Acceleration of the direct reconstruction of linear parametric images using nested algorithms

Direct Patlak Reconstruction of [68Ga]Ga-PSMA PET for the Evaluation of Primary Prostate Cancer Prior Total Prostatectomy: Results of a Pilot Study

To investigate the use of kinetic parameters derived from direct Patlak reconstructions of [68Ga]Ga-PSMA-11 positron emission tomography/computed tomography (PET/CT) to predict the histological grade of malignancy of the primary tumor of patients with prostate cancer (PCa). Thirteen patients (mean age 66 ± 10 years) with a primary, therapy-naïve PCa (median PSA 9.3 [range: 6.3-130 µg/L]) prior radical prostatectomy, were recruited in this exploratory prospective study. A dynamic whole-body [68Ga]Ga-PSMA-11 PET/CT scan was performed for all patients. Measured quantification parameters included Patlak slope (Ki: absolute rate of tracer consumption) and Patlak intercept (Vb: degree of tracer perfusion in the tumor). Additionally, the mean and maximum standardized uptake values (SUVmean and SUVmax) of the tumor were determined from a static PET 60 min post tracer injection. In every patient, initial PSA (iPSA) values that were also the PSA level at the time of the examination and final histology results with Gleason score (GS) grading were correlated with the quantitative readouts. Collectively, 20 individual malignant prostate lesions were ascertained and histologically graded for GS with ISUP classification. Six lesions were classified as ISUP 5, two as ISUP 4, eight as ISUP 3, and four as ISUP 2. In both static and dynamic PET/CT imaging, the prostate lesions could be visually distinguished from the background. The average values of the SUVmean, slope, and intercept of the background were 2.4 (±0.4), 0.015 1/min (±0.006), and 52% (±12), respectively. These were significantly lower than the corresponding parameters extracted from the prostate lesions (all p < 0.01). No significant differences were found between these values and the various GS and ISUP (all p > 0.05). Spearman correlation coefficient analysis demonstrated a strong correlation between static and dynamic PET/CT parameters (all r ≥ 0.70, p < 0.01). Both GS and ISUP grading revealed only weak correlations with the mean and maximum SUV and tumor-to-background ratio derived from static images and dynamic Patlak slope. The iPSA demonstrated no significant correlation with GS and ISUP grading or with dynamic and static PET parameter values. In this cohort of mainly high-risk PCa, no significant correlation between [68Ga]Ga-PSMA-11 perfusion and consumption and the aggressiveness of the primary tumor was observed. This suggests that the association between SUV values and GS may be more distinctive when distinguishing clinically relevant from clinically non-relevant PCa.

Four-dimensional quantitative analysis using FDG-PET in clinical oncology

Positron emission tomography (PET) with F-18 fluorodeoxyglucose (FDG) has been commonly used in many oncological areas. High-resolution PET permits a three-dimensional analysis of FDG distributions on various lesions in vivo, which can be applied for tissue characterization, risk analysis, and treatment monitoring after chemoradiotherapy and immunotherapy. Metabolic changes can be assessed using the tumor absolute FDG uptake as standardized uptake value (SUV) and metabolic tumor volume (MTV). In addition, tumor heterogeneity assessment can potentially estimate tumor aggressiveness and resistance to chemoradiotherapy. Attempts have been made to quantify intratumoral heterogeneity using radiomics. Recent reports have indicated the clinical feasibility of a dynamic FDG PET-computed tomography (CT) in pilot cohort studies of oncological cases. Dynamic imaging permits the assessment of temporal changes in FDG uptake after administration, which is particularly useful for differentiating pathological from physiological uptakes with high diagnostic accuracy. In addition, several new parameters have been introduced for the in vivo quantitative analysis of FDG metabolic processes. Thus, a four-dimensional FDG PET-CT is available for precise tissue characterization of various lesions. This review introduces various new techniques for the quantitative analysis of FDG distribution and glucose metabolism using a four-dimensional FDG analysis with PET-CT. This elegant study reveals the important role of tissue characterization and treatment strategies in oncology.

Parametric Imaging of Biologic Activity of Atherosclerosis Using Dynamic Whole-Body Positron Emission Tomography

BACKGROUND

For molecular imaging of atherosclerotic vessel wall activity, tracer kinetic analysis may yield improved contrast versus blood, more robust quantitative parameters, and more reliable characterization of systems biology.

OBJECTIVES

The authors introduce a novel dynamic whole-body positron emission tomography (PET) protocol that is enabled by rapid continuous camera table motion, followed by reconstruction of parametric data sets using voxel-based Patlak graphical analysis.

METHODS

Twenty-five subjects were prospectively enrolled and underwent dynamic PET up to 90 minutes after injection of 2-[¹⁸F]fluoro-2-deoxy-D-glucose (FDG). Two sets of images were generated: 1) the established standard of static standardized uptake value (SUV) images; and 2) parametric images of the metabolic rate of FDG (MR_FDG) using the Patlak plot-derived influx rate. Arterial wall signal was measured and compared using the volume-of-interest technique, and its association with hematopoietic and lymphoid organ signal and atherosclerotic risk factors was explored.

RESULTS

Parametric MR_FDG images provided excellent arterial wall visualization, with elimination of blood-pool activity, and enhanced focus detectability and reader confidence. Target-to-background ratio (TBR) from MR_FDG images was significantly higher compared with SUV images (2.6 ± 0.8 vs 1.4 ± 0.2; P < 0.0001), confirming improved arterial wall contrast. On MR_FDG images, arterial wall signal showed improved correlation with hematopoietic and lymphoid organ activity (spleen P = 0.0009; lymph nodes P = 0.0055; and bone marrow P = 0.0202) and increased with the number of atherosclerotic risk factors (r = 0.49; P = 0.0138), where signal from SUV images (SUV_maxP = 0.9754; TBR_maxP = 0.8760) did not.

