Maximuma posteriorireconstruction of the Patlak parametric image from sinograms in dynamic PET

Optimization and impact of sensitivity mode on abbreviated scan protocols with population-based input function for parametric imaging of [18F]-FDG for a long axial FOV PET scanner

BACKGROUND

The long axial field of view, combined with the high sensitivity of the Biograph Vision Quadra PET/CT scanner enables the precise deviation of an image derived input function (IDIF) required for parametric imaging. Traditionally, this requires an hour-long dynamic PET scan for [18F]-FDG, which can be significantly reduced by using a population-based input function (PBIF). In this study, we expand these examinations and include the scanner's ultra-high sensitivity (UHS) mode in comparison to the high sensitivity (HS) mode and evaluate the potential for further shortening of the scan time.

METHODS

Patlak Ki and DV estimates were determined by the indirect and direct Patlak methods using dynamic [18F]-FDG data of 6 oncological patients with 26 lesions (0-65 min p.i.). Both sensitivity modes for different number/duration of PET data frames were compared, together with the potential of using abbreviated scan durations of 20, 15 and 10 min by using a PBIF. The differences in parametric images and tumour-to-background ratio (TBR) due to the shorter scans using the PBIF method and between the sensitivity modes were assessed.

RESULTS

A difference of 3.4 ± 7.0% (Ki) and 1.2 ± 2.6% (DV) was found between both sensitivity modes using indirect Patlak and the full IDIF (0-65 min). For the abbreviated protocols and indirect Patlak, the UHS mode resulted in a lower bias and higher precision, e.g., 45-65 min p.i. 3.8 ± 4.4% (UHS) and 6.4 ± 8.9% (HS), allowing shorter scan protocols, e.g. 50-65 min p.i. 4.4 ± 11.2% (UHS) instead of 7.3 ± 20.0% (HS). The variation of Ki and DV estimates for both Patlak methods was comparable, e.g., UHS mode 3.8 ± 4.4% and 2.7 ± 3.4% (Ki) and 14.4 ± 2.7% and 18.1 ± 7.5% (DV) for indirect and direct Patlak, respectively. Only a minor impact of the number of Patlak frames was observed for both sensitivity modes and Patlak methods. The TBR obtained with direct Patlak and PBIF was not affected by the sensitivity mode, was higher than that derived from the SUV image (6.2 ± 3.1) and degraded from 20.2 ± 12.0 (20 min) to 10.6 ± 5.4 (15 min). Ki and DV estimate images showed good agreement (UHS mode, RC: 6.9 ± 2.3% (Ki), 0.1 ± 3.1% (DV), peak signal-to-noise ratio (PSNR): 64.5 ± 3.3 dB (Ki), 61.2 ± 10.6 dB (DV)) even for abbreviated scan protocols of 50-65 min p.i.

CONCLUSIONS

Both sensitivity modes provide comparable results for the full 65 min dynamic scans and abbreviated scans using the direct Patlak reconstruction method, with good Ki and DV estimates for 15 min short scans. For the indirect Patlak approach the UHS mode improved the Ki estimates for the abbreviated scans.

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.

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.

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.

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.

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.

Quantifying bias and precision of kinetic parameter estimation on the PennPET Explorer, a long axial field-of-view scanner

Long axial field-of-view (AFOV) PET scanners allow for full-body dynamic imaging in a single bed-position at very high sensitivity. However, the benefits for kinetic parameter estimation have yet to be studied. This work uses (1) a dynamic GATE simulation of [¹⁸F]-fluorothymidine (FLT) in a modified NEMA IQ phantom and (2) a lesion embedding study of spheres in a dynamic [¹⁸F]-fluorodeoxyglucose (FDG) human subject imaged on the PennPET Explorer. Both studies were designed using published kinetic data of lung and liver cancers and modeled using two tissue compartments. Data were reconstructed at various emulated doses. Sphere time-activity curves (TACs) were measured on resulting dynamic images, and TACs were fit using a two-tissue-compartment model (k₄ ≠ 0) for the FLT study and both a two-tissue-compartment model (k₄ = 0) and Patlak graphical analysis for the FDG study to estimate flux (K_i) and delivery (K₁) parameters. Quantification of flux and K1 shows lower bias and better precision for both radiotracers on the long AFOV scanner, especially at low doses. Dynamic imaging on a long AFOV system can be achieved for a greater range of injected doses, as low as 0.5-2 mCi depending on the sphere size and flux, compared to a standard AFOV scanner, while maintaining good kinetic parameter estimation.

