Imaging radiotracer model parameters in PET: a mixture analysis approach

Mapping 18F-FDG Kinetics Together with Patient-Specific Bootstrap Assessment of Uncertainties: An Illustration with Data from a PET/CT Scanner with a Long Axial Field of View

The purpose of this study was to examine a nonparametric approach to mapping kinetic parameters and their uncertainties with data from the emerging generation of dynamic whole-body PET/CT scanners. Methods: Dynamic PET 18F-FDG data from a set of 24 cancer patients studied on a long-axial-field-of-view PET/CT scanner were considered. Kinetics were mapped using a nonparametric residue mapping (NPRM) technique. Uncertainties were evaluated using an image-based bootstrapping methodology. Kinetics and bootstrap-derived uncertainties are reported for voxels, maximum-intensity projections, and volumes of interest (VOIs) corresponding to several key organs and lesions. Comparisons between NPRM and standard 2-compartment (2C) modeling of VOI kinetics are carefully examined. Results: NPRM-generated kinetic maps were of good quality and well aligned with vascular and metabolic 18F-FDG patterns, reasonable for the range of VOIs considered. On a single 3.2-GHz processor, the specification of the bootstrapping model took 140 min; individual bootstrap replicates required 80 min each. VOI time-course data were much more accurately represented, particularly in the early time course, by NPRM than by 2C modeling constructs, and improvements in fit were statistically highly significant. Although 18F-FDG flux values evaluated by NPRM and 2C modeling were generally similar, significant deviations between vascular blood and distribution volume estimates were found. The bootstrap enables the assessment of quite complex summaries of mapped kinetics. This is illustrated with maximum-intensity maps of kinetics and their uncertainties. Conclusion: NPRM kinetics combined with image-domain bootstrapping is practical with large whole-body dynamic 18F-FDG datasets. The information provided by bootstrapping could support more sophisticated uses of PET biomarkers used in clinical decision-making for the individual patient.

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

BACKGROUND

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

CHALLENGES

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

CONCLUSIONS

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

Total-Body PET Multiparametric Imaging of Cancer Using a Voxelwise Strategy of Compartmental Modeling

Quantitative dynamic PET with compartmental modeling has the potential to enable multiparametric imaging and more accurate quantification than static PET imaging. Conventional methods for parametric imaging commonly use a single kinetic model for all image voxels and neglect the heterogeneity of physiologic models, which can work well for single-organ parametric imaging but may significantly compromise total-body parametric imaging on a scanner with a long axial field of view. In this paper, we evaluate the necessity of voxelwise compartmental modeling strategies, including time delay correction (TDC) and model selection, for total-body multiparametric imaging. Methods: Ten subjects (5 patients with metastatic cancer and 5 healthy volunteers) were scanned on a total-body PET/CT system after injection of 370 MBq of 18F-FDG. Dynamic data were acquired for 60 min. Total-body parametric imaging was performed using 2 approaches. One was the conventional method that uses a single irreversible 2-tissue-compartment model with and without TDC. The second approach selects the best kinetic model from 3 candidate models for individual voxels. The differences between the 2 approaches were evaluated for parametric imaging of microkinetic parameters and the 18F-FDG net influx rate, KiResults: TDC had a nonnegligible effect on kinetic quantification of various organs and lesions. The effect was larger in lesions with a higher blood volume. Parametric imaging of Ki with the standard 2-tissue-compartment model introduced vascular-region artifacts, which were overcome by the voxelwise model selection strategy. Conclusion: The time delay and appropriate kinetic model vary in different organs and lesions. Modeling of the time delay of the blood input function and model selection improved total-body multiparametric imaging.

Principles of Tracer Kinetic Analysis in Oncology, Part I: Principles and Overview of Methodology

