Generalized algorithms for direct reconstruction of parametric images from dynamic PET data

Total-Body Perfusion Imaging with [11C]-Butanol

Tissue perfusion can be affected by physiology or disease. With the advent of total-body PET, quantitative measurement of perfusion across the entire body is possible. [11C]-butanol is a perfusion tracer with a superior extraction fraction compared with [15O]-water and [13N]-ammonia. To develop the methodology for total-body perfusion imaging, a pilot study using [11C]-butanol on the uEXPLORER total-body PET/CT scanner was conducted. Methods: Eight participants (6 healthy volunteers and 2 patients with peripheral vascular disease [PVD]) were injected with a bolus of [11C]-butanol and underwent 30-min dynamic acquisitions. Three healthy volunteers underwent repeat studies at rest (baseline) to assess test-retest reproducibility; 1 volunteer underwent paired rest and cold pressor test (CPT) studies. Changes in perfusion were measured in the paired rest-CPT study. For PVD patients, local changes in perfusion were investigated and correlated with patient medical history. Regional and parametric kinetic analysis methods were developed using a 1-tissue compartment model and leading-edge delay correction. Results: Estimated baseline perfusion values ranged from 0.02 to 1.95 mL·min-1·cm-3 across organs. Test-retest analysis showed that repeat baseline perfusion measurements were highly correlated (slope, 0.99; Pearson r = 0.96, P < 0.001). For the CPT subject, the largest regional increases were in skeletal muscle (psoas, 142%) and the myocardium (64%). One of the PVD patients showed increased collateral vessel growth in the calf because of a peripheral stenosis. Comorbidities including myocardial infarction, hypothyroidism, and renal failure were correlated with variations in organ-specific perfusion. Conclusion: This pilot study demonstrates the ability to obtain reproducible measurements of total-body perfusion using [11C]-butanol. The methods are sensitive to local perturbations in flow because of physiologic stressors and disease.

Quantitation of dynamic total-body PET imaging: recent developments and future perspectives

BACKGROUND

Positron emission tomography (PET) scanning is an important diagnostic imaging technique used in disease diagnosis, therapy planning, treatment monitoring, and medical research. The standardized uptake value (SUV) obtained at a single time frame has been widely employed in clinical practice. Well beyond this simple static measure, more detailed metabolic information can be recovered from dynamic PET scans, followed by the recovery of arterial input function and application of appropriate tracer kinetic models. Many efforts have been devoted to the development of quantitative techniques over the last couple of decades.

CHALLENGES

The advent of new-generation total-body PET scanners characterized by ultra-high sensitivity and long axial field of view, i.e., uEXPLORER (United Imaging Healthcare), PennPET Explorer (University of Pennsylvania), and Biograph Vision Quadra (Siemens Healthineers), further stimulates valuable inspiration to derive kinetics for multiple organs simultaneously. But some emerging issues also need to be addressed, e.g., the large-scale data size and organ-specific physiology. The direct implementation of classical methods for total-body PET imaging without proper validation may lead to less accurate results.

CONCLUSIONS

In this contribution, the published dynamic total-body PET datasets are outlined, and several challenges/opportunities for quantitation of such types of studies are presented. An overview of the basic equation, calculation of input function (based on blood sampling, image, population or mathematical model), and kinetic analysis encompassing parametric (compartmental model, graphical plot and spectral analysis) and non-parametric (B-spline and piece-wise basis elements) approaches is provided. The discussion mainly focuses on the feasibilities, recent developments, and future perspectives of these methodologies for a diverse-tissue environment.

Total-body PET: a new paradigm for molecular imaging

Total body (TB) positron emission tomography (PET) instruments have dramatically changed the paradigm of PET clinical and research studies due to their very high sensitivity and capability to image dynamic radiopharmaceutical distributions in the major organs of the body simultaneously. In this manuscript, we review the design of these systems and discuss general challenges and trade-offs to maximize the performance gains of current TB-PET systems. We then describe new concepts and technology that may impact future TB-PET systems. The manuscript summarizes what has been learned from the initial sites with TB-PET and explores potential research and clinical applications of TB-PET. The current generation of TB-PET systems range in axial field-of-view (AFOV) from 1 to 2 m and serve to illustrate the benefits and opportunities of a longer AFOV for various applications in PET. In only a few years of use these new TB-PET systems have shown that they will play an important role in expanding the field of molecular imaging and benefiting clinical practice.

Deep Kernel Representation for Image Reconstruction in PET

Image reconstruction for positron emission tomography (PET) is challenging because of the ill-conditioned tomographic problem and low counting statistics. Kernel methods address this challenge by using kernel representation to incorporate image prior information in the forward model of iterative PET image reconstruction. Existing kernel methods construct the kernels commonly using an empirical process, which may lead to unsatisfactory performance. In this paper, we describe the equivalence between the kernel representation and a trainable neural network model. A deep kernel method is then proposed by exploiting a deep neural network to enable automated learning of an improved kernel model and is directly applicable to single subjects in dynamic PET. The training process utilizes available image prior data to form a set of robust kernels in an optimized way rather than empirically. The results from computer simulations and a real patient dataset demonstrate that the proposed deep kernel method can outperform the existing kernel method and neural network method for dynamic PET image reconstruction.

Positronium Lifetime Image Reconstruction for TOF PET

Positron emission tomography is widely used in clinical and preclinical applications. Positronium lifetime carries information about the tissue microenvironment where positrons are emitted, but such information has not been captured because of two technical challenges. One challenge is the low sensitivity in detecting triple coincidence events. This problem has been mitigated by the recent developments of PET scanners with long (1-2 m) axial field of view. The other challenge is the low spatial resolution of the positronium lifetime images formed by existing methods that is determined by the time-of-flight (TOF) resolution (200-500 ps) of existing PET scanners. This paper solves the second challenge by developing a new image reconstruction method to generate high-resolution positronium lifetime images using existing TOF PET. Simulation studies demonstrate that the proposed method can reconstruct positronium lifetime images at much better spatial resolution than the limit set by the TOF resolution of the PET scanner. The proposed method opens up the possibility of performing positronium lifetime imaging using existing TOF PET scanners. The lifetime information can be used to understand the tissue microenvironment in vivo which could facilitate the study of disease mechanism and selection of proper treatments.

