-hole collimation. Two approaches to optimizing the SPECT system were then compared in a lesion quantification task: sequential optimization, where collimation was optimized on projection data using the Cramer–Rao bound, and joint optimization, which simultaneously optimized collimator and reconstruction parameters. For every condition, quantification performance in reconstructed images was evaluated using the root-mean-squared-error of 400 estimates of lesion activity. Compared to the joint-optimization approach, the sequential-optimization approach favoured a poorer resolution collimator, which, under some conditions, resulted in sub-optimal estimation performance. This implies that inclusion of the reconstruction parameters in the optimization procedure is important in obtaining the best possible task performance; in this study, this was achieved with a collimator resolution similar to that of a general-purpose (LEGP) collimator. This collimator was found to outperform the more commonly used high-resolution (LEHR) collimator, in agreement with other task-based studies, using both quantification and detection tasks.

Evaluation of a method for projection-based tissue-activity estimation within small volumes of interest

A new method of compensating for tissue-fraction and count-spillover effects, which require tissue segmentation only within a small volume surrounding the primary lesion of interest, was evaluated for SPECT imaging. Tissue-activity concentration estimates are obtained by fitting the measured projection data to a statistical model of the segmented tissue projections. Multiple realizations of two simulated human-torso phantoms, each containing 20 spherical 'tumours', 1.6 cm in diameter, with tumour-to-background ratios of 8:1 and 4:1, were simulated. Estimates of tumour- and background-activity concentration values for homogeneous as well as inhomogeneous tissue activities were compared to the standard uptake value (SUV) metrics on the basis of accuracy and precision. For perfectly registered, high-contrast, superficial lesions in a homogeneous background without scatter, the method yielded accurate (<0.4% bias) and precise (<6.1%) recovery of the simulated activity values, significantly outperforming the SUV metrics. Tissue inhomogeneities, greater tumour depth and lower contrast ratios degraded precision (up to 11.7%), but the estimates remained almost unbiased. The method was comparable in accuracy but more precise than a well-established matrix inversion approach, even when errors in tumour size and position were introduced to simulate moderate inaccuracies in segmentation and image registration. Photon scatter in the object did not significantly affect the accuracy or precision of the estimates.

Finding Optimized Conditions of Slit-Slat and Multislit-Slat Collimation for Breast Imaging

In order to develop a breast-imaging system for Single Photon Emission Computed Tomography (SPECT) using slit-slat and multislit-slat collimators, we searched for optimized geometric parameters of the collimators. For this study, we employed two independent metrics to validate each result: 1) Signal to Noise Ratio (SNR) based on the Cramer-Rao lower Bound (CRB) and 2) contrast at the same noise level from an ensemble. We calculated SNR values using forward-projection data of an anthropomorphic digital phantom containing two lesions in the breast (one at the chest wall and the other at the center) with a simulated slit-slat collimator as a function of the collimator's geometric parameters. We also calculated contrast values from reconstructed images with noise. Based on the results from the slit-slat case, we investigated angular range, SNR, and contrast for the multislit-slat. We saw similar trends of the two metrics. One interesting property of the multislit-slat is that the imaging performance depends on the orientation of the field of view (FOV) of the side slits. When we compared the metric values for the slit-slat and multislit-slat, improvement was seen only when the lesion was in the FOV of the side slits. Therefore, tuning the parameters of the multislit-slat to optimally detect lesions at the chest wall might be a sensible option since the slit-slat already provides good image quality for center and superficial lesions.

Joint optimization of collimator and reconstruction parameters in SPECT imaging for lesion quantification

