BACKGROUND AND PURPOSE:Sodium (23Na) MRI provides unique information about ionic homeostasis in the brain. However, in vivo quantification of regional brain sodium is highly challenging due to low SNR and limited spatial resolution. Here, we use our novel anatomically guided reconstruction (AGR) method to overcome these challenges and enable precise quantification of regional brain total sodium concentration (TSC). MATERIALS AND METHODS:Thirty-four healthy subjects were studied by using a 3T clinical MRI scanner with a dual-tuned (1H-23Na) birdcage coil. 23Na images were acquired by using a twisted projection imaging sequence (TR = 100 ms, TE1/TE2 = 0.5/5 ms), while proton (1H) images were obtained with a standard T1-weighted MPRAGE sequence. AGR was performed with regularization parameters βr = 0.67, 2.0, and 6.0. As a baseline comparison, standard reconstruction (SR) was also performed by using a regridding algorithm with compensation for nonuniform sampling. To assess partial volume effects (PVEs) on the reconstruction methods, an erosion experiment was conducted. Internal linear calibration using noise-only background and vitreous humor regions was applied to calculate TSC in ROIs including lobar cortical GM, subcortical (including hippocampus, caudate, pallidum, putamen and thalamus), callosal, and whole-brain WM. Bonferroni-corrected pair-wise comparison was performed by using Multivariate Analysis of Variance at a significance level P < .05. RESULTS:The WM erosion experiments confirmed that TSCAGR was stabilized beyond 1-voxel erosion in the WM, but TSCSR was decreasing with erosion increasing, showing a reduced PVE in the AGR images. AGR also shows greater separation in TSC between GM and WM compared with SR (GM TSCSR = 49.2 ± 4.6 mmol/L, WM TSCSR = 38.1 ± 3.0 mmol/L; GM TSCAGR = 48.6 ± 4.9 mmol/L, WM TSCAGR = 30.5 ± 2.8 mmol/L). We also found smaller variance of TSCAGR in WM and GMsubcortical compared with TSCSR. CONCLUSIONS:The AGR helps sodium quantification in healthy human brains by reducing the PVE and variance of TSC in noncortical brain regions. Our normative values of TSC in the brain regions set the stage to better understand derangements of 23Na metabolism and homeostasis in neurologic disease.

Objective.Scattered coincidences are a major source of quantitative bias in positron emission tomography (PET) and must be compensated during reconstruction using an estimate of scattered coincidences per line-of-response and time-of-flight bin. Such estimates are typically obtained from simulators with simple cylindrical scanner models that omit detector physics. Incorporating detector sensitivities for scatter is challenging, as scattered coincidences have less constrained properties (e.g. incidence angles) than true coincidences.Approach.We integrated a 5D single-photon detection probability lookup table (photon energy, incidence angle, detector location) into the simulator logic. The resulting scatter sinogram is multiplied by a precomputed, lookup table-specific scatter sensitivity sinogram to yield the scatter estimate. Scatter was simulated with MCGPU-PET, a fast Monte Carlo (MC) simulator with a simplified scanner model, and applied to phantom data from a simulated GE Signa PET/MR in GATE. We evaluated three scenarios:Long, high-count MCGPU-PET simulations from a known activity distribution (reference).Same distribution with limited simulation time and counts.Same low-count data with joint estimation of activity and scatter during reconstruction.We also adapted the approach to test it on two acquisitions from a real Signa PET/MR.Main result.In scenario 1, scatter-compensated reconstructions achieved<1%global bias in all active regions relative to true-only reconstructions. In scenario 2, noisy scatter estimates caused strong positive bias, but Gaussian smoothing restored accuracy to scenario 1 levels. In scenario 3, joint estimation under low-count conditions maintained<1%global bias in nearly all regions. For real scans, the Monte Carlo-based scatter estimate was very similar to the vendor scatter estimate.Significance.Although demonstrated with a fast MC simulator, the proposed scatter sensitivity modeling could enhance existing single scatter simulators used clinically, which typically neglect detector physics. This proof-of-concept also supports the feasibility of scatter estimation for real scans using fast MC simulation, offering potentially greater accuracy and robustness to acquisition noise.