Efficient Delay Correction for Total-Body PET Kinetic Modeling Using Pulse Timing Methods

Quantitative kinetic modeling requires an input function. A noninvasive image-derived input function (IDIF) can be obtained from dynamic PET images. However, a robust IDIF location (e.g., aorta) may be far from a tissue of interest, particularly in total-body PET, introducing a time delay between the IDIF and the tissue. The standard practice of joint estimation (JE) of delay, along with model fitting, is computationally expensive. To improve the efficiency of delay correction for total-body PET parametric imaging, this study investigated the use of pulse timing methods to estimate and correct for delay. Methods: Simulation studies were performed with a range of delay values, frame lengths, and noise levels to test the tolerance of 2 pulse timing methods-leading edge (LE) and constant fraction discrimination and their thresholds. The methods were then applied to data from 21 subjects (14 healthy volunteers, 7 cancer patients) who underwent a 60-min dynamic total-body ¹⁸F-FDG PET acquisition. Region-of-interest kinetic analysis was performed and parametric images were generated to compare LE and JE methods of delay correction, as well as no delay correction. Results: Simulations demonstrated that a 10% LE threshold resulted in biases and SDs at tolerable levels for all noise levels tested, with 2-s frames. Pooled region-of-interest-based results (n = 154) showed strong agreement between LE (10% threshold) and JE methods in estimating delay (Pearson r = 0.96, P < 0.001) and the kinetic parameters v_b (r = 0.96, P < 0.001), K_i (r = 1.00, P < 0.001), and K₁ (r = 0.97, P < 0.001). When tissues with minimal delay were excluded from pooled analyses, there were reductions in v_b (69.4%) and K₁ (4.8%) when delay correction was not performed. Similar results were obtained for parametric images; additionally, lesion K_i contrast was improved overall with LE and JE delay correction compared with no delay correction and Patlak analysis. Conclusion: This study demonstrated the importance of delay correction in total-body PET. LE delay correction can be an efficient surrogate for JE, requiring a fraction of the computational time and allowing for rapid delay correction across more than 10⁶ voxels in total-body PET datasets.

Unsupervised PET logan parametric image estimation using conditional deep image prior

Recently, deep learning-based denoising methods have been gradually used for PET images denoising and have shown great achievements. Among these methods, one interesting framework is conditional deep image prior (CDIP) which is an unsupervised method that does not need prior training or a large number of training pairs. In this work, we combined CDIP with Logan parametric image estimation to generate high-quality parametric images. In our method, the kinetic model is the Logan reference tissue model that can avoid arterial sampling. The neural network was utilized to represent the images of Logan slope and intercept. The patient's computed tomography (CT) image or magnetic resonance (MR) image was used as the network input to provide anatomical information. The optimization function was constructed and solved by the alternating direction method of multipliers (ADMM) algorithm. Both simulation and clinical patient datasets demonstrated that the proposed method could generate parametric images with more detailed structures. Quantification results showed that the proposed method results had higher contrast-to-noise (CNR) improvement ratios (PET/CT datasets: 62.25%±29.93%; striatum of brain PET datasets : 129.51%±32.13%, thalamus of brain PET datasets: 128.24%±31.18%) than Gaussian filtered results (PET/CT datasets: 23.33%±18.63%; striatum of brain PET datasets: 74.71%±8.71%, thalamus of brain PET datasets: 73.02%±9.34%) and nonlocal mean (NLM) denoised results (PET/CT datasets: 37.55%±26.56%; striatum of brain PET datasets: 100.89%±16.13%, thalamus of brain PET datasets: 103.59%±16.37%).

Direct Reconstruction of Linear Parametric Images From Dynamic PET Using Nonlocal Deep Image Prior

Direct reconstruction methods have been developed to estimate parametric images directly from the measured PET sinograms by combining the PET imaging model and tracer kinetics in an integrated framework. Due to limited counts received, signal-to-noise-ratio (SNR) and resolution of parametric images produced by direct reconstruction frameworks are still limited. Recently supervised deep learning methods have been successfully applied to medical imaging denoising/reconstruction when large number of high-quality training labels are available. For static PET imaging, high-quality training labels can be acquired by extending the scanning time. However, this is not feasible for dynamic PET imaging, where the scanning time is already long enough. In this work, we proposed an unsupervised deep learning framework for direct parametric reconstruction from dynamic PET, which was tested on the Patlak model and the relative equilibrium Logan model. The training objective function was based on the PET statistical model. The patient's anatomical prior image, which is readily available from PET/CT or PET/MR scans, was supplied as the network input to provide a manifold constraint, and also utilized to construct a kernel layer to perform non-local feature denoising. The linear kinetic model was embedded in the network structure as a 1 ×1 ×1 convolution layer. Evaluations based on dynamic datasets of ¹⁸F-FDG and ¹¹C-PiB tracers show that the proposed framework can outperform the traditional and the kernel method-based direct reconstruction methods.

Dynamic PET image reconstruction incorporating a median nonlocal means kernel method

In dynamic positron emission tomography (PET) imaging, the reconstructed image of a single frame often exhibits high noise due to limited counting statistics of projection data. This study proposed a median nonlocal means (MNLM)-based kernel method for dynamic PET image reconstruction. The kernel matrix is derived from median nonlocal means of pre-reconstructed composite images. Then the PET image intensities in all voxels were modeled as a kernel matrix multiplied by coefficients and incorporated into the forward model of PET projection data. Then, the coefficients of each feature were estimated by the maximum likelihood method. Using simulated low-count dynamic data of Zubal head phantom, the quantitative performance of the proposed MNLM kernel method was investigated and compared with the maximum-likelihood method, conventional kernel method with and without median filter, and nonlocal means (NLM) kernel method. Simulation results showed that the MNLM kernel method achieved visual and quantitative accuracy improvements (in terms of the ensemble mean squared error, bias versus variance, and contrast versus noise performances). Especially for frame 2 with the lowest count level of a single frame, the MNLM kernel method achieves lower ensemble mean squared error (10.43%) than the NLM kernel method (13.68%), conventional kernel method with and without median filter (11.88% and 23.50%), and MLEM algorithm (24.77%). The study on real low-dose ¹⁸F-FDG rat data also showed that the MNLM kernel method outperformed other methods in visual and quantitative accuracy improvements (in terms of regional noise versus intensity mean performance).

Rapid high-quality PET Patlak parametric image generation based on direct reconstruction and temporal nonlocal neural network

Parametric imaging based on dynamic positron emission tomography (PET) has wide applications in neurology. Compared to indirect methods, direct reconstruction methods, which reconstruct parametric images directly from the raw PET data, have superior image quality due to better noise modeling and richer information extracted from the PET raw data. For low-dose scenarios, the advantages of direct methods are more obvious. However, the wide adoption of direct reconstruction is inevitably impeded by the excessive computational demand and deficiency of the accessible raw data. In addition, motion modeling inside dynamic PET image reconstruction raises more computational challenges for direct reconstruction methods. In this work, we focused on the ¹⁸F-FDG Patlak model, and proposed a data-driven approach which can estimate the motion corrected full-dose direct Patlak images from the dynamic PET reconstruction series, based on a proposed novel temporal non-local convolutional neural network. During network training, direct reconstruction with motion correction based on full-dose dynamic PET sinograms was performed to obtain the training labels. The reconstructed full-dose /low-dose dynamic PET images were supplied as the network input. In addition, a temporal non-local block based on the dynamic PET images was proposed to better recover the structural information and reduce the image noise. During testing, the proposed network can directly output high-quality Patlak parametric images from the full-dose /low-dose dynamic PET images in seconds. Experiments based on 15 full-dose and 15 low-dose ¹⁸F-FDG brain datasets were conducted and analyzed to validate the feasibility of the proposed framework. Results show that the proposed framework can generate better image quality than reference methods.