Learning Objectives: On successful completion of this activity, participants should be able to describe (1) describe principles of PET tracer kinetic analysis for oncologic applications; (2) list methods used for PET kinetic analysis for oncology; and (3) discuss application of kinetic modeling for cancer-specific diagnostic needs.Financial Disclosure: This work was supported by KL2 TR001879, R01 CA211337, R01 CA113941, R33 CA225310, Komen SAC130060, R50 CA211270, and K01 DA040023. Dr. Pantel is a consultant or advisor for Progenics and Blue Earth Diagnostics and is a meeting participant or lecturer for Blue Earth Diagnostics. Dr. Mankoff is on the scientific advisory boards of GE Healthcare, Philips Healthcare, Reflexion, and ImaginAb and is the owner of Trevarx; his wife is the chief executive officer of Trevarx. The authors of this article have indicated no other relevant relationships that could be perceived as a real or apparent conflict of interest.CME Credit: SNMMI is accredited by the Accreditation Council for Continuing Medical Education (ACCME) to sponsor continuing education for physicians. SNMMI designates each JNM continuing education article for a maximum of 2.0 AMA PRA Category 1 Credits. Physicians should claim only credit commensurate with the extent of their participation in the activity. For CE credit, SAM, and other credit types, participants can access this activity through the SNMMI website (http://www.snmmilearningcenter.org) through March 2025PET enables noninvasive imaging of regional in vivo cancer biology. By engineering a radiotracer to target specific biologic processes of relevance to cancer (e.g., cancer metabolism, blood flow, proliferation, and tumor receptor expression or ligand binding), PET can detect cancer spread, characterize the cancer phenotype, and assess its response to treatment. For example, imaging of glucose metabolism using the radiolabeled glucose analog ¹⁸F-FDG has widespread applications to all 3 of these tasks and plays an important role in cancer care. However, the current clinical practice of imaging at a single time point remote from tracer injection (i.e., static imaging) does not use all the information that PET cancer imaging can provide, especially to address questions beyond cancer detection. Reliance on tracer measures obtained only from static imaging may also lead to misleading results. In this 2-part continuing education paper, we describe the principles of tracer kinetic analysis for oncologic PET (part 1), followed by examples of specific implementations of kinetic analysis for cancer PET imaging that highlight the added benefits over static imaging (part 2). This review is designed to introduce nuclear medicine clinicians to basic concepts of kinetic analysis in oncologic imaging, with a goal of illustrating how kinetic analysis can augment our understanding of in vivo cancer biology, improve our approach to clinical decision making, and guide the interpretation of quantitative measures derived from static images.

Quantitation of multiple injection dynamic PET scans: an investigation of the benefits of pooling data from separate scans when mapping kinetics

Multiple injection dynamic positron emission tomography (PET) scanning is used in the clinical management of certain groups of patients and in medical research. The analysis of these studies can be approached in two ways: (i) separate analysis of data from individual tracer injections, or (ii), concatenate/pool data from separate injections and carry out a combined analysis. The simplicity of separate analysis has some practical appeal but may not be statistically efficient. We use a linear model framework associated with a kinetic mapping scheme to develop a simplified theoretical understanding of separate and combined analysis. The theoretical framework is explored numerically using both 1D and 2D simulation models. These studies are motivated by the breast cancer flow-metabolism mismatch studies involving15O-water (H2O) and18F-Fluorodeoxyglucose (FDG) and repeat15O-H2O injections used in brain activation investigations. Numerical results are found to be substantially in line with the simple theoretical analysis: mean square error characteristics of alternative methods are well described by factors involving the local voxel-level resolution of the imaging data, the relative activities of the individual scans and the number of separate injections involved. While voxel-level resolution has dependence on scan dose, after adjustment for this effect, the impact of a combined analysis is understood in simple terms associated with the linear model used for kinetic mapping. This is true for both data reconstructed by direct filtered backprojection or iterative maximum likelihood. The proposed analysis has potential to be applied to the emerging long axial field-of-view PET scanners.

A Generalized Linear modeling approach to bootstrapping multi-frame PET image data

PET imaging is an important diagnostic tool for management of patients with cancer and other diseases. Medical decisions based on quantitative PET information could potentially benefit from the availability of tools for evaluation of associated uncertainties. Raw PET data can be viewed as a sample from an inhomogeneous Poisson process so there is the possibility to directly apply bootstrapping to raw projection-domain list-mode data. Unfortunately this is computationally impractical, particularly if data reconstruction is iterative or the acquisition protocol is dynamic. We develop a flexible statistical linear model analysis to be used with multi-frame PET image data to create valid bootstrap samples. The technique is illustrated using data from dynamic PET studies with fluoro-deoxyglucose (FDG) and fluoro-thymidine (FLT) in brain and breast cancer patients. As is often the case with dynamic PET studies, data have been archived without raw list-mode information. Using the bootstrapping technique maps of kinetic parameters and associated uncertainties are obtained. The quantitative performance of the approach is assessed by simulation. The proposed image-domain bootstrap is found to substantially match the projection-domain alternative. Analysis of results points to a close relation between relative uncertainty in voxel-level kinetic parameters and local reconstruction error. This is consistent with statistical theory.

