Analytic determination of the resolution-equivalent effective diameter of a pinhole collimator

Characterization of accurate 3D collimator-detector response function for single- and multi-lofthole collimated SPECT cameras

PURPOSE

Collimator-detector response function (CDRF) of a SPECT scanner refers to the image generated from a point source of activity. This research aims to characterize the CDRF of a breast-dedicated SPECT imager equipped with a lofthole collimator using GATE Monte Carlo simulation.

MATERIALS AND METHODS

To do so, a cylindrical multi-lofthole collimation system with lofthole apertures dedicated to breast imaging was modeled using the GATE Monte Carlo simulator. The dependency of the CDRF on the source-to-collimator distance of a single-lofthole as well as 8-lofthole collimations was assessed and then compared. In addition, the 3D-sensitivity map of the 8-lofthole collimation was derived. Finally, fair comparisons were conducted between the response of the 8-lofthole collimator and that of an 8-pinhole and also existing analytical derivations. In all cases, a data acquisition period of 5.0 min with an in-air 99mTc point source was considered.

RESULTS

For the single-lofthole collimator, 4.5 times increasing the magnification factor leads to a 16- and twofold improvement in the sensitivity and spatial resolution, respectively. In the single-lofthole collimator, the resolution and sensitivity are degraded as the source-to-aperture distance increases. For the cylindrical 8-lofthole collimator, the findings confirm that CDRF strongly depends on source-to-aperture distance and angle of photon incidence. For a 30 mm in-plane offset point, a 25% increase in sensitivity is observed compared to that of the center of the FOV. Increasing the angle from 0∘ to 34∘ results in a 50% reduction in sensitivity. Furthermore, the findings illustrate that spatial resolution follows a quadratic function as10 - 3 d 2 + 2 × 10 - 4 d + R 0 where d is an offset along the x-, y-, and z-axis, and R0 is the spatial resolution at the center of the FOV.

CONCLUSION

In conclusion, both spatial resolution and sensitivity of the lofthole collimation are considerably angle- and offset-dependent within the FOV of single- and multi-lofthole collimated SPECT imagers.

Correction of multiplexing artefacts in multi-pinhole SPECT through temporal shuttering, de-multiplexing of projections, and alternating reconstruction

Objective.Single-photon emission computed tomography (SPECT) with pinhole collimators can provide high-resolution imaging, but is often limited by low sensitivity. Acquiring projections simultaneously through multiple pinholes affords both high resolution and high sensitivity. However, the overlap of projections from different pinholes on detectors, known as multiplexing, has been shown to cause artefacts which degrade reconstructed images.Approach.Multiplexed projection sets were considered here using an analytic simulation model of AdaptiSPECT-C-a brain-dedicated multi-pinhole SPECT system. AdaptiSPECT-C has fully adaptable aperture shutters, so can acquire projections with a combination of multiplexed and non-multiplexed frames using temporal shuttering. Two strategies for reducing multiplex artefacts were considered: an algorithm to de-multiplex projections, and an alternating reconstruction strategy for projections acquired with a combination of multiplexed and non-multiplexed frames. Geometric and anthropomorphic digital phantoms were used to assess a number of metrics.Main results.Both de-multiplexing strategies showed a significant reduction in image artefacts and improved fidelity, image uniformity, contrast recovery and activity recovery (AR). In all cases, the two de-multiplexing strategies resulted in superior metrics to those from images acquired with only mux-free frames. The de-multiplexing algorithm provided reduced image noise and superior uniformity, whereas the alternating strategy improved contrast and AR.Significance.The use of these de-multiplexing algorithms means that multi-pinhole SPECT systems can acquire projections with more multiplexing without degradation of images.

A novel reconstruction method combining multi-detector SPECT with an elliptical orbit and computer tomography for cardiac imaging

The myocardial single photon emission computed tomography (SPECT) is a good study due to its clinical significance in the diagnosis of myocardial disease and the requirement for improving image quality. However, SPECT imaging faces challenges related to low spatial resolution and significant statistical noise, which concerns patient radiation safety. In this paper, a novel reconstruction system combining multi-detector elliptical SPECT (ME-SPECT) and computer tomography (CT) is proposed to enhance spatial resolution and sensitivity. The hybrid imaging system utilizes a slit-slat collimator and elliptical orbit to improve sensitivity and signal-to-noise ratio (SNR), obtains accurate attenuation mapping matrices, and requires prior information from integrated CT. Collimator parameters are corrected based on CT reconstruction results. The SPECT imaging system employs an iterative reconstruction algorithm that utilizes prior knowledge. An iterative reconstruction algorithm based on prior knowledge is applied to the SPECT imaging system, and a method for prioritizing the reconstruction of regions of interest (ROI) is introduced to deal with severely truncated data from ME-SPECT. Simulation results show that the proposed method can significantly improve the system's spatial resolution, SNR, and image fidelity. The proposed method can effectively suppress distortion and artifacts with the higher spatial resolution ordered subsets expectation maximization (OSEM); slit-slat collimation.

Radiation Source Localization Using a Model-Based Approach

The procedure is practically an optimization method, during which it is assumed that the gamma dose values detected at different points above the area come from the background radiation and from a single source found in the area. Accordingly, the procedure searches within the area for a geographical coordinate for which the distance law for the spatial propagation of radiation will be true. In order to validate the procedure, we performed measurements in a test area in such a way that all parameters of the source, including its location, were well defined. However, these data were not taken into account during the processing, i.e., the search procedure did not have these data. We can estimate the radiation position without a positional parameter. The exact coordinate and the intensity of the radiating sample were only used when checking the results. We have also applied the method to the raw data of our experiments carried out in the past if we used one source for them. The results confirmed our assumptions. The method is suitable for determining the starting parameters of more complex processes that can even detect multiple sources, but assuming one source, it has proven to be a reliable analytical method on its own.

Intraoperative Gamma Cameras: A Review of Development in the Last Decade and Future Outlook

Portable gamma cameras suitable for intraoperative imaging are in active development and testing. These cameras utilise a range of collimation, detection, and readout architectures, each of which can have significant and interacting impacts on the performance of the system as a whole. In this review, we provide an analysis of intraoperative gamma camera development over the past decade. The designs and performance of 17 imaging systems are compared in depth. We discuss where recent technological developments have had the greatest impact, identify emerging technological and scientific requirements, and predict future research directions. This is a comprehensive review of the current and emerging state-of-the-art as more devices enter clinical practice.