Direct and indirect parameter imaging methods for dynamic PET

The method of reconstructing parametric images from dynamic positron emission tomography (PET) data with the linear Patlak model has been widely used in scientific research and clinical practice. Whether for direct or indirect image reconstruction, researchers have deeply investigated the associated methods and effects. Among the existing methods, the traditional maximum likelihood expectation maximization (MLEM) reconstruction algorithm is fast but produces a substantial amount of noise. If the parameter images obtained by the MLEM algorithm are postfiltered, a large amount of image edge information is lost. Additionally, although the kernel method has a better noise reduction effect, its calculation costs are very high due to the complexity of the algorithm. Therefore, to obtain parametric images with a high signal-to-noise ratio (SNR) and good retention of detailed information, here, we use guided kernel means (GKM) and dynamic PET image information to conduct guided filtering and perform parametric image reconstruction. We apply this method to direct and indirect reconstruction, and through computer simulations, we show that our proposed method has higher identifiability and a greater SNR than conventional direct and indirect reconstruction methods. We also show that our method produces better images with direct than with indirect reconstruction.

Neural MLAA for PET-enabled Dual-Energy CT Imaging

The PET-enabled dual-energy CT method allows dual-energy CT imaging on PET/CT scanners without the need for a second x-ray CT scan. A 511 keV γ-ray attenuation image can be reconstructed from time-of-flight PET emission data using the maximum-likelihood attenuation and activity (MLAA) algorithm. However, the attenuation image reconstructed by standard MLAA is commonly noisy. To suppress noise, we propose a neural-network approach for MLAA reconstruction. The PET attenuation image is described as a function of kernelized neural networks with the flexibility of incorporating the available x-ray CT image as anatomical prior. By applying optimization transfer, the complex optimization problem of the proposed neural MLAA reconstruction is solved by a modularized iterative algorithm with each iteration decomposed into three steps: PET activity image update, attenuation image update, and neural-network learning using a weighed mean squared-error loss. The optimization algorithm is guaranteed to monotonically increase the data likelihood. The results from computer simulations demonstrated the neural MLAA algorithm can achieve a significant improvement on the γ-ray CT image quality as compared to other algorithms.

3D/4D Reconstruction and Quantitative Total Body Imaging

Total-body PET image reconstruction follows a similar procedure to the image reconstruction process for standard whole-body PET scanners. One unique aspect of total-body imaging is simultaneous coverage of the entire human body, which makes it convenient to perform total-body dynamic PET scans. Therefore, four-dimensional dynamic PET reconstruction and parametric imaging are of great interest in total-body imaging. This article covers some basics of PET image reconstruction and then focuses on three- and four-dimensional PET reconstruction for total-body imaging. Methods for image formation from raw measurements in total-body PET are described. Challenges and opportunities in total-body PET image reconstruction are discussed.

PET imaging of neurotransmission using direct parametric reconstruction

Receptor ligand-based dynamic Positron Emission Tomography (PET) permits the measurement of neurotransmitter release in the human brain. For single-scan paradigms, the conventional method of estimating changes in neurotransmitter levels relies on fitting a pharmacokinetic model to activity concentration histories extracted after PET image reconstruction. However, due to the statistical fluctuations of activity concentration data at the voxel scale, parametric images computed using this approach often exhibit low signal-to-noise ratio, impeding characterization of neurotransmitter release. Numerous studies have shown that direct parametric reconstruction (DPR) approaches, which combine image reconstruction and kinetic analysis in a unified framework, can improve the signal-to-noise ratio of parametric mapping. However, there is little experience with DPR in imaging of neurotransmission and the performance of the approach in this application has not been evaluated before in humans. In this report, we present and evaluate a DPR methodology that computes 3-D distributions of ligand transport, binding potential (BP_ND) and neurotransmitter release magnitude (γ) from a dynamic sequence of PET sinograms. The technique employs the linear simplified reference region model (LSRRM) of Alpert et al. (2003), which represents an extension of the simplified reference region model that incorporates time-varying binding parameters due to radioligand displacement by release of neurotransmitter. Estimation of parametric images is performed by gradient-based optimization of a Poisson log-likelihood function incorporating LSRRM kinetics and accounting for the effects of head movement, attenuation, detector sensitivity, random and scattered coincidences. A ¹¹C-raclopride simulation study showed that the proposed approach substantially reduces the bias and variance of voxel-wise γ estimates as compared to standard methods. Moreover, simulations showed that detection of release could be made more reliable and/or conducted using a smaller sample size using the proposed DPR estimator. Likewise, images of BP_ND computed using DPR had substantially improved bias and variance properties. Application of the method in human subjects was demonstrated using ¹¹C-raclopride dynamic scans and a reward task, confirming the improved quality of the estimated parametric images using the proposed approach.

Probabilistic Graphical Models for Dynamic PET: A Novel Approach to Direct Parametric Map Estimation and Image Reconstruction

In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single-time frames, followed by the application of a suitable kinetic model to time-activity curves (TACs) at the voxel or region-of-interest level. Direct 4D positron emission tomography (PET) reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple time frames within the reconstruction task. Established direct methods are based on a deterministic description of voxelwise TACs, captured by the chosen kinetic model, considering the photon counting process the only source of uncertainty. In this paper, we introduce a new probabilistic modeling strategy based on the key assumption that activity time course would be subject to uncertainty even if the parameters of the underlying dynamic process are known. This leads to a hierarchical model that we formulate using the formalism of probabilistic graphical modeling. The inference is addressed using a new iterative algorithm, in which kinetic modeling results are treated as prior expectation of activity time course, rather than as a deterministic match, making it possible to control the trade-off between a data-driven and a model-driven reconstruction. The proposed method is flexible to an arbitrary choice of (linear and nonlinear) kinetic models, it enables the inclusion of arbitrary (sub)differentiable priors for parametric maps, and it is simple to implement. Computer simulations and an application to a real-patient scan show how the proposed method is able to generalize over conventional indirect and direct approaches, providing a bridge between them by properly tuning the impact of the kinetic modeling step on image reconstruction.

Direct List Mode Parametric Reconstruction for Dynamic Cardiac SPECT

Recently introduced stationary dedicated cardiac SPECT scanners provide new opportunities to quantify myocardial blood flow (MBF) using dynamic SPECT. However, comparing to PET, the low sensitivity of SPECT scanners affects MBF quantification due to the high noise level, especially for 201 Thallium (201Tl) due to its typically low injected dose. The conventional indirect method for generating parametric images typically starts by reconstructing a time series of frame images followed by fitting the time-activity curve (TAC) for each voxel or segment with an appropriate kinetic model. The indirect method is simple and easy to implement; however, it usually suffers from substantial image noise that could also lead to bias. In this paper, we developed a list mode direct parametric image reconstruction algorithm to substantially reduce noise in MBF quantification using dynamic SPECT and allow for patient radiation dose reduction. GPU-based parallel computing was used to achieve more than 2000-fold acceleration. The proposed method was evaluated in both simulation and in vivo canine studies. Compared with the indirect method, the proposed direct method achieved substantially lower image noise and variability, particularly at large number of iterations and at low-count levels.