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.

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.

Relative Patlak plot for dynamic PET parametric imaging without the need for early-time input function

The Patlak graphical method is widely used in parametric imaging for modeling irreversible radiotracer kinetics in dynamic PET. The net influx rate of radiotracer can be determined from the slope of the Patlak plot. The implementation of the standard Patlak method requires the knowledge of full-time input function from the injection time until the scan end time, which presents a challenge for use in the clinic. This paper proposes a new relative Patlak plot method that does not require early-time input function and therefore can be more efficient for parametric imaging. Theoretical analysis proves that the effect of early-time input function is a constant scaling factor on the Patlak slope estimation. Thus, the parametric image of the slope of the relative Patlak plot is related to the parametric image of standard Patlak slope by a global scaling factor. This theoretical finding has been further demonstrated by computer simulation and real patient data. The study indicates that parametric imaging of the relative Patlak slope can be used as a substitute of parametric imaging of standard Patlak slope for tasks that do not require absolute quantification, such as lesion detection and tumor volume segmentation.

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.

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.

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.

MR-guided dynamic PET reconstruction with the kernel method and spectral temporal basis functions

Recent advances in dynamic positron emission tomography (PET) reconstruction have demonstrated that it is possible to achieve markedly improved end-point kinetic parameter maps by incorporating a temporal model of the radiotracer directly into the reconstruction algorithm. In this work we have developed a highly constrained, fully dynamic PET reconstruction algorithm incorporating both spectral analysis temporal basis functions and spatial basis functions derived from the kernel method applied to a co-registered T1-weighted magnetic resonance (MR) image. The dynamic PET image is modelled as a linear combination of spatial and temporal basis functions, and a maximum likelihood estimate for the coefficients can be found using the expectation-maximization (EM) algorithm. Following reconstruction, kinetic fitting using any temporal model of interest can be applied. Based on a BrainWeb T1-weighted MR phantom, we performed a realistic dynamic [(18)F]FDG simulation study with two noise levels, and investigated the quantitative performance of the proposed reconstruction algorithm, comparing it with reconstructions incorporating either spectral analysis temporal basis functions alone or kernel spatial basis functions alone, as well as with conventional frame-independent reconstruction. Compared to the other reconstruction algorithms, the proposed algorithm achieved superior performance, offering a decrease in spatially averaged pixel-level root-mean-square-error on post-reconstruction kinetic parametric maps in the grey/white matter, as well as in the tumours when they were present on the co-registered MR image. When the tumours were not visible in the MR image, reconstruction with the proposed algorithm performed similarly to reconstruction with spectral temporal basis functions and was superior to both conventional frame-independent reconstruction and frame-independent reconstruction with kernel spatial basis functions. Furthermore, we demonstrate that a joint spectral/kernel model can also be used for effective post-reconstruction denoising, through the use of an EM-like image-space algorithm. Finally, we applied the proposed algorithm to reconstruction of real high-resolution dynamic [(11)C]SCH23390 data, showing promising results.

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.

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.

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.

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.

Dynamic positron emission tomography image restoration via a kinetics-induced bilateral filter

Dynamic positron emission tomography (PET) imaging is a powerful tool that provides useful quantitative information on physiological and biochemical processes. However, low signal-to-noise ratio in short dynamic frames makes accurate kinetic parameter estimation from noisy voxel-wise time activity curves (TAC) a challenging task. To address this problem, several spatial filters have been investigated to reduce the noise of each frame with noticeable gains. These filters include the Gaussian filter, bilateral filter, and wavelet-based filter. These filters usually consider only the local properties of each frame without exploring potential kinetic information from entire frames. Thus, in this work, to improve PET parametric imaging accuracy, we present a kinetics-induced bilateral filter (KIBF) to reduce the noise of dynamic image frames by incorporating the similarity between the voxel-wise TACs using the framework of bilateral filter. The aim of the proposed KIBF algorithm is to reduce the noise in homogeneous areas while preserving the distinct kinetics of regions of interest. Experimental results on digital brain phantom and in vivo rat study with typical ¹⁸F-FDG kinetics have shown that the present KIBF algorithm can achieve notable gains over other existing algorithms in terms of quantitative accuracy measures and visual inspection.