Fast and Accurate Gamma Imaging System Calibration Based on Deep Denoising Networks and Self-Adaptive Data Clustering

Gamma imagers play a key role in both industrial and medical applications. Modern gamma imagers typically employ iterative reconstruction methods in which the system matrix (SM) is a key component to obtain high-quality images. An accurate SM could be acquired from an experimental calibration step with a point source across the FOV, but at a cost of long calibration time to suppress noise, posing challenges to real-world applications. In this work, we propose a time-efficient SM calibration approach for a 4π-view gamma imager with short-time measured SM and deep-learning-based denoising. The key steps include decomposing the SM into multiple detector response function (DRF) images, categorizing DRFs into multiple groups with a self-adaptive K-means clustering method to address sensitivity discrepancy, and independently training separate denoising deep networks for each DRF group. We investigate two denoising networks and compare them against a conventional Gaussian filtering method. The results demonstrate that the denoised SM with deep networks faithfully yields a comparable imaging performance with the long-time measured SM. The SM calibration time is reduced from 1.4 h to 8 min. We conclude that the proposed SM denoising approach is promising and effective in enhancing the productivity of the 4π-view gamma imager, and it is also generally applicable to other imaging systems that require an experimental calibration step.

Improved Performance of a Multipinhole SPECT for DAT Imaging by Increasing Number of Pinholes at the Expense of Increased Multiplexing

SPECT imaging of dopamine transporters (DAT) in the brain is a widely utilized study to improve the diagnosis of Parkinsonian syndromes, where conventional (parallel-hole and fan-beam) collimators on dual-head scanners are commonly employed. We have designed a multi-pinhole (MPH) collimator to improve the performance of DAT imaging. The MPH collimator focuses on the striatum and hence offers a better trade-off for sensitivity and spatial resolution than the conventional collimators within this clinically most relevant region for DAT imaging. Our original MPH design consisted of 9 pinholes with a background-to-striatal (Bkg/Str) projection multiplexing of 1% only. In this simulation study, we investigated whether further improvements in the performance of MPH imaging could be obtained by increasing the number of pinholes, hence by enhancing the sensitivity and sampling, despite the ambiguity in reconstructing images due to increased multiplexing. We performed analytic simulations of the MPH configurations with 9, 13, and 16 pinholes (aperture diameters: 4-6mm) using a digital phantom modeling DAT imaging. Our quantitative analyses indicated that using 13 (Bkg/Str: 12%) and 16 (Bkg/Str: 22%) pinholes provided better performance than the original 9-pinhole configuration for the acquisition with 2 or 4 angular views, but a similar performance with 8 and 16 views.

Inclusion of quasi-vertex views in a brain-dedicated multi-pinhole SPECT system for improved imaging performance

With brain-dedicated multi-detector systems employing pinhole apertures the usage of detectors facing the top of the patient's head (i.e. quasi-vertex (QV) views) can provide the advantage of additional viewing from close to the brain for improved detector coverage. In this paper, we report the results of simulation and reconstruction studies to investigate the impact of the QV views on the imaging performance of AdaptiSPECT-C, a brain-dedicated stationary SPECT system under development. In this design, both primary and scatter photons from regions located inferior to the brain can contribute to SPECT projections acquired by the QV views, and thus degrade AdaptiSPECT-C imaging performance. In this work, we determined the proportion, origin, and nature (i.e. primary, scatter, and multiple-scatter) of counts emitted from structures within the head and throughout the body contributing to projections from the different AdaptiSPECT-C detector rings, as well as from a true vertex view detector. We simulated phantoms used to assess different aspects of image quality (i.e. uniform activity concentration sphere, and Derenzo), as well as anthropomorphic phantoms with different count levels emulating clinical ¹²³I activity distributions (i.e. DaTscan and perfusion). We determined that attenuation and scatter in the patient's body greatly diminish the probability of the photons emitted outside the volume of interest reaching to detectors and being recorded within the 15% photopeak energy window. In addition, we demonstrated that the inclusion of the residual of such counts in the system acquisition does not degrade visual interpretation or quantitative analysis. The addition of the QV detectors improves volumetric sensitivity, angular sampling, and spatial resolution leading to significant enhancement in image quality, especially in the striato-thalamic and superior regions of the brain. Besides, the use of QV detectors improves the recovery of clinically relevant metrics such as the striatal binding ratio and mean activity in selected cerebral structures. Our findings proving the usefulness of the QV ring for brain imaging with ¹²³I agents can be generalized to other commonly used SPECT imaging agents labelled with isotopes, such as ^99mTc and likely ¹¹¹In.

System geometry optimization for molecular breast tomosynthesis with focusing multi-pinhole collimators

Imaging of ^99mTc-labelled tracers is gaining popularity for detecting breast tumours. Recently, we proposed a novel design for molecular breast tomosynthesis (MBT) based on two sliding focusing multi-pinhole collimators that scan a modestly compressed breast. Simulation studies indicate that MBT has the potential to improve the tumour-to-background contrast-to-noise ratio significantly over state-of-the-art planar molecular breast imaging. The aim of the present paper is to optimize the collimator-detector geometry of MBT. Using analytical models, we first optimized sensitivity at different fixed system resolutions (ranging from 5 to 12 mm) by tuning the pinhole diameters and the distance between breast and detector for a whole series of automatically generated multi-pinhole designs. We evaluated both MBT with a conventional continuous crystal detector with 3.2 mm intrinsic resolution and with a pixelated detector with 1.6 mm pixels. Subsequently, full system simulations of a breast phantom containing several lesions were performed for the optimized geometry at each system resolution for both types of detector. From these simulations, we found that tumour-to-background contrast-to-noise ratio was highest for systems in the 7 mm-10 mm system resolution range over which it hardly varied. No significant differences between the two detector types were found.

Design of a Tri-PET collimator for high-resolution whole-body mouse imaging

PURPOSE

Tri-PET refers to high-resolution 511-keV emission tomography using a multipinhole collimator in conjunction with lower resolution PET detectors operating in coincidence mode. Tri-PET is unique in that three spatial locations are associated with each event (two detector coordinates and one pinhole location). Spatial resolution and sensitivity are similar to that of 511-keV SPECT and are governed mainly by the collimator design. However because of a third spatial location in Tri-PET, the line-of-response is overdetermined. This feature permits new opportunities in data processing which impact collimator design. In particular, multiplexing can be avoided since the coincidence data identify the pinhole through which the photon passed. In this paper, the principles of Tri-PET collimator design are reviewed and then applied to the case of high-resolution imaging of a small animal in a clinical PET scanner.

