A technique for extracting physiological parameters and the required input function simultaneously from PET image measurements: theory and simulation study

Exact parameter identification in PET pharmacokinetic modeling using the irreversible two tissue compartment model. Phys Med Biol 2024;69:165008. [PMID: 38830366 PMCID: PMC11288174 DOI: 10.1088/1361-6560/ad539e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Objective.In quantitative dynamic positron emission tomography (PET), time series of images, reflecting the tissue response to the arterial tracer supply, are reconstructed. This response is described by kinetic parameters, which are commonly determined on basis of the tracer concentration in tissue and the arterial input function. In clinical routine the latter is estimated by arterial blood sampling and analysis, which is a challenging process and thus, attempted to be derived directly from reconstructed PET images. However, a mathematical analysis about the necessity of measurements of the common arterial whole blood activity concentration, and the concentration of free non-metabolized tracer in the arterial plasma, for a successful kinetic parameter identification does not exist. Here we aim to address this problem mathematically.Approach.We consider the identification problem in simultaneous pharmacokinetic modeling of multiple regions of interests of dynamic PET data using the irreversible two-tissue compartment model analytically. In addition to this consideration, the situation of noisy measurements is addressed using Tikhonov regularization. Furthermore, numerical simulations with a regularization approach are carried out to illustrate the analytical results in a synthetic application example.Main results.We provide mathematical proofs showing that, under reasonable assumptions, all metabolic tissue parameters can be uniquely identified without requiring additional blood samples to measure the arterial input function. A connection to noisy measurement data is made via a consistency result, showing that exact reconstruction of the ground-truth tissue parameters is stably maintained in the vanishing noise limit. Furthermore, our numerical experiments suggest that an approximate reconstruction of kinetic parameters according to our analytic results is also possible in practice for moderate noise levels.Significance.The analytical result, which holds in the idealized, noiseless scenario, suggests that for irreversible tracers, fully quantitative dynamic PET imaging is in principle possible without costly arterial blood sampling and metabolite analysis.

Kinetic model-informed deep learning for multiplexed PET image separation

BACKGROUND

Multiplexed positron emission tomography (mPET) imaging can measure physiological and pathological information from different tracers simultaneously in a single scan. Separation of the multiplexed PET signals within a single PET scan is challenging due to the fact that each tracer gives rise to indistinguishable 511 keV photon pairs, and thus no unique energy information for differentiating the source of each photon pair.

METHODS

Recently, many applications of deep learning for mPET image separation have been concentrated on pure data-driven methods, e.g., training a neural network to separate mPET images into single-tracer dynamic/static images. These methods use over-parameterized networks with only a very weak inductive prior. In this work, we improve the inductive prior of the deep network by incorporating a general kinetic model based on spectral analysis. The model is incorporated, along with deep networks, into an unrolled image-space version of an iterative fully 4D PET reconstruction algorithm.

RESULTS

The performance of the proposed method was evaluated on a simulated brain image dataset for dual-tracer [18 F]FDG+[11 C]MET PET image separation. The results demonstrate that the proposed method can achieve separation performance comparable to that obtained with single-tracer imaging. In addition, the proposed method outperformed the model-based separation methods (the conventional voxel-wise multi-tracer compartment modeling method (v-MTCM) and the image-space dual-tracer version of the fully 4D PET image reconstruction algorithm (IS-F4D)), as well as a pure data-driven separation [using a convolutional encoder-decoder (CED)], with fewer training examples.

CONCLUSIONS

This work proposes a kinetic model-informed unrolled deep learning method for mPET image separation. In simulation studies, the method proved able to outperform both the conventional v-MTCM method and a pure data-driven CED with less training data.

Non-Invasive Quantification of the Brain [¹⁸F]FDG-PET Using Inferred Blood Input Function Learned From Total-Body Data With Physical Constraint

Full quantification of brain PET requires the blood input function (IF), which is traditionally achieved through an invasive and time-consuming arterial catheter procedure, making it unfeasible for clinical routine. This study presents a deep learning based method to estimate the input function (DLIF) for a dynamic brain FDG scan. A long short-term memory combined with a fully connected network was used. The dataset for training was generated from 85 total-body dynamic scans obtained on a uEXPLORER scanner. Time-activity curves from 8 brain regions and the carotid served as the input of the model, and labelled IF was generated from the ascending aorta defined on CT image. We emphasize the goodness-of-fitting of kinetic modeling as an additional physical loss to reduce the bias and the need for large training samples. DLIF was evaluated together with existing methods in terms of RMSE, area under the curve, regional and parametric image quantifications. The results revealed that the proposed model can generate IFs that closer to the reference ones in terms of shape and amplitude compared with the IFs generated using existing methods. All regional kinetic parameters calculated using DLIF agreed with reference values, with the correlation coefficient being 0.961 (0.913) and relative bias being 1.68±8.74% (0.37±4.93%) for [Formula: see text] ( [Formula: see text]. In terms of the visual appearance and quantification, parametric images were also highly identical to the reference images. In conclusion, our experiments indicate that a trained model can infer an image-derived IF from dynamic brain PET data, which enables subsequent reliable kinetic modeling.

Optimization-derived blood input function using a kernel method and its evaluation with total-body PET for brain parametric imaging

Dynamic PET allows quantification of physiological parameters through tracer kinetic modeling. For dynamic imaging of brain or head and neck cancer on conventional PET scanners with a short axial field of view, the image-derived input function (ID-IF) from intracranial blood vessels such as the carotid artery (CA) suffers from severe partial volume effects. Alternatively, optimization-derived input function (OD-IF) by the simultaneous estimation (SIME) method does not rely on an ID-IF but derives the input function directly from the data. However, the optimization problem is often highly ill-posed. We proposed a new method that combines the ideas of OD-IF and ID-IF together through a kernel framework. While evaluation of such a method is challenging in human subjects, we used the uEXPLORER total-body PET system that covers major blood pools to provide a reference for validation.

METHODS

The conventional SIME approach estimates an input function using a joint estimation together with kinetic parameters by fitting time activity curves from multiple regions of interests (ROIs). The input function is commonly parameterized with a highly nonlinear model which is difficult to estimate. The proposed kernel SIME method exploits the CA ID-IF as a priori information via a kernel representation to stabilize the SIME approach. The unknown parameters are linear and thus easier to estimate. The proposed method was evaluated using 18F-fluorodeoxyglucose studies with both computer simulations and 20 human-subject scans acquired on the uEXPLORER scanner. The effect of the number of ROIs on kernel SIME was also explored.