CONCLUSIONS

Absolute quantification of MR_FDG is feasible for arterial wall using dynamic whole-body PET imaging. Parametric images provide superior arterial wall contrast, and they might be better suited to explore the relationship between arterial wall activity, systemic organ networks, and cardiovascular risk. This novel methodology may serve as a platform for future diagnostic and therapeutic clinical studies targeting the biology of arterial wall disease.

Clinical validation of a population-based input function for 20-min dynamic whole-body 18F-FDG multiparametric PET imaging

Purpose

Contemporary PET/CT scanners can use 70-min dynamic whole-body (D-WB) PET to generate more quantitative information about FDG uptake than just the SUV by generating parametric images of FDG metabolic rate (MR_FDG). The analysis requires the late (50–70 min) D-WB tissue data combined with the full (0–70 min) arterial input function (AIF). Our aim was to assess whether the use of a scaled population-based input function (sPBIF) obviates the need for the early D-WB PET acquisition and allows for a clinically feasible 20-min D-WB PET examination.

Methods

A PBIF was calculated based on AIFs from 20 patients that were D-WB PET scanned for 120 min with simultaneous arterial blood sampling. MR_FDG imaging using PBIF requires that the area under the curve (AUC) of the sPBIF is equal to the AUC of the individual patient’s input function because sPBIF AUC bias translates into MR_FDG bias. Special patient characteristics could affect the shape of their AIF. Thus, we validated the use of PBIF in 171 patients that were divided into 12 subgroups according to the following characteristics: diabetes, cardiac ejection fraction, blood pressure, weight, eGFR and age. For each patient, the PBIF was scaled to the aorta image-derived input function (IDIF) to calculate a sPBIF, and the AUC bias was calculated.

Results

We found excellent agreement between the AIF and IDIF at all times. For the clinical validation, the use of sPBIF led to an acceptable AUC bias of 1–5% in most subgroups except for patients with diabetes or patients with low eGFR, where the biases were marginally higher at 7%. Multiparametric MR_FDG images based on a short 20-min D-WB PET and sPBIF were visually indistinguishable from images produced by the full 70-min D-WB PET and individual IDIF.

Conclusions

A short 20-min D-WB PET examination using PBIF can be used for multiparametric imaging without compromising the image quality or precision of MR_FDG. The D-WB PET examination may therefore be used in clinical routine for a wide range of patients, potentially allowing for more precise quantification in e.g. treatment response imaging.

Supplementary Information

The online version contains supplementary material available at 10.1186/s40658-022-00490-y.

Normal values for 18F-FDG uptake in organs and tissues measured by dynamic whole body multiparametric FDG PET in 126 patients

BACKGROUND

Dynamic whole-body (D-WB) FDG PET/CT is a recently developed technique that allows direct reconstruction of multiparametric images of metabolic rate of FDG uptake (MR_FDG) and "free" FDG (DV_FDG). Multiparametric images have a markedly different appearance than the conventional SUV images obtained by static PET imaging, and normal values of MR_FDG and DV_FDG in frequently used reference tissues and organs are lacking. The aim of this study was therefore to: (1) provide an overview of normal MR_FDG and DV_FDG values and range of variation in organs and tissues; (2) analyse organ time-activity curves (TACs); (3) validate the accuracy of directly reconstructed MR_FDG tissue values versus manually calculated K_i (and MR_FDG) values; and (4) explore correlations between demographics, blood glucose levels and MR_FDG values. D-WB data from 126 prospectively recruited patients (100 without diabetes and 26 with diabetes) were retrospectively analysed. Participants were scanned using a 70-min multiparametric PET acquisition protocol on a Siemens Biograph Vision 600 PET/CT scanner. 13 regions (bone, brain grey and white matter, colon, heart, kidney, liver, lung, skeletal muscle of the back and thigh, pancreas, spleen, and stomach) as well as representative pathological findings were manually delineated, and values of static PET (SUV), D-WB PET (K_i, MR_FDG and DV_FDG) and individual TACs were extracted. Multiparametric values were compared with manual TAC-based calculations of K_i and MR_FDG, and correlations with blood glucose, age, weight, BMI, and injected tracer dose were explored.

RESULTS

Tissue and organ MR_FDG values showed little variation, comparable to corresponding SUV variation. All regional TACs were in line with previously published FDG kinetics, and the multiparametric metrics correlated well with manual TAC-based calculations (r² = 0.97, p < 0.0001). No correlations were observed between glucose levels and MR_FDG in tissues known not to be substrate driven, while tissues with substrate driven glucose uptake had significantly correlated glucose levels and MR_FDG values.

CONCLUSION

The multiparametric D-WB PET scan protocol provides normal MR_FDG values with little inter-subject variation and in agreement with manual TAC-based calculations and literature values. The technique therefore facilitates both accurate clinical reports and simpler acquisition of quantitative estimates of whole-body tissue glucose metabolism.

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 whole-body FDG-PET imaging for oncology studies

Introduction

Recent PET/CT systems have improved sensitivity and spatial resolution by smaller PET detectors and improved reconstruction software. In addition, continuous-bed-motion mode is now available in some PET systems for whole-body PET imaging. In this review, we describe the advantages of dynamic whole-body FDG-PET in oncology studies.

Methods

PET–CT imaging was obtained at 60 min after FDG administration. Dynamic whole-body imaging with continuous bed motion in 3 min each with flow motion was obtained over 400 oncology cases. For routine image analysis, these dynamic phases (usually four phases) were summed as early FDG imaging. The image quality of each serial dynamic imaging was visually evaluated. In addition, changes in FDG uptake were analyzed in consecutive dynamic imaging and also in early delayed (90 min after FDG administration) time point imaging (dual-time-point imaging; DTPI). Image interpretation was performed by consensus of two nuclear medicine physicians.