Direct Parametric Maps Estimation from Dynamic PET Data: An Iterated Conditional Modes Approach

We propose and test a novel approach for direct parametric image reconstruction of dynamic PET data. We present a theoretical description of the problem of PET direct parametric maps estimation as an inference problem, from a probabilistic point of view, and we derive a simple iterative algorithm, based on the Iterated Conditional Mode (ICM) framework, which exploits the simplicity of a two-step optimization and the efficiency of an analytic method for estimating kinetic parameters from a nonlinear compartmental model. The resulting method is general enough to be flexible to an arbitrary choice of the kinetic model, and unlike many other solutions, it is capable to deal with nonlinear compartmental models without the need for linearization. We tested its performance on a two-tissue compartment model, including an analytical solution to the kinetic parameters evaluation, based on an auxiliary parameter set, with the aim of reducing computation errors and approximations. The new method is tested on simulated and clinical data. Simulation analysis led to the conclusion that the proposed algorithm gives a good estimation of the kinetic parameters in any noise condition. Furthermore, the application of the proposed method to clinical data gave promising results for further studies.

Direct Estimation of Voxel-Wise Neurotransmitter Response Maps From Dynamic PET Data

Computational methods, such as the linear parametric neurotransmitter PET (lp-ntPET) method, have been developed to characterize the transient changes in radiotracer kinetics in the target tissue during endogenous neurotransmitter release. In this paper, we describe and evaluate a parametric reconstruction algorithm that uses an expectation maximization framework, along with the lp-ntPET model, to estimate the endogenous neurotransmitter response to stimuli directly from the measured PET data. Computer simulations showed that the proposed direct reconstruction method offers improved accuracy and precision for the estimated timing parameters of the neurotransmitter response at the voxel level ( t_d=1±2 min, for activation onset bias and standard deviation) compared with conventional post reconstruction modeling ( t_d=4±7 min). In addition, we applied the proposed direct parameter estimation methodology to a [¹¹C]raclopride displacement study of an awake rat and generated parametric maps illustrating the magnitude of ligand displacement from striatum. Although the estimated parametric maps of activation magnitude obtained from both direct and post reconstruction methodologies suffered from false positive activations, the proposed direct reconstruction framework offered more reliable parametric maps when the activation onset parameter was constrained.

A kernel-based image denoising method for improving parametric image generation

One of the main challenges in the pixel-wise modeling analysis is the presence of high noise levels. Wang and Qi proposed a kernel-based method for dynamic positron emission tomgraphy reconstruction. Inspired by this method, we propose a kernel-based image denoising method based on the minimization of a kernel-based lp-norm regularized problem. To solve the kernel-based image denoising problem, we used the general-threshold filtering algorithm in combination with total difference. In the present study, we investigated whether diffusion-weighted magnetic resonance imaging (DW-MRI) data denoised using the proposed method can provide improved intravoxel incoherent motion (IVIM) parametric images. We also compared the proposed method with the method using the local principal component analysis (LPCA). The simulated DW-MR magnitude images are assumed to have Rician distributed noise. Computer simulations show that the proposed image denoising method can achieve a better bias-variance trade-off than the LPCA method. Moreover, the proposed method can reduce variance while simultaneously preserving edges in the parametric images. We tested our image denoising method on in vivo DW-MRI data, and the result showed that the denoised DWI-MRI data obtained using the proposed method can substantially improve the quality of IVIM parametric images.

Simultaneous estimation and segmentation from projection data in dynamic PET

PURPOSE

Dynamic positron emission tomography (PET) is known for its ability to extract spatiotemporal information of a radio tracer in living tissue. Information of different functional regions based on an accurate reconstruction of the activity images and kinetic parametric images has been widely studied and can be useful in research and clinical setting for diagnosis and other quantitative tasks. In this paper, our purpose is to present a novel framework for estimating the kinetic parametric images directly from the raw measurement data together with a simultaneous segmentation accomplished through kinetic parameters clustering.

METHOD

An iterative framework is proposed to estimate the kinetic parameter image, activity map and do the segmentation simultaneously from the complete dynamic PET projection data. The clustering process is applied to the kinetic parameter variable rather than to the traditional activity distribution so as to achieve accurate discrimination between different functional areas. Prior information such as total variation regularization is incorporated to reduce the noise in the PET images and a sparseness constraint is integrated to guarantee the solution for kinetic parameters due to the over complete dictionary. Alternating direction method of multipliers (ADMM) method is used to solve the optimization problem. The proposed algorithm was validated with experiments on Monte Carlo-simulated phantoms and real patient data. Symbol error rate (SER) was defined to evaluate the performance of clustering. Bias and variance of the reconstruction activity images were calculated based on ground truth. Relative mean square error (MSE) was used to evaluate parametric results quantitatively.

RESULT

In brain phantom experiment, when counting rate is 1 × 10⁶ , the bias (variance) of our method is 0.1270 (0.0281), which is lower than maximum likelihood expectation maximization (MLEM) 0.1637 (0.0410) and direct estimation without segmentation (DE) 0.1511 (0.0326). In the Zubal phantom experiment, our method has the lowest bias (variance) 0.1559 (0.0354) with 1 × 10⁵ counting rate, compared with DE 0.1820 (0.0435) and MLEM 0.3043 (0.0644). As for classification, the SER of our method is 18.87% which is the lowest among MLEM + k-means, DE + k-means, and kinetic spectral clustering (KSC). Brain data with MR reference and real patient results also show that the proposed method can get images with clear structure by visual inspection.

CONCLUSION

In this paper, we presented a joint reconstruction framework for simultaneously estimating the activity distribution, parametric images, and parameter-based segmentation of the ROIs into different functional areas. Total variation regularization is performed on the activity distribution domain to suppress noise and preserve the edges between ROIs. An over complete dictionary for time activity curve basis is constructed. SER, bias, variance, and MSE were calculated to show the effectiveness of the proposed method.

Parameterized level-set based pharmacokinetic fluorescence optical tomography using the regularized Gauss-Newton filter

Pharmacokinetic tomography is emerging as an important methodology for detecting abnormalities in tissue based upon spatially varying estimation of the pharmacokinetic rates governing the leakage of an injected fluorophore between blood plasma and tissue. We present a shape-based reconstruction framework of a compartment-model based formulation of this dynamic fluorescent optical tomography problem to solve for the pharmacokinetic rates and concentrations of the fluorophore from time-varying log intensity measurements of the optical signal. The compartment-model based state variable model is set up in a radial basis function parameterized level set setting. The state (concentrations) and (pharmacokinetic) parameter estimation problem is solved with an iteratively regularized Gauss-Newton filter in a trust-region framework. Reconstructions obtained using this scheme for noisy data obtained from cancer mimicking numerical phantoms of near/sub-cm sizes show a good localization of the affected regions and reasonable estimates of the pharmacokinetic rates and concentration curves.