RESULTS

The estimated OD-IF by kernel SIME showed a good match with the reference input function and provided more accurate estimation of kinetic parameters for both simulation and human-subject data. The kernel SIME led to the highest correlation coefficient (R = 0.97) and the lowest mean absolute error (MAE = 10.5 %) compared to using the CA ID-IF (R = 0.86, MAE = 108.2 %) and conventional SIME (R = 0.57, MAE = 78.7 %) in the human-subject evaluation. Adding more ROIs improved the overall performance of the kernel SIME method.

CONCLUSION

The proposed kernel SIME method shows promise to provide an accurate estimation of the blood input function and kinetic parameters for brain PET parametric imaging.

Deep-learning-derived input function in dynamic [18F]FDG PET imaging of mice

Dynamic positron emission tomography and kinetic modeling play a critical role in tracer development research using small animals. Kinetic modeling from dynamic PET imaging requires accurate knowledge of an input function, ideally determined through arterial blood sampling. Arterial cannulation in mice, however, requires complex, time-consuming and terminal surgery, meaning that longitudinal studies are impossible. The aim of the current work was to develop and evaluate a non-invasive, deep-learning-based prediction model (DLIF) that directly takes the PET data as input to predict a usable input function. We first trained and evaluated the DLIF model on 68 [18F]Fluorodeoxyglucose mouse scans with image-derived targets using cross validation. Subsequently, we evaluated the performance of a trained DLIF model on an external dataset consisting of 8 mouse scans where the input function was measured by continuous arterial blood sampling. The results showed that the predicted DLIF and image-derived targets were similar, and the net influx rate constants following from Patlak modeling using DLIF as input function were strongly correlated to the corresponding values obtained using the image-derived input function. There were somewhat larger discrepancies when evaluating the model on the external dataset, which could be attributed to systematic differences in the experimental setup between the two datasets. In conclusion, our non-invasive DLIF prediction method may be a viable alternative to arterial blood sampling in small animal [18F]FDG imaging. With further validation, DLIF could overcome the need for arterial cannulation and allow fully quantitative and longitudinal experiments in PET imaging studies of mice.

Deep learned triple-tracer multiplexed PET myocardial image separation

Introduction

In multiplexed positron emission tomography (mPET) imaging, physiological and pathological information from different radiotracers can be observed simultaneously in a single dynamic PET scan. The separation of mPET signals within a single PET scan is challenging due to the fact that the PET scanner measures the sum of the PET signals of all the tracers. The conventional multi-tracer compartment modeling (MTCM) method requires staggered injections and assumes that the arterial input functions (AIFs) of each tracer are known.

Methods

In this work, we propose a deep learning-based method to separate triple-tracer PET images without explicitly knowing the AIFs. A dynamic triple-tracer noisy MLEM reconstruction was used as the network input, and dynamic single-tracer noisy MLEM reconstructions were used as training labels.

Results

A simulation study was performed to evaluate the performance of the proposed framework on triple-tracer ([ F 18 ]FDG+ Rb 82 +[ Tc 99m ]sestamibi) PET myocardial imaging. The results show that the proposed methodology substantially reduced the noise level compared to the results obtained from single-tracer imaging. Additionally, it achieved lower bias and standard deviation in the separated single-tracer images compared to the MTCM-based method at both the voxel and region of interest (ROI) levels.

Discussion

As compared to MTCM separation, the proposed method uses spatiotemporal information for separation, which improves the separation performance at both the voxel and ROI levels. The simulation study also demonstrates the feasibility and potential of the proposed DL-based method for the application to pre-clinical and clinical studies.

Automated extraction of the arterial input function from brain images for parametric PET studies

BACKGROUND

Accurate measurement of the arterial input function (AIF) is crucial for parametric PET studies, but the AIF is commonly derived from invasive arterial blood sampling. It is possible to use an image-derived input function (IDIF) obtained by imaging a large blood pool, but IDIF measurement in PET brain studies performed on standard field of view scanners is challenging due to lack of a large blood pool in the field-of-view. Here we describe a novel automated approach to estimate the AIF from brain images.

RESULTS

Total body 18F-FDG PET data from 12 subjects were split into a model adjustment group (n = 6) and a validation group (n = 6). We developed an AIF estimation framework using wavelet-based methods and unsupervised machine learning to distinguish arterial and venous activity curves, compared to the IDIF from the descending aorta. All of the automatically extracted AIFs in the validation group had similar shape to the IDIF derived from the descending aorta IDIF. The average area under the curve error and normalised root mean square error across validation data were - 1.59 ± 2.93% and 0.17 ± 0.07.

CONCLUSIONS

Our automated AIF framework accurately estimates the AIF from brain images. It reduces operator-dependence, and could facilitate the clinical adoption of parametric PET.

ParaPET: non-invasive deep learning method for direct parametric brain PET reconstruction using histoimages

BACKGROUND

The indirect method for generating parametric images in positron emission tomography (PET) involves the acquisition and reconstruction of dynamic images and temporal modelling of tissue activity given a measured arterial input function. This approach is not robust, as noise in each dynamic image leads to a degradation in parameter estimation. Direct methods incorporate into the image reconstruction step both the kinetic and noise models, leading to improved parametric images. These methods require extensive computational time and large computing resources. Machine learning methods have demonstrated significant potential in overcoming these challenges. But they are limited by the requirement of a paired training dataset. A further challenge within the existing framework is the use of state-of-the-art arterial input function estimation via temporal arterial blood sampling, which is an invasive procedure, or an additional magnetic resonance imaging (MRI) scan for selecting a region where arterial blood signal can be measured from the PET image. We propose a novel machine learning approach for reconstructing high-quality parametric brain images from histoimages produced from time-of-flight PET data without requiring invasive arterial sampling, an MRI scan, or paired training data from standard field-of-view scanners.

