Fully 3D Monte Carlo reconstruction in SPECT: a feasibility study

Future trends for patient-specific dosimetry methodology in molecular radiotherapy

Molecular radiotherapy is rapidly expanding, and new radiotherapeutics are emerging. The majority of treatments is still performed using empirical fixed activities and not tailored for individual patients. Molecular radiotherapy dosimetry is often seen as a promising candidate that would allow personalisation of treatments as outcome should ultimately depend on the absorbed doses delivered and not the activities administered. The field of molecular radiotherapy dosimetry has made considerable progress towards the feasibility of routine clinical dosimetry with reasonably accurate absorbed-dose estimates for a range of molecular radiotherapy dosimetry applications. A range of challenges remain with respect to the accurate quantification, assessment of time-integrated activity and absorbed dose estimation. In this review, we summarise a range of technological and methodological advancements, mainly focussed on beta-emitting molecular radiotherapeutics, that aim to improve molecular radiotherapy dosimetry to achieve accurate, reproducible, and streamlined dosimetry. We describe how these new technologies can potentially improve the often time-consuming considered process of dosimetry and provide suggestions as to what further developments might be required.

Monte Carlo methods for device simulations in radiation therapy

Monte Carlo (MC) simulations play an important role in radiotherapy, especially as a method to evaluate physical properties that are either impossible or difficult to measure. For example, MC simulations (MCSs) are used to aid in the design of radiotherapy devices or to understand their properties. The aim of this article is to review the MC method for device simulations in radiation therapy. After a brief history of the MC method and popular codes in medical physics, we review applications of the MC method to model treatment heads for neutral and charged particle radiation therapy as well as specific in-room devices for imaging and therapy purposes. We conclude by discussing the impact that MCSs had in this field and the role of MC in future device design.

Advances in multimodal data fusion in neuroimaging: Overview, challenges, and novel orientation

Multimodal fusion in neuroimaging combines data from multiple imaging modalities to overcome the fundamental limitations of individual modalities. Neuroimaging fusion can achieve higher temporal and spatial resolution, enhance contrast, correct imaging distortions, and bridge physiological and cognitive information. In this study, we analyzed over 450 references from PubMed, Google Scholar, IEEE, ScienceDirect, Web of Science, and various sources published from 1978 to 2020. We provide a review that encompasses (1) an overview of current challenges in multimodal fusion (2) the current medical applications of fusion for specific neurological diseases, (3) strengths and limitations of available imaging modalities, (4) fundamental fusion rules, (5) fusion quality assessment methods, and (6) the applications of fusion for atlas-based segmentation and quantification. Overall, multimodal fusion shows significant benefits in clinical diagnosis and neuroscience research. Widespread education and further research amongst engineers, researchers and clinicians will benefit the field of multimodal neuroimaging.

Joint Optimization of Collimator and Reconstruction Parameters in X-Ray Fluorescence Computed Tomography Using Analytical Point Spread Function and Model Observer

OBJECTIVE

To jointly optimize collimator design and image reconstruction algorithm in X-ray Fluorescence Computed Tomography (XFCT) for imaging low concentrations of high atomic number (Z) elements in small animal models.

METHODS

Single pinhole (SPH) collimator and three types of multi-pinhole (MPH) collimators were evaluated. MPH collimators with 5, 7, and 9 pinholes using lead, stainless steel and brass were considered. A digital cylindrical phantom (0.5 mm3 voxels) of 25 mm diameter and 25 mm height with a central 5 mm diameter and 12.5 mm height cylindrical insert containing gold nanoparticles (2:1 insert: background concentration) was modeled. A 125 kVp, 2 mm Sn filtered x-ray spectrum (0.5 cGy/projection) for gold K-shell XFCT was considered. System matrices were implemented using analytical point spread functions (PSF) for each pinhole collimator. Poisson noise was added to the projection data (16 equiangular views) before image reconstruction using Maximum-Likelihood Expectation-Maximization (ML-EM) algorithm. Signal-present and signal-absent images were generated for the detection task performed by a channelized Hotelling observer (CHO) with 10 Dense Difference-of-Gaussian channels. The area under the curve (AUC) in receiver operating characteristic was used as the image quality metric.