Result

All consecutive dynamic whole-body PET images of 3 min duration had acceptable image quality. Many of the areas with physiologically high FDG uptake had altered uptake on serial images. On the other hand, most of the benign and malignant lesions did not show visual changes on serial images. In the study of 60 patients with suspected colorectal cancer, unchanged uptake was noted in almost all regions with pathologically proved FDG uptake, indicating high sensitivity with high negative predictive value on both serial dynamic imaging and on DTPI. We proposed another application of serial dynamic imaging for minimizing motion artifacts for patients who may be likely to move during PET studies.

Discussion

Dynamic whole-body imaging has several advantages over the static imaging. Serial assessment of changes in FDG uptake over a short period of time is useful for distinguishing pathological from physiological uptake, especially in the abdominal regions. These dynamic PET studies may minimize the need for DPTI. In addition, continuous dynamic imaging has the potential to reduce motion artifacts in patients who are likely to move during PET imaging. Furthermore, kinetic analysis of the FDG distribution in tumor areas has a potential for precise tissue characterization.

Conclusion

Dynamic whole-body FDG-PET imaging permits assessment of serial FDG uptake change which is particularly useful for differentiation of pathological uptake from physiological uptake with high diagnostic accuracy. This imaging can be applied for minimizing motion artifacts. Wide clinical applications of such serial, dynamic whole-body PET imaging is expected in oncological studies in the near future.

First results on kinetic modelling and parametric imaging of dynamic 18F-FDG datasets from a long axial FOV PET scanner in oncological patients

PURPOSE

To investigate the kinetics of ¹⁸F-fluorodeoxyglucose (¹⁸F-FDG) by positron emission tomography (PET) in multiple organs and test the feasibility of total-body parametric imaging using an image-derived input function (IDIF).

METHODS

Twenty-four oncological patients underwent dynamic ¹⁸F-FDG scans lasting 65 min using a long  axial FOV (LAFOV) PET/CT system. Time activity curves (TAC) were extracted from semi-automated segmentations of multiple organs, cerebral grey and white matter, and from vascular structures. The tissue and tumor lesion TACs were fitted using an irreversible two-tissue compartment (2TC) and a Patlak model. Parametric images were also generated using direct and indirect Patlak methods and their performances were evaluated.

RESULTS

We report estimates of kinetic parameters and metabolic rate of glucose consumption (MR_FDG) for different organs and tumor lesions. In some organs, there were significant differences between MR_FDG values estimated using 2TC and Patlak models. No statistically significant difference was seen between MR_FDG values estimated using 2TC and Patlak methods in tumor lesions (paired t-test, P = 0.65). Parametric imaging showed that net influx (K_i) images generated using direct and indirect Patlak methods had superior tumor-to-background ratio (TBR) to standard uptake value (SUV) images (3.1- and 3.0-fold mean increases in TBR_mean, respectively). Influx images generated using the direct Patlak method had twofold higher contrast-to-noise ratio in tumor lesions compared to images generated using the indirect Patlak method.

CONCLUSION

We performed pharmacokinetic modelling of multiple organs using linear and non-linear models using dynamic total-body ¹⁸F-FDG images. Although parametric images did not reveal more tumors than SUV images, the results confirmed that parametric imaging furnishes improved tumor contrast. We thus demonstrate the feasibility of total-body kinetic modelling and parametric imaging in basic research and oncological studies. LAFOV PET can enhance dynamic imaging capabilities by providing high sensitivity parametric images and allowing total-body pharmacokinetic analysis.

Dictionary Learning Constrained Direct Parametric Estimation in Dynamic Myocardial Perfusion PET

In myocardial perfusion imaging with dynamic positron emission tomography (PET), direct parametric reconstruction from the projection data allows accurate modeling of the Poisson noise in the projection domain to provide more reliable estimate of the parametric images. In this study, we propose to incorporate a superior denoiser to efficiently suppress the unfavorable noise propagation during the direct reconstruction. The dictionary learning (DL) based sparse representation serves as a regularization term to constrain the intermediate K₁ estimation. We rewrite the DL regularizer into a voxel-separable form to facilitate the decoupling of a DL penalized curve fitting from the reconstruction of dynamic frames. The nonlinear fitting is then solved by a damped Newton method with uniform initialization. Using simulated and patient ⁸²Rb dynamic PET data, we study the performance of the proposed DL direct algorithm and quantitatively compare it with the indirect method with or without post-filtering, the direct reconstruction without regularization, and the quadratic penalty regularized direct algorithm. The DL regularized direct reconstruction achieves improved noise versus bias performance in the reconstructed K₁ images as well as superior recovery of a reduced myocardial blood flow defect. The dictionary learned from a 3D self-created hollow sphere image yields comparable results to those using the dictionary learned from the corresponding magnetic resonance image. The uniform initializations converge to K₁ estimations similar to the result from initializing with the indirect reconstruction. To summarize, we demonstrate the potential of the proposed DL constrained direct parametric reconstruction in improving quantitative dynamic PET imaging.

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).