METHODS

The design of a 148-pinhole collimator for whole-body imaging of a mouse is presented. Two pinhole designs were investigated: knife-edge pinholes with 1.1 mm aperture and novel hyperboloidal pinholes with 1.2 mm aperture, both having 18° cone angle. The pinhole configuration is unfocused, covering a whole-body mouse field of view with nearly uniform sensitivity. Computer simulations were performed of a micro hot rods phantom imaged with this collimator in a clinical PET scanner. Sensitivity was estimated by simulating a point source centered on-axis at locations spanning a 70-mm axial range, similar to the NEMA NU-4 standard for whole-body mouse imaging.

RESULTS

Reconstructed images of the hot rods phantom demonstrated the ability to resolve 1.1 mm structures with the knife-edge pinholes and 1.0 mm structures with the hyperboloidal pinholes. Sensitivity was found to be 0.093% and 0.054% for the knife-edge and hyperboloidal pinholes, respectively.

CONCLUSIONS

With a properly designed multipinhole collimator, high-resolution and acceptable sensitivity are achievable with Tri-PET using ordinary clinical PET detectors.

Analytically based photon scatter modeling for a multipinhole cardiac SPECT camera

PURPOSE

Dedicated cardiac SPECT scanners have improved performance over standard gamma cameras allowing reductions in acquisition times and/or injected activity. One approach to improving performance has been to use pinhole collimators, but this can cause position-dependent variations in attenuation, sensitivity, and spatial resolution. CT attenuation correction (AC) and an accurate system model can compensate for many of these effects; however, scatter correction (SC) remains an outstanding issue. In addition, in cameras using cadmium-zinc-telluride-based detectors, a large portion of unscattered photons is detected with reduced energy (low-energy tail). Consequently, application of energy-based SC approaches in these cameras leads to a higher increase in noise than with standard cameras due to the subtraction of true counts detected in the low-energy tail. Model-based approaches with parallel-hole collimator systems accurately calculate scatter based on the physics of photon interactions in the patient and camera and generate lower-noise estimates of scatter than energy-based SC. In this study, the accuracy of a model-based SC method was assessed using physical phantom studies on the GE-Discovery NM530c and its performance was compared to a dual energy window (DEW)-SC method.

METHODS

The analytical photon distribution (APD) method was used to calculate the distribution of probabilities that emitted photons will scatter in the surrounding scattering medium and be subsequently detected. APD scatter calculations for ^99mTc-SPECT (140 ± 14 keV) were validated with point-source measurements and 15 anthropomorphic cardiac-torso phantom experiments and varying levels of extra-cardiac activity causing scatter inside the heart. The activity inserted into the myocardial compartment of the phantom was first measured using a dose calibrator. CT images were acquired on an Infinia Hawkeye (GE Healthcare) SPECT/CT and coregistered with emission data for AC. For comparison, DEW scatter projections (120 ± 6 keV ) were also extracted from the acquired list-mode SPECT data. Either APD or DEW scatter projections were subtracted from corresponding 140 keV measured projections and then reconstructed with AC (APD-SC and DEW-SC). Quantitative accuracy of the activity measured in the heart for the APD-SC and DEW-SC images was assessed against dose calibrator measurements. The difference between modeled and acquired projections was measured as the root-mean-squared-error (RMSE). APD-modeled projections for a clinical cardiac study were also evaluated.

RESULTS

APD-modeled projections showed good agreement with SPECT measurements and had reduced noise compared to DEW scatter estimates. APD-SC reduced mean error in activity measurement compared to DEW-SC in images and the reduction was statistically significant where the scatter fraction (SF) was large (mean SF = 28.5%, T-test p = 0.007). APD-SC reduced measurement uncertainties as well; however, the difference was not found to be statistically significant (F-test p > 0.5). RMSE comparisons showed that elevated levels of scatter did not significantly contribute to a change in RMSE (p > 0.2).

CONCLUSIONS

Model-based APD scatter estimation is feasible for dedicated cardiac SPECT scanners with pinhole collimators. APD-SC images performed better than DEW-SC images and improved the accuracy of activity measurement in high-scatter scenarios.

Development and Evaluation of Image Reconstruction Algorithms for a Novel Desktop SPECT System

OBJECTIVE S

Various iterative reconstruction algorithms in nuclear medicine have been introduced in the last three decades. For each new imaging system, it is wise to select appropriate image reconstruction algorithms and evaluate their performance. In this study, three approaches of image reconstruction were developed for a novel desktop open-gantry SPECT system, PERSPECT, to assess their performance in terms of the quality of the resultant reconstructed images.

METHODS

In the present work, a proposed image reconstruction algorithm for the PERSPECT, referred to as quasi-simultaneous multiplicative algebraic reconstruction technique (qSMART), together with two popular image reconstruction methods, maximum-likelihood expectation-maximization (MLEM) and ordered-subsets EM (OSEM), were implemented and compared. Analytic and Monte Carlo simulations were applied for data acquisition of various phantoms including a micro-Derenzo phantom. All acquired data were reconstructed by the three algorithms using different number of iterations (1-40 ). A thorough set of figures-of-merit was utilized to quantitatively compare the generated images.

RESULTS

OSEM depicted reconstructed images of higher (or matching) quality in comparison to qSMART. MLEM also reached nearly similar quality as OSEM but at higher number of iterations. The graph of data discrepancy revealed that the ranking of the three approaches in terms of convergence speed is as qSMART, OSEM, and MLEM. Furthermore, bias-versus-noise curves indicated that optimal bias-noise results were achieved using OSEM.

CONCLUSION

The results showed that although qSMART can be applied for image reconstruction if being halted in the early iterations (up to 5), the best achievable quality of images is obtained using the OSEM.

Simulation study of a novel target oriented SPECT design using a variable pinhole collimator

PURPOSE

In the past decade, demands for organ specific (target oriented) single-photon emission computed tomography (SPECT) is increasing, and several groups have conducted studies on developing clinical dedicated SPECT with pinhole collimator to improve the spatial resolution. However, acceptance angle of the collimator cannot be adjusted to fit the different ROIs of target objects because the shape of pinhole could not be changed, and the magnifying factor cannot be maximized as the collimator-to-detector distance is fixed. Furthermore, those dedicated pinhole SPECTs are typically made for a single purpose and therefore possess a drawback in that it cannot be utilized for any other purpose. In this study, we propose a novel SPECT system using variable pinhole collimator (VP SPECT) whose parameters are flexible.