By the time of the first published issue of Physics in Medicine and Biology in 1956, the fundamentals of nuclear medicine were well established. The nature of radioactivity and its nuclear origins had been discovered, the tracer principle had been invented, radiation detectors had been developed and methods for generating diagnostic images and exploiting the therapeutic eTects of radionuclides were already in their infancy. Despite this, a practitioner in the 1950s would find it almost impossible to imagine the technology used in nuclear medicine today, the quality of the images produced, or the breadth of clinical and research applications it has enabled. Over the last 7 decades nuclear medicine has been transformed from a medical curiosity into a mainstream component of the modern healthcare system globally and an important tool in clinical research and therapeutic trials. This article highlights the landmark discoveries and technological advances since 1956 that have significantly shaped the field and got us to where we are today.

PET requires accurate, precise, and efficient scatter correction techniques. Conventional scatter estimation typically relies on tail-fitted single-scatter simulation (SSS) strategy. However, the accuracy of tail-fitted SSS is limited, for example, by mismatches between the attenuation image and the PET emission data or by the presence of activity outside the FOV. These shortcomings can be addressed using energy-based scatter estimation (EBSE), as recently proposed by Efthimiou et al. and Hamill et al. The aim of this work is to 1. improve the accuracy of EBSE by accounting for the LOR dependence of the energy spectrum of unscattered photons, 2. improve the computational speed of EBSE through better initialization and a more efficient optimization algorithm. The proposed improved EBSE method models the energy probability density function (PDF) of both single and multiple scattered photons, and incorporates a position-dependent energy PDF for unscattered photons. These energy PDFs form the basis of two forward models used for scatter estimation based on 2D energy histograms. The performance of these models were evaluated using GATE Monte Carlo simulations and a NEMA phantom acquisition on a GE SIGNA PET/MR scanner. Furthermore, we assessed the stability of EBSE across the forward models by varying the number of counts in the 2D energy histograms via data mashing. EBSE outperformed tail-fitted SSS, particularly in regions near out-of-FOV activity. Our GATE simulations showed that incorporating a local energy for unscattered photons improves off-center regional quantification by approximately 2 Additionally, improved initialization combined with the NEGML optimizer enabling execution on a mashed TOF sinogram in 12 minutes on six-core CPU. The proposed method enhances both the accuracy and computational efficiency of EBSE, making it well-suited for clinical applications.

BACKGROUND:A number of studies have suggested that there is a need for improved understanding of dento-maxillofacial cone beam computed tomography (CBCT) technology, and to establish optimized imaging protocols. While several ex vivo/in vitro studies, along with a few in vivo studies, have addressed this topic, virtual imaging trials could form a powerful alternative but have not yet been introduced within the field of dento-maxillofacial imaging. PURPOSE:To introduce and illustrate the potential of utilizing a virtual imaging trial (VIT) platform for dento-maxillofacial CBCT imaging through a number of case studies. METHODS:A framework developed in-house, simulating an existing CBCT scanner, and the necessary digital patient phantoms were prepared for the following potential studies: I) the impact of intracanal material type (Ni-Cr alloy, fiberglass, gutta-percha) and acquisition settings (tube current (mA), tube voltage (kVp)) on root fracture (RF) visibility; II) image artefact levels from candidate new restorative materials, such as graphene; III) the effect of patient rigid motion on image artifacts; IV) the effect of a metal artifact reduction algorithm on RF visibility in a tooth treated endodontically and restored with a metal post. In addition, features not available on the real system, including automatic exposure control and extended tube current and tube voltage ranges, were added to study the impact of these parameters. Patient dose levels were also quantified. RESULTS:The generated images showed the influence of different restorative materials, dose levels, rigid motion, and image processing on the quality of the final images. Results of these simulated conditions were consistent with findings in the literature. Patient effective dose levels ranged between 22 and 138 μ Sv $\mu{\rm Sv}$ for all simulated scenarios. Images were considered sufficiently realistic according to an experienced oral radiologist. Furthermore, the platform was able to simulate scenarios that are difficult or impossible to replicate physically in a controlled and repeatable way. CONCLUSIONS:A virtual imaging trial platform has the potential to improve the understanding and use of CBCT technology. Improved insight into system performance can lead to optimized imaging protocols, and help to reduce the large variation in system setup and performance currently seen in clinical practice in dento-maxillofacial CBCT imaging.