Use of dynamic reconstruction for parametric Patlak imaging in dynamic whole body PET

Dynamic whole body (DWB) PET acquisition protocols enable the use of whole body parametric imaging for clinical applications. In FDG imaging, accurate parametric images of PatlakK_ican be complementary to regular standardised uptake value images and improve on current applications or enable new ones. In this study we consider DWB protocols implemented on clinical scanners with a limited axial field of view with the use of multiple whole body sweeps. These protocols result in temporal gaps in the dynamic data which produce noisier and potentially more biased parametric images, compared to single bed (SB) dynamic protocols. Dynamic reconstruction using the Patlak model has been previously proposed to overcome these limits and shown improved DWB parametric images ofK_i. In this work, we propose and make use of a spectral analysis based model for dynamic reconstruction and parametric imaging of PatlakK_i. Both dynamic reconstruction methods were evaluated for DWB FDG protocols and compared against 3D reconstruction based parametric imaging from SB dynamic protocols. This work was conducted on simulated data and results were tested against real FDG dynamic data. We showed that dynamic reconstruction can achieve levels of parametric image noise and bias comparable to 3D reconstruction in SB dynamic studies, with the spectral model offering additional flexibility and further reduction of image noise. Comparisons were also made between step and shoot and continuous bed motion (CBM) protocols, which showed that CBM can achieve lower parametric image noise due to reduced acquisition temporal gaps. Finally, our results showed that dynamic reconstruction improved VOI parametric mean estimates but did not result to fully converged values before resulting in undesirable levels of noise. Additional regularisation methods need to be considered for DWB protocols to ensure both accurate quantification and acceptable noise levels for clinical applications.

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.

Simplified protocol for whole-body Patlak parametric imaging with 18 F-FDG PET/CT: Feasibility and error analysis

PURPOSE

Parametric imaging using the Patlak model has been shown to provide improved lesion detectability and specificity. The Patlak model requires both tissue time-activity curves (TACs) after equilibrium and knowledge of the input function from the start of injection. Therefore, the conventional dynamic scanning protocol typically starts from the radiotracer injection all the way to equilibrium. In this paper, we propose the use of hybrid population-based and model-based input function estimation and evaluate its use for whole-body Patlak analysis, in order to reduce the total scan time and simplify clinical Patlak parametric imaging protocols. Possible quantitative errors caused by the simplified scanning protocol were also analyzed both theoretically and with the use of clinical data.

MATERIALS AND METHODS

Clinical data from 24 patients referred for tumor staging were included in this study. The patients underwent a whole-body dynamic PET study, 20 min after FDG injection (0.13 mCi/kg). The proposed whole-body scanning protocol includes 6 passes with 4-5 bed positions, depending on the size of the patient, with 2 min for each bed position. An input function from the literature was selected as the shape of the population-based input function. The descending aorta from the corresponding CT image was segmented and applied on the reconstructed dynamic PET images to acquire an image-based input function, which was later fitted using an exponential model. Due to the late scan time, only the later portion of the input function was available, which was used to scale the population-based input function. The hybrid input function was used to derive the whole-body Patlak images. Assuming a given error in the population-based input function, its influence on the final Patlak images were also derived theoretically and verified using the clinical data sets. Finally, the image quality of the reconstructed Patlak slope image was evaluated by an experienced radiologist in four different aspects: image artifacts, image noise, lesion sharpness, and lesion detectability.

RESULTS

It was found that errors in the population-based input function only affect the absolute scale of the Patlak slope image. The induced error is proportional to the percentage area-under-curve (AUC) error in the input function. These findings were also confirmed by numerical analysis. The predicted global scale was in good agreement with results from both image-based Patlak and direct Patlak approach. The fractions of the AUC from the early portion population-based input function were also found to be around 18% of the total AUC of the input function, further limiting the propagation of quantitation error from population-based input function to the final Patlak slope image. The reconstructed Patlak images were also found by the radiologist to provide excellent confidence in lesion detection tasks.

CONCLUSIONS

We have proposed a simplified whole-body scanning protocol that utilizes both population-based input function and model-based input function. The error from the population-based function was found to only affect the global scale and the overall quantitative impact can be predicted using our proposed formulas.

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.

PET Parametric Imaging: Past, Present, and Future

Positron emission tomography (PET) is actively used in a diverse range of applications in oncology, cardiology, and neurology. The use of PET in the clinical setting focuses on static (single time frame) imaging at a specific time-point post radiotracer injection and is typically considered as semi-quantitative; e.g. standardized uptake value (SUV) measures. In contrast, dynamic PET imaging requires increased acquisition times but has the advantage that it measures the full spatiotemporal distribution of a radiotracer and, in combination with tracer kinetic modeling, enables the generation of multiparametric images that more directly quantify underlying biological parameters of interest, such as blood flow, glucose metabolism, and receptor binding. Parametric images have the potential for improved detection and for more accurate and earlier therapeutic response assessment. Parametric imaging with dynamic PET has witnessed extensive research in the past four decades. In this paper, we provide an overview of past and present activities and discuss emerging opportunities in the field of parametric imaging for the future.

Bootstrap-Optimised Regularised Image Reconstruction for Emission Tomography

In emission tomography, iterative image reconstruction from noisy measured data usually results in noisy images, and so regularisation is often used to compensate for noise. However, in practice, an appropriate, automatic and precise specification of the strength of regularisation for image reconstruction from a given noisy measured dataset remains unresolved. Existing approaches are either empirical approximations with no guarantee of generalisation, or else are computationally intensive cross-validation methods requiring full reconstructions for a limited set of preselected regularisation strengths. In contrast, we propose a novel methodology embedded within iterative image reconstruction, using one or more bootstrapped replicates of the measured data for precise optimisation of the regularisation. The approach uses a conventional unregularised iterative update of a current image estimate from the noisy measured data, and then also uses the bootstrap replicate to obtain a bootstrap update of the current image estimate. The method then seeks the regularisation hyperparameters which, when applied to the bootstrap update of the image, lead to a best fit of the regularised bootstrap update to the conventional measured data update. This corresponds to estimating the degree of regularisation needed in order to map the noisy update to a model of the mean of an ensemble of noisy updates. For a given regularised objective function (e.g. penalised likelihood), no hyperparameter selection or tuning is required. The method is demonstrated for positron emission tomography (PET) data at different noise levels, and delivers near-optimal reconstructions (in terms of reconstruction error) without any knowledge of the ground truth, nor any form of training data.