METHODS

The proposed variable pinhole collimator is modeled on conventional pinhole by piling several tungsten layers of different apertures. Depending on the combination of the holes in each layer, a variety of hole diameters and acceptance angles of the pinhole can be made. In addition, VP SPECT system allows attaching the collimator to the object as close as possible to maximize the sensitivity and adjust the distance of the pinhole from the scintillation detector to optimize the system resolution for each rotation angle, automatically. For quantitative measurement, we compared the sensitivity and spatial resolution of VP SPECT with those of conventional pinhole SPECT. To determine the possibility of the clinical and preclinical use of proposed system, a digital mouse whole-body (MOBY) phantom is used for simulating the live mouse model.

RESULTS

The result of simulation using ultra-micro hot spot phantom shows that the sensitivity of the proposed VP SPECT system is about 297% of that of the conventional system. While hot rods of diameter 0.6 mm can be distinguished in the image with the proposed VP SPECT system, 1.2-mm hot rods are barely discernible in the conventional pinhole SPECT image. According to the result of MOBY phantom simulation, heart walls separated by 3 mm were not distinguished in conventional pinhole SPECT images, but were clearly discerned in VP SPECT images.

CONCLUSIONS

In this study, we designed a novel pinhole collimator for SPECT and presented preliminary results of target oriented imaging with a simulation study. Currently, we are pursuing strategies to realize the proposed system, with the goal to apply the technology into a high-sensitivity and high-resolution preclinical SPECT. Should VP SPECT be applied to the clinical setting, we anticipate a high-sensitivity, high-resolution system for applications such as heart dedicated SPECT or related fields.

Design of a dual-resolution collimator for preclinical cardiac SPECT with a stationary triple-detector system

PURPOSE

One approach to preclinical single-photon emission computed tomography (SPECT) imaging that provides both high resolution and high sensitivity is based on imaging a mouse inside a collimating tube; many magnified pinhole projection images from a small target region, e.g., the heart, can be recorded simultaneously on multiple detectors with little multiplexing since each pinhole aperture's opening angle is restricted to view mostly the target organ. However, to obtain complete data for reconstruction, it may be necessary to scan the mouse through the target region of the tube. The authors are developing a different approach based on acquisition and reconstruction of both low-resolution and high-resolution projection data acquired sequentially through many pinholes embedded in two tungsten tube sections of different diameters, a "scout" section and a high-resolution section, placed end-to-end along the axis of a triple-head clinical SPECT scanner. This paper describes the design procedures used to determine the geometric parameters of two new collimator-tube sections, as well as one approach for joint reconstruction of data acquired from both sections.

METHODS

The high-resolution section was designed by projecting as many pinhole views of a simulated mouse heart as possible over each detector's camera, with no overlapping of heart projections and minimal overlapping between adjacent "hot" organ and cardiac projections. The authors then jointly optimized the geometric design of the scout section for a triple-detector camera system, as well as the number of maximum-likelihood expectation maximization (MLEM) iterations required to provide minimum mean-squared error of reconstructed voxel counts throughout a 7-cm axial range, with the constraints of fixed, 2.4-mm scout system resolution at the tube center for all apertures, limited multiplexing, and no detector motion. Simulated mouse projection data from both tube sections were then reconstructed to illustrate a simple approach for using high-resolution data to improve the whole-body scout images within a cylindrical region surrounding the heart.

RESULTS

The 2-cm-inner-radius high-resolution tube section accommodated 87 platinum-iridium pinhole inserts, each with a 0.3-mm square aperture; their radial distances from the centerline of the system ranged from 2.2 to 3.0 cm. The optimal radial distance to the closest scout pinhole and optimal number of MLEM iterations were 4.4 cm and 35 iterations, respectively, and the radial distances of the 39 scout pinholes ranged from 4.4 to 4.8 cm; aperture sizes ranged from 1.1 to 1.7 mm transaxially and 0.9-1.5 mm axially. After including data from the high-resolution section viewing the heart region into whole-body mouse reconstructions from scout data, the authors obtained high-resolution images of the heart, embedded within lower resolution images of the body, with minimal artifacts.

CONCLUSIONS

The authors have optimized a dual-resolution collimator tube that provides both whole-body projections of a mouse and more targeted projections centered on the heart that can be jointly reconstructed to obtain high-resolution images of the heart embedded within lower-resolution whole-body images.

Investigation of imaging properties for submillimeter rectangular pinholes

PURPOSE

Recently, a multipinhole collimator with inserts that have both rectangular apertures and rectangular fields of view (FOVs) has been proposed for SPECT imaging since it can tile the projection onto the detector efficiently and the FOVs in transverse and axial directions become separable. The purpose of this study is to investigate the image properties of rectangular-aperture pinholes with submillimeter apertures sizes.

METHODS

In this work, the authors have conducted sensitivity and FOV experiments for 18 replicates of a prototype insert fabricated in platinum/iridium (Pt/Ir) alloy with submillimeter square-apertures. A sin(q)θ fit to the experimental sensitivity has been performed for these inserts. For the FOV measurement, the authors have proposed a new formula to calculate the projection intensity of a flood image on the detector, taking into account the penumbra effect. By fitting this formula to the measured projection data, the authors obtained the acceptance angles.

RESULTS

The mean (standard deviation) of fitted sensitivity exponents q and effective edge lengths we were, respectively, 10.8 (1.8) and 0.38 mm (0.02 mm), which were close to the values, 7.84 and 0.396 mm, obtained from Monte Carlo calculations using the parameters of the designed inserts. For the FOV measurement, the mean (standard deviation) of the transverse and axial acceptances were 35.0° (1.2°) and 30.5° (1.6°), which are in good agreement with the designed values (34.3° and 29.9°).

CONCLUSIONS

These results showed that the physical properties of the fabricated inserts with submillimeter aperture size matched our design well.

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.