PET-ABC: fully Bayesian likelihood-free inference for kinetic models

Aims.We describe an intuitive, easy to use method called PET-ABC that enables full Bayesian statistical inference from single subject dynamic PET data. The performance of PET-ABC was compared with weighted non-linear least squares (WNLS) in terms of reliability of kinetic parameter estimation and statistical power for model selection.Methods.Dynamic PET data based on 1-tissue and 2-tissue compartmental models were simulated with 2 noise models and 3 noise levels. PET-ABC was used to evaluate the reliability of parameter estimates under each condition. It was also used to perform model selection for a simulated noisy dataset composed of a mixture of 1- and 2-tissue compartment kinetics. Finally, PET-ABC was used to analyze a non-steady state dynamic [¹¹C] raclopride study performed on a fully conscious rat administered either 2 mg.kg^-1amphetamine or saline 20 min after tracer injection.Results.PET-ABC yielded posterior point estimates for model parameters with smaller variance than WNLS, as well as probability density functions indicating confidence intervals for those estimates. It successfully identified the superiority of a 2-tissue compartment model to fit the simulated mixed model data. For the drug challenge study, the post observation probability of striatal displacement of the PET signal was 0.9 for amphetamine and approximately 0 for saline, indicating a high probability of amphetamine-induced endogenous dopamine release in the striatum. PET-ABC also demonstrated superior statistical power to WNLS (0.87 versus 0.09) for selecting the correct model in a simulated ligand displacement study.Conclusions.PET-ABC is a simple and intuitive method that provides complete Bayesian statistical analysis of single subject dynamic PET data, including the extent to which model parameter estimates and model choice are supported by the data. Software for PET-ABC is freely available as part of thePETabcpackagehttps://github.com/cgrazian/PETabc.

Analysis of Four-Dimensional Data for Total Body PET Imaging

The high sensitivity and total-body coverage of total-body PET scanners will be valuable for a number of clinical and research applications outlined in this article.

Machine learning-based kinetic modeling: a robust and reproducible solution for quantitative analysis of dynamic PET data

A variety of compartment models are used for the quantitative analysis of dynamic positron emission tomography (PET) data. Traditionally, these models use an iterative fitting (IF) method to find the least squares between the measured and calculated values over time, which may encounter some problems such as the overfitting of model parameters and a lack of reproducibility, especially when handling noisy data or error data. In this paper, a machine learning (ML) based kinetic modeling method is introduced, which can fully utilize a historical reference database to build a moderate kinetic model directly dealing with noisy data but not trying to smooth the noise in the image. Also, due to the database, the presented method is capable of automatically adjusting the models using a multi-thread grid parameter searching technique. Furthermore, a candidate competition concept is proposed to combine the advantages of the ML and IF modeling methods, which could find a balance between fitting to historical data and to the unseen target curve. The machine learning based method provides a robust and reproducible solution that is user-independent for VOI-based and pixel-wise quantitative analysis of dynamic PET data.

VOXEL-LEVEL MAPPING OF TRACER KINETICS IN PET STUDIES: A STATISTICAL APPROACH EMPHASIZING TISSUE LIFE TABLES

Most radiotracers used in dynamic positron emission tomography (PET) scanning act in a linear time-invariant fashion so that the measured time-course data are a convolution between the time course of the tracer in the arterial supply and the local tissue impulse response, known as the tissue residue function. In statistical terms the residue is a life table for the transit time of injected radiotracer atoms. The residue provides a description of the tracer kinetic information measurable by a dynamic PET scan. Decomposition of the residue function allows separation of rapid vascular kinetics from slower blood-tissue exchanges and tissue retention. For voxel-level analysis, we propose that residues be modeled by mixtures of nonparametrically derived basis residues obtained by segmentation of the full data volume. Spatial and temporal aspects of diagnostics associated with voxel-level model fitting are emphasized. Illustrative examples, some involving cancer imaging studies, are presented. Data from cerebral PET scanning with 18F fluoro-deoxyglucose (FDG) and 15O water (H2O) in normal subjects is used to evaluate the approach. Cross-validation is used to make regional comparisons between residues estimated using adaptive mixture models with more conventional compartmental modeling techniques. Simulations studies are used to theoretically examine mean square error performance and to explore the benefit of voxel-level analysis when the primary interest is a statistical summary of regional kinetics. The work highlights the contribution that multivariate analysis tools and life-table concepts can make in the recovery of local metabolic information from dynamic PET studies, particularly ones in which the assumptions of compartmental-like models, with residues that are sums of exponentials, might not be certain.