Dynamic PET of human liver inflammation: impact of kinetic modeling with optimization-derived dual-blood input function

The hallmark of nonalcoholic steatohepatitis is hepatocellular inflammation and injury in the setting of hepatic steatosis. Recent work has indicated that dynamic 18F-FDG PET with kinetic modeling has the potential to assess hepatic inflammation noninvasively, while static FDG-PET is less promising. Because the liver has dual blood supplies, kinetic modeling of dynamic liver PET data is challenging in human studies. This paper aims to identify the optimal dual-input kinetic modeling approach for dynamic FDG-PET of human liver inflammation. Fourteen patients with nonalcoholic fatty liver disease were included. Each patient underwent 1 h dynamic FDG-PET/CT scan and had liver biopsy within six weeks. Three models were tested for kinetic analysis: the traditional two-tissue compartmental model with an image-derived single-blood input function (SBIF), a model with population-based dual-blood input function (DBIF), and a new model with optimization-derived DBIF through a joint estimation framework. The three models were compared using Akaike information criterion (AIC), F test and histopathologic inflammation score. Results showed that the optimization-derived DBIF model improved liver time activity curve fitting and achieved lower AIC values and higher F values than the SBIF and population-based DBIF models in all patients. The optimization-derived model significantly increased FDG K1 estimates by 101% and 27% as compared with traditional SBIF and population-based DBIF. K1 by the optimization-derived model was significantly associated with histopathologic grades of liver inflammation while the other two models did not provide a statistical significance. In conclusion, modeling of DBIF is critical for dynamic liver FDG-PET kinetic analysis in human studies. The optimization-derived DBIF model is more appropriate than SBIF and population-based DBIF for dynamic FDG-PET of liver inflammation.

Direct Patlak Reconstruction From Dynamic PET Data Using the Kernel Method With MRI Information Based on Structural Similarity

Positron emission tomography (PET) is a functional imaging modality widely used in oncology, cardiology, and neuroscience. It is highly sensitive, but suffers from relatively poor spatial resolution, as compared with anatomical imaging modalities, such as magnetic resonance imaging (MRI). With the recent development of combined PET/MR systems, we can improve the PET image quality by incorporating MR information into image reconstruction. Previously, kernel learning has been successfully embedded into static and dynamic PET image reconstruction using either PET temporal or MRI information. Here, we combine both PET temporal and MRI information adaptively to improve the quality of direct Patlak reconstruction. We examined different approaches to combine the PET and MRI information in kernel learning to address the issue of potential mismatches between MRI and PET signals. Computer simulations and hybrid real-patient data acquired on a simultaneous PET/MR scanner were used to evaluate the proposed methods. Results show that the method that combines PET temporal information and MRI spatial information adaptively based on the structure similarity index has the best performance in terms of noise reduction and resolution improvement.

Enhancement of dynamic myocardial perfusion PET images based on low-rank plus sparse decomposition

BACKGROUND AND OBJECTIVE

The absolute quantification of dynamic myocardial perfusion (MP) PET imaging is challenged by the limited spatial resolution of individual frame images due to division of the data into shorter frames. This study aims to develop a method for restoration and enhancement of dynamic PET images.

METHODS

We propose that the image restoration model should be based on multiple constraints rather than a single constraint, given the fact that the image characteristic is hardly described by a single constraint alone. At the same time, it may be possible, but not optimal, to regularize the image with multiple constraints simultaneously. Fortunately, MP PET images can be decomposed into a superposition of background vs. dynamic components via low-rank plus sparse (L + S) decomposition. Thus, we propose an L + S decomposition based MP PET image restoration model and express it as a convex optimization problem. An iterative soft thresholding algorithm was developed to solve the problem. Using realistic dynamic ⁸²Rb MP PET scan data, we optimized and compared its performance with other restoration methods.

RESULTS

The proposed method resulted in substantial visual as well as quantitative accuracy improvements in terms of noise versus bias performance, as demonstrated in extensive ⁸²Rb MP PET simulations. In particular, the myocardium defect in the MP PET images had improved visual as well as contrast versus noise tradeoff. The proposed algorithm was also applied on an 8-min clinical cardiac ⁸²Rb MP PET study performed on the GE Discovery PET/CT, and demonstrated improved quantitative accuracy (CNR and SNR) compared to other algorithms.

CONCLUSIONS

The proposed method is effective for restoration and enhancement of dynamic PET images.

Simplified estimation of binding parameters based on image-derived reference tissue models for dopamine transporter bindings in non-human primates using [18F]FE-PE2I and PET

The aim of this study on dopamine transporter binding by [¹⁸F]FE-PE2I and PET was to describe an image-derived approach using reference tissue models: the Logan DVR approach and simplified reference tissue model (SRTM), the features of which were simple to operate and precise in the measurements. Using the approach, the authors sought to obtain binding images and parameters. [¹⁸F]FE-PE2I and dynamic PET as well as an MRI was performed on three rhesus monkeys, and metabolite corrected arterial plasma inputs were obtained. After co-registering of PET to MR images, both image sets were resliced. The time-activity curve of the cerebellum was used as indirect input, and binding parametric images were computed voxel-by-voxel. Voxel-wise linear calculations were used for the Logan DVR approach, and nonlinear least squares fittings for the SRTM. To determine the best linear regression in the Logan DVR approach, the distribution volume ratio was obtained using the optimal starting frame analysis. The obtained binding parameters were compared with those obtained by the other independent ROI-based numerical approaches: two-tissue compartment model (2TCM), Logan DVR approach and SRTM using PMOD software. Binding potentials (BP) obtained by the present approach agreed well with those obtained by ROI-based numerical approaches, although reference tissue models tended to underestimate the BP value than 2TCM. Image-derived Logan approach provided a low-noise image, the computation time was short, and the error in the optimal starting frame analysis was small. The present approach provides a high-quality binding parametric image and reliable parameter value easily.

Population Pharmacokinetics of Tracers: A New Tool for Medical Imaging?

Positron emission tomography-computed tomography is a medical imaging method measuring the activity of a radiotracer chosen to accumulate in cancer cells. A recent trend of medical imaging analysis is to account for the radiotracer's pharmacokinetic properties at a voxel (three-dimensional-pixel) level to separate the different tissues. These analyses are closely linked to population pharmacokinetic-pharmacodynamic modelling. Kineticists possess the cultural background to improve medical imaging analysis. This article stresses the common points with population pharmacokinetics and highlights the methodological locks that need to be lifted.