Improved image quality in pinhole SPECT by accurate modeling of the point spread function in low magnification systems

PURPOSE

Single photon emission computed tomography (SPECT) has become an important noninvasive imaging technique in small-animal research. Due to the high resolution required in small-animal SPECT systems, the spatially variant system response needs to be included in the reconstruction algorithm. Accurate modeling of the system response should result in a major improvement in the quality of reconstructed images. The aim of this study was to quantitatively assess the impact that an accurate modeling of spatially variant collimator/detector response has on image-quality parameters, using a low magnification SPECT system equipped with a pinhole collimator and a small gamma camera.

METHODS

Three methods were used to model the point spread function (PSF). For the first, only the geometrical pinhole aperture was included in the PSF. For the second, the septal penetration through the pinhole collimator was added. In the third method, the measured intrinsic detector response was incorporated. Tomographic spatial resolution was evaluated and contrast, recovery coefficients, contrast-to-noise ratio, and noise were quantified using a custom-built NEMA NU 4-2008 image-quality phantom.

RESULTS

A high correlation was found between the experimental data corresponding to intrinsic detector response and the fitted values obtained by means of an asymmetric Gaussian distribution. For all PSF models, resolution improved as the distance from the point source to the center of the field of view increased and when the acquisition radius diminished. An improvement of resolution was observed after a minimum of five iterations when the PSF modeling included more corrections. Contrast, recovery coefficients, and contrast-to-noise ratio were better for the same level of noise in the image when more accurate models were included. Ring-type artifacts were observed when the number of iterations exceeded 12.

CONCLUSIONS

Accurate modeling of the PSF improves resolution, contrast, and recovery coefficients in the reconstructed images. To avoid the appearance of ring-type artifacts, the number of iterations should be limited. In low magnification systems, the intrinsic detector PSF plays a major role in improvement of the image-quality parameters.

The evaluation of data completeness and image quality in multiplexing multi-pinhole SPECT

Multi-pinhole collimators are often used in pre-clinical SPECT systems because they have a better resolution-sensitivity tradeoff than parallel hole collimators when imaging small objects. Most multi-pinhole collimators are designed to allow no or only a limited amount of overlap between the different pinhole projections because the ambiguity introduced by multiplexing pinholes can result in artifacts. The origin of these artifacts is still not fully understood, but previous research has already shown that data incompleteness could be part of the explanation. Therefore, we developed a method to investigate data completeness in multiplexing multi-pinhole systems and showed that a certain activity distribution can be successfully reconstructed when the nonmultiplexed data is complete or when the overlap can be sufficiently de-multiplexed. We validated this method using computer simulated phantom data of different multiplexing systems. We also studied contrast-to-noise and nonprewhitening matched filter signal-to-noise ratio (NPW-SNR) to compare the image quality in a single pinhole system with multiplexing systems. We found that our method can indeed be used to evaluate data completeness in multiplexing systems and found no artifacts in the systems that had complete data. Sensitivity increased significantly with multiplexing but we found only small, nonsignificant differences in contrast-to-noise ratio. However, the NPW-SNR did slightly improve in the multiplexing setups. We conclude that more multiplexing does not necessarily result in more artifacts and that even a high amount of multiplexing can still result in artifact-free images if the nonmultiplexed data is complete or when the overlap can be sufficiently de-multiplexed.

Advances in pinhole and multi-pinhole collimators for single photon emission computed tomography imaging

The collimator in single photon emission computed tomography (SPECT), is an important part of the imaging chain. One of the most important collimators that used in research, preclinical study, small animal, and organ imaging is the pinhole collimator. Pinhole collimator can improve the tradeoff between sensitivity and resolution in comparison with conventional parallel-hole collimator and facilities diagnosis. However, a major problem with pinhole collimator is a small field of view (FOV). Multi-pinhole collimator has been investigated in order to increase the sensitivity and FOV with a preserved spatial resolution. The geometry of pinhole and multi-pinhole collimators is a critical factor in the image quality and plays a key role in SPECT imaging. The issue of the material and geometry for pinhole and multi-pinhole collimators have been a controversial and much disputed subject within the field of SPECT imaging. On the other hand, recent developments in collimator optimization have heightened the need for appropriate reconstruction algorithms for pinhole SPECT imaging. Therefore, iterative reconstruction algorithms were introduced to minimize the undesirable effect on image quality. Current researches have focused on geometry and configuration of pinhole and multi-pinhole collimation rather than reconstruction algorithm. The lofthole and multi-lofthole collimator are samples of novel designs. The purpose of this paper is to provide a review on recent researches in the pinhole and multi-pinhole collimators for SPECT imaging.

Design and performance of a compact and stationary microSPECT system

PURPOSE

Over the last ten years, there has been an extensive growth in the development of microSPECT imagers. Most of the systems are based on the combination of conventional, relatively large gamma cameras with poor intrinsic spatial resolution and multipinhole collimators working in large magnification mode. Spatial resolutions range from 0.58 to 0.76 mm while peak sensitivities vary from 0.06% to 0.4%. While pushing the limits of performance is of major importance, the authors believe that there is a need for smaller and less complex systems that bring along a reduced cost. While low footprint and low-cost systems can make microSPECT available to more researchers, the ease of operation and calibration and low maintenance cost are additional factors that can facilitate the use of microSPECT in molecular imaging. In this paper, the authors simulate the performance of a microSPECT imager that combines high space-bandwidth detectors and pinholes with truncated projection, resulting in a small and stationary system.

METHODS

A system optimization algorithm is used to determine the optimal SPECT systems, given our high resolutions detectors and a fixed field-of-view. These optimal system geometries are then used to simulate a Defrise disk phantom and a hot rod phantom. Finally, a MOBY mouse phantom, with realistic concentrations of Tc99m-tetrofosmin is simulated.

RESULTS

Results show that the authors can successfully reconstruct a Defrise disk phantom of 24 mm in diameter without any rotating system components or translation of the object. Reconstructed spatial resolution is approximately 800 μm while the peak sensitivity is 0.23%. Finally, the simulation of the MOBY mouse phantom shows that the authors can accurately reconstruct mouse images.

CONCLUSIONS

These results show that pinholes with truncated projections can be used in small magnification or minification mode to obtain a compact and stationary microSPECT system. The authors showed that they can reach state-of-the-art system performance and can successfully reconstruct images with realistic noise levels in a preclinical context. Such a system can be useful for dynamic SPECT imaging.