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.

Dynamic whole-body PET imaging: principles, potentials and applications

PURPOSE

In this article, we discuss dynamic whole-body (DWB) positron emission tomography (PET) as an imaging tool with significant clinical potential, in relation to conventional standard uptake value (SUV) imaging.

BACKGROUND

DWB PET involves dynamic data acquisition over an extended axial range, capturing tracer kinetic information that is not available with conventional static acquisition protocols. The method can be performed within reasonable clinical imaging times, and enables generation of multiple types of PET images with complementary information in a single imaging session. Importantly, DWB PET can be used to produce multi-parametric images of (i) Patlak slope (influx rate) and (ii) intercept (referred to sometimes as "distribution volume"), while also providing (iii) a conventional 'SUV-equivalent' image for certain protocols.

RESULTS

We provide an overview of ongoing efforts (primarily focused on FDG PET) and discuss potential clinically relevant applications.

CONCLUSION

Overall, the framework of DWB imaging [applicable to both PET/CT(computed tomography) and PET/MRI (magnetic resonance imaging)] generates quantitative measures that may add significant value to conventional SUV image-derived measures, with limited pitfalls as we also discuss in this work.

Accelerated PET kinetic maps estimation by analytic fitting method

In this work, we propose and test a new approach for non-linear kinetic parameters' estimation from dynamic PET data. A technique is discussed, to derive an analytical closed-form expression of the compartmental model used for kinetic parameters' evaluation, using an auxiliary parameter set, with the aim of reducing the computational burden and speeding up the fitting of these complex mathematical expressions to noisy TACs. Two alternative algorithms based on numeric calculations are considered and compared to the new proposal. We perform a simulation study aimed at (i) assessing agreement between the proposed method and other conventional ways of implementing compartmental model fitting, and (ii) quantifying the reduction in computational time required for convergence. It results in a speed-up factor of ∼120 when compared to a fully numeric version, or ∼38, with respect to a more conventional implementation, while converging to very similar values for the estimated model parameters. The proposed method is also tested on dynamic 3D PET clinical data of four control subjects. The results obtained supported those of the simulation study, and provided input and promising perspectives for the application of the proposed technique in clinical practice.

4D-PET reconstruction using a spline-residue model with spatial and temporal roughness penalties

4D reconstruction of dynamic positron emission tomography (dPET) data can improve the signal-to-noise ratio in reconstructed image sequences by fitting smooth temporal functions to the voxel time-activity-curves (TACs) during the reconstruction, though the optimal choice of function remains an open question. We propose a spline-residue model, which describes TACs as weighted sums of convolutions of the arterial input function with cubic B-spline basis functions. Convolution with the input function constrains the spline-residue model at early time-points, potentially enhancing noise suppression in early time-frames, while still allowing a wide range of TAC descriptions over the entire imaged time-course, thus limiting bias. Spline-residue based 4D-reconstruction is compared to that of a conventional (non-4D) maximum a posteriori (MAP) algorithm, and to 4D-reconstructions based on adaptive-knot cubic B-splines, the spectral model and an irreversible two-tissue compartment ('2C3K') model. 4D reconstructions were carried out using a nested-MAP algorithm including spatial and temporal roughness penalties. The algorithms were tested using Monte-Carlo simulated scanner data, generated for a digital thoracic phantom with uptake kinetics based on a dynamic [18F]-Fluromisonidazole scan of a non-small cell lung cancer patient. For every algorithm, parametric maps were calculated by fitting each voxel TAC within a sub-region of the reconstructed images with the 2C3K model. Compared to conventional MAP reconstruction, spline-residue-based 4D reconstruction achieved  >50% improvements for five of the eight combinations of the four kinetics parameters for which parametric maps were created with the bias and noise measures used to analyse them, and produced better results for 5/8 combinations than any of the other reconstruction algorithms studied, while spectral model-based 4D reconstruction produced the best results for 2/8. 2C3K model-based 4D reconstruction generated the most biased parametric maps. Inclusion of a temporal roughness penalty function improved the performance of 4D reconstruction based on the cubic B-spline, spectral and spline-residue models.

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.

Cardiac-gated parametric images from 82 Rb PET from dynamic frames and direct 4D reconstruction

PURPOSE

Cardiac perfusion PET data can be reconstructed as a dynamic sequence and kinetic modeling performed to quantify myocardial blood flow, or reconstructed as static gated images to quantify function. Parametric images from dynamic PET are conventionally not gated, to allow use of all events with lower noise. An alternative method for dynamic PET is to incorporate the kinetic model into the reconstruction algorithm itself, bypassing the generation of a time series of emission images and directly producing parametric images. So-called "direct reconstruction" can produce parametric images with lower noise than the conventional method because the noise distribution is more easily modeled in projection space than in image space. In this work, we develop direct reconstruction of cardiac-gated parametric images for ⁸² Rb PET with an extension of the Parametric Motion compensation OSEM List mode Algorithm for Resolution-recovery reconstruction for the one tissue model (PMOLAR-1T).

METHODS

PMOLAR-1T was extended to accommodate model terms to account for spillover from the left and right ventricles into the myocardium. The algorithm was evaluated on a 4D simulated ⁸² Rb dataset, including a perfusion defect, as well as a human ⁸² Rb list mode acquisition. The simulated list mode was subsampled into replicates, each with counts comparable to one gate of a gated acquisition. Parametric images were produced by the indirect (separate reconstructions and modeling) and direct methods for each of eight low-count and eight normal-count replicates of the simulated data, and each of eight cardiac gates for the human data. For the direct method, two initialization schemes were tested: uniform initialization, and initialization with the filtered iteration 1 result of the indirect method. For the human dataset, event-by-event respiratory motion compensation was included. The indirect and direct methods were compared for the simulated dataset in terms of bias and coefficient of variation as a function of iteration.