Sparsity Constrained Mixture Modeling for the Estimation of Kinetic Parameters in Dynamic PET

The estimation and analysis of kinetic parameters in dynamic positron emission tomography (PET) is frequently confounded by tissue heterogeneity and partial volume effects. We propose a new constrained model of dynamic PET to address these limitations. The proposed formulation incorporates an explicit mixture model in which each image voxel is represented as a mixture of different pure tissue types with distinct temporal dynamics. We use Cramér-Rao lower bounds to demonstrate that the use of prior information is important to stabilize parameter estimation with this model. As a result, we propose a constrained formulation of the estimation problem that we solve using a two-stage algorithm. In the first stage, a sparse signal processing method is applied to estimate the rate parameters for the different tissue compartments from the noisy PET time series. In the second stage, tissue fractions and the linear parameters of different time activity curves are estimated using a combination of spatial-regularity and fractional mixture constraints. A block coordinate descent algorithm is combined with a manifold search to robustly estimate these parameters. The method is evaluated with both simulated and experimental dynamic PET data.

Quantitative assessment of dynamic PET imaging data in cancer imaging

Clinical imaging in positron emission tomography (PET) is often performed using single-time-point estimates of tracer uptake or static imaging that provides a spatial map of regional tracer concentration. However, dynamic tracer imaging can provide considerably more information about in vivo biology by delineating both the temporal and spatial pattern of tracer uptake. In addition, several potential sources of error that occur in static imaging can be mitigated. This review focuses on the application of dynamic PET imaging to measuring regional cancer biologic features and especially in using dynamic PET imaging for quantitative therapeutic response monitoring for cancer clinical trials. Dynamic PET imaging output parameters, particularly transport (flow) and overall metabolic rate, have provided imaging end points for clinical trials at single-center institutions for years. However, dynamic imaging poses many challenges for multicenter clinical trial implementations from cross-center calibration to the inadequacy of a common informatics infrastructure. Underlying principles and methodology of PET dynamic imaging are first reviewed, followed by an examination of current approaches to dynamic PET image analysis with a specific case example of dynamic fluorothymidine imaging to illustrate the approach.

Component analysis approach to estimation of tissue intensity distributions of 3D images

Many segmentation algorithms in medical imaging rely on accurate modeling and estimation of tissue intensity probability density functions. Gaussian mixture modeling, currently the most common approach, has several drawbacks, such as reliance on a Gaussian model and iterative local optimization used to estimate the model parameters. It also does not take advantage of substantially larger amount of data provided by 3D acquisitions, which are becoming standard in clinical environment. We propose a novel and completely non-parametric algorithm to estimate the tissue intensity probabilities in 3D images. Instead of relying on traditional framework of iterating between classification and estimation, we pose the problem as an instance of a blind source separation problem, where the unknown distributions are treated as sources and histograms of image subvolumes as mixtures. The new approach performed well on synthetic data and real magnetic resonance imaging (MRI) scans of the brain, robustly capturing intensity distributions of even small image structures and partial volume voxels.

PET tumor metabolism in locally advanced breast cancer patients undergoing neoadjuvant chemotherapy: value of static versus kinetic measures of fluorodeoxyglucose uptake

PURPOSE

Changes in tumor metabolism from positron emission tomography (PET) in locally advanced breast cancer (LABC) patients treated with neoadjuvant chemotherapy (NC) are predictive of pathologic response. Serial dynamic [(18)F]-FDG (fluorodeoxyglucose) PET scans were used to compare kinetic parameters with the standardized uptake value (SUV) as predictors of pathologic response, disease-free survival (DFS), and overall survival (OS).

EXPERIMENTAL DESIGN

Seventy-five LABC patients underwent FDG PET prior to and at midpoint of NC. FDG delivery (K(1)), FDG flux (K(i)), and SUV measures were calculated and compared by clinical and pathologic tumor characteristics using regression methods and area under the receiver operating characteristic curve (AUC). Associations between K(1), K(i), and SUV and DFS and OS were evaluated using the Cox proportional hazards model.