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.

Direct 4-D PET list mode parametric reconstruction with a novel EM algorithm

The production of images of kinetic parameters is often the ultimate goal of positron emission tomography (PET) imaging. The indirect method of PET parametric imaging, also called the frame-based method (FM), is performed by fitting the time-activity curve (TAC) for each voxel with an appropriate compartment model after image reconstruction. The indirect method is simple and easily implemented, however, it usually leads to some loss of accuracy or precision, due to the use of two separate steps. This paper presents a direct 4-D method for producing 3-D images of kinetic parameters from list mode PET data. In this application, the TAC for each voxel is described by a one-tissue compartment model (1T). Extending previous EM algorithms, a new spatiotemporal complete data space was introduced to optimize the maximum likelihood function. This leads to a straightforward closed-form parametric image update equation. This method was implemented by extending the current list mode platform MOLAR to produce a parametric algorithm PMOLAR-1T. Using an ordered subset approach, qualitative and quantitative evaluations were performed using 2-D (x, t) and 4-D (x, y, z, t) simulated list mode data based on brain receptor tracers and also with a human brain study. Comparisons with the indirect method showed that the proposed direct method can lead to accurate estimation of the parametric image values with reduced variance, especially at low count levels. In the 2-D test, the direct method showed similar bias to the frame-based method but with variance reduction of 23%-60%. In the 4-D test, bias values of both methods were no more than 4% and the direct method had lower variability (coefficient of variation reduction of 0%-64% compared to the frame-based method) at the normal count level. The direct method had a larger reduction in variability (27%-81%) and lower bias (1%-5% for 4-D and 1%-19% for FM) at low count levels. The results in the human brain study are similar with PMOLAR-1T showing lower noise than FM.

3.5D dynamic PET image reconstruction incorporating kinetics-based clusters

Standard 3D dynamic positron emission tomographic (PET) imaging consists of independent image reconstructions of individual frames followed by application of appropriate kinetic model to the time activity curves at the voxel or region-of-interest (ROI). The emerging field of 4D PET reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple frames within the image reconstruction task. Here we propose a novel reconstruction framework aiming to enhance quantitative accuracy of parametric images via introduction of priors based on voxel kinetics, as generated via clustering of preliminary reconstructed dynamic images to define clustered neighborhoods of voxels with similar kinetics. This is then followed by straightforward maximum a posteriori (MAP) 3D PET reconstruction as applied to individual frames; and as such the method is labeled '3.5D' image reconstruction. The use of cluster-based priors has the advantage of further enhancing quantitative performance in dynamic PET imaging, because: (a) there are typically more voxels in clusters than in conventional local neighborhoods, and (b) neighboring voxels with distinct kinetics are less likely to be clustered together. Using realistic simulated (11)C-raclopride dynamic PET data, the quantitative performance of the proposed method was investigated. Parametric distribution-volume (DV) and DV ratio (DVR) images were estimated from dynamic image reconstructions using (a) maximum-likelihood expectation maximization (MLEM), and MAP reconstructions using (b) the quadratic prior (QP-MAP), (c) the Green prior (GP-MAP) and (d, e) two proposed cluster-based priors (CP-U-MAP and CP-W-MAP), followed by graphical modeling, and were qualitatively and quantitatively compared for 11 ROIs. Overall, the proposed dynamic PET reconstruction methodology resulted in substantial visual as well as quantitative accuracy improvements (in terms of noise versus bias performance) for parametric DV and DVR images. The method was also tested on a 90 min (11)C-raclopride patient study performed on the high-resolution research tomography. The proposed method was shown to outperform the conventional method in visual as well as quantitative accuracy improvements (in terms of noise versus regional DVR value performance).