RESULTS

A stainless steel focusing type MPH with 7 pinholes and 20 iterations of ML-EM provided the highest AUC.

CONCLUSION

MPH collimators outperformed SPH collimators for XFCT and consistently high AUCs were observed with focusing type MPH designs with 7 pinholes.

SIGNIFICANCE

The combinations of collimator design and image reconstruction parameters that maximized AUC were identified, which could improve the performance of XFCT.

Image reconstruction using multi-energy system matrices with a scintillator-based gamma camera for nuclear security applications

The system response of a gamma camera is dependent on the photon energy, thus the energy-dependent response function needs to be considered to improve the quality and fidelity of reconstructed images for identifying radionuclides in security applications. In this study, two reconstruction strategies using the maximum-likelihood expectation maximization (MLEM) algorithm with the multi-energy system matrices calculated by Monte Carlo simulations are proposed. The difference between the two is in data acquisition; one uses the sum of all events into a single projection image while the other sorts them into separate energy windows. Various radiation images of gamma-ray sources were simulated with a Monte Carlo code, and an actual image was acquired with a gamma camera. Both simulation and experiment results demonstrated the feasibility of the presented multi-energy reconstruction strategies in the detection of orphan sources.

Development and validation of a full model of a four-headed neuroimaging single-photon emission computed tomography scanner

Objective

The Nucline X-Ring 4R is a four-headed gamma camera dedicated to neuroimaging. In this paper, we describe and validate a GATE (Geant4 Application for Tomographic Emission) model of the Nucline X-Ring 4R.

Materials and methods

Images produced during model simulations were compared with those acquired experimentally to confirm the model was an accurate representation of the scanner. The most commonly reported measurements used to validate a GATE model include energy resolution, spatial resolution and sensitivity. In addition to the commonly reported static imaging measures, single-photon emission computed tomography (SPECT) spatial resolution was investigated to confirm that the model produces similar SPECT images to the experimental output.

Results

The experimental full-width at half-maximum was calculated to be 12.3 keV, which corresponds to an energy resolution of 8.8%. The simulated full-width at half-maximum was measured to be 12 keV, giving an energy resolution of 8.6%. The average spatial resolutions were found to be well matched (5.69 mm – simulated and 5.64 mm – experimental). However, the sensitivity was overestimated using the GATE model (47.8 and 54.3 cps/MBq) compared with the values obtained experimentally (42.7 and 44.3 cps/MBq). Finally, the simulated SPECT spatial resolution images were found to produce qualitatively comparable results.

Conclusion

The model developed has been shown to produce similar results and images to those obtained experimentally. This model has the potential to simulate patient scans with the aim of improving patient care by optimizing scanner protocols.

Monte Carlo-based SPECT reconstruction within the SIMIND framework

This paper presents the development and validation of a Monte Carlo-based singe photon emission computed tomography reconstruction program for parallel-hole collimation contained within the SIMIND Monte Carlo framework. The Monte Carlo code is used as an accurate forward-projector and is combined with a simplified back-projector to perform iterative tomographic reconstruction using the Maximum Likelihood Expectation Maximization and Ordered Subsets Expectation Maximization algorithms, together forming a program called SIMREC. The Monte Carlo simulation transforms the estimated source distribution directly from activity to counts in its projections. Hence, the reconstructed image is expressed in activity without reference to an external calibration. The program is tested using phantom measurements of spheres filled with ^99mTc, ¹⁷⁷Lu and ¹³¹I placed in air and centrally and peripherally in a water-filled elliptical phantom. The feasibility of applying the reconstruction to patients is also demonstrated for a range of radiopharmaceuticals. The deviation in total activity in the spheres ranged between  -4.1% and 6.2% compared with the activity determined when preparing the phantom. The SIMREC program was found to be accurate with respect to activity estimation and to reconstruct visually acceptable images within a few hours when applied to patient examples.