RESULT

The proposed is tested on a simulated phantom and five oncological subjects undergoing an 18F-FDG-PET scan of the brain using Siemens Biograph Vision Quadra. Kinetic parameters set in the brain phantom correlated strongly with the estimated parameters (K1, k2 and k3, Pearson correlation coefficient of 0.91, 0.92 and 0.93) and a mean squared error of less than 0.0004. In addition, our method significantly outperforms (p < 0.05, paired t-test) the conventional nonlinear least squares method in terms of contrast-to-noise ratio. At last, the proposed method was found to be 37% faster than the conventional method.

CONCLUSION

We proposed a direct non-invasive DL-based reconstruction method and produced high-quality parametric maps of the brain. The use of histoimages holds promising potential for enhancing the estimation of parametric images, an area that has not been extensively explored thus far. The proposed method can be applied to subject-specific dynamic PET data alone.

Simultaneous estimation of a model-derived input function for quantifying cerebral glucose metabolism with [18F]FDG PET

BACKGROUND

Quantification of the cerebral metabolic rate of glucose (CMRGlu) by dynamic [18F]FDG PET requires invasive arterial sampling. Alternatives to using an arterial input function (AIF) include the simultaneous estimation (SIME) approach, which models the image-derived input function (IDIF) by a series of exponentials with coefficients obtained by fitting time activity curves (TACs) from multiple volumes-of-interest. A limitation of SIME is the assumption that the input function can be modelled accurately by a series of exponentials. Alternatively, we propose a SIME approach based on the two-tissue compartment model to extract a high signal-to-noise ratio (SNR) model-derived input function (MDIF) from the whole-brain TAC. The purpose of this study is to present the MDIF approach and its implementation in the analysis of animal and human data.

METHODS

Simulations were performed to assess the accuracy of the MDIF approach. Animal experiments were conducted to compare derived MDIFs to measured AIFs (n = 5). Using dynamic [18F]FDG PET data from neurologically healthy volunteers (n = 18), the MDIF method was compared to the original SIME-IDIF. Lastly, the feasibility of extracting parametric images was investigated by implementing a variational Bayesian parameter estimation approach.

RESULTS

Simulations demonstrated that the MDIF can be accurately extracted from a whole-brain TAC. Good agreement between MDIFs and measured AIFs was found in the animal experiments. Similarly, the MDIF-to-IDIF area-under-the-curve ratio from the human data was 1.02 ± 0.08, resulting in good agreement in grey matter CMRGlu: 24.5 ± 3.6 and 23.9 ± 3.2 mL/100 g/min for MDIF and IDIF, respectively. The MDIF method proved superior in characterizing the first pass of [18F]FDG. Groupwise parametric images obtained with the MDIF showed the expected spatial patterns.

CONCLUSIONS

A model-driven SIME method was proposed to derive high SNR input functions. Its potential was demonstrated by the good agreement between MDIFs and AIFs in animal experiments. In addition, CMRGlu estimates obtained in the human study agreed to literature values. The MDIF approach requires fewer fitting parameters than the original SIME method and has the advantage that it can model the shape of any input function. In turn, the high SNR of the MDIFs has the potential to facilitate the extraction of voxelwise parameters when combined with robust parameter estimation methods such as the variational Bayesian approach.

A short 18F-FDG imaging window triple injection neuroimaging protocol for parametric mapping in PET

BACKGROUND

In parametric PET, kinetic parameters are extracted from dynamic PET images. It is not commonly used in clinical practice because of long scan times and the requirement for an arterial input function (AIF). To address these limitations, we designed an 18F-fluorodeoxyglucose (18F-FDG) triple injection dynamic PET protocol for brain imaging with a standard field of view PET scanner using a 24-min imaging window and an input function modeled using measurements from a region of interest placed over the left ventricle.

METHODS

To test the protocol in 6 healthy participants, we examined the quality of voxel-based maps of kinetic parameters in the brain generated using the two-tissue compartment model and compared estimated parameter values with previously published values. We also utilized data from a 36-min validation imaging window to compare (1) the modeled AIF against the input function measured in the validation window; and (2) the net influx rate ([Formula: see text]) computed using parameter estimates from the short imaging window against the net influx rate obtained using Patlak analysis in the validation window.

RESULTS

Compared to the AIF measured in the validation window, the input function estimated from the short imaging window achieved a mean area under the curve error of 9%. The voxel-wise Pearson's correlation between [Formula: see text] estimates from the short imaging window and the validation imaging window exceeded 0.95.

CONCLUSION

The proposed 24-min triple injection protocol enables parametric 18F-FDG neuroimaging with noninvasive estimation of the AIF from cardiac images using a standard field of view PET scanner.

Parametric and non-parametric Poisson regression for modelling of the arterial input function in positron emission tomography

Full quantification of Positron Emission Tomography (PET) requires an arterial input function (AIF) for measurement of certain targets, or using particular radiotracers, or for the quantification of specific outcome measures. The AIF represents the measurement of radiotracer concentrations in the arterial blood plasma over the course of the PET examination. Measurement of the AIF is prone to error as it is a composite measure created from the combination of multiple measurements of different samples with different equipment, each of which can be sources of measurement error. Moreover, its measurement requires a high degree of temporal granularity for early time points, which necessitates a compromise between quality and quantity of recorded samples. For these reasons, it is often desirable to fit models to this data in order to improve its quality before using it for quantification of radiotracer binding in the tissue. The raw observations of radioactivity in arterial blood and plasma samples are derived from radioactive decay, which is measured as a number of recorded counts. Count data have several specific properties, including the fact that they cannot be negative as well as a particular mean-variance relationship. Poisson regression is the most principled modelling strategy for working with count data, as it both incorporates and exploits these properties. However, no previous studies to our knowledge have taken this approach, despite the advantages of greater efficiency and accuracy which result from using the appropriate distributional assumptions. Here, we implement a Poisson regression modelling approach for the AIF as proof-of-concept of its application. We applied both parametric and non-parametric models for the input function curve. We show that a negative binomial distribution is a more appropriate error distribution for handling overdispersion. Furthermore, we extend this approach to a hierarchical non-parametric model which is shown to be highly resilient to missing data. We thus demonstrate that Poisson regression is both feasible and effective when applied to AIF data, and propose that this is a promising strategy for modelling blood count data for PET in future.

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.