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.

Direct 4D parametric imaging for linearized models of reversibly binding PET tracers using generalized AB-EM reconstruction

Due to high noise levels in the voxel kinetics, development of reliable parametric imaging algorithms remains one of most active areas in dynamic brain PET imaging, which in the vast majority of cases involves receptor/transporter studies with reversibly binding tracers. As such, the focus of this work has been to develop a novel direct 4D parametric image reconstruction scheme for such tracers. Based on a relative equilibrium (RE) graphical analysis formulation (Zhou et al 2009b Neuroimage 44 661-70), we developed a closed-form 4D EM algorithm to directly reconstruct distribution volume (DV) parametric images within a plasma input model, as well as DV ratio (DVR) images within a reference tissue model scheme (wherein an initial reconstruction was used to estimate the reference tissue time-activity curves). A particular challenge with the direct 4D EM formulation is that the intercept parameters in graphical (linearized) analysis of reversible tracers (e.g. Logan or RE analysis) are commonly negative (unlike for irreversible tracers, e.g. using Patlak analysis). Subsequently, we focused our attention on the AB-EM algorithm, derived by Byrne (1998, Inverse Problems 14 1455-67) to allow inclusion of prior information about the lower (A) and upper (B) bounds for image values. We then generalized this algorithm to the 4D EM framework, thus allowing negative intercept parameters. Furthermore, our 4D AB-EM algorithm incorporated and emphasized the use of spatially varying lower bounds to achieve enhanced performance. As validation, the means of parameters estimated from 55 human (11)C-raclopride dynamic PET studies were used for extensive simulations using a mathematical brain phantom. Images were reconstructed using conventional indirect as well as proposed direct parametric imaging methods. Noise versus bias quantitative measurements were performed in various regions of the brain. Direct 4D EM reconstruction resulted in notable qualitative and quantitative accuracy improvements (over 35% noise reduction, with matched bias, in both plasma and reference-tissue input models). Similar improvements were also observed in the coefficient of variation of the estimated DV and DVR values even for relatively low uptake cortical regions, suggesting the enhanced ability for robust parameter estimation. The method was also tested on a 90 min (11)C-raclopride patient study performed on the high-resolution research tomograph wherein the proposed method was shown across a variety of regions to outperform the conventional method in the sense that for a given DVR value, improved noise levels were observed.

A robust state-space kinetics-guided framework for dynamic PET image reconstruction

Dynamic PET image reconstruction is a challenging issue due to the low SNR and the large quantity of spatio-temporal data. We propose a robust state-space image reconstruction (SSIR) framework for activity reconstruction in dynamic PET. Unlike statistically-based frame-by-frame methods, tracer kinetic modeling is incorporated to provide physiological guidance for the reconstruction, harnessing the temporal information of the dynamic data. Dynamic reconstruction is formulated in a state-space representation, where a compartmental model describes the kinetic processes in a continuous-time system equation, and the imaging data are expressed in a discrete measurement equation. Tracer activity concentrations are treated as the state variables, and are estimated from the dynamic data. Sampled-data H(∞) filtering is adopted for robust estimation. H(∞) filtering makes no assumptions on the system and measurement statistics, and guarantees bounded estimation error for finite-energy disturbances, leading to robust performance for dynamic data with low SNR and/or errors. This alternative reconstruction approach could help us to deal with unpredictable situations in imaging (e.g. data corruption from failed detector blocks) or inaccurate noise models. Experiments on synthetic phantom and patient PET data are performed to demonstrate feasibility of the SSIR framework, and to explore its potential advantages over frame-by-frame statistical reconstruction approaches.

Inference with minimal Gibbs free energy in information field theory

Non-linear and non-gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the gaussian approximation to the full posterior probability, which has maximal cross information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a gaussian signal with unknown spectrum, and (iii) inference of a poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-gaussian posterior.