A comparison between GATE4 results and MCNP4B published data for internal radiation dosimetry

Aim: GATE, has been designed as upper layer of the GEANT4 toolkit for nuclear medicine application including internal dosimetry. However, its results have not been fully compared to the well-developed codes and anthropomorphic voxel phantoms have never been used with GATE/GEANT for internal dosimetry. The aim of present study was to compare the internal dose calculated by GATE/GEANT with the MCNP4B published data. Methods: The Zubal phantom was used to model a typical adult male. Activity was assumed uniformly distributed in liver, kidneys, lungs, spleen, pancreas and adrenals. GATE/ GEANT Monte Carlo package was used for estimation of doses in the phantom. Simulations were performed for photon energy of 0.01–1 MeV and mono-energetic electrons of 935 keV. Specific absorbed fractions for photons and S-factors for electrons were calculated. Results: On average, GATE/GEANT produces higher photon SAF (Specific Absorbed Fraction) values (+2.7%) for self-absorption and lower values (-2.9%) for cross-absorption. The difference was higher for paired organs particularly lungs. Moreover the photon SAF values for lungs as source organ at the energy of 200 and 500 keV was considerably higher with MCNP4B compared to GATE. Conclusion: Despite of differences between the GATE4 and MCNP4B, the results can be considered ensuring. This may be considered as validation of GATE/GEANT as a proprietary code in nuclear medicine for radionuclide dosimetry applications.

Monte Carlo-based quantitative pinhole SPECT reconstruction using a ray-tracing back-projector

Background

Monte Carlo simulations provide accurate models of nuclear medicine imaging systems as they can properly account for the full physics of photon transport. The accuracy of the model included in the maximum-likelihood–expectation-maximization (ML-EM) reconstruction limits the overall accuracy of the reconstruction results. In this paper, we present a Monte Carlo-based ML-EM reconstruction method for pinhole single-photon emission computed tomography (SPECT) that has been incorporated into the SIMIND Monte Carlo program. The Monte Carlo-based model, which accounts for all of the physical and geometrical characteristics of the camera system, is used in the forward-projection step of the reconstruction, while a simpler model based on ray-tracing is used for back-projection. The aim of this work was to investigate the quantitative accuracy of this combination of forward- and back-projectors in the clinical pinhole camera GE Discovery NM 530c.

Results

The total activity was estimated in ^99mTc-filled spheres with volumes between 0.5 and 16 mL. The total sphere activity was generally overestimated but remained within 10% of the reference activity defined by the phantom preparation. The recovered activity converged towards the reference activity as the number of iterations increased. Furthermore, the recovery of the activity concentrations within the physical boundaries of the spheres increased with increasing sphere volume. Additionally, the Monte Carlo-based reconstruction enabled recovery of the true activity concentration in the myocardium of a cardiac phantom mounted in a torso phantom regardless of whether the torso was empty or water-filled. A qualitative comparison to data reconstructed using the clinical reconstruction algorithm showed that the two methods performed similarly, although the images reconstructed using the clinical software were more uniform due to the incorporation of noise regularization and post-filtration in that reconstruction technique.

Conclusions

We developed a Monte Carlo-based reconstruction method for pinhole SPECT and evaluated it using phantom measurements. The combination of a Monte Carlo-based forward-projector and a simplified analytical ray-tracing back-projector produced quantitative images of acceptable image quality. No explicit calibration is necessary in this method since the forward-projector model maintains a relationship between the number of counts and activity.