RESULTS

Tumors that were hormone receptor negative, high grade, highly proliferative, or of ductal histology had higher FDG K(i) and SUV values; on an average, FDG K(1) did not differ systematically by tumor features. Predicting pathologic response in conjunction with estrogen receptor (ER) and axillary lymph node positivity, kinetic measures (AUC = 0.97) were more robust predictors than SUV (AUC = 0.84, P = 0.005). Changes in K(1) and K(i) predicted both DFS and OS, whereas changes in SUV predicted OS only. In multivariate modeling, only changes in K(1) remained an independent prognosticator of DFS and OS.

CONCLUSION

Kinetic measures of FDG PET for LABC patients treated with NC accurately measured treatment response and predicted outcome compared with static SUV measures, suggesting that kinetic analysis may hold advantage of static uptake measures for response assessment.

Imaging of cyclosporine inhibition of P-glycoprotein activity using 11C-verapamil in the brain: studies of healthy humans

The multiple-drug resistance (MDR) transporter P-glycoprotein (P-gp) is highly expressed at the human blood-brain barrier (BBB). P-gp actively effluxes a wide variety of drugs from the central nervous system, including anticancer drugs. We have previously demonstrated P-gp activity at the human BBB using PET of (11)C-verapamil distribution into the brain in the absence and presence of the P-gp inhibitor cyclosporine-A (CsA). Here we extend the initial noncompartmental analysis of these data and apply compartmental modeling to these human verapamil imaging studies.

METHODS

Healthy volunteers were injected with (15)O-water to assess blood flow, followed by (11)C-verapamil to assess BBB P-gp activity. Arterial blood samples and PET images were obtained at frequent intervals for 5 and 45 min, respectively, after injection. After a 60-min infusion of CsA (intravenously, 2.5 mg/kg/h) to inhibit P-gp, a second set of water and verapamil PET studies was conducted, followed by (11)C-CO imaging to measure regional blood volume. Blood flow was estimated using dynamic (15)O-water data and a flow-dispersion model. Dynamic (11)C-verapamil data were assessed by a 2-tissue-compartment (2C) model of delivery and retention and a 1-tissue-compartment model using the first 10 min of data (1C(10)).

RESULTS

The 2C model was able to fit the full dataset both before and during P-pg inhibition. CsA modulation of P-gp increased blood-brain transfer (K(1)) of verapamil into the brain by 73% (range, 30%-118%; n = 12). This increase was significantly greater than changes in blood flow (13%; range, 12%-49%; n = 12, P < 0.001). Estimates of K(1) from the 1C(10) model correlated to estimates from the 2C model (r = 0.99, n = 12), indicating that a short study could effectively estimate P-gp activity.

CONCLUSION

(11)C-verapamil and compartmental analysis can estimate P-gp activity at the BBB by imaging before and during P-gp inhibition by CsA, indicated by a change in verapamil transport (K(1)). Inhibition of P-gp unmasks verapamil trapping in brain tissue that requires a 2C model for long imaging times; however, transport can be effectively measured using a short scan time with a 1C(10) model, avoiding complications with labeled metabolites and tracer retention.

Nonparametric Residue Analysis of Dynamic PET Data With Application to Cerebral FDG Studies in Normals

Kinetic analysis is used to extract metabolic information from dynamic positron emission tomography (PET) uptake data. The theory of indicator dilutions, developed in the seminal work of Meier and Zierler (1954), provides a probabilistic framework for representation of PET tracer uptake data in terms of a convolution between an arterial input function and a tissue residue. The residue is a scaled survival function associated with tracer residence in the tissue. Nonparametric inference for the residue, a deconvolution problem, provides a novel approach to kinetic analysis-critically one that is not reliant on specific compartmental modeling assumptions. A practical computational technique based on regularized cubic B-spline approximation of the residence time distribution is proposed. Nonparametric residue analysis allows formal statistical evaluation of specific parametric models to be considered. This analysis needs to properly account for the increased flexibility of the nonparametric estimator. The methodology is illustrated using data from a series of cerebral studies with PET and fluorodeoxyglucose (FDG) in normal subjects. Comparisons are made between key functionals of the residue, tracer flux, flow, etc., resulting from a parametric (the standard two-compartment of Phelps et al. 1979) and a nonparametric analysis. Strong statistical evidence against the compartment model is found. Primarily these differences relate to the representation of the early temporal structure of the tracer residence-largely a function of the vascular supply network. There are convincing physiological arguments against the representations implied by the compartmental approach but this is the first time that a rigorous statistical confirmation using PET data has been reported. The compartmental analysis produces suspect values for flow but, notably, the impact on the metabolic flux, though statistically significant, is limited to deviations on the order of 3%-4%. The general advantage of the nonparametric residue analysis is the ability to provide a valid kinetic quantitation in the context of studies where there may be heterogeneity or other uncertainty about the accuracy of a compartmental model approximation of the tissue residue.