Onboard functional and molecular imaging: a design investigation for robotic multipinhole SPECT

PURPOSE

Onboard imaging-currently performed primarily by x-ray transmission modalities-is essential in modern radiation therapy. As radiation therapy moves toward personalized medicine, molecular imaging, which views individual gene expression, may also be important onboard. Nuclear medicine methods, such as single photon emission computed tomography (SPECT), are premier modalities for molecular imaging. The purpose of this study is to investigate a robotic multipinhole approach to onboard SPECT.

METHODS

Computer-aided design (CAD) studies were performed to assess the feasibility of maneuvering a robotic SPECT system about a patient in position for radiation therapy. In order to obtain fast, high-quality SPECT images, a 49-pinhole SPECT camera was designed which provides high sensitivity to photons emitted from an imaging region of interest. This multipinhole system was investigated by computer-simulation studies. Seventeen hot spots 10 and 7 mm in diameter were placed in the breast region of a supine female phantom. Hot spot activity concentration was six times that of background. For the 49-pinhole camera and a reference, more conventional, broad field-of-view (FOV) SPECT system, projection data were computer simulated for 4-min scans and SPECT images were reconstructed. Hot-spot localization was evaluated using a nonprewhitening forced-choice numerical observer.

RESULTS

The CAD simulation studies found that robots could maneuver SPECT cameras about patients in position for radiation therapy. In the imaging studies, most hot spots were apparent in the 49-pinhole images. Average localization errors for 10-mm- and 7-mm-diameter hot spots were 0.4 and 1.7 mm, respectively, for the 49-pinhole system, and 3.1 and 5.7 mm, respectively, for the reference broad-FOV system.

CONCLUSIONS

A robot could maneuver a multipinhole SPECT system about a patient in position for radiation therapy. The system could provide onboard functional and molecular imaging with 4-min scan times.

Design and simulation of a full-ring multi-lofthole collimator for brain SPECT

Currently, clinical brain single photon emission computed tomography (SPECT) is mostly performed using rotating dual-head gamma cameras equipped with low-energy-high-resolution parallel-beam collimators (LEHR PAR). The resolution of these systems is rather poor (8-10 mm) and the rotation of the heavy gamma cameras can introduce misalignment errors. Therefore, we designed a static full-ring multi-lofthole brain SPECT insert for an existing ring of LaBr3 (5% Ce) detectors. The novelty of the design is found in the shutter mechanism that makes the system very flexible and eliminates the need for rotating parts. A stationary SPECT insert is not only more robust, it is also easier to integrate in a magnetic resonance imaging system (MRI) for simultaneous SPECT-MRI. The target spatial resolution of our design is 6 mm. In this study we used analytical calculations to optimize the collimator for an existing ring of LaBr3 (5% Ce) detectors. We fixed the target spatial resolution at 6 mm in the center of the field-of-view and maximized the volume sensitivity by changing the collimator radius, the aperture and the number of loftholes. Based on these optimal parameters we simulated phantom data and evaluated the image quality of our multi-lofthole system. We simulated a noiseless uniform and Defrise phantom to assess artifacts and sampling completeness and a noiseless hot-rod phantom to assess the reconstructed spatial resolution. We visually evaluated a simulated noisy Hoffman phantom with two lesions. Then, we evaluated the non-prewhitening matched filter signal-to-noise ratio (NPW-SNR) in two lesion detectability phantoms: one with hot lesions and one with cold lesions. Finally, a contrast-to-noise (CNR) study was performed on a phantom with both hot and cold lesions of different sizes (6-16 mm). All results were compared to a LEHR PAR system. The optimization resulted in a final collimator design with a volume sensitivity of 1.55 × 10(-4) cps Bq(-1), which is 2.5 times lower than the sensitivity of a dual-head system with LEHR PAR collimators. Spatial resolution, on the other hand, has clearly improved compared to LEHR PAR: with the multi-lofthole system we successfully reconstructed 4 mm hot rods. Although this improved resolution did not result in an unambiguous improvement in CNR or NPW-SNR, we believe that the flexibility of the shutter mechanism opens interesting perspectives toward time-multiplexing and integration with MRI.

A detector response function design in pinhole SPECT including geometrical calibration

Clinical single photon emission computed tomography (SPECT) equipped with pinhole collimators have a magnification factor that results in high spatial resolution images for small animal imaging. Using Monte Carlo simulations to model the acquisition process and the propagation of the photons from their point of emission to their detection point then integrating the model into an iterative reconstruction algorithm improves the signal-to-noise ratio, the contrast and the spatial resolution in the reconstructed images. However, pinhole SPECT systems are known to be very sensitive to geometrical misalignments. Geometrical misalignments are defined as the radial or axial shift of the collimator pinhole and/or twist and tilt of the detector heads and are introduced in the system each time the collimation device is changed (pinhole to parallel holes or vice versa). In this work, we present a flexible detector response function table (DRFT) design that takes into account the geometrical misalignments and avoids performing new Monte Carlo simulations for each exam in order to calculate a geometrical study-dependent system matrix. The utilization of the DRFT for the calculation of the system matrix speeds up its computation time by two orders of magnitude making it acceptable for preclinical and clinical applications.

Improvement of Performance of Cardiac SPECT Camera Using Curved Detectors With Pinholes

SPECT is primarily used in the clinic for cardiac myocardial perfusion imaging. However, for SPECT, sensitivity is impaired due to the need for collimation. System resolution FWHM is poor as well (~ 1 cm). In this work the resolution of a curved detector was theoretically derived. The advantage of a curved detector over a flat detector with pinhole collimation was demonstrated for cardiac applications using theoretical derivations as well as a ray-tracing voxel-based forward projector. For the flat detector using parameters close to what was expected for the new multi-pinhole GE Discovery system, it is shown that using a paraboloid detector one may obtain a better system resolution (about 29% better on the average), keeping same pinhole opening. Alternately, sensitivity gains of as much as 2.25 may be obtained, for similar resolutions as a flat detector by just using a different pinhole with higher hole-diameter.