Dynamic single photon emission computed tomography--basic principles and cardiac applications

The very nature of nuclear medicine, the visual representation of injected radiopharmaceuticals, implies imaging of dynamic processes such as the uptake and wash-out of radiotracers from body organs. For years, nuclear medicine has been touted as the modality of choice for evaluating function in health and disease. This evaluation is greatly enhanced using single photon emission computed tomography (SPECT), which permits three-dimensional (3D) visualization of tracer distributions in the body. However, to fully realize the potential of the technique requires the imaging of in vivo dynamic processes of flow and metabolism. Tissue motion and deformation must also be addressed. Absolute quantification of these dynamic processes in the body has the potential to improve diagnosis. This paper presents a review of advancements toward the realization of the potential of dynamic SPECT imaging and a brief history of the development of the instrumentation. A major portion of the paper is devoted to the review of special data processing methods that have been developed for extracting kinetics from dynamic cardiac SPECT data acquired using rotating detector heads that move as radiopharmaceuticals exchange between biological compartments. Recent developments in multi-resolution spatiotemporal methods enable one to estimate kinetic parameters of compartment models of dynamic processes using data acquired from a single camera head with slow gantry rotation. The estimation of kinetic parameters directly from projection measurements improves bias and variance over the conventional method of first reconstructing 3D dynamic images, generating time-activity curves from selected regions of interest and then estimating the kinetic parameters from the generated time-activity curves. Although the potential applications of SPECT for imaging dynamic processes have not been fully realized in the clinic, it is hoped that this review illuminates the potential of SPECT for dynamic imaging, especially in light of new developments that enable measurement of dynamic processes directly from projection measurements.

Direct 4D reconstruction of parametric images incorporating anato-functional joint entropy

We developed an anatomy-guided 4D closed-form algorithm to directly reconstruct parametric images from projection data for (nearly) irreversible tracers. Conventional methods consist of individually reconstructing 2D/3D PET data, followed by graphical analysis on the sequence of reconstructed image frames. The proposed direct reconstruction approach maintains the simplicity and accuracy of the expectation-maximization (EM) algorithm by extending the system matrix to include the relation between the parametric images and the measured data. A closed-form solution was achieved using a different hidden complete-data formulation within the EM framework. Furthermore, the proposed method was extended to maximum a posterior reconstruction via incorporation of MR image information, taking the joint entropy between MR and parametric PET features as the prior. Using realistic simulated noisy [(11)C]-naltrindole PET and MR brain images/data, the quantitative performance of the proposed methods was investigated. Significant improvements in terms of noise versus bias performance were demonstrated when performing direct parametric reconstruction, and additionally upon extending the algorithm to its Bayesian counterpart using the MR-PET joint entropy measure.

Small-animal molecular imaging methods

The ability to trace or identify specific molecules within a specific anatomic location provides insight into metabolic pathways, tissue components, and tracing of solute transport mechanisms. With the increasing use of small animals for research, such imaging must have sufficiently high spatial resolution to allow anatomic localization as well as sufficient specificity and sensitivity to provide an accurate description of the molecular distribution and concentration.

METHODS

Imaging methods based on electromagnetic radiation, such as PET, SPECT, MRI, and CT, are increasingly applicable because of recent advances in novel scanner hardware and image reconstruction software and the availability of novel molecules that have enhanced sensitivity in these methodologies.

RESULTS

Small-animal PET has been advanced by the development of detector arrays that provide higher resolution and positron-emitting elements that allow new molecular tracers to be labeled. Micro-MRI has been improved in terms of spatial resolution and sensitivity through increased magnet field strength and the development of special-purpose coils and associated scan protocols. Of particular interest is the associated ability to image local mechanical function and solute transport processes, which can be directly related to the molecular information. This ability is further strengthened by the synergistic integration of PET with MRI. Micro-SPECT has been improved through the use of coded aperture imaging approaches as well as image reconstruction algorithms that can better deal with the photon-limited scan data. The limited spatial resolution can be partially overcome by integrating SPECT with CT. Micro-CT by itself provides exquisite spatial resolution of anatomy, but recent developments in high-spatial-resolution photon counting and spectrally sensitive imaging arrays, combined with x-ray optical devices, hold promise for actual molecular identification by virtue of the chemical bond lengths of molecules, especially biopolymers.