NCI-sponsored trial for the evaluation of safety and preliminary efficacy of 3'-deoxy-3'-[18F]fluorothymidine (FLT) as a marker of proliferation in patients with recurrent gliomas: preliminary efficacy studies

PURPOSE

3'-Deoxy-3'-[18F]fluorothymidine ([18F]FLT) is being developed for imaging cellular proliferation. The goals were to explore the capacity of FLT-positron emission tomography (PET) to distinguish between recurrence and radionecrosis in gliomas and compare the results to those obtained with 2-fluoro-2-deoxy-D: -glucose (FDG).

PROCEDURES

Fifteen patients with tumor recurrence and four with radionecrosis, determined by clinical course and magnetic resonance imaging results, were studied by dynamic [18F]FLT-PET with arterial blood sampling. A two-tissue compartment four-rate constant model was used to determine metabolic flux (K (FLT)), blood to tissue transport (K (1)), and phosphorylation (k (3)). FDG-PET scans were obtained 75-90 min postinjection.

RESULTS

K (FLT) and k (3), but not K (1) or k (3)/k (2) + k (3), reached significance for separating the recurrence from radionecrosis groups. Standardized uptake value and visual analyses of FLT or FDG images did not reach significance.

CONCLUSIONS

K (FLT) (flux) appears to distinguish recurrence from radionecrosis better than other parameters, FLT and FDG semiquantitative approaches, or visual analysis of images of either tracer.

Joint penalized-likelihood reconstruction of time-activity curves and regions-of-interest from projection data in brain PET

This paper presents a novel statistical approach for joint estimation of regions-of-interest (ROIs) and the corresponding time-activity curves (TACs) from dynamic positron emission tomography (PET) brain projection data. It is based on optimizing the joint objective function that consists of a data log-likelihood term and two penalty terms reflecting the available a priori information about the human brain anatomy. The developed local optimization strategy iteratively updates both the ROI and TAC parameters and is guaranteed to monotonically increase the objective function. The quantitative evaluation of the algorithm is performed with numerically and Monte Carlo-simulated dynamic PET brain data of the 11C-Raclopride and 18F-FDG tracers. The results demonstrate that the method outperforms the existing sequential ROI quantification approaches in terms of accuracy, and can noticeably reduce the errors in TACs arising due to the finite spatial resolution and ROI delineation.

Segmentation of VOI from multidimensional dynamic PET images by integrating spatial and temporal features

Segmentation of multidimensional dynamic positron emission tomography (PET) images into volumes of interest (VOIs) exhibiting similar temporal behavior and spatial features is a challenging task due to inherently poor signal-to-noise ratio and spatial resolution. In this study, we propose VOI segmentation of dynamic PET images by utilizing both the three-dimensional (3-D) spatial and temporal domain information in a hybrid technique that integrates two independent segmentation techniques of cluster analysis and region growing. The proposed technique starts with a cluster analysis that partitions the image based on temporal similarities. The resulting temporal partitions, together with the 3-D spatial information are utilized in the region growing segmentation. The technique was evaluated with dynamic 2-[18F] fluoro-2-deoxy-D-glucose PET simulations and clinical studies of the human brain and compared with the k-means and fuzzy c-means cluster analysis segmentation methods. The quantitative evaluation with simulated images demonstrated that the proposed technique can segment the dynamic PET images into VOIs of different kinetic structures and outperforms the cluster analysis approaches with notable improvements in the smoothness of the segmented VOIs with fewer disconnected or spurious segmentation clusters. In clinical studies, the hybrid technique was only superior to the other techniques in segmenting the white matter. In the gray matter segmentation, the other technique tended to perform slightly better than the hybrid technique, but the differences did not reach significance. The hybrid technique generally formed smoother VOIs with better separation of the background. Overall, the proposed technique demonstrated potential usefulness in the diagnosis and evaluation of dynamic PET neurological imaging studies.