Direct parametric reconstruction in dynamic PET myocardial perfusion imaging: in vivo studies

Dynamic PET myocardial perfusion imaging (MPI) used in conjunction with tracer kinetic modeling enables the quantification of absolute myocardial blood flow (MBF). However, MBF maps computed using the traditional indirect method (i.e. post-reconstruction voxel-wise fitting of kinetic model to PET time-activity-curves-TACs) suffer from poor signal-to-noise ratio (SNR). Direct reconstruction of kinetic parameters from raw PET projection data has been shown to offer parametric images with higher SNR compared to the indirect method. The aim of this study was to extend and evaluate the performance of a direct parametric reconstruction method using in vivo dynamic PET MPI data for the purpose of quantifying MBF. Dynamic PET MPI studies were performed on two healthy pigs using a Siemens Biograph mMR scanner. List-mode PET data for each animal were acquired following a bolus injection of ~7-8 mCi of 18F-flurpiridaz, a myocardial perfusion agent. Fully-3D dynamic PET sinograms were obtained by sorting the coincidence events into 16 temporal frames covering ~5 min after radiotracer administration. Additionally, eight independent noise realizations of both scans-each containing 1/8th of the total number of events-were generated from the original list-mode data. Dynamic sinograms were then used to compute parametric maps using the conventional indirect method and the proposed direct method. For both methods, a one-tissue compartment model accounting for spillover from the left and right ventricle blood-pools was used to describe the kinetics of 18F-flurpiridaz. An image-derived arterial input function obtained from a TAC taken in the left ventricle cavity was used for tracer kinetic analysis. For the indirect method, frame-by-frame images were estimated using two fully-3D reconstruction techniques: the standard ordered subset expectation maximization (OSEM) reconstruction algorithm on one side, and the one-step late maximum a posteriori (OSL-MAP) algorithm on the other side, which incorporates a quadratic penalty function. The parametric images were then calculated using voxel-wise weighted least-square fitting of the reconstructed myocardial PET TACs. For the direct method, parametric images were estimated directly from the dynamic PET sinograms using a maximum a posteriori (MAP) parametric reconstruction algorithm which optimizes an objective function comprised of the Poisson log-likelihood term, the kinetic model and a quadratic penalty function. Maximization of the objective function with respect to each set of parameters was achieved using a preconditioned conjugate gradient algorithm with a specifically developed pre-conditioner. The performance of the direct method was evaluated by comparing voxel- and segment-wise estimates of [Formula: see text], the tracer transport rate (ml · min-1 · ml-1), to those obtained using the indirect method applied to both OSEM and OSL-MAP dynamic reconstructions. The proposed direct reconstruction method produced [Formula: see text] maps with visibly lower noise than the indirect method based on OSEM and OSL-MAP reconstructions. At normal count levels, the direct method was shown to outperform the indirect method based on OSL-MAP in the sense that at matched level of bias, reduced regional noise levels were obtained. At lower count levels, the direct method produced [Formula: see text] estimates with significantly lower standard deviation across noise realizations than the indirect method based on OSL-MAP at matched bias level. In all cases, the direct method yielded lower noise and standard deviation than the indirect method based on OSEM. Overall, the proposed direct reconstruction offered a better bias-variance tradeoff than the indirect method applied to either OSEM and OSL-MAP. Direct parametric reconstruction as applied to in vivo dynamic PET MPI data is therefore a promising method for producing MBF maps with lower variance.

Direct Parametric Reconstruction With Joint Motion Estimation/Correction for Dynamic Brain PET Data

Direct reconstruction of parametric images from raw photon counts has been shown to improve the quantitative analysis of dynamic positron emission tomography (PET) data. However it suffers from subject motion which is inevitable during the typical acquisition time of 1-2 hours. In this work we propose a framework to jointly estimate subject head motion and reconstruct the motion-corrected parametric images directly from raw PET data, so that the effects of distorted tissue-to-voxel mapping due to subject motion can be reduced in reconstructing the parametric images with motion-compensated attenuation correction and spatially aligned temporal PET data. The proposed approach is formulated within the maximum likelihood framework, and efficient solutions are derived for estimating subject motion and kinetic parameters from raw PET photon count data. Results from evaluations on simulated [¹¹C]raclopride data using the Zubal brain phantom and real clinical [¹⁸F]florbetapir data of a patient with Alzheimer's disease show that the proposed joint direct parametric reconstruction motion correction approach can improve the accuracy of quantifying dynamic PET data with large subject motion.

A Bayesian spatial temporal mixtures approach to kinetic parametric images in dynamic positron emission tomography

PURPOSE

Estimation of parametric maps is challenging for kinetic models in dynamic positron emission tomography. Since voxel kinetics tend to be spatially contiguous, the authors consider groups of homogeneous voxels together. The authors propose a novel algorithm to identify the groups and estimate kinetic parameters simultaneously. Uncertainty estimates for kinetic parameters are also obtained.

METHODS

Mixture models were used to fit the time activity curves. In order to borrow information from spatially nearby voxels, the Potts model was adopted. A spatial temporal model was built incorporating both spatial and temporal information in the data. Markov chain Monte Carlo was used to carry out parameter estimation. Evaluation and comparisons with existing methods were carried out on cardiac studies using both simulated data sets and a pig study data. One-compartment kinetic modeling was used, in which K1 is the parameter of interest, providing a measure of local perfusion.

RESULTS

Based on simulation experiments, the median standard deviation across all image voxels, of K1 estimates were 0, 0.13, and 0.16 for the proposed spatial mixture models (SMMs), standard curve fitting, and spatial K-means methods, respectively. The corresponding median mean squared biases for K1 were 0.04, 0.06, and 0.06 for abnormal region of interest (ROI); 0.03, 0.03, and 0.04 for normal ROI; and 0.007, 0.02, and 0.05 for the noise region.

CONCLUSIONS

SMM is a fully Bayesian algorithm which determines the optimal number of homogeneous voxel groups, voxel group membership, parameter estimation, and parameter uncertainty estimation simultaneously. The voxel membership can also be used for classification purposes. By borrowing information from spatially nearby voxels, SMM substantially reduces the variability of parameter estimates. In some ROIs, SMM also reduces mean squared bias.

Dynamic positron emission tomography restoration with low-rank representation incorporating edge preservation

BACKGROUND

Dynamic positron emission tomography (PET) is a powerful tool that provides useful quantitative information on physiological and biochemical processes. However, the low signal-to-noise ratio (SNR) in short dynamic frames is a challenge.

OBJECTIVE

To get high SNR in the dynamic PET and to achieve high-quality PET parametric image are the objective of this study.

METHODS

Low-rank (LR) modeling and edge-preserving prior are incorporated in this study with a unified mathematical framework to improve the SNR of a dynamic PET image series. The proposed algorithm is designed to reduce noise in homogeneous areas while preserving the edges of regions of interest.

RESULTS

The performance of the proposed method (LRH) is compared both visually and quantitatively by using the classic Gaussian filter and an LR expression filter on a digital brain phantom and in vivo rat study. Experimental results demonstrate that the proposed filter can achieve superior visual and quantitative performance without sacrificing spatial resolution.

CONCLUSIONS

The proposed LRH is considerably effective and exhibits great potential in processing dynamic PET data with high noise levels.

Investigation of optimization-based reconstruction with an image-total-variation constraint in PET

Interest remains in reconstruction-algorithm research and development for possible improvement of image quality in current PET imaging and for enabling innovative PET systems to enhance existing, and facilitate new, preclinical and clinical applications. Optimization-based image reconstruction has been demonstrated in recent years of potential utility for CT imaging applications. In this work, we investigate tailoring the optimization-based techniques to image reconstruction for PET systems with standard and non-standard scan configurations. Specifically, given an image-total-variation (TV) constraint, we investigated how the selection of different data divergences and associated parameters impacts the optimization-based reconstruction of PET images. The reconstruction robustness was explored also with respect to different data conditions and activity up-takes of practical relevance. A study was conducted particularly for image reconstruction from data collected by use of a PET configuration with sparsely populated detectors. Overall, the study demonstrates the robustness of the TV-constrained, optimization-based reconstruction for considerably different data conditions in PET imaging, as well as its potential to enable PET configurations with reduced numbers of detectors. Insights gained in the study may be exploited for developing algorithms for PET-image reconstruction and for enabling PET-configuration design of practical usefulness in preclinical and clinical applications.