Guided block matching and 4-D transform domain filter projection denoising method for dynamic PET image reconstruction

PURPOSE

Dynamic PET is an essential tool in oncology due to its ability to visualize and quantify radiotracer uptake, which has the potential to improve imaging quality. However, image noise caused by a low photon count in dynamic PET is more significant than in static PET. This study aims to develop a novel denoising method, namely the Guided Block Matching and 4-D Transform Domain Filter (GBM4D) projection, to enhance dynamic PET image reconstruction.

METHODS

The sinogram was first transformed using the Anscombe method, then denoised using a combination of hard thresholding and Wiener filtering. Each denoising step involved guided block matching and grouping, collaborative filtering, and weighted averaging. The guided block matching was performed on accumulated PET sinograms to prevent mismatching due to low photon counts. The performance of the proposed denoising method (GBM4D) was compared to other methods such as wavelet, total variation, non-local means, and BM3D using computer simulations on the Shepp-Logan and digital brain phantoms. The denoising methods were also applied to real patient data for evaluation.

RESULTS

In all phantom studies, GBM4D outperformed other denoising methods in all time frames based on the structural similarity and peak signal-to-noise ratio. Moreover, GBM4D yielded the lowest root mean square error in the time-activity curve of all tissues and produced the highest image quality when applied to real patient data.

CONCLUSION

GBM4D demonstrates excellent denoising and edge-preserving capabilities, as validated through qualitative and quantitative assessments of both temporal and spatial denoising performance.

PET AIF estimation when available ROI data is impacted by dispersive and/or background effects

Objective.Blood pool region of interest (ROI) data extracted from the field of view of a PET scanner can be impacted by both dispersive and background effects. This circumstance compromises the ability to correctly extract the arterial input function (AIF) signal. The paper explores a novel approach to addressing this difficulty.Approach.The method involves representing the AIF in terms of the whole-body impulse response (IR) to the injection profile. Analysis of a collection/population of directly sampled arterial data sets allows the statistical behaviour of the tracer's impulse response to be evaluated. It is proposed that this information be used to develop a penalty term for construction of a data-adaptive method of regularisation estimator of the AIF when dispersive and/or background effects maybe impacting the blood pool ROI data.Main results.Computational efficiency of the approach derives from the linearity of the impulse response representation of the AIF and the ability to substantially rely on quadratic programming techniques for numerical implementation. Data from eight different tracers, used in PET cancer imaging studies, are considered. Sample image-based AIF extractions for brain studies with:18F-labeled fluoro-deoxyglucose and fluoro-thymidine (FLT),11C-labeled carbon dioxide (CO2) and15O-labeled water (H2O) are presented. Results are compared to the true AIF based on direct arterial sampling. Formal numerical simulations are used to evaluate the performance of the AIF extraction method when the ROI data has varying amounts of contamination, in comparison to a direct approach that ignores such effects. It is found that even with quite small amounts of contamination, the mean squared error of the regularised AIF is significantly better than the error associated with direct use of the ROI data.Significance.The proposed IR-based AIF extraction scheme offers a practical methodological approach for situations where the available image ROI data may be contaminated by background and/or dispersion effects.

Non-invasive kinetic modelling approaches for quantitative analysis of brain PET studies

Pharmacokinetic modelling with arterial sampling is the gold standard for analysing dynamic PET data of the brain. However, the invasive character of arterial sampling prevents its widespread clinical application. Several methods have been developed to avoid arterial sampling, in particular reference region methods. Unfortunately, for some tracers or diseases, no suitable reference region can be defined. For these cases, other potentially non-invasive approaches have been proposed: (1) a population based input function (PBIF), (2) an image derived input function (IDIF), or (3) simultaneous estimation of the input function (SIME). This systematic review aims to assess the correspondence of these non-invasive methods with the gold standard. Studies comparing non-invasive pharmacokinetic modelling methods with the current gold standard methods using an input function derived from arterial blood samples were retrieved from PubMed/MEDLINE (until December 2021). Correlation measurements were extracted from the studies. The search yielded 30 studies that correlated outcome parameters (V_T, DVR, or BP_ND for reversible tracers; K_i or CMR_glu for irreversible tracers) from a potentially non-invasive method with those obtained from modelling using an arterial input function. Some studies provided similar results for PBIF, IDIF, and SIME-based methods as for modelling with an arterial input function (R² = 0.59-1.00, R² = 0.71-1.00, R² = 0.56-0.96, respectively), if the non-invasive input curve was calibrated with arterial blood samples. Even when the non-invasive input curve was calibrated with venous blood samples or when no calibration was applied, moderate to good correlations were reported, especially for the IDIF and SIME (R² = 0.71-1.00 and R² = 0.36-0.96, respectively). Overall, this systematic review illustrates that non-invasive methods to generate an input function are still in their infancy. Yet, IDIF and SIME performed well, not only with arterial blood calibration, but also with venous or no blood calibration, especially for some tracers without plasma metabolites, which would potentially make these methods better suited for clinical application. However, these methods should still be properly validated for each individual tracer and application before implementation.

Dynamic PET images denoising using spectral graph wavelet transform

Positron emission tomography (PET) is a non-invasive molecular imaging method for quantitative observation of physiological and biochemical changes in living organisms. The quality of the reconstructed PET image is limited by many different physical degradation factors. Various denoising methods including Gaussian filtering (GF) and non-local mean (NLM) filtering have been proposed to improve the image quality. However, image denoising usually blurs edges, of which high frequency components are filtered as noises. On the other hand, it is well-known that edges in a PET image are important to detection and recognition of a lesion. Denoising while preserving the edges of PET images remains an important yet challenging problem in PET image processing. In this paper, we propose a novel denoising method with good edge-preserving performance based on spectral graph wavelet transform (SGWT) for dynamic PET images denoising. We firstly generate a composite image from the entire time series, then perform SGWT on the PET images, and finally reconstruct the low graph frequency content to get the denoised dynamic PET images. Experimental results on simulation and in vivo data show that the proposed approach significantly outperforms the GF, NLM and graph filtering methods. Compared with deep learning-based method, the proposed method has the similar denoising performance, but it does not need lots of training data and has low computational complexity.