Assessment of a fully 3D Monte Carlo reconstruction method for preclinical PET with iodine-124

Iodine-124 is a radionuclide well suited to the labeling of intact monoclonal antibodies. Yet, accurate quantification in preclinical imaging with I-124 is challenging due to the large positron range and a complex decay scheme including high-energy gammas. The aim of this work was to assess the quantitative performance of a fully 3D Monte Carlo (MC) reconstruction for preclinical I-124 PET. The high-resolution small animal PET Inveon (Siemens) was simulated using GATE 6.1. Three system matrices (SM) of different complexity were calculated in addition to a Siddon-based ray tracing approach for comparison purpose. Each system matrix accounted for a more or less complete description of the physics processes both in the scanned object and in the PET scanner. One homogeneous water phantom and three heterogeneous phantoms including water, lungs and bones were simulated, where hot and cold regions were used to assess activity recovery as well as the trade-off between contrast recovery and noise in different regions. The benefit of accounting for scatter, attenuation, positron range and spurious coincidences occurring in the object when calculating the system matrix used to reconstruct I-124 PET images was highlighted. We found that the use of an MC SM including a thorough modelling of the detector response and physical effects in a uniform water-equivalent phantom was efficient to get reasonable quantitative accuracy in homogeneous and heterogeneous phantoms. Modelling the phantom heterogeneities in the SM did not necessarily yield the most accurate estimate of the activity distribution, due to the high variance affecting many SM elements in the most sophisticated SM.

Assessment of a Monte-Carlo simulation of SPECT recordings from a new-generation heart-centric semiconductor camera: from point sources to human images

Geant4 application for tomographic emission (GATE), a Monte-Carlo simulation platform, has previously been used for optimizing tomoscintigraphic images recorded with scintillation Anger cameras but not with the new-generation heart-centric cadmium-zinc-telluride (CZT) cameras. Using the GATE platform, this study aimed at simulating the SPECT recordings from one of these new CZT cameras and to assess this simulation by direct comparison between simulated and actual recorded data, ranging from point sources to human images. Geometry and movement of detectors, as well as their respective energy responses, were modeled for the CZT 'D.SPECT' camera in the GATE platform. Both simulated and actual recorded data were obtained from: (1) point and linear sources of (99m)Tc for compared assessments of detection sensitivity and spatial resolution, (2) a cardiac insert filled with a (99m)Tc solution for compared assessments of contrast-to-noise ratio and sharpness of myocardial borders and (3) in a patient with myocardial infarction using segmented cardiac magnetic resonance imaging images. Most of the data from the simulated images exhibited high concordance with the results of actual images with relative differences of only: (1) 0.5% for detection sensitivity, (2) 6.7% for spatial resolution, (3) 2.6% for contrast-to-noise ratio and 5.0% for sharpness index on the cardiac insert placed in a diffusing environment. There was also good concordance between actual and simulated gated-SPECT patient images for the delineation of the myocardial infarction area, although the quality of the simulated images was clearly superior with increases around 50% for both contrast-to-noise ratio and sharpness index. SPECT recordings from a new heart-centric CZT camera can be simulated with the GATE software with high concordance relative to the actual physical properties of this camera. These simulations may be conducted up to the stage of human SPECT-images even if further refinement is needed in this setting.

Quantitative simultaneous 111In∕99mTc SPECT-CT of osteomyelitis

PURPOSE

A well-established approach for diagnostic imaging of osteomyelitis (OM), a bone infection, is simultaneous SPECT-CT of 99mTc sulfur colloid (SC) and 111In white blood cells (WBC). This method provides essentially perfect spatial registration of the tracers within anatomic sites of interest. Currently, diagnosis is based purely on a visual assessment-where relative discordance between 99mTc and 111In uptake in bone, i.e., high 111In and low 99mTc, suggests OM. To achieve more quantitative images, noise, scatter, and crosstalk between radionuclides must be addressed through reconstruction. Here the authors compare their Monte Carlo-based joint OSEM (MC-JOSEM) algorithm, which reconstructs both radionuclides simultaneously, to a more conventional triple-energy window-based reconstruction (TEW-OSEM), and to iterative reconstruction with no compensation for scatter (NC-OSEM).