RESULTS

Convergence of direct reconstruction was slow with uniform initialization; lower bias was achieved in fewer iterations by initializing with the filtered indirect iteration 1 images. For most parameters and regions evaluated, the direct method achieved the same or lower absolute bias at matched iteration as the indirect method, with 23%-65% lower noise. Additionally, the direct method gave better contrast between the perfusion defect and surrounding normal tissue than the indirect method. Gated parametric images from the human dataset had comparable relative performance of indirect and direct, in terms of mean parameter values per iteration. Changes in myocardial wall thickness and blood pool size across gates were readily visible in the gated parametric images, with higher contrast between myocardium and left ventricle blood pool in parametric images than gated SUV images.

CONCLUSIONS

Direct reconstruction can produce parametric images with less noise than the indirect method, opening the potential utility of gated parametric imaging for perfusion PET.

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.

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.

Theoretical Analysis of Penalized Maximum-Likelihood Patlak Parametric Image Reconstruction in Dynamic PET for Lesion Detection

Detecting cancerous lesions is a major clinical application of emission tomography. In a previous work, we studied penalized maximum-likelihood (PML) image reconstruction for lesion detection in static PET. Here we extend our theoretical analysis of static PET reconstruction to dynamic PET. We study both the conventional indirect reconstruction and direct reconstruction for Patlak parametric image estimation. In indirect reconstruction, Patlak parametric images are generated by first reconstructing a sequence of dynamic PET images, and then performing Patlak analysis on the time activity curves (TACs) pixel-by-pixel. In direct reconstruction, Patlak parametric images are estimated directly from raw sinogram data by incorporating the Patlak model into the image reconstruction procedure. PML reconstruction is used in both the indirect and direct reconstruction methods. We use a channelized Hotelling observer (CHO) to assess lesion detectability in Patlak parametric images. Simplified expressions for evaluating the lesion detectability have been derived and applied to the selection of the regularization parameter value to maximize detection performance. The proposed method is validated using computer-based Monte Carlo simulations. Good agreements between the theoretical predictions and the Monte Carlo results are observed. Both theoretical predictions and Monte Carlo simulation results show the benefit of the indirect and direct methods under optimized regularization parameters in dynamic PET reconstruction for lesion detection, when compared with the conventional static PET reconstruction.

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.

Generalized whole-body Patlak parametric imaging for enhanced quantification in clinical PET

We recently developed a dynamic multi-bed PET data acquisition framework to translate the quantitative benefits of Patlak voxel-wise analysis to the domain of routine clinical whole-body (WB) imaging. The standard Patlak (sPatlak) linear graphical analysis assumes irreversible PET tracer uptake, ignoring the effect of FDG dephosphorylation, which has been suggested by a number of PET studies. In this work: (i) a non-linear generalized Patlak (gPatlak) model is utilized, including a net efflux rate constant kloss, and (ii) a hybrid (s/g)Patlak (hPatlak) imaging technique is introduced to enhance contrast to noise ratios (CNRs) of uptake rate Ki images. Representative set of kinetic parameter values and the XCAT phantom were employed to generate realistic 4D simulation PET data, and the proposed methods were additionally evaluated on 11 WB dynamic PET patient studies. Quantitative analysis on the simulated Ki images over 2 groups of regions-of-interest (ROIs), with low (ROI A) or high (ROI B) true kloss relative to Ki, suggested superior accuracy for gPatlak. Bias of sPatlak was found to be 16-18% and 20-40% poorer than gPatlak for ROIs A and B, respectively. By contrast, gPatlak exhibited, on average, 10% higher noise than sPatlak. Meanwhile, the bias and noise levels for hPatlak always ranged between the other two methods. In general, hPatlak was seen to outperform all methods in terms of target-to-background ratio (TBR) and CNR for all ROIs. Validation on patient datasets demonstrated clinical feasibility for all Patlak methods, while TBR and CNR evaluations confirmed our simulation findings, and suggested presence of non-negligible kloss reversibility in clinical data. As such, we recommend gPatlak for highly quantitative imaging tasks, while, for tasks emphasizing lesion detectability (e.g. TBR, CNR) over quantification, or for high levels of noise, hPatlak is instead preferred. Finally, gPatlak and hPatlak CNR was systematically higher compared to routine SUV values.

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.

PET image reconstruction using kernel method

Image reconstruction from low-count positron emission tomography (PET) projection data is challenging because the inverse problem is ill-posed. Prior information can be used to improve image quality. Inspired by the kernel methods in machine learning, this paper proposes a kernel based method that models PET image intensity in each pixel as a function of a set of features obtained from prior information. The kernel-based image model is incorporated into the forward model of PET projection data and the coefficients can be readily estimated by the maximum likelihood (ML) or penalized likelihood image reconstruction. A kernelized expectation-maximization algorithm is presented to obtain the ML estimate. Computer simulations show that the proposed approach can achieve better bias versus variance trade-off and higher contrast recovery for dynamic PET image reconstruction than the conventional maximum likelihood method with and without post-reconstruction denoising. Compared with other regularization-based methods, the kernel method is easier to implement and provides better image quality for low-count data. Application of the proposed kernel method to a 4-D dynamic PET patient dataset showed promising results.

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.