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

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

Image Quantification for TSPO PET with a Novel Image-Derived Input Function Method

There is a growing interest in using 18F-DPA-714 PET to study neuroinflammation and microglial activation through imaging the 18-kDa translocator protein (TSPO). Although quantification of 18F-DPA-714 binding can be achieved through kinetic modeling analysis with an arterial input function (AIF) measured with blood sampling procedures, the invasiveness of such procedures has been an obstacle for wide application. To address these challenges, we developed an image-derived input function (IDIF) that noninvasively estimates the arterial input function from the images acquired for 18F-DPA-714 quantification. Methods: The method entails three fully automatic steps to extract the IDIF, including a segmentation of voxels with highest likelihood of being the arterial blood over the carotid artery, a model-based matrix factorization to extract the arterial blood signal, and a scaling optimization procedure to scale the extracted arterial blood signal into the activity concentration unit. Two cohorts of human subjects were used to evaluate the extracted IDIF. In the first cohort of five subjects, arterial blood sampling was performed, and the calculated IDIF was validated against the measured AIF through the comparison of distribution volumes from AIF (VT,AIF) and IDIF (VT,IDIF). In the second cohort, PET studies from twenty-eight healthy controls without arterial blood sampling were used to compare VT,IDIF with VT,REF measured using a reference region-based analysis to evaluate whether it can distinguish high-affinity (HAB) and mixed-affinity (MAB) binders. Results: In the arterial blood-sampling cohort, VT derived from IDIF was found to be an accurate surrogate of the VT from AIF. The bias of VT, IDIF was −5.8 ± 7.8% when compared to VT,AIF, and the linear mixed effect model showed a high correlation between VT,AIF and VT, IDIF (p < 0.001). In the nonblood-sampling cohort, VT, IDIF showed a significance difference between the HAB and MAB healthy controls. VT, IDIF and standard uptake values (SUV) showed superior results in distinguishing HAB from MAB subjects than VT,REF. Conclusions: A novel IDIF method for 18F-DPA-714 PET quantification was developed and evaluated in this study. This IDIF provides a noninvasive alternative measurement of VT to quantify the TSPO binding of 18F-DPA-714 in the human brain through dynamic PET scans.

Temporal information guided dynamic dual-tracer PET signal separation network

PURPOSE

The difficulty of dynamic dual-tracer positron emission tomography (PET) technology is to separate the complete single-tracer information from mixed dual-tracer. Traditional methods cannot separate single injection single-scan dynamic dual-tracer PET images. In this paper, we propose a deep learning framework based on gated recurrent unit (GRU) network and evaluate its performance with simulation experiments and realistic monkey data.

METHODS

The proposed single-scan dynamic dual-tracer PET image separation network consists of three parts, including encoder, separation and decoder module. Encoder part is to map the mixed time activity curves (TACs) from the low-dimensional space to the high-dimensional space to get mixed weight vector matrix. Separation part is to capture the temporal information of mixed weight vector matrix using bi-directional GRU (bi-GRU) layer to obtain the single-tracer masks, and the decoding part remaps the high-dimensional single-tracer weight vector matrix to the low-dimensional space to obtain two separated single tracers.

RESULTS

In the simulation experiments under different tracers, phantoms, noise levels, arterial input function (AIF) and k-parameter with Gaussian random, compared to the stacked auto encoder (SAE) network and traditional background subtraction method, GRU-based network has better performance with low bias and mean squared error (MSE). In the realistic study, the image results of GRU network have higher mean structural similarity (MSSIM), and peak signal to noise ratio (PSNR).

CONCLUSIONS

This study demonstrates the feasibility of temporal information guided neural network in single-injection single-scan dynamic dual-tracer PET images separation. The GRU-based network uses TAC temporal information without AIFs to make the separation results more robust and accurate, which significantly outperforms state-of-the-art method qualitatively and quantitatively. This article is protected by copyright. All rights reserved.

Machine Learning-Based Noninvasive Quantification of Single-Imaging Session Dual-Tracer 18F-FDG and 68Ga-DOTATATE Dynamic PET-CT in Oncology

⁶⁸Ga-DOTATATE PET-CT is routinely used for imaging neuroendocrine tumor (NET) somatostatin receptor subtype 2 (SSTR2) density in patients, and is complementary to FDG PET-CT for improving the accuracy of NET detection, characterization, grading, staging, and predicting/monitoring NET responses to treatment. Performing sequential ¹⁸F-FDG and ⁶⁸Ga-DOTATATE PET scans would require 2 or more days and can delay patient care. To align temporal and spatial measurements of ¹⁸F-FDG and ⁶⁸Ga-DOTATATE PET, and to reduce scan time and CT radiation exposure to patients, we propose a single-imaging session dual-tracer dynamic PET acquisition protocol in the study. A recurrent extreme gradient boosting (rXGBoost) machine learning algorithm was proposed to separate the mixed ¹⁸F-FDG and ⁶⁸Ga-DOTATATE time activity curves (TACs) for the region of interest (ROI) based quantification with tracer kinetic modeling. A conventional parallel multi-tracer compartment modeling method was also implemented for reference. Single-scan dual-tracer dynamic PET was simulated from 12 NET patient studies with ¹⁸F-FDG and ⁶⁸Ga-DOTATATE 45-min dynamic PET scans separately obtained within 2 days. Our experimental results suggested an ¹⁸F-FDG injection first followed by ⁶⁸Ga-DOTATATE with a minimum 5 min delayed injection protocol for the separation of mixed ¹⁸F-FDG and ⁶⁸Ga-DOTATATE TACs using rXGBoost algorithm followed by tracer kinetic modeling is highly feasible.

Source-to-Target Automatic Rotating Estimation (STARE) - a publicly-available, blood-free quantification approach for PET tracers with irreversible kinetics: Theoretical framework and validation for [18F]FDG

INTRODUCTION

Full quantification of positron emission tomography (PET) data requires an input function. This generally means arterial blood sampling, which is invasive, labor-intensive and burdensome. There is no current, standardized method to fully quantify PET radiotracers with irreversible kinetics in the absence of blood data. Here, we present Source-to-Target Automatic Rotating Estimation (STARE), a novel, data-driven approach to quantify the net influx rate (K_i) of irreversible PET radiotracers, that requires only individual-level PET data and no blood data. We validate STARE with human [¹⁸F]FDG PET scans and assess its performance using simulations.