METHODS

The authors created numerical phantoms of the foot and torso. Multiple bone-infection sites were modeled using high-count Monte Carlo simulation. Counts per voxel were then scaled to values appropriate for 111In WBC and 99mTc SC imaging. Ten independent noisy projection image sets were generated by drawing random Poisson deviates from these very low-noise images. Data were reconstructed using the two iterative scatter-compensation methods, TEW-OSEM and MC-JOSEM, as well as the uncorrected method (NC-OSEM). Mean counts in volumes of interest (VOIs) were used to evaluate the bias and precision of each method. Data were also acquired using a phantom, approximately the size of an adult ankle, consisting of regions representing infected and normal bone marrow, within a bone-like attenuator and surrounding soft tissue; each compartment contained a mixture of 111In and 99mTc. Low-noise data were acquired during multiple short scans over 29 h on a Siemens Symbia T6 SPECT-CT with medium-energy collimators. Pure 99mTc and 111In projection datasets were derived by fitting the acquired projections to the sum of 99mTc and 111In contributions, using the known half-lives. Uncontaminated data were scaled and recombined into six datasets with different activity ratios; ten Poisson noise realizations were then generated for each ratio. VOIs in each of the compartments were used to evaluate the bias and precision of each method with respect to reconstructions of uncontaminated datasets. In addition to the simulated and acquired phantom images, the authors reconstructed patient images with MC-JOSEM and TEW-OSEM. Patient reconstructions were assessed qualitatively for lesion contrast, spatial definition, and scatter.

RESULTS

For all simulated and acquired infection phantoms, the root-mean squared-error of measured 99mTc activity was significantly improved with MC-JOSEM and TEW-OSEM in comparison to NC-OSEM reconstructions. While MC-JOSEM trended toward outperforming TEW-OSEM, the improvement was only found to be significant (p<0.001) for the acquired bone phantom in which a wide range of 111In∕99mTc concentration ratios were tested. In all cases, scatter correction did not significantly improve 111In quantitation.

CONCLUSIONS

Compensation for scatter and crosstalk is useful for improving quality, bias, and precision of 99mTc activity estimates in simultaneous dual-radionuclide imaging of OM. The use of the more rigorous MC-based estimates provided marginal improvements over TEW. While the phantom results were encouraging, more subjects are needed to evaluate the usefulness of quantitative 111In∕99mTc SPECT-CT in the clinic.

Accurate and efficient modeling of the detector response in small animal multi-head PET systems

In fully three-dimensional PET imaging, iterative image reconstruction techniques usually outperform analytical algorithms in terms of image quality provided that an appropriate system model is used. In this study we concentrate on the calculation of an accurate system model for the YAP-(S)PET II small animal scanner, with the aim to obtain fully resolution- and contrast-recovered images at low levels of image roughness. For this purpose we calculate the system model by decomposing it into a product of five matrices: (1) a detector response component obtained via Monte Carlo simulations, (2) a geometric component which describes the scanner geometry and which is calculated via a multi-ray method, (3) a detector normalization component derived from the acquisition of a planar source, (4) a photon attenuation component calculated from x-ray computed tomography data, and finally, (5) a positron range component is formally included. This system model factorization allows the optimization of each component in terms of computation time, storage requirements and accuracy. The main contribution of this work is a new, efficient way to calculate the detector response component for rotating, planar detectors, that consists of a GEANT4 based simulation of a subset of lines of flight (LOFs) for a single detector head whereas the missing LOFs are obtained by using intrinsic detector symmetries. Additionally, we introduce and analyze a probability threshold for matrix elements of the detector component to optimize the trade-off between the matrix size in terms of non-zero elements and the resulting quality of the reconstructed images. In order to evaluate our proposed system model we reconstructed various images of objects, acquired according to the NEMA NU 4-2008 standard, and we compared them to the images reconstructed with two other system models: a model that does not include any detector response component and a model that approximates analytically the depth of interaction as detector response component. The comparisons confirm previous research results, showing that the usage of an accurate system model with a realistic detector response leads to reconstructed images with better resolution and contrast recovery at low levels of image roughness.

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.