CONCLUSION

Given the increasing use of small animals for evaluating new clinical imaging techniques and providing more insight into pathophysiologic phenomena as well as the availability of improved detection systems, scanning protocols, and associated software, the sensitivity and specificity of molecular imaging are increasing.

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

Parametric imaging using dynamic positron emission tomography (PET) provides important information for biological research and clinical diagnosis. Indirect and direct methods have been developed for reconstructing linear parametric images from dynamic PET data. Indirect methods are relatively simple and easy to implement because the image reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from raw PET data and are statistically more efficient. However, the convergence rate of direct algorithms can be slow due to the coupling between the reconstruction and kinetic modeling. Here we present two fast gradient-type algorithms for direct reconstruction of linear parametric images. The new algorithms decouple the reconstruction and linear parametric modeling at each iteration by employing the principle of optimization transfer. Convergence speed is accelerated by running more sub-iterations of linear parametric estimation because the computation cost of the linear parametric modeling is much less than that of the image reconstruction. Computer simulation studies demonstrated that the new algorithms converge much faster than the traditional expectation maximization (EM) and the preconditioned conjugate gradient algorithms for dynamic PET.

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

Indirect and direct methods have been developed for reconstructing parametric images from dynamic positron emission tomography (PET) data. Indirect methods are simple and easy to implement because reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from dynamic PET sinograms and, in theory, can be statistically more efficient, but the algorithms are often difficult to implement and are very specific to the kinetic model being used. This paper presents a class of generalized algorithms for direct reconstruction of parametric images that are relatively easy to implement and can be adapted to different kinetic models. The proposed algorithms use optimization transfer principle to convert the maximization of a penalized likelihood into a pixel-wise weighted least squares (WLS) kinetic fitting problem at each iteration. Thus, it can employ existing WLS algorithms developed for kinetic models. The proposed algorithms resemble the empirical iterative implementation of the indirect approach, but converge to a solution of the direct formulation. Computer simulations showed that the proposed direct reconstruction algorithms are flexible and achieve a better bias-variance tradeoff than indirect reconstruction methods.

Initial Evaluation of Direct 4D Parametric Reconstruction with Human PET Data

Previously, we presented a direct EM method for producing kinetic parameter images from list mode PET data, where the time-activity curve for each voxel is described by a one-tissue compartment model (1T). The initial evaluations were performed with simulations, without motion, randoms, or scatter effects included. By extension of our previous frame-based physics correction methods, a practical direct 4D parametric reconstruction algorithm is now proposed and implemented for human data. Initial evaluations were performed using 3 human subjects with the serotonin transporter tracer [(11)C]AFM. Comparisons with the 2-step approach (frame-based reconstruction followed by voxel-by-voxel parameter estimation) provided encouraging initial results. Regional analysis showed that the 2-step and 4D methods have similar K(1) and V(T) values, but with a consistent difference. Visual analysis showed some noise reduction in 4D. These initial results suggest that direct 4D parametric reconstruction can be performed with real data, and offers the potential for improved accuracy and precision over the 2-step frame method.

DIRECT RECONSTRUCTION OF DYNAMIC PET PARAMETRIC IMAGES USING SPARSE SPECTRAL REPRESENTATION

To generate parametric images for dynamic PET, direct reconstruction from projection data is statistically more efficient than conventional indirect methods that perform image reconstruction and kinetic modeling in two separate steps. Existing direct reconstruction methods often use nonlinear compartmental models, which require the knowledge of model order. This paper presents a direct reconstruction approach using a linear spectral representation and does not require model order assumption. A Laplacian prior is used to ensure sparsity in the spectral representation. The resultant maximum a posteriori (MAP) formulation is solved by an expectation maximization shrinkage algorithm. A bias correction step is developed to improve the MAP estimate. Computer simulations show that the proposed method achieves better bias-variance tradeoff than a conventional indirect method for estimating parametric images from dynamic PET data.