Scattered coincidences introduce quantitative bias in positron emission tomography and must be compensated during reconstruction using an estimated scatter sinogram. These estimates are typically derived from simulators with simplified cylindrical scanner models that omit detector physics. Incorporating detector sensitivities for scatter is challenging, as scattered coincidences exhibit less constrained properties (e.g., incidence angles) than true events. We integrated a 5D single-photon detection probability lookup table (LUT; based on photon properties) into the simulator logic. The resulting scatter sinogram is scaled by a precomputed, LUT-specific scatter sensitivity sinogram to yield the final estimate. Scatter was simulated using MCGPU-PET, a fast Monte Carlo (MC) simulator with a simplified scanner model, and applied to phantom data from a simulated GE Signa PET/MR in GATE. We evaluated three scenarios: (1) long, high-count simulations from a known activity distribution (reference); (2) same distribution with limited simulation time and counts; (3) same low-count data with joint estimation of activity and scatter during reconstruction. In scenario 1, scatter-compensated reconstructions achieved <1

Objective. Whole-body positron emission tomography (PET) imaging is often hindered by respiratory motion during acquisition, causing significant degradation in the quality of reconstructed activity images. An additional challenge in PET/CT imaging arises from the respiratory phase mismatch between CT-based attenuation correction and PET acquisition, leading to attenuation artifacts. To address these issues, we propose two new, purely data-driven methods for the joint estimation of activity, attenuation, and motion in respiratory self-gated time-of-flight PET. These methods enable the reconstruction of a single activity image free from motion and attenuation artifacts.Approach. The proposed methods were evaluated using data from the anthropomorphic Wilhelm phantom acquired on a Siemens mCT PET/CT system, as well as three clinical [18F]FDG PET/CT datasets acquired on a GE DMI PET/CT system. Image quality was assessed visually to identify motion and attenuation artifacts. Lesion uptake values were quantitatively compared across reconstructions without motion modeling, with motion modeling but 'static' attenuation correction, and with our proposed methods.Main results. For the Wilhelm phantom, the proposed methods delivered image quality closely matching the reference reconstruction from a static acquisition. The lesion-to-background contrast for a liver dome lesion improved from 2.0 (no motion correction) to 5.2 (using our proposed methods), matching the contrast from the static acquisition (5.2). In contrast, motion modeling with 'static' attenuation correction yielded a lower contrast of 3.5. In patient datasets, the proposed methods successfully reduced motion artifacts in lung and liver lesions and mitigated attenuation artifacts, demonstrating superior lesion to background separation.Significance. Our proposed methods enable the reconstruction of a single, high-quality activity image that is motion-corrected and free from attenuation artifacts, without the need for external hardware.