Quality and precision of parametric images created from PET sinogram data by direct reconstruction: proof of concept

We have previously implemented the direct reconstruction of dense kinetic model parameter images ("parametric images") from sinogram data, and compared it to conventional image domain kinetic parameter estimation methods . Although it has been shown that the direct reconstruction algorithm estimates the kinetic model parameters with lower root mean squared error than the conventional image domain techniques, some theoretical obstacles remain. These obstacles include the difficulty of evaluating the accuracy and precision of the estimated parameters. In image domain techniques, the reconstructed time activity curve (TAC) and the model predicted TAC are compared, and the goodness-of-fit is evaluated as a measure of the accuracy and precision of the estimated parameters. This approach cannot be applied to the direct reconstruction technique as there are no reconstructed TACs. In this paper, we propose ways of evaluating the precision and goodness-of-fit of the kinetic model parameters estimated by the direct reconstruction algorithm. Specifically, precision of the estimates requires the calculation of variance images for each parameter, and goodness-of-fit is addressed by reconstructing the difference between the measured and the fitted sinograms. We demonstrate that backprojecting the difference from sinogram space to image space creates error images that can be examined for goodness-of-fit and model selection purposes. The presence of nonrandom structures in the error images may indicate an inadequacy of the kinetic model that has been incorporated into the direct reconstruction algorithm. We introduce three types of goodness-of-fit images. We propose and demonstrate a number-of-runs image as a means of quantifying the adequacy or deficiency of the model. We further propose and demonstrate images of the F statistic and the change in the Akaike Information Criterion as devices for identifying the statistical advantage of one model over another at each voxel. As direct reconstruction to parametric images proliferates, it will be essential for imagers to adopt methods such as those proposed herein to assess the accuracy and precision of their parametric images.

Joint parametric reconstruction and motion correction framework for dynamic PET data

In this paper we propose a novel algorithm for jointly performing data based motion correction and direct parametric reconstruction of dynamic PET data. We derive a closed form update for the penalised likelihood maximisation which greatly enhances the algorithm's computational efficiency for practical use. Our algorithm achieves sub-voxel motion correction residual with noisy data in the simulation-based validation and reduces the bias of the direct estimation of the kinetic parameter of interest. A preliminary evaluation on clinical brain data using [18F]Choline shows improved contrast for regions of high activity. The proposed method is based on a data-driven kinetic modelling method and is directly applicable to reversible and irreversible PET tracers, covering a range of clinical applications.

Preclinical evaluation of parametric image reconstruction of [18F]FMISO PET: correlation with ex vivo immunohistochemistry

Compared to indirect methods, direct parametric image reconstruction (PIR) has the advantage of high quality and low statistical errors. However, it is not yet clear if this improvement in quality is beneficial for physiological quantification. This study aimed to evaluate direct PIR for the quantification of tumor hypoxia using the hypoxic fraction (HF) assessed from immunohistological data as a physiological reference. Sixteen mice with xenografted human squamous cell carcinomas were scanned with dynamic [18F]FMISO PET. Afterward, tumors were sliced and stained with H&E and the hypoxia marker pimonidazole. The hypoxic signal was segmented using k-means clustering and HF was specified as the ratio of the hypoxic area over the viable tumor area. The parametric Patlak slope images were obtained by indirect voxel-wise modeling on reconstructed images using filtered back projection and ordered-subset expectation maximization (OSEM) and by direct PIR (e.g., parametric-OSEM, POSEM). The mean and maximum Patlak slopes of the tumor area were investigated and compared with HF. POSEM resulted in generally higher correlations between slope and HF among the investigated methods. A strategy for the delineation of the hypoxic tumor volume based on thresholding parametric images at half maximum of the slope is recommended based on the results of this study.

Direct estimation of kinetic parametric images for dynamic PET

Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed.

Dynamic whole-body PET parametric imaging: I. Concept, acquisition protocol optimization and clinical application

Static whole-body PET/CT, employing the standardized uptake value (SUV), is considered the standard clinical approach to diagnosis and treatment response monitoring for a wide range of oncologic malignancies. Alternative PET protocols involving dynamic acquisition of temporal images have been implemented in the research setting, allowing quantification of tracer dynamics, an important capability for tumor characterization and treatment response monitoring. Nonetheless, dynamic protocols have been confined to single-bed-coverage limiting the axial field-of-view to ~15-20 cm, and have not been translated to the routine clinical context of whole-body PET imaging for the inspection of disseminated disease. Here, we pursue a transition to dynamic whole-body PET parametric imaging, by presenting, within a unified framework, clinically feasible multi-bed dynamic PET acquisition protocols and parametric imaging methods. We investigate solutions to address the challenges of: (i) long acquisitions, (ii) small number of dynamic frames per bed, and (iii) non-invasive quantification of kinetics in the plasma. In the present study, a novel dynamic (4D) whole-body PET acquisition protocol of ~45 min total length is presented, composed of (i) an initial 6 min dynamic PET scan (24 frames) over the heart, followed by (ii) a sequence of multi-pass multi-bed PET scans (six passes × seven bed positions, each scanned for 45 s). Standard Patlak linear graphical analysis modeling was employed, coupled with image-derived plasma input function measurements. Ordinary least squares Patlak estimation was used as the baseline regression method to quantify the physiological parameters of tracer uptake rate Ki and total blood distribution volume V on an individual voxel basis. Extensive Monte Carlo simulation studies, using a wide set of published kinetic FDG parameters and GATE and XCAT platforms, were conducted to optimize the acquisition protocol from a range of ten different clinically acceptable sampling schedules examined. The framework was also applied to six FDG PET patient studies, demonstrating clinical feasibility. Both simulated and clinical results indicated enhanced contrast-to-noise ratios (CNRs) for Ki images in tumor regions with notable background FDG concentration, such as the liver, where SUV performed relatively poorly. Overall, the proposed framework enables enhanced quantification of physiological parameters across the whole body. In addition, the total acquisition length can be reduced from 45 to ~35 min and still achieve improved or equivalent CNR compared to SUV, provided the true Ki contrast is sufficiently high. In the follow-up companion paper, a set of advanced linear regression schemes is presented to particularly address the presence of noise, and attempt to achieve a better trade-off between the mean-squared error and the CNR metrics, resulting in enhanced task-based imaging.