METHODS

STARE builds upon a source-to-target tissue model, where the tracer time activity curves (TACs) in multiple "target" regions are expressed at once as a function of a "source" region, based on the two-tissue irreversible compartment model, and separates target region K_i from source K_i by fitting the source-to-target model across all target regions simultaneously. To ensure identifiability, data-driven, subject-specific anchoring is used in the STARE minimization, which takes advantage of the PET signal in a vasculature cluster in the field of view (FOV) that is automatically extracted and partial volume-corrected. To avoid the need for any a priori determination of a single source region, each of the considered regions acts in turn as the source, and a final K_i is estimated in each region by averaging the estimates obtained in each source rotation.

RESULTS

In a large dataset of human [¹⁸F]FDG scans (N=69), STARE K_i estimates were correlated with corresponding arterial blood-based K_i estimates (r=0.80), with an overall regression slope of 0.88, and were precisely estimated, as assessed by comparing STARE K_i estimates across several runs of the algorithm (coefficient of variation across runs=6.74 ± 2.48%). In simulations, STARE K_i estimates were largely robust to factors that influence the individualized anchoring used within its algorithm.

CONCLUSION

Through simulations and application to [¹⁸F]FDG PET data, feasibility is demonstrated for STARE blood-free, data-driven quantification of K_i. Future work will include applying STARE to PET data obtained with a portable PET camera and to other irreversible radiotracers.

Kernel graph filtering-A new method for dynamic sinogram denoising

Low count PET (positron emission tomography) imaging is often desirable in clinical diagnosis and biomedical research, but its images are generally very noisy, due to the very weak signals in the sinograms used in image reconstruction. To address this issue, this paper presents a novel kernel graph filtering method for dynamic PET sinogram denoising. This method is derived from treating the dynamic sinograms as the signals on a graph, and learning the graph adaptively from the kernel principal components of the sinograms to construct a lowpass kernel graph spectrum filter. The kernel graph filter thus obtained is then used to filter the original sinogram time frames to obtain the denoised sinograms for PET image reconstruction. Extensive tests and comparisons on the simulated and real life in-vivo dynamic PET datasets show that the proposed method outperforms the existing methods in sinogram denoising and image enhancement of dynamic PET at all count levels, especially at low count, with a great potential in real life applications of dynamic PET imaging.

Cerebral blood flow measurements with 15O-water PET using a non-invasive machine-learning-derived arterial input function

Cerebral blood flow (CBF) can be measured with dynamic positron emission tomography (PET) of 15O-labeled water by using tracer kinetic modelling. However, for quantification of regional CBF, an arterial input function (AIF), obtained from arterial blood sampling, is required. In this work we evaluated a novel, non-invasive approach for input function prediction based on machine learning (MLIF), against AIF for CBF PET measurements in human subjects.Twenty-five subjects underwent two 10 min dynamic 15O-water brain PET scans with continuous arterial blood sampling, before (baseline) and following acetazolamide medication. Three different image-derived time-activity curves were automatically segmented from the carotid arteries and used as input into a Gaussian process-based AIF prediction model, considering both baseline and acetazolamide scans as training data. The MLIF approach was evaluated by comparing AIF and MLIF curves, as well as whole-brain grey matter CBF values estimated by kinetic modelling derived with either AIF or MLIF.The results showed that AIF and MLIF curves were similar and that corresponding CBF values were highly correlated and successfully differentiated before and after acetazolamide medication. In conclusion, our non-invasive MLIF method shows potential to replace the AIF obtained from blood sampling for CBF measurements using 15O-water PET and kinetic modelling.

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.

Validation of a combined image derived input function and venous sampling approach for the quantification of [18F]GE-179 PET binding in the brain

Blood-based kinetic analysis of PET data relies on an accurate estimate of the arterial plasma input function (PIF). An alternative to invasive measurements from arterial sampling is an image-derived input function (IDIF). However, an IDIF provides the whole blood radioactivity concentration, rather than the required free tracer radioactivity concentration in plasma. To estimate the tracer PIF, we corrected an IDIF from the carotid artery with estimates of plasma parent fraction (PF) and plasma-to-whole blood (PWB) ratio obtained from five venous samples. We compared the combined IDIF+venous approach to gold standard data from arterial sampling in 10 healthy volunteers undergoing [¹⁸F]GE-179 brain PET imaging of the NMDA receptor. Arterial and venous PF and PWB ratio estimates determined from 7 patients with traumatic brain injury (TBI) were also compared to assess the potential effect of medication. There was high agreement between areas under the curves of the estimates of PF (r = 0.99, p<0.001), PWB ratio (r = 0.93, p<0.001), and the PIF (r = 0.92, p<0.001) as well as total distribution volume (V_T) in 11 regions across the brain (r = 0.95, p<0.001). IDIF+venous V_T had a mean bias of -1.7% and a comparable regional coefficient of variation (arterial: 21.3 ± 2.5%, IDIF+venous: 21.5 ± 2.0%). Simplification of the IDIF+venous method to use only one venous sample provided less accurate V_T estimates (mean bias 9.9%; r = 0.71, p<0.001). A version of the method that avoids the need for blood sampling by combining the IDIF with population-based PF and PWB ratio estimates systematically underestimated V_T (mean bias -20.9%), and produced V_T estimates with a poor correlation to those obtained using arterial data (r = 0.45, p<0.001). Arterial and venous blood data from 7 TBI patients showed high correlations for PF (r = 0.92, p = 0.003) and PWB ratio (r = 0.93, p = 0.003). In conclusion, the IDIF+venous method with five venous samples provides a viable alternative to arterial sampling for quantification of [¹⁸F]GE-179 V_T.

Voxelwise Principal Component Analysis of Dynamic [S-Methyl-11C]Methionine PET Data in Glioma Patients

Recent works have demonstrated the added value of dynamic amino acid positron emission tomography (PET) for glioma grading and genotyping, biopsy targeting, and recurrence diagnosis. However, most of these studies are based on hand-crafted qualitative or semi-quantitative features extracted from the mean time activity curve within predefined volumes. Voxelwise dynamic PET data analysis could instead provide a better insight into intra-tumor heterogeneity of gliomas. In this work, we investigate the ability of principal component analysis (PCA) to extract relevant quantitative features from a large number of motion-corrected [S-methyl-¹¹C]methionine ([¹¹C]MET) PET frames. We first demonstrate the robustness of our methodology to noise by means of numerical simulations. We then build a PCA model from dynamic [¹¹C]MET acquisitions of 20 glioma patients. In a distinct cohort of 13 glioma patients, we compare the parametric maps derived from our PCA model to these provided by the classical one-compartment pharmacokinetic model (1TCM). We show that our PCA model outperforms the 1TCM to distinguish characteristic dynamic uptake behaviors within the tumor while being less computationally expensive and not requiring arterial sampling. Such methodology could be valuable to assess the tumor aggressiveness locally with applications for treatment planning and response evaluation. This work further supports the added value of dynamic over static [¹¹C]MET PET in gliomas.