Multi-resolution Bayesian regression in PET dynamic studies using wavelets

In the kinetic analysis of dynamic PET data, one usually posits that the variation of the data through one dimension, time, can be described by a mathematical model encapsulating the relevant physiological features of the radioactive tracer. In this work, we posit that the remaining dimension, space, can also be modeled as a physiological feature, and we introduce this concept into a new computational procedure for the production of parametric maps. An organ and, in the instance considered here, the brain presents similarities in the physiological properties of its elements across scales: computationally, this similarity can be implemented in two stages. Firstly, a multi-scale decomposition of the dynamic frames is created through the wavelet transform. Secondly, kinetic analysis is performed in wavelet space and the kinetic parameters estimated at low resolution are used as priors to inform estimates at higher resolutions. Kinetic analysis in the above scheme is achieved by extension of the Patlak analysis through Bayesian linear regression that retains the simplicity and speed of the original procedure. Application to artificial and real data (FDG and FDOPA) demonstrates the ability of the procedure to reduce remarkably the variance of parametric maps (up to 4-fold reduction) without introducing sizeable bias. Significance of the methodology and extension of the procedure to other data (fMRI) and models are discussed.

MAP-based kinetic analysis for voxel-by-voxel compartment model estimation: Detailed imaging of the cerebral glucose metabolism using FDG

We propose a novel algorithm for voxel-by-voxel compartment model analysis based on a maximum a posteriori (MAP) algorithm. Voxel-by-voxel compartment model analysis can derive functional images of living tissues, but it suffers from high noise statistics in voxel-based PET data and extended calculation times. We initially set up a feature space of the target radiopharmaceutical composed of a measured plasma time activity curve and a set of compartment model parameters, and measured the noise distribution of the PET data. The dynamic PET data were projected onto the feature space, and then clustered using the Mahalanobis distance. Our method was validated using simulation studies, and compared with ROI-based ordinary kinetic analysis for FDG. The parametric images exhibited an acceptable linear relation with the simulations and the ROI-based results, and the calculation time took about 10 min. We therefore concluded that our proposed MAP-based algorithm is practical.

Locally constrained mixture representation of dynamic imaging data from PET and MR studies

Dynamic positron emission tomography (PET) studies provide measurements of the kinetics of radiotracers in living tissue. This is a powerful technology which can play a major role in the study of biological processes, potentially leading to better understanding and treatment of disease. Dynamic PET data relate to complex spatiotemporal processes and its analysis poses significant challenges. In previous work, mixture models that expressed voxel-level PET time course data as a convex linear combination of a finite number of dominant time course characteristics (called sub-TACs) were introduced. This paper extends that mixture model formulation to allow for a weighted combination of scaled sub-TACs and also considers the imposition of local constraints in the number of sub-TACs that can be active at any one voxel. An adaptive 3D scaled segmentation algorithm is developed for model initialization. Increases in the weighted residual sums of squares is used to guide the choice of the number of segments and the number of sub-TACs in the final mixture model. The methodology is applied to five data sets from representative PET imaging studies. The methods are also applicable to other contexts in which dynamic image data are acquired. To illustrate this, data from an echo-planar magnetic resonance (MR) study of cerebral hemodynamics are considered. Our analysis shows little indication of departure from a locally constrained mixture model representation with at most two active components at any voxel. Thus, the primary sources of spatiotemporal variation in representative dynamic PET and MR imaging studies would appear to be accessible to a substantially simplified representation in terms of the generalized locally constrained mixture model introduced.

PET imaging of cellular proliferation

PET cellular proliferation imaging has its roots in a long history of in vitro cellular proliferation studies to characterize cancer and in the understanding of the biology of thymidine incorporation into DNA gained from these studies. PET imaging represents the logical translation of the in vitro work to measure in vivo tumor proliferation. Preclinical studies of [11C]-thymidine and other PET-labeled thymidine analogues set the stage for early clinical studies that provided very promising results. Recent progress in the application of [18F]-FLT, a clinically practical PET thymidine analogue, to patient studies sets the next stage for clinical PET cellular proliferation imaging. Further mechanistic studies of the imaging agents and well-designed clinical trials will be important in moving PET proliferation imaging into what is likely to be a significant role in the care of cancer patients by providing a quantitative measure of tumor response to cytotoxic or cytostatic therapy.