Comparison of pinhole collimator materials based on sensitivity equivalence

Pinhole SPECT often provides an excellent resolution sensitivity trade-off for radionuclide imaging compared to SPECT with parallel holes, particularly when imaging small experimental animals like rodents. High absorption pinhole materials are often chosen because of their low edge penetration and therefore good system resolution. Capturing more photons in the edges however results in decreased system sensitivity if the pinhole diameter remains the same, which may partly undo the beneficial effect on the resolution. In the search for an optimal trade-off we have compared pinhole projection data and reconstructed images of different materials with pinhole aperture diameters adjusted to obtain equal sensitivity. Monte Carlo calculations modeling the transmission, penetration and scattering of gamma radiation in single pinholes of uranium, gold, tungsten and lead were performed for a range of pinhole opening angles, diameters and gamma ray energies. In addition, reconstructed images of a hot rod phantom were determined for a multipinhole SPECT system and for a system that can image the 511 keV annihilation photons of positron emitting tracers with clustered pinholes. Our results indicate that, under the condition of equal sensitivity, tungsten and for SPECT also lead pinholes perform just as well as gold and uranium ones, indicating that a significant cost reduction can be achieved in pinhole collimator manufacturing while the use of rare or impractical materials can be avoided.

Assessing antibody pharmacokinetics in mice with in vivo imaging

Recent advances in small-animal molecular imaging instrumentation combined with well characterized antibody-labeling chemistry have enabled detailed in vivo measurements of antibody distribution in mouse models. This article reviews the strengths and limitations of in vivo antibody imaging methods with a focus on positron emission tomography and single-photon emission computed tomography and a brief discussion of the role of optical imaging in this application. A description of the basic principles behind the imaging techniques is provided along with a discussion of radiolabeling methods relevant to antibodies. Practical considerations of study design and execution are presented through a discussion of sensitivity and resolution tradeoffs for these techniques as defined by modality, signaling probe (isotope or fluorophore) selection, labeling method, and radiation dosimetry. Images and analysis results from a case study are presented with a discussion of output data content and relevant informatics gained with this approach to studying antibody pharmacokinetics.

New principles in nuclear medicine imaging: a full aperture stereoscopic imaging technique

In nuclear medicine, images of planar scintigraphy and single photon emission computerized tomography (SPECT) obtained through gamma camera (GC) appear to be blurred. Alternatively, coded aperture imaging (CAI) can surpass the quality of GC images, but still it is not extensively used due to the decoding complexity of some images and the difficulty in controlling the noise. Summing up, the images obtained through GC are low quality and it is still difficult to implement CAI technique. Here we present a full aperture imaging (FAI) technique which overcomes the problems of CAI ordinary systems. The gamma radiation transmitted through a large single aperture is edge-encoded, taking advantage of the fact that nuclear radiation is spatially incoherent. The novel technique is tested by means of Monte Carlo method with simple and complex sources. Spatial resolution tests and parallax tests of GC versus FAI were made, and three-dimensional capacities of GC versus FAI were analyzed. Simulations have allowed comparison of both techniques under ideal, identical conditions. The results show that FAI technique has greater sensitivity (approximately 100 times) and greater spatial resolution (>2.6 times at 40 cm source-detector distance) than that of GC. FAI technique allows to obtain images with typical resolution of GC short source-detector distance but at longer source-detector distance. The FAI decoding algorithm simultaneously reconstructs four different projections, while GC produces only one projection per acquisition. Our results show it is possible to apply an extremely simple encoded imaging technique, and get three-dimensional radioactivity information. Thus GC-based systems could be substituted, given that FAI technique is simple and it produces four images which may feed stereoscopic systems, substituting in some cases, tomographic reconstructions.

Theoretical bounds and system design for multipinhole SPECT

The pinhole camera in single photon emission computed tomography (SPECT) has an inherent trade-off between resolution and sensitivity. Recent systems overcome this to some extent by utilizing multiple pinholes distributed around the imaging object. The present work is a theoretical study on how to optimally construct such systems. We use an analytic model to analyze the multipinhole SPECT geometry and identify the underlying trade-offs. One of the results is the derivation of the upper bound for the sensitivity, given the geometric resolution and field-of-view (FOV). Reaching this bound requires an infinitely large detector. However, a sensitivity very close to the upper bound can be achieved by a system with realistic proportions. We show that it is usually possible to get a sensitivity that is 95%-99% of the upper bound. Further analysis reveals a trade-off between sensitivity, magnification, and the number of pinholes. Based on this new theory, we develop a strategy for multipinhole SPECT design, from which a number of example systems are computed. Penetration in the pinhole knife edge is accounted for by using the resolution and sensitivity equivalent apertures.

Theoretical analysis of full-ring multi-pinhole brain SPECT

Presently used clinical brain SPECT suffers from limited spatio-temporal resolution. Here we investigate the feasibility of high-resolution and high-sensitivity full-ring multi-pinhole brain SPECT (MP-SPECT). Using an analytical model we optimized pinhole-detector geometries of MP-SPECT for different detector intrinsic resolutions R(i). System resolution and sensitivity of optimized MP-SPECT were compared to conventional clinical SPECT. The comparison of the system resolution of different systems was done at matched sensitivity, which was achieved by tuning pinhole diameters. Similarly, sensitivities were compared at matched system resolution. For MP-SPECT that uses detectors with intrinsic resolutions of 4 mm > R(i) 0.5 mm a sensitivity can be achieved that is 6.0 times higher than the sensitivity of conventional dual-head SPECT systems with parallel-hole collimators (DualPar), while system resolution can be improved by a factor of 2.4. To achieve these improvements a large detector-to-collimator distance is needed. In contrast, for detectors with intrinsic resolutions <0.2 mm, it is beneficial to place the detectors close to the pinholes, resulting in a high number of de-magnified projections. For a detector intrinsic resolution of 0.05 mm, a 14.5-fold improvement in sensitivity and a 3.8-fold improvement in system resolution compared to DualPar is predicted. Furthermore, we found that for optimized MP-SPECT the sensitivity scales proportionally to system resolution squared, with the proportionality constant depending on R(i). From our sensitivity-system resolution trade-off equations we deduced that MP-SPECT with an ideal detector (R(i) --> 0) can have a system resolution that is 2.0 times better than optimized MP-SPECT with a conventional detector (R(i) approximately 3 mm). The high performance of optimized MP-SPECT may open up completely new molecular imaging applications.

Multidivergent-beam stationary cardiac SPECT

This article develops a stationary cardiac single photon emission computed tomography (SPECT) system using a novel multidivergent-beam collimator. This stationary SPECT system is inexpensive to build, small, and able to acquire true dynamic SPECT data. Stationary cardiac SPECT systems with multipinhole technology already exist. The proposed approach is to replace the multipinhole collimators with the originally designed multidivergent-beam collimators. The motivation for replacing the pinhole technology by divergent-beam technology is based on the following facts. The resolution/sensitivity trade-off for the pinhole is excellent (good resolution and good sensitivity) only in small object (e.g., small animal) imaging when it operates in the image magnifying mode. However, in large object (e.g., human) imaging, the resolution/sensitivity trade-off is poor (poor resolution and poor sensitivity) when the pinhole operates in the image reducing mode. In a stationary system, the number of angular views is limited; thus, image reduction is necessary to obtain more view angles. In this image reducing situation, divergent-beam collimation is able to provide better resolution and detection sensitivity than pinhole collimation. Computer simulations are carried out to verified the claims.