Whole-body direct 4D parametric PET imaging employing nested generalized Patlak expectation-maximization reconstruction

Whole-body (WB) dynamic PET has recently demonstrated its potential in translating the quantitative benefits of parametric imaging to the clinic. Post-reconstruction standard Patlak (sPatlak) WB graphical analysis utilizes multi-bed multi-pass PET acquisition to produce quantitative WB images of the tracer influx rate K i as a complimentary metric to the semi-quantitative standardized uptake value (SUV). The resulting K i images may suffer from high noise due to the need for short acquisition frames. Meanwhile, a generalized Patlak (gPatlak) WB post-reconstruction method had been suggested to limit K i bias of sPatlak analysis at regions with non-negligible (18)F-FDG uptake reversibility; however, gPatlak analysis is non-linear and thus can further amplify noise. In the present study, we implemented, within the open-source software for tomographic image reconstruction platform, a clinically adoptable 4D WB reconstruction framework enabling efficient estimation of sPatlak and gPatlak images directly from dynamic multi-bed PET raw data with substantial noise reduction. Furthermore, we employed the optimization transfer methodology to accelerate 4D expectation-maximization (EM) convergence by nesting the fast image-based estimation of Patlak parameters within each iteration cycle of the slower projection-based estimation of dynamic PET images. The novel gPatlak 4D method was initialized from an optimized set of sPatlak ML-EM iterations to facilitate EM convergence. Initially, realistic simulations were conducted utilizing published (18)F-FDG kinetic parameters coupled with the XCAT phantom. Quantitative analyses illustrated enhanced K i target-to-background ratio (TBR) and especially contrast-to-noise ratio (CNR) performance for the 4D versus the indirect methods and static SUV. Furthermore, considerable convergence acceleration was observed for the nested algorithms involving 10-20 sub-iterations. Moreover, systematic reduction in K i % bias and improved TBR were observed for gPatlak versus sPatlak. Finally, validation on clinical WB dynamic data demonstrated the clinical feasibility and superior K i CNR performance for the proposed 4D framework compared to indirect Patlak and SUV imaging.

A Functional Approach to Deconvolve Dynamic Neuroimaging Data

Positron emission tomography (PET) is an imaging technique which can be used to investigate chemical changes in human biological processes such as cancer development or neurochemical reactions. Most dynamic PET scans are currently analyzed based on the assumption that linear first-order kinetics can be used to adequately describe the system under observation. However, there has recently been strong evidence that this is not the case. To provide an analysis of PET data which is free from this compartmental assumption, we propose a nonparametric deconvolution and analysis model for dynamic PET data based on functional principal component analysis. This yields flexibility in the possible deconvolved functions while still performing well when a linear compartmental model setup is the true data generating mechanism. As the deconvolution needs to be performed on only a relative small number of basis functions rather than voxel by voxel in the entire three-dimensional volume, the methodology is both robust to typical brain imaging noise levels while also being computationally efficient. The new methodology is investigated through simulations in both one-dimensional functions and 2D images and also applied to a neuroimaging study whose goal is the quantification of opioid receptor concentration in the brain.

Dynamic PET reconstruction using temporal patch-based low rank penalty for ROI-based brain kinetic analysis

Dynamic positron emission tomography (PET) is widely used to measure changes in the bio-distribution of radiopharmaceuticals within particular organs of interest over time. However, to retain sufficient temporal resolution, the number of photon counts in each time frame must be limited. Therefore, conventional reconstruction algorithms such as the ordered subset expectation maximization (OSEM) produce noisy reconstruction images, thus degrading the quality of the extracted time activity curves (TACs). To address this issue, many advanced reconstruction algorithms have been developed using various spatio-temporal regularizations. In this paper, we extend earlier results and develop a novel temporal regularization, which exploits the self-similarity of patches that are collected in dynamic images. The main contribution of this paper is to demonstrate that the correlation of patches can be exploited using a low-rank constraint that is insensitive to global intensity variations. The resulting optimization framework is, however, non-Lipschitz and nonconvex due to the Poisson log-likelihood and low-rank penalty terms. Direct application of the conventional Poisson image deconvolution by an augmented Lagrangian (PIDAL) algorithm is, however, problematic due to its large memory requirements, which prevents its parallelization. Thus, we propose a novel optimization framework using the concave-convex procedure (CCCP)

Direct Parametric Reconstruction Using Anatomical Regularization for Simultaneous PET/MRI Data

Pharmacokinetic analysis of dynamic positron emission tomography (PET) imaging data maps the measured time activity curves to a set of model-specific pharmacokinetic parameters. Voxel-based parameter estimation via curve fitting is conventionally performed indirectly on a sequence of independently reconstructed PET images, leading to high variance and bias in the parametric images. We propose a direct parametric reconstruction algorithm with raw projection data as input that leverages high-resolution anatomical information simultaneously obtained from magnetic resonance (MR) imaging in a PET/MRI scanner for regularization. The reconstruction problem is formulated in a flexible Bayesian framework with Gaussian Markov Random field modeling of activity, parameters, or both simultaneously. MR information is incorporated through a Bowsher-like prior function. Optimization transfer using an expectation-maximization surrogate and a new Bowsher-like penalty surrogate is applied to obtain a voxel-separable algorithm that interleaves a reconstruction with a fitting step. An analytical input function model is used. The algorithm is evaluated on simulated [(18)F]FDG and clinical [(18)F]FET brain data acquired with a Biograph mMR. The results indicate that direct and simultaneously regularized parametric reconstruction increases image quality. Anatomical regularization leads to higher contrast than conventional distance-weighted regularization.

Direct Parametric Image Reconstruction in Reduced Parameter Space for Rapid Multi-Tracer PET Imaging

The separation of multiple PET tracers within an overlapping scan based on intrinsic differences of tracer pharmacokinetics is challenging, due to limited signal-to-noise ratio (SNR) of PET measurements and high complexity of fitting models. In this study, we developed a direct parametric image reconstruction (DPIR) method for estimating kinetic parameters and recovering single tracer information from rapid multi-tracer PET measurements. This is achieved by integrating a multi-tracer model in a reduced parameter space (RPS) into dynamic image reconstruction. This new RPS model is reformulated from an existing multi-tracer model and contains fewer parameters for kinetic fitting. Ordered-subsets expectation-maximization (OSEM) was employed to approximate log-likelihood function with respect to kinetic parameters. To incorporate the multi-tracer model, an iterative weighted nonlinear least square (WNLS) method was employed. The proposed multi-tracer DPIR (MT-DPIR) algorithm was evaluated on dual-tracer PET simulations ([18F]FDG and [11C]MET) as well as on preclinical PET measurements ([18F]FLT and [18F]FDG). The performance of the proposed algorithm was compared to the indirect parameter estimation method with the original dual-tracer model. The respective contributions of the RPS technique and the DPIR method to the performance of the new algorithm were analyzed in detail. For the preclinical evaluation, the tracer separation results were compared with single [18F]FDG scans of the same subjects measured two days before the dual-tracer scan. The results of the simulation and preclinical studies demonstrate that the proposed MT-DPIR method can improve the separation of multiple tracers for PET image quantification and kinetic parameter estimations.