Objective.Sensitivity is a key feature of positron emission tomography (PET). Here, sensitivity can be defined as the reciprocal of the amount of injected radioactivity needed to obtain a sufficient image quality for a particular scan duration. PET sensitivity can not only be increased by increasing the solid angle covered by the detectors, but also by improving their spatial and the temporal resolution, which in turn determines the time-of-flight (TOF) resolution. This paper analyzes how the interplay between the spatial detector resolution, the TOF resolution and the required imaging resolution affects the sensitivity of a TOF-PET system.Approach.Two approaches are studied. The first computes the performance of the Hoteling observer for discriminating a small hot spot from a less small and less hot spot with the same total activity. This approach is flexible, and elegant closed form equations are obtained. In the second approach, analytical equations are derived for the variance of the reconstructed voxel values as a function of the TOF and spatial detector resolutions and of the reconstruction point spread function. To keep the mathematics tractable, the derivations are done for the center of a uniform sphere or cylinder, which is placed in the center of a cylindrical or spherical PET system. The results are verified with simulation experiments for 2D PET and 3D PET with septa.Main results.Both approaches confirm that the sensitivity of the PET system increases, when the spatial detector resolution is improved, in agreement with simulation results published by Muehllehner (1985Phys. Med. Biol.30163). The same is true for improvements of the TOF resolution. Remarkably, when the TOF resolution (converted to a distance) approaches the spatial resolution, further improving it increases the sensitivity more than expected based on experience with current TOF-PET systems and on the analysis for moderate TOF resolution (Tomitani 1981IEEE Trans. Nucl. Sci.NS-284582-9). This agrees with simulation results published recently by Toussaintet al(2020IEEE Trans. Radiat. Plasma Med. Sci.5729-37). Finally, our new Equations confirm that the value of a TOF-kernel is well characterized by the integral of its square, as was reported previously (Nuytset al2022IEEE Trans. Med. Imaging421254-64; Nuytset al2022Phys. Med. Biol.69015011).Significance.This analysis explains how spatial detector resolution and TOF accuracy contribute to the sensitivity of PET systems, and predicts that pushing the TOF resolution well below 100 ps will produce a larger benefit than expected based on current rules of thumb.

Comparing positron emission tomography (PET) systems which have different features is not straightforward. To address this, we propose to image the same object with all considered PET systems using a fixed scan time, and reconstruct from each scan an image at the same predefined spatial resolution. With such resolution matched reconstructions, the images should be identical except for their noise. Therefore, the PET system that produces the image with the lowest variance has the best performance. An analytical model is described to compute this variance, assuming that the PET system is (approximately) cylindrical, the imaged object is a uniform cylinder centered in the field of view, and the variance is only computed at the center of the reconstructed image. The model takes into account the solid angle covered by the detectors, the detector stopping power, the time-of-flight (TOF) resolution, the scatter fraction and the spatial resolution of the system, the attenuation and diameter of the cylinder and the desired spatial resolution of the reconstructed image. The inverse of this variance can be considered as the effective sensitivity of the system. This effective sensitivity can be calibrated based on the NEMA line source sensitivity. As a performance metric for scanning long objects, the minimum sensitivity achieved over the object is computed, with an optimal number of bed positions and optimal overlap between them. The influence of the spatial and TOF resolution on the effective sensitivity is verified with simulations.

Scatter compensation is a key part of image reconstruction in positron emission tomography (PET). It currently relies on tail-fitted single scatter simulations, which are prone to errors in low count frames. Up until recently, more accurate scatter estimation methods based on Monte Carlo (MC) simulation were not feasible due to their very long calculation times. We showed, using the newly developed MCGPU-PET simulator, that it is possible to get a reliable scatter sinogram estimate using just $3^{*} 10^{8} \mathrm{MC}$-simulated scatter coincidences, for dynamic emission frames as short as 1 second. This requires a simulation time of 5 minutes, but can be reduced even further, so that image reconstruction with Monte Carlo based scatter compensation can be done in clinically acceptable computation times.

Scatter correction (SC) is essential for obtaining quantitative images in Positron Emission Tomography (PET), and is routinely performed using tail-fitted single scatter simulation (SSS). While this method is usually robust and accurate, it can fail when there is a strong scatter contribution from activity outside the field of view (FOV) or when the attenuation map is not well aligned due to patient motion. As an alternative, energy-based scatter estimation has recently been proposed [1, 2]. Hamill et al. [2] model the joint photon energy histogram as a sum of nine basis functions. An iterative expectation maximization approach determines the coefficients and estimates the scatter. In this study, we investigate possible improvements to the approach by Hamill et al. including: (i) modeling the position dependence of the trues energy spectrum and (ii) invoking time-of-flight TOF to reduce the number of model parameters to 5. Using GATE simulations, we show that the trues energy spectrum depends on the photon incidence angle and therefore on position. We provide arguments for the parameter reduction; the evaluation of its effect on the final reconstructed image is ongoing.