Comparison of blind deconvolution- and Patlak analysis-based methods for determining vascular permeability

This study describes a computational algorithm to determine vascular permeability constants from time-lapse imaging data without concurrent knowledge of the arterial input function. The algorithm is based on "blind" deconvolution of imaging data, which were generated with analytical and finite-element models of bidirectional solute transport between a capillary and its surrounding tissue. Compared to the commonly used Patlak analysis, the blind algorithm is substantially more accurate in the presence of solute delay and dispersion. We also compared the performance of the blind algorithm with that of a simpler one that assumed unidirectional transport from capillary to tissue [as described in Truslow et al., Microvasc. Res. 90, 117-120 (2013)]. The algorithm based on bidirectional transport was more accurate than the one based on unidirectional transport for more permeable vessels and smaller extravascular distribution volumes, and less accurate for less permeable vessels and larger extravascular distribution volumes. Our results indicate that blind deconvolution is superior to Patlak analysis for permeability mapping under clinically relevant conditions, and can thus potentially improve the detection of tissue regions with a compromised vascular barrier.

Reproducibility of compartmental modelling of 18F-FDG PET/CT to evaluate lung inflammation

Introduction

Compartmental modelling is an established method of quantifying ¹⁸F-FDG uptake; however, only recently has it been applied to evaluate pulmonary inflammation. Implementation of compartmental models remains challenging in the lung, partly due to the low signal-to-noise ratio compared to other organs and the lack of standardisation. Good reproducibility is a key requirement of an imaging biomarker which has yet to be demonstrated in pulmonary compartmental models of ¹⁸F-FDG; in this paper, we address this unmet need.

Methods

Retrospective subject data were obtained from the EVOLVE observational study: Ten COPD patients (age =66±9; 8M/2F), 10 α₁ATD patients (age =63±8; 7M/3F) and 10 healthy volunteers (age =68±8; 9M/1F) never smokers. PET and CT images were co-registered, and whole lung regions were extracted from CT using an automated algorithm; the descending aorta was defined using a manually drawn region. Subsequent stages of the compartmental analysis were performed by two independent operators using (i) a MIAKAT^TM based pipeline and (ii) an in-house developed pipeline. We evaluated the metabolic rate constant of ¹⁸F-FDG (K_im) and the fractional blood volume (V_b); Bland-Altman plots were used to compare the results. Further, we adjusted the in-house pipeline to identify the salient features in the analysis which may help improve the standardisation of this technique in the lung.

Results

The initial agreement on a subject level was poor: Bland-Altman coefficients of reproducibility for K_im and V_b were 0.0031 and 0.047 respectively. However, the effect size between the groups (i.e. COPD, α₁ATD and healthy subjects) was similar using either pipeline. We identified the key drivers of this difference using an incremental approach: ROI methodology, modelling of the IDIF and time delay estimation. Adjustment of these factors led to improved Bland-Altman coefficients of reproducibility of 0.0015 and 0.027 for K_im and V_b respectively.

Conclusions

Despite similar methodology, differences in implementation can lead to disparate results in the outcome parameters. When reporting the outcomes of lung compartmental modelling, we recommend the inclusion of the details of ROI methodology, input function fitting and time delay estimation to improve reproducibility.

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.

Iterative PET Image Reconstruction Using Convolutional Neural Network Representation

PET image reconstruction is challenging due to the ill-poseness of the inverse problem and limited number of detected photons. Recently, the deep neural networks have been widely and successfully used in computer vision tasks and attracted growing interests in medical imaging. In this paper, we trained a deep residual convolutional neural network to improve PET image quality by using the existing inter-patient information. An innovative feature of the proposed method is that we embed the neural network in the iterative reconstruction framework for image representation, rather than using it as a post-processing tool. We formulate the objective function as a constrained optimization problem and solve it using the alternating direction method of multipliers algorithm. Both simulation data and hybrid real data are used to evaluate the proposed method. Quantification results show that our proposed iterative neural network method can outperform the neural network denoising and conventional penalized maximum likelihood methods.

Hybrid PET/MRI Methodology

The hybrid PET/MR scanner represents the first implementation of the effective integration of two modalities allowing truly synchronous/simultaneous acquisition of their imaging signals. This integration, resulting from the innovation and development of specific hardware components has paved the way for new approaches in the study of neurodegenerative diseases. This chapter will describe the hardware development that has led to the availability of different clinical solutions for PET/MR imaging as well as the still-open technological challenges and opportunities related to the processing and exploitation of the simultaneous acquisition in neurological studies.

Non-invasive kinetic modelling of PET tracers with radiometabolites using a constrained simultaneous estimation method: evaluation with 11C-SB201745

Background

Kinetic analysis of dynamic PET data requires an accurate knowledge of available PET tracer concentration within blood plasma over time, known as the arterial input function (AIF). The gold standard method used to measure the AIF requires serial arterial blood sampling over the course of the PET scan, which is an invasive procedure and makes this method less practical in clinical settings. Traditional image-derived methods are limited to specific tracers and are not accurate if metabolites are present in the plasma.

Results

In this work, we utilise an image-derived whole blood curve measurement to reduce the computational complexity of the simultaneous estimation method (SIME), which is capable of estimating the AIF directly from tissue time activity curves (TACs). This method was applied to data obtained from a serotonin receptor study (¹¹C-SB207145) and estimated parameter results are compared to results obtained using the original SIME and gold standard AIFs derived from arterial samples. Reproducibility of the method was assessed using test-retest data. It was shown that the incorporation of image-derived information increased the accuracy of total volume of distribution (V _T) estimates, averaged across all regions, by 40% and non-displaceable binding potential (BP _ND) estimates by 16% compared to the original SIME. Particular improvements were observed in K₁ parameter estimates. BP _ND estimates, based on the proposed method and the gold standard arterial sample-derived AIF, were not significantly different (P=0.7).