Feasibility of whole-body functional mouse imaging using helical pinhole SPECT

PURPOSE

Detailed in vivo whole-body biodistributions of radiolabeled tracers may characterize the longitudinal progression of disease, and changes with therapeutic interventions. Small-animal imaging in mice is particularly attractive due to the wide array of well characterized genetically and surgically created models of disease. Single Photon Emission Computed Tomography (SPECT) imaging using pinhole collimation provides high resolution and sensitivity, but conventional methods using circular acquisitions result in severe image truncation and incomplete sampling of data, which prevent the accurate determination of whole-body radiotracer biodistributions. This study describes the feasibility of helical acquisition paths to mitigate these effects.

PROCEDURES

Helical paths of pinhole apertures were implemented using an external robotic stage aligned with the axis of rotation (AOR) of the scanner. Phantom and mouse scans were performed using helical paths and either circular or bi-circular orbits at the same radius of rotation (ROR). The bi-circular orbits consisted of two 360-degree scans separated by an axial shift to increase the axial field of view (FOV) and to improve the complete-sampling properties.

RESULTS

Reconstructions of phantoms and mice acquired with helical paths show good image quality and are visually free of both truncation and axial-blurring artifacts. Circular orbits yielded reconstructions with both artifacts and a limited effective FOV. The bi-circular scans enlarged the axial FOV, but still suffered from truncation and sampling artifacts.

CONCLUSIONS

Helical paths can provide complete sampling data and large effective FOV, yielding 3D full-body in vivo biodistributions while still maintaining a small distance from the aperture to the object for good sensitivity and resolution.

A pinhole gamma camera with optical depth-of-interaction elimination

The performance of pinhole single photon emission computed tomography (SPECT) depends on the spatial resolution of the gamma-ray detectors used. Pinhole cameras suffer from strong resolution loss due to the varying depth-of-interaction (DOI) of gamma quanta that enter the detector material at an angle. We eliminate DOI effects in a scintillation gamma camera via a dedicated optic fiber bundle that acts as a focusing collimator for light generated in a scintillation crystal. A curved crystal is connected to a concavely shaped fiber-optic bundle such that the fibers connect perpendicularly to the crystal's convex surface and point straight at the pinhole opening. Limiting the fiber numerical apertures can be used to suppress resolution losses due to light spread. Here we demonstrate experimentally that this prototype position-sensitive gamma sensor successfully eliminates DOI effects, and has an intrinsic resolution of better than 280 microm full width at half maximum with an interaction probability of 67% for 140 keV photons. Therefore, the detector has great potential for increasing the resolution of pinhole SPECT.

Feasibility of whole-body functional mouse imaging using helical pinhole SPECT

PURPOSE

Detailed in vivo whole-body biodistributions of radiolabeled tracers may characterize the longitudinal progression of disease, and changes with therapeutic interventions. Small-animal imaging in mice is particularly attractive due to the wide array of well characterized genetically and surgically created models of disease. Single Photon Emission Computed Tomography (SPECT) imaging using pinhole collimation provides high resolution and sensitivity, but conventional methods using circular acquisitions result in severe image truncation and incomplete sampling of data, which prevent the accurate determination of whole-body radiotracer biodistributions. This study describes the feasibility of helical acquisition paths to mitigate these effects.

PROCEDURES

Helical paths of pinhole apertures were implemented using an external robotic stage aligned with the axis of rotation (AOR) of the scanner. Phantom and mouse scans were performed using helical paths and either circular or bi-circular orbits at the same radius of rotation (ROR). The bi-circular orbits consisted of two 360-degree scans separated by an axial shift to increase the axial field of view (FOV) and to improve the complete-sampling properties.

RESULTS

Reconstructions of phantoms and mice acquired with helical paths show good image quality and are visually free of both truncation and axial-blurring artifacts. Circular orbits yielded reconstructions with both artifacts and a limited effective FOV. The bi-circular scans enlarged the axial FOV, but still suffered from truncation and sampling artifacts.

CONCLUSIONS

Helical paths can provide complete sampling data and large effective FOV, yielding 3D full-body in vivo biodistributions while still maintaining a small distance from the aperture to the object for good sensitivity and resolution.

Multi-pinhole collimator design for small-object imaging with SiliSPECT: a high-resolution SPECT

We have designed a multi-pinhole collimator for a dual-headed, stationary SPECT system that incorporates high-resolution silicon double-sided strip detectors. The compact camera design of our system enables imaging at source-collimator distances between 20 and 30 mm. Our analytical calculations show that using knife-edge pinholes with small-opening angles or cylindrically shaped pinholes in a focused, multi-pinhole configuration in combination with this camera geometry can generate narrow sensitivity profiles across the field of view that can be useful for imaging small objects at high sensitivity and resolution. The current prototype system uses two collimators each containing 127 cylindrically shaped pinholes that are focused toward a target volume. Our goal is imaging objects such as a mouse brain, which could find potential applications in molecular imaging.

Derivation and validation of a sensitivity formula for slit-slat collimation

An analytic formula is derived for the sensitivity of collimators achieving transverse collimation with a slit and axial collimation with a slat assembly whose septa may be parallel or focus on a line. The formula predicts sin(3) phi dependence on the incidence angle and, in the particular case of parallel slats, 1/h dependence on the distance from the slit. More complex expressions for sensitivity that do not diverge at points near the slit or the focal line of the slat assembly are also derived. The predictions of the formulas are checked against simple cases for which solutions are available from direct calculation as well as against Monte Carlo simulation and published experimental data. Agreement is good in all cases analyzed. An approximate penetration model is also introduced: it involves the use of a sensitivity-effective slit width and septal length. Its predictions are compared to simulation results. Agreement was found to be compatible with statistical fluctuation (+/- 0.3%) for geometric sensitivity and better than 3% of total sensitivity in the worst case of septa designed for high-energy (364.5 keV) photons.