In order to achieve quantitatively reliable images from Positron Emission Tomography (PET), scatter correction is necessary. By studying the energy measured for each event, useful information about the energy spectrum of the events is obtained. This information can be used for scatter correction. Efthimiou et al [1] proposed a method based on energy spectrum of scatter and a moments method to estimate scatter. In this study, we checked the effects of mashing data on scatter estimation based on this model. Mashing is the combination of multiple lines of response into a single one, to reduce the noise. Efthimiou et al. used the Delayed Window method to perform random corrections. In our study, the energy spectrum of random events was estimated experimentally. Our results indicate that mashing was useful for estimating the scatter contribution accurately.

There is a large variability in the features of existing (and future) positron emission tomography (PET) systems. This complicates comparison of the performance of different systems for different tasks. We propose a mathematical model that estimates the relative performance of a PET system for imaging a uniform cylinder of a particular diameter, attenuation and length, and producing a reconstructed image with a particular spatial resolution. The PET system is assumed to be (approximately) cylindrical. The model computes an "effective sensitivity", taking into account the solid angle covered by the detectors, the detector stopping power, the time-of-flight resolution, the scatter fraction and the spatial resolution of the system, the attenuation and diameter of the cylinder and the desired spatial resolution of the reconstructed image. This effective sensitivity can be calibrated based on the NEMA line source sensitivity. The PET systems are compared at matched scantime. Systems with the same effective sensitivity are predicted to produce reconstructed images with the same pixel variance. As performance metric for scanning long objects, the minimum sensitivity achieved over the object is computed, with an optimal number of bed positions and optimal overlap between them. The influence of the spatial and TOF resolution on the effective sensitivity is verified with simulations.

Purpose: Sodium MRI is challenging because of the low tissue concentration of the 23 Na nucleus and its extremely fast biexponential transverse relaxation rate. In this article, we present an iterative reconstruction framework using dual-echo 23Na data and exploiting anatomical prior information (AGR) from high-resolution, low-noise, 1 H MR images. This framework enables the estimation and modeling of the spatially-varying signal decay due to transverse relaxation during readout (AGRdm), which leads to images of better resolution and reduced noise resulting in improved quantification of the reconstructed 23Na images. Methods: The proposed framework was evaluated using reconstructions of 30 noise realizations of realistic simulations of dual echo twisted projection imaging (TPI) 23 Na data. Moreover, three dual echo 23 Na TPI brain data sets of healthy controls acquired on a 3T Siemens Prisma system were reconstructed using conventional reconstruction, AGR and AGRdm. Results: Our simulations show that compared to conventional reconstructions, AGR and AGRdm show improved bias-noise characteristics in several regions of the brain. Moreover, AGR and AGRdm images show more anatomical detail and less noise in the reconstructions of the experimental data sets. Compared to AGR and the conventional reconstruction, AGRdm shows higher contrast in the sodium concentration ratio between gray and white matter and between gray matter and the brain stem. Conclusion: AGR and AGRdm generate 23 Na images with high resolution, high levels of anatomical detail, and low levels of noise, potentially enabling high-quality 23 Na MR imaging at 3T.

Deep learning-based medical image segmentation is widely used and has achieved the state-of-the-art segmentation performance, in which nnU-Net is a particularly successful pipeline due to its pre-processing and auto-configuration features. However, the output predicted probabilities from neural networks are generally not properly calibrated and don’t necessarily indicate segmentation errors, which are problematic for clinical use. Bayesian deep learning is a promising way to address these problems by improving the probability calibration and error localisation ability. In this paper, we proposed a novel Bayesian approach based on posterior bootstrap theory to sample the neural network parameters from a posterior distribution. Based on nnU-Net, we implemented our method and other Bayesian approaches, and evaluated their uncertainty estimation quality. The results show that the proposed posterior bootstrap method provides improvement on uncertainty estimation with equivalent segmentation performance. The proposed method is easy to implement, compatible with any deep learning-based image segmentation pipeline, and doesn’t require additional hyper-parameter tuning, enabling it to totally preserve nnU-Net’s auto-configuration feature.