A residual correction method for high-resolution PET reconstruction with application to on-the-fly Monte Carlo based model of positron range

PURPOSE

The quality of tomographic images is directly affected by the system model being used in image reconstruction. An accurate system matrix is desirable for high-resolution image reconstruction, but it often leads to high computation cost. In this work the authors present a maximum a posteriori reconstruction algorithm with residual correction to alleviate the tradeoff between the model accuracy and the computation efficiency in image reconstruction.

METHODS

Unlike conventional iterative methods that assume that the system matrix is accurate, the proposed method reconstructs an image with a simplified system matrix and then removes the reconstruction artifacts through residual correction. Since the time-consuming forward and back projection operations using the accurate system matrix are not required in every iteration, image reconstruction time can be greatly reduced.

RESULTS

The authors apply the new algorithm to high-resolution positron emission tomography reconstruction with an on-the-fly Monte Carlo (MC) based positron range model. Computer simulations show that the new method is an order of magnitude faster than the traditional MC-based method, whereas the visual quality and quantitative accuracy of the reconstructed images are much better than that obtained by using the simplified system matrix alone.

CONCLUSIONS

The residual correction method can reconstruct high-resolution images and is computationally efficient.

Accuracy of quantitative reconstructions in SPECT/CT imaging

The goal of this study was to determine the quantitative accuracy of our OSEM-APDI reconstruction method based on SPECT/CT imaging for Tc-99m, In-111, I-123, and I-131 isotopes. Phantom studies were performed on a SPECT/low-dose multislice CT system (Infinia-Hawkeye-4 slice, GE Healthcare) using clinical acquisition protocols. Two radioactive sources were centrally and peripherally placed inside an anthropometric Thorax phantom filled with non-radioactive water. Corrections for attenuation, scatter, collimator blurring and collimator septal penetration were applied and their contribution to the overall accuracy of the reconstruction was evaluated. Reconstruction with the most comprehensive set of corrections resulted in activity estimation with error levels of 3-5% for all the isotopes.

Advances in PET Image Reconstruction

Until recently, the most widely used methods for image reconstruction were direct analytic techniques. Iterative techniques, although computationally much more intensive, produce improved images (principally arising from more accurate modeling of the acquired projection data), enabling these techniques to replace analytic techniques not only in research settings but also in the clinic. This article offers an overview of image reconstruction theory and algorithms for PET, with a particular emphasis on statistical iterative reconstruction techniques. Future directions for image reconstruction in PET are considered, which concern mainly improving the modeling of the data acquisition process and task-specific specification of the parameters to be estimated in image reconstruction.

Computational Anthropomorphic Models of the Human Anatomy: The Path to Realistic Monte Carlo Modeling in Radiological Sciences

The widespread availability of high-performance computing and popularity of simulations stimulated the development of computational anthropomorphic models of the human anatomy for medical imaging modalities and dosimetry calculations. The widespread interest in molecular imaging spurred the development of more realistic three- to five-dimensional computational models based on the actual anatomy and physiology of individual humans and small animals. These can be defined by either mathematical (analytical) functions or digital (voxel-based) volume arrays (or a combination of both), thus allowing the simulation of medical imaging data that are ever closer to actual patient data. The paradigm shift away from the stylized human models is imminent with the development of more than 30 voxel-based tomographic models in recent years based on anatomical medical images. We review the fundamental and technical challenges of designing computational models of the human anatomy, and focus particularly on the latest developments and future directions of their application in the simulation of radiological imaging systems and dosimetry calculations.

A parallelizable compression scheme for Monte Carlo scatter system matrices in PET image reconstruction

Scatter correction techniques in iterative positron emission tomography (PET) reconstruction increasingly utilize Monte Carlo (MC) simulations which are very well suited to model scatter in the inhomogeneous patient. Due to memory constraints the results of these simulations are not stored in the system matrix, but added or subtracted as a constant term or recalculated in the projector at each iteration. This implies that scatter is not considered in the back-projector. The presented scheme provides a method to store the simulated Monte Carlo scatter in a compressed scatter system matrix. The compression is based on parametrization and B-spline approximation and allows the formation of the scatter matrix based on low statistics simulations. The compression as well as the retrieval of the matrix elements are parallelizable. It is shown that the proposed compression scheme provides sufficient compression so that the storage in memory of a scatter system matrix for a 3D scanner is feasible. Scatter matrices of two different 2D scanner geometries were compressed and used for reconstruction as a proof of concept. Compression ratios of 0.1% could be achieved and scatter induced artifacts in the images were successfully reduced by using the compressed matrices in the reconstruction algorithm.