Obtaining the best possible task performance using reconstructed SPECT images requires optimization of both the collimator and reconstruction parameters. The goal of this study is to determine how to perform this optimization, namely whether the collimator parameters can be optimized solely from projection data, or whether reconstruction parameters should also be considered. In order to answer this question, and to determine the optimal collimation, a digital phantom representing a human torso with 16 mm diameter hot lesions (activity ratio 8:1) was generated and used to simulate clinical SPECT studies with parallel-hole collimation. Two approaches to optimizing the SPECT system were then compared in a lesion quantification task: sequential optimization, where collimation was optimized on projection data using the Cramer–Rao bound, and joint optimization, which simultaneously optimized collimator and reconstruction parameters. For every condition, quantification performance in reconstructed images was evaluated using the root-mean-squared-error of 400 estimates of lesion activity. Compared to the joint-optimization approach, the sequential-optimization approach favoured a poorer resolution collimator, which, under some conditions, resulted in sub-optimal estimation performance. This implies that inclusion of the reconstruction parameters in the optimization procedure is important in obtaining the best possible task performance; in this study, this was achieved with a collimator resolution similar to that of a general-purpose (LEGP) collimator. This collimator was found to outperform the more commonly used high-resolution (LEHR) collimator, in agreement with other task-based studies, using both quantification and detection tasks.

Collimator optimization in SPECT based on a joint detection and localization task

In SPECT the collimator is a crucial element of the imaging chain and controls the noise-resolution tradeoff of the collected data. Optimizing collimator design has been a long studied topic, with many different criteria used to evaluate the design. One class of criteria is task based, in which the collimator is designed to optimize detection of a signal (lesion). Here we consider a new, more realistic task, the joint detection and localization of a signal. Furthermore, we use an ideal observer-one that attains a theoretically maximum task performance-to optimize collimator design. The ideal observer operates on the sinogram data. We consider a family of parallel-hole low-energy collimators of varying resolution and efficiency and optimize over this set. We observe that for a 2D object characterized by noise due to background variability and a sinogram with photon noise, the optimal collimator tends to be of lower resolution and higher efficiency than equivalent commercial collimators. Furthermore, this optimal design is insensitive to the tolerance radius within which the signal must be localized. So for this scenario, the addition of a localization task does not change the optimal collimator. Optimal collimator resolution gets worse as signal size grows, and improves as the level of background variability noise increases. These latter two trends are also observed when the detection task is signal-known-exactly and background variable.

Collimator optimization in SPECT based on a joint detection and localization task

In SPECT the collimator is a crucial element of the imaging chain and controls the noise-resolution tradeoff of the collected data. Optimizing collimator design has been a long studied topic, with many different criteria used to evaluate the design. One class of criteria is task based, in which the collimator is designed to optimize detection of a signal (lesion). Here we consider a new, more realistic task, the joint detection and localization of a signal. Furthermore, we use an ideal observer-one that attains a theoretically maximum task performance-to optimize collimator design. The ideal observer operates on the sinogram data. We consider a family of parallel-hole low-energy collimators of varying resolution and efficiency and optimize over this set. We observe that for a 2D object characterized by noise due to background variability and a sinogram with photon noise, the optimal collimator tends to be of lower resolution and higher efficiency than equivalent commercial collimators. Furthermore, this optimal design is insensitive to the tolerance radius within which the signal must be localized. So for this scenario, the addition of a localization task does not change the optimal collimator. Optimal collimator resolution gets worse as signal size grows, and improves as the level of background variability noise increases. These latter two trends are also observed when the detection task is signal-known-exactly and background variable.

Estimating random signal parameters from noisy images with nuisance parameters: linear and scanning-linear methods

In a pure estimation task, an object of interest is known to be present, and we wish to determine numerical values for parameters that describe the object. This paper compares the theoretical framework, implementation method, and performance of two estimation procedures. We examined the performance of these estimators for tasks such as estimating signal location, signal volume, signal amplitude, or any combination of these parameters. The signal is embedded in a random background to simulate the effect of nuisance parameters. First, we explore the classical Wiener estimator, which operates linearly on the data and minimizes the ensemble mean-squared error. The results of our performance tests indicate that the Wiener estimator can estimate amplitude and shape once a signal has been located, but is fundamentally unable to locate a signal regardless of the quality of the image. Given these new results on the fundamental limitations of Wiener estimation, we extend our methods to include more complex data processing. We introduce and evaluate a scanning-linear estimator that performs impressively for location estimation. The scanning action of the estimator refers to seeking a solution that maximizes a linear metric, thereby requiring a global-extremum search. The linear metric to be optimized can be derived as a special case of maximum a posteriori (MAP) estimation when the likelihood is Gaussian and a slowly varying covariance approximation is made.