BACKGROUND Optimization of dental cone beam computed tomography (CBCT) imaging is still in a preliminary stage and should be addressed using task-based methods. Dedicated models containing relevant clinical tasks for image quality studies have yet to be developed. PURPOSE To present a methodology to develop and validate a virtual adult anthropomorphic voxel phantom for use in task-based image quality optimization studies in dental CBCT imaging research, focusing on root fracture (RF) detection tasks in the presence of metal artefacts. METHODS The phantom was developed from a CBCT scan with an isotropic voxel size of 0.2 mm, from which the main dental structures, mandible and maxilla were segmented. The missing large anatomical structures, including the spine, skull and remaining soft tissues, were segmented from a lower resolution full skull scan. Anatomical abnormalities were absent in the areas of interest. Fine detailed dental structures, that could not be segmented due to the limited resolution and noise in the clinical data, were modelled using a-priori anatomical knowledge. Model resolution of the teeth was therefore increased to 0.05 mm. Models of RFs as well as dental restorations to create the artefacts, were developed, and could be inserted in the phantom in any desired configuration. Simulated CBCT images of the models were generated using a newly developed multi-resolution simulation framework that incorporated the geometry, beam quality, noise and spatial resolution characteristics of a real dental CBCT scanner. Ray-tracing and Monte Carlo techniques were used to create the projection images, which were reconstructed using the classical FDK algorithm. Validation of the models was assessed by measurements of different tooth lengths, the pulp volume and the mandible, and comparison with reference values. Additionally, the simulated images were used in a reader study in which two oral radiologists had to score the realism level of the model's normal anatomy, as well as the modelled RFs and restorations. RESULTS A model of an adult head, as well as models of RFs and different types of dental restorations were created. Anatomical measurements were consistent with ranges reported in literature. For the tooth length measurements, the deviations from the mean reference values were less than 20%. In 77% of all the measurements, the deviations were within 10.1%. The pulp volumes, and mandible measurements were within one standard deviation of the reference values. Regarding the normal anatomy, both readers considered the realism level of the dental structures to be good. Background structures received a lower realism score due to the lack of detailed enough trabecular bone structure, which was expected but not the focus of this study. All modelled RFs were scored at least adequate by at least one of the readers, both in appearance and position. The realism level of the modelled restorations was considered to be good. CONCLUSIONS A methodology was proposed to develop and validate an anthropomorphic voxel phantom for image quality optimization studies in dental CBCT imaging, with a main focus on RF detection tasks. The methodology can be extended further to create more models representative of the clinical population.

Objective. Measurement of the time-of-flight (TOF) difference of each coincident pair of photons increases the effective sensitivity of positron emission tomography (PET). Many authors have analyzed the benefit of TOF for quantification and hot spot detection in the reconstructed activity images. However, TOF not only improves the effective sensitivity, it also enables the joint reconstruction of the tracer concentration and attenuation images. This can be used to correct for errors in CT- or MR-derived attenuation maps, or to apply attenuation correction without the help of a second modality. This paper presents an analysis of the effect of TOF on the variance of the jointly reconstructed attenuation and (attenuation corrected) tracer concentration images. Approach. The analysis is performed for PET systems that have a distribution of possibly non-Gaussian TOF-kernels, and includes the conventional Gaussian TOF-kernel as a special case. Non-Gaussian TOF-kernels are often observed in novel detector designs, which make use of two (or more) different mechanisms to convert the incoming 511 keV photon to optical photons. The analytical result is validated with a simple 2D simulation. Main results. We show that if two different TOF-kernels are equivalent for image reconstruction with known attenuation, then they are also equivalent for joint reconstruction of the activity and the attenuation images. The variance increase in the activity, caused by also jointly reconstructing the attenuation image, vanishes when the TOF-resolution approaches perfection. Significance. These results are of interest for PET detector development and for the development of stand-alone PET systems.