Fast hybrid SPECT simulation including efficient septal penetration modelling (SP-PSF)

Single photon emission computed tomography (SPECT) images are degraded by the detection of scattered photons and photons that penetrate the collimator septa. In this paper, a previously proposed Monte Carlo software that employs fast object scatter simulation using convolution-based forced detection (CFD) is extended towards a wide range of medium and high energy isotopes measured using various collimators. To this end, a fast method was developed for incorporating effects of septal penetrating (SP) photons. The SP contributions are obtained by calculating the object attenuation along the path from primary emission to detection followed by sampling a pre-simulated and scalable septal penetration point spread function (SP-PSF). We found that with only a very slight reduction in accuracy, we could accelerate the SP simulation by four orders of magnitude. To achieve this, we combined: (i) coarse sampling of the activity and attenuation distribution; (ii) simulation of the penetration only for a coarse grid of detector pixels followed by interpolation and (iii) neglection of SP-PSF elements below a certain threshold. By inclusion of this SP-PSF-based simulation it became possible to model both primary and septal penetrated photons while only 10% extra computation time was added to the CFD-based Monte Carlo simulator. As a result, a SPECT simulation of a patient-like distribution including SP now takes less than 5 s per projection angle on a dual processor PC. Therefore, the simulator is well-suited as an efficient projector for fully 3D model-based reconstruction or as a fast data-set generator for applications such as image processing optimization or observer studies.

High accuracy multiple scatter modelling for 3D whole body PET

A new technique for modelling multiple-order Compton scatter which uses the absolute probabilities relating the image space to the projection space in 3D whole body PET is presented. The details considered in this work give a valuable insight into the scatter problem, particularly for multiple scatter. Such modelling is advantageous for large attenuating media where scatter is a dominant component of the measured data, and where multiple scatter may dominate the total scatter depending on the energy threshold and object size. The model offers distinct features setting it apart from previous research: (1) specification of the scatter distribution for each voxel based on the transmission data, the physics of Compton scattering and the specification of a given PET system; (2) independence from the true activity distribution; (3) in principle no scaling or iterative process is required to find the distribution; (4) explicit multiple scatter modelling; (5) no scatter subtraction or addition to the forward model when included in the system matrix used with statistical image reconstruction methods; (6) adaptability to many different scatter compensation methods from simple and fast to more sophisticated and therefore slower methods; (7) accuracy equivalent to that of a Monte Carlo model. The scatter model has been validated using Monte Carlo simulation (SimSET).