Dynamic whole-body PET parametric imaging: II. Task-oriented statistical estimation

In the context of oncology, dynamic PET imaging coupled with standard graphical linear analysis has been previously employed to enable quantitative estimation of tracer kinetic parameters of physiological interest at the voxel level, thus, enabling quantitative PET parametric imaging. However, dynamic PET acquisition protocols have been confined to the limited axial field-of-view (~15-20 cm) of a single-bed position and have not been translated to the whole-body clinical imaging domain. On the contrary, standardized uptake value (SUV) PET imaging, considered as the routine approach in clinical oncology, commonly involves multi-bed acquisitions, but is performed statically, thus not allowing for dynamic tracking of the tracer distribution. Here, we pursue a transition to dynamic whole-body PET parametric imaging, by presenting, within a unified framework, clinically feasible multi-bed dynamic PET acquisition protocols and parametric imaging methods. In a companion study, we presented a novel clinically feasible dynamic (4D) multi-bed PET acquisition protocol as well as the concept of whole-body PET parametric imaging employing Patlak ordinary least squares (OLS) regression to estimate the quantitative parameters of tracer uptake rate Ki and total blood distribution volume V. In the present study, we propose an advanced hybrid linear regression framework, driven by Patlak kinetic voxel correlations, to achieve superior trade-off between contrast-to-noise ratio (CNR) and mean squared error (MSE) than provided by OLS for the final Ki parametric images, enabling task-based performance optimization. Overall, whether the observer's task is to detect a tumor or quantitatively assess treatment response, the proposed statistical estimation framework can be adapted to satisfy the specific task performance criteria, by adjusting the Patlak correlation-coefficient (WR) reference value. The multi-bed dynamic acquisition protocol, as optimized in the preceding companion study, was employed along with extensive Monte Carlo simulations and an initial clinical (18)F-deoxyglucose patient dataset to validate and demonstrate the potential of the proposed statistical estimation methods. Both simulated and clinical results suggest that hybrid regression in the context of whole-body Patlak Ki imaging considerably reduces MSE without compromising high CNR. Alternatively, for a given CNR, hybrid regression enables larger reductions than OLS in the number of dynamic frames per bed, allowing for even shorter acquisitions of ~30 min, thus further contributing to the clinical adoption of the proposed framework. Compared to the SUV approach, whole-body parametric imaging can provide better tumor quantification, and can act as a complement to SUV, for the task of tumor detection.

Acceleration of image-based resolution modelling reconstruction using an expectation maximization nested algorithm

Recent studies have demonstrated the benefits of a resolution model within iterative reconstruction algorithms in an attempt to account for effects that degrade the spatial resolution of the reconstructed images. However, these algorithms suffer from slower convergence rates, compared to algorithms where no resolution model is used, due to the additional need to solve an image deconvolution problem. In this paper, a recently proposed algorithm, which decouples the tomographic and image deconvolution problems within an image-based expectation maximization (EM) framework, was evaluated. This separation is convenient, because more computational effort can be placed on the image deconvolution problem and therefore accelerate convergence. Since the computational cost of solving the image deconvolution problem is relatively small, multiple image-based EM iterations do not significantly increase the overall reconstruction time. The proposed algorithm was evaluated using 2D simulations, as well as measured 3D data acquired on the high-resolution research tomograph. Results showed that bias reduction can be accelerated by interleaving multiple iterations of the image-based EM algorithm solving the resolution model problem, with a single EM iteration solving the tomographic problem. Significant improvements were observed particularly for voxels that were located on the boundaries between regions of high contrast within the object being imaged and for small regions of interest, where resolution recovery is usually more challenging. Minor differences were observed using the proposed nested algorithm, compared to the single iteration normally performed, when an optimal number of iterations are performed for each algorithm. However, using the proposed nested approach convergence is significantly accelerated enabling reconstruction using far fewer tomographic iterations (up to 70% fewer iterations for small regions). Nevertheless, the optimal number of nested image-based EM iterations is hard to be defined and it should be selected according to the given application.

Resolution modeling in PET imaging: theory, practice, benefits, and pitfalls

In this paper, the authors review the field of resolution modeling in positron emission tomography (PET) image reconstruction, also referred to as point-spread-function modeling. The review includes theoretical analysis of the resolution modeling framework as well as an overview of various approaches in the literature. It also discusses potential advantages gained via this approach, as discussed with reference to various metrics and tasks, including lesion detection observer studies. Furthermore, attention is paid to issues arising from this approach including the pervasive problem of edge artifacts, as well as explanation and potential remedies for this phenomenon. Furthermore, the authors emphasize limitations encountered in the context of quantitative PET imaging, wherein increased intervoxel correlations due to resolution modeling can lead to significant loss of precision (reproducibility) for small regions of interest, which can be a considerable pitfall depending on the task of interest.

An optimization transfer algorithm for nonlinear parametric image reconstruction from dynamic PET data

Direct reconstruction of kinetic parameters from raw projection data is a challenging task in molecular imaging using dynamic positron emission tomography (PET). This paper presents a new optimization transfer algorithm for penalized likelihood direct reconstruction of nonlinear parametric images that is easy to use and has a fast convergence rate. Each iteration of the proposed algorithm can be implemented in three simple steps: a frame-by-frame maximum likelihood expectation-maximization (EM)-like image update, a frame-by-frame image smoothing, and a pixel-by-pixel time activity curve fitting. Computer simulation shows that the direct algorithm can achieve a better bias-variance performance than the indirect reconstruction algorithm. The convergence rate of the new algorithm is substantially faster than our previous algorithm that is based on a separable paraboloidal surrogate function. The proposed algorithm has been applied to real 4-D PET data.