Conclusions

The results of this work indicate that the proposed method with prior AIF information obtained from a partial volume corrected image-derived whole blood curve, and modelled parent fraction, has the potential to be used as an alternative non-invasive method to perform kinetic analysis of tracers with metabolite products.

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.

An improved optimization algorithm of the three-compartment model with spillover and partial volume corrections for dynamic FDG PET images of small animal hearts in vivo

The three-compartment model with spillover (SP) and partial volume (PV) corrections has been widely used for noninvasive kinetic parameter studies of dynamic 2-[18F] fluoro-2deoxy-D-glucose (FDG) positron emission tomography images of small animal hearts in vivo. However, the approach still suffers from estimation uncertainty or slow convergence caused by the commonly used optimization algorithms. The aim of this study was to develop an improved optimization algorithm with better estimation performance. Femoral artery blood samples, image-derived input functions from heart ventricles and myocardial time-activity curves (TACs) were derived from data on 16 C57BL/6 mice obtained from the UCLA Mouse Quantitation Program. Parametric equations of the average myocardium and the blood pool TACs with SP and PV corrections in a three-compartment tracer kinetic model were formulated. A hybrid method integrating artificial immune-system and interior-reflective Newton methods were developed to solve the equations. Two penalty functions and one late time-point tail vein blood sample were used to constrain the objective function. The estimation accuracy of the method was validated by comparing results with experimental values using the errors in the areas under curves (AUCs) of the model corrected input function (MCIF) and the 18F-FDG influx constant K _i . Moreover, the elapsed time was used to measure the convergence speed. The overall AUC error of MCIF for the 16 mice averaged  -1.4  ±  8.2%, with correlation coefficients of 0.9706. Similar results can be seen in the overall K _i error percentage, which was 0.4  ±  5.8% with a correlation coefficient of 0.9912. The t-test P value for both showed no significant difference. The mean and standard deviation of the MCIF AUC and K _i percentage errors have lower values compared to the previously published methods. The computation time of the hybrid method is also several times lower than using just a stochastic algorithm. The proposed method significantly improved the model estimation performance in terms of the accuracy of the MCIF and K _i , as well as the convergence speed.

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.

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.

Improved simultaneous estimation of tracer kinetic models with artificial immune network based optimization method

Tracer kinetic modeling (TKM) is a promising quantitative method for physiological and biochemical processes in vivo. In this paper, we investigated the applications of an immune-inspired method to better address the issues of Simultaneous Estimation (SIME) of TKM with multimodal optimization. Experiments of dynamic FDG PET imaging experiments and simulation studies were carried out. The proposed artificial immune network (TKM_AIN) shows more scalable and effective when compared with the gradient-based Marquardt-Levenberg algorithm and the scholastic-based simulated annealing method.

Quantitative amyloid imaging using image-derived arterial input function

Amyloid PET imaging is an indispensable tool widely used in the investigation, diagnosis and monitoring of Alzheimer’s disease (AD). Currently, a reference region based approach is used as the mainstream quantification technique for amyloid imaging. This approach assumes the reference region is amyloid free and has the same tracer influx and washout kinetics as the regions of interest. However, this assumption may not always be valid. The goal of this work is to evaluate an amyloid imaging quantification technique that uses arterial region of interest as the reference to avoid potential bias caused by specific binding in the reference region. 21 participants, age 58 and up, underwent Pittsburgh compound B (PiB) PET imaging and MR imaging including a time-of-flight (TOF) MR angiography (MRA) scan and a structural scan. FreeSurfer based regional analysis was performed to quantify PiB PET data. Arterial input function was estimated based on coregistered TOF MRA using a modeling based technique. Regional distribution volume (V_T) was calculated using Logan graphical analysis with estimated arterial input function. Kinetic modeling was also performed using the estimated arterial input function as a way to evaluate PiB binding (DVR_kinetic) without a reference region. As a comparison, Logan graphical analysis was also performed with cerebellar cortex as reference to obtain DVR_REF. Excellent agreement was observed between the two distribution volume ratio measurements (r>0.89, ICC>0.80). The estimated cerebellum V_T was in line with literature reported values and the variability of cerebellum V_T in the control group was comparable to reported variability using arterial sampling data. This study suggests that image-based arterial input function is a viable approach to quantify amyloid imaging data, without the need of arterial sampling or a reference region. This technique can be a valuable tool for amyloid imaging, particularly in population where reference normalization may not be accurate.

Network dynamics for optimal compressive-sensing input-signal recovery

By using compressive sensing (CS) theory, a broad class of static signals can be reconstructed through a sequence of very few measurements in the framework of a linear system. For networks with nonlinear and time-evolving dynamics, is it similarly possible to recover an unknown input signal from only a small number of network output measurements? We address this question for pulse-coupled networks and investigate the network dynamics necessary for successful input signal recovery. Determining the specific network characteristics that correspond to a minimal input reconstruction error, we are able to achieve high-quality signal reconstructions with few measurements of network output. Using various measures to characterize dynamical properties of network output, we determine that networks with highly variable and aperiodic output can successfully encode network input information with high fidelity and achieve the most accurate CS input reconstructions. For time-varying inputs, we also find that high-quality reconstructions are achievable by measuring network output over a relatively short time window. Even when network inputs change with time, the same optimal choice of network characteristics and corresponding dynamics apply as in the case of static inputs.

Recent advances in parametric neuroreceptor mapping with dynamic PET: basic concepts and graphical analyses

Tracer kinetic modeling in dynamic positron emission tomography (PET) has been widely used to investigate the characteristic distribution patterns or dysfunctions of neuroreceptors in brain diseases. Its practical goal has progressed from regional data quantification to parametric mapping that produces images of kinetic-model parameters by fully exploiting the spatiotemporal information in dynamic PET data. Graphical analysis (GA) is a major parametric mapping technique that is independent on any compartmental model configuration, robust to noise, and computationally efficient. In this paper, we provide an overview of recent advances in the parametric mapping of neuroreceptor binding based on GA methods. The associated basic concepts in tracer kinetic modeling are presented, including commonly-used compartment models and major parameters of interest. Technical details of GA approaches for reversible and irreversible radioligands are described, considering both plasma input and reference tissue input models. Their statistical properties are discussed in view of parametric imaging.