Hybrid scatter correction applied to quantitative holmium-166 SPECT

Ho-166 is a combined beta-gamma emitter of which the betas can be used therapeutically. From the 81 keV gammas of Ho-166, SPECT images can be obtained, which give opportunities to guide Ho-166 therapy. Accurate reconstruction of Ho-166 images is currently hampered by photopeak-scatter in the patient, down-scatter in the detector, collimator and patient caused by the 1.4 MeV photons and by bremsstrahlung. We developed and validated a method for quantitative SPECT of Ho-166 that involves correction for both types of scatter plus non-uniform attenuation correction using attenuation maps. Photopeak-scatter (S) is compensated for by a rapid 3D Monte Carlo (MC) method that is incorporated in ordered subset (OS) reconstruction of the emission data, together with simultaneous correction for attenuation (A) and detector response (D); this method is referred to as OS-ADS. Additionally, for correction of down-scatter, we use a 14 keV wide energy window centred at 118 keV (OS-ADSS). Due to a limited number of available energy windows, the same 118 keV energy window was used for down-scatter correction of the simultaneously acquired Gd-153 transmission data. Validations were performed using physical phantom experiments carried out on a dual-head SPECT system; Gd-153 transmission line sources were used for acquiring attenuation maps. For quantitative comparison of OS-ADS and OS-ADSS, bottles filled with Ho-166 were placed in both a cylindrical phantom and an anthropomorphic thorax phantom. Both OS-ADS and OS-ADSS were compared with an ordered subset reconstruction without any scatter correction (OS-AD). Underestimations of about 20% in the attenuation map were reduced to a few per cent after down-scatter correction. The average deviation from the true activity contained in the bottles was +72% with OS-AD. Using OS-ADS, this average overestimation was reduced to +28% and with OS-ADSS the deviation was further reduced to 16%. With OS-AD and OS-ADS, these numbers were more sensitive to the choice of volumes of interest than with OS-ADSS. For the reconstructed activity distributions, erroneous background activity found with OS-AD was reduced by a factor of approximately 2 by applying OS-ADS and reduced by a factor of approximately 4 by applying OS-ADSS. The combined attenuation, photopeak-scatter and down-scatter correction framework proposed here greatly enhanced the quantitative accuracy of Ho-166 imaging, which is of the uppermost importance for image-guided therapies. It is expected that the method, with adapted window settings, also can be applied to other isotopes with high energy peaks that contaminate the photopeak data, such as I-131 or In-111.

The influence of noise in full Monte Carlo ML-EM and dual matrix reconstructions in positron emission tomography

Monte Carlo (MC) simulations in positron emission tomography (PET) play an important role in detector modeling and algorithm testing. Whereas the simulations are widely used in a forward projection manner to accomplish this task, ideally they should be included into the reconstruction process itself. It is therefore desirable to investigate the convergence properties and the propagation of MC noise of these kinds of reconstruction algorithms. MC simulations were integrated into the maximum likelihood expectation maximization (ML-EM) algorithm in two different ways. In the full matrix approach the system matrix was calculated by running MC simulations, including scatter. This matrix was used in both the projector and the backprojector. In the dual matrix (DM) approach, MC simulations were used to incorporate scatter in the projector, whereas the backprojector only comprised attenuation. Repeated reconstructions with different MC seeds allowed a statistical analysis of the error at each iteration step and made it possible to investigate separately the propagation of the MC noise that was introduced by the sinogram, by the projector, and by the matrix. Both approaches resulted in similar images, but the DM approach with unmatched projector and backprojector yielded a faster initial convergence when compared to the ideal full matrix approach. The analysis of the noise sources for the modeled single ring scanner in full matrix reconstruction showed that the noise introduced by the matrix became comparable to the noise introduced by the sinogram when using a matrix that was simulated with 10,000 emissions/voxel.

Fully 3-D PET reconstruction with system matrix derived from point source measurements

The quality of images reconstructed by statistical iterative methods depends on an accurate model of the relationship between image space and projection space through the system matrix The elements of the system matrix for the clinical Hi-Rez scanner were derived by processing the data measured for a point source at different positions in a portion of the field of view. These measured data included axial compression and azimuthal interleaving of adjacent projections. Measured data were corrected for crystal and geometrical efficiency. Then, a whole system matrix was derived by processing the responses in projection space. Such responses included both geometrical and detection physics components of the system matrix. The response was parameterized to correct for point source location and to smooth for projection noise. The model also accounts for axial compression (span) used on the scanner. The forward projector for iterative reconstruction was constructed using the estimated response parameters. This paper extends our previous work to fully three-dimensional. Experimental data were used to compare images reconstructed by the standard iterative reconstruction software and the one modeling the response function. The results showed that the modeling of the response function improves both spatial resolution and noise properties.

Image reconstruction

We give an overview of the role of Physics in Medicine and Biology in the development of tomographic reconstruction algorithms. We focus on imaging modalities involving ionizing radiation, CT, PET and SPECT, and cover a wide spectrum of reconstruction problems, starting with classical 2D tomography in the 1970s up to 4D and 5D problems involving dynamic imaging of moving organs.