Bayesian Framework Based Direct Reconstruction of Fluorescence Parametric Images

Fluorescence imaging has been successfully used in the study of pharmacokinetic analysis, while dynamic fluorescence molecular tomography (FMT) is an attractive imaging technique for three-dimensionally resolving the metabolic process of fluorescent biomarkers in small animals in vivo. Parametric images obtained by combining dynamic FMT with compartmental modeling can provide quantitative physiological information for biological studies and drug development. However, images obtained with conventional indirect methods suffer from poor image quality because of failure in utilizing the temporal correlations of boundary measurements. Besides, FMT suffers from low spatial resolution due to its ill-posed nature, which further reduces the image quality. In this paper, we propose a novel method to directly reconstruct parametric images from boundary measurements based on maximum a posteriori (MAP) estimation with structural priors in a Bayesian framework. The proposed method can utilize structural priors obtained from an X-ray computed tomography system to mitigate the ill-posedness of dynamic FMT inverse problem, and use direct reconstruction strategy to make full use of temporal correlations of boundary measurements. The results of numerical simulations and in vivo mouse experiments demonstrate that the proposed method leads to significant improvements in the reconstruction quality of parametric images as compared with the conventional indirect method and a previously developed direct method.

Acceleration of dynamic fluorescence molecular tomography with principal component analysis

Dynamic fluorescence molecular tomography (FMT) is an attractive imaging technique for three-dimensionally resolving the metabolic process of fluorescent biomarkers in small animal. When combined with compartmental modeling, dynamic FMT can be used to obtain parametric images which can provide quantitative pharmacokinetic information for drug development and metabolic research. However, the computational burden of dynamic FMT is extremely huge due to its large data sets arising from the long measurement process and the densely sampling device. In this work, we propose to accelerate the reconstruction process of dynamic FMT based on principal component analysis (PCA). Taking advantage of the compression property of PCA, the dimension of the sub weight matrix used for solving the inverse problem is reduced by retaining only a few principal components which can retain most of the effective information of the sub weight matrix. Therefore, the reconstruction process of dynamic FMT can be accelerated by solving the smaller scale inverse problem. Numerical simulation and mouse experiment are performed to validate the performance of the proposed method. Results show that the proposed method can greatly accelerate the reconstruction of parametric images in dynamic FMT almost without degradation in image quality.

Application of adaptive kinetic modelling for bias propagation reduction in direct 4D image reconstruction

Parametric imaging in thoracic and abdominal PET can provide additional parameters more relevant to the pathophysiology of the system under study. However, dynamic data in the body are noisy due to the limiting counting statistics leading to suboptimal kinetic parameter estimates. Direct 4D image reconstruction algorithms can potentially improve kinetic parameter precision and accuracy in dynamic PET body imaging. However, construction of a common kinetic model is not always feasible and in contrast to post-reconstruction kinetic analysis, errors in poorly modelled regions may spatially propagate to regions which are well modelled. To reduce error propagation from erroneous model fits, we implement and evaluate a new approach to direct parameter estimation by incorporating a recently proposed kinetic modelling strategy within a direct 4D image reconstruction framework. The algorithm uses a secondary more general model to allow a less constrained model fit in regions where the kinetic model does not accurately describe the underlying kinetics. A portion of the residuals then is adaptively included back into the image whilst preserving the primary model characteristics in other well modelled regions using a penalty term that trades off the models. Using fully 4D simulations based on dynamic [(15)O]H2O datasets, we demonstrate reduction in propagation-related bias for all kinetic parameters. Under noisy conditions, reductions in bias due to propagation are obtained at the cost of increased noise, which in turn results in increased bias and variance of the kinetic parameters. This trade-off reflects the challenge of separating the residuals arising from poor kinetic modelling fits from the residuals arising purely from noise. Nonetheless, the overall root mean square error is reduced in most regions and parameters. Using the adaptive 4D image reconstruction improved model fits can be obtained in poorly modelled regions, leading to reduced errors potentially propagating to regions of interest which the primary biologic model accurately describes. The proposed methodology, however, depends on the secondary model and choosing an optimal model on the residual space is critical in improving model fits.

Direct reconstruction of cardiac PET kinetic parametric images using a preconditioned conjugate gradient approach

PURPOSE

Our research goal is to develop an algorithm to reconstruct cardiac positron emission tomography (PET) kinetic parametric images directly from sinograms and compare its performance with the conventional indirect approach.

METHODS

Time activity curves of a NCAT phantom were computed according to a one-tissue compartmental kinetic model with realistic kinetic parameters. The sinograms at each time frame were simulated using the activity distribution for the time frame. The authors reconstructed the parametric images directly from the sinograms by optimizing a cost function, which included the Poisson log-likelihood and a spatial regularization terms, using the preconditioned conjugate gradient (PCG) algorithm with the proposed preconditioner. The proposed preconditioner is a diagonal matrix whose diagonal entries are the ratio of the parameter and the sensitivity of the radioactivity associated with parameter. The authors compared the reconstructed parametric images using the direct approach with those reconstructed using the conventional indirect approach.

RESULTS

At the same bias, the direct approach yielded significant relative reduction in standard deviation by 12%-29% and 32%-70% for 50 × 10(6) and 10 × 10(6) detected coincidences counts, respectively. Also, the PCG method effectively reached a constant value after only 10 iterations (with numerical convergence achieved after 40-50 iterations), while more than 500 iterations were needed for CG.

CONCLUSIONS

The authors have developed a novel approach based on the PCG algorithm to directly reconstruct cardiac PET parametric images from sinograms, and yield better estimation of kinetic parameters than the conventional indirect approach, i.e., curve fitting of reconstructed images. The PCG method increases the convergence rate of reconstruction significantly as compared to the conventional CG method.

Patlak image estimation from dual time-point list-mode PET data

We investigate using dual time-point PET data to perform Patlak modeling. This approach can be used for whole body dynamic PET studies in which we compute voxel-wise estimates of Patlak parameters using two frames of data for each bed position. Our approach directly uses list-mode arrival times for each event to estimate the Patlak parametric image. We use a penalized likelihood method in which the penalty function uses spatially variant weighting to ensure a count independent local impulse response. We evaluate performance of the method in comparison to fractional changes in SUV values (%DSUV) between the two frames using Cramer Rao analysis and Monte Carlo simulation. Receiver operating characteristic (ROC) curves are used to compare performance in differentiating tumors relative to background based on the dynamic data sets. Using area under the ROC curve as a performance metric, we show superior performance of Patlak relative to %DSUV over a range of dynamic data sets and parameters. These results suggest that Patlak analysis may be appropriate for analysis of dual time-point whole body PET data and could lead to superior detection of tumors relative to %DSUV metrics.