Kinetic Analysis of 2-[11C]Thymidine PET Imaging Studies of Malignant Brain Tumors: Preliminary Patient Results

2-[11C]Thymidine (TdR), a PET tracer for cellular proliferation, may be advantageous for monitoring brain tumor progression and response to therapy. Kinetic analysis of dynamic TdR images was performed to estimate the rate of thymidine transport ( K1t) and thymidine flux ( KTdR) into brain tumors and normal brain. These estimates were compared to MRI and pathologic results. Methods: Twenty patients underwent sequential [11C]CO2 (major TdR metabolite) and TdR PET studies with arterial blood sampling and metabolite analysis. The data were fitted using the five-compartment model described in the companion article. Results: Comparison of model estimates with clinical and pathologic data shows that K1t is higher for MRI contrast enhancing tumors ( p > .001), and KTdR increases with tumor grade ( p > .02). On average, TdR retention was lower after treatment in high-grade tumors. The model was able to distinguish between increased thymidine transport due to blood–brain barrier breakdown and increased tracer retention associated with tumor cell proliferation. Conclusion: Initial analysis of model estimates of thymidine retention and transport show good agreement with the clinical and pathological features of a wide range of brain tumors. Ongoing studies will evaluate its role in measuring response to treatment and predicting outcome.

Spatiotemporal reconstruction of list-mode PET data

We describe a method for computing a continuous time estimate of tracer density using list-mode positron emission tomography data. The rate function in each voxel is modeled as an inhomogeneous Poisson process whose rate function can be represented using a cubic B-spline basis. The rate functions are estimated by maximizing the likelihood of the arrival times of detected photon pairs over the control vertices of the spline, modified by quadratic spatial and temporal smoothness penalties and a penalty term to enforce nonnegativity. Randoms rate functions are estimated by assuming independence between the spatial and temporal randoms distributions. Similarly, scatter rate functions are estimated by assuming spatiotemporal independence and that the temporal distribution of the scatter is proportional to the temporal distribution of the trues. A quantitative evaluation was performed using simulated data and the method is also demonstrated in a human study using 11C-raclopride.

Correction for ambiguous solutions in factor analysis using a penalized least squares objective

Factor analysis is a powerful tool used for the analysis of dynamic studies. One of the major drawbacks of factor analysis of dynamic structures (FADS) is that the solution is not mathematically unique when only nonnegativity constraints are used to determine factors and factor coefficients. In this paper, a method to correct for ambiguous FADS solutions has been developed. A nonambiguous solution (to within certain scaling factors) is obtained by constructing and minimizing a new objective function. The most common objective function consists of a least squares term that when minimized with nonnegativity constraints, forces agreement between the applied factor model and the measured data. In our method, this objective function is modified by adding a term that penalizes multiple components in the images of the factor coefficients. Due to nonuniqueness effects, these factor coefficients consist of more than one physiological component. The technique was tested on computer simulations, an experimental canine cardiac study using 99mTc-teboroxime, and a patient planar 99mTc-MAG3 renal study. The results show that the technique works well in comparison to the truth in computer simulations and to region of interest (ROI) measurements in the experimental studies.

Direct recovery of regional tracer kinetics from temporally inconsistent dynamic ECT projections using dimension-reduced time-activity basis

We present an algorithm of reduced computational cost which is able to estimate kinetic model parameters directly from dynamic ECT sinograms made up of temporally inconsistent projections. The algorithm exploits the extreme degree of parameter redundancy inherent in linear combinations of the exponential functions which represent the modes of first-order compartmental systems. The singular value decomposition is employed to find a small set of orthogonal functions, the linear combinations of which are able to accurately represent all modes within the physiologically anticipated range in a given study. The reduced dimension basis is formed as the convolution of this orthogonal set with a measured input function. The Moore-Penrose pseudoinverse is used to find coefficients of this basis. Algorithm performance is evaluated at realistic count rates using MCAT phantom and clinical 99mTc-teboroxime myocardial study data. Phantom data are modelled as originating from a Poisson process. For estimates recovered from a single slice projection set containing 2.5 x 10(5) total counts, recovered tissue responses compare favourably with those obtained using more computationally intensive methods. The corresponding kinetic parameter estimates (coefficients of the new basis) exhibit negligible bias, while parameter variances are low, falling within 30% of the Cramér-Rao lower bound.

Direct least-squares estimation of spatiotemporal distributions from dynamic SPECT projections using a spatial segmentation and temporal B-splines

Artifacts can result when reconstructing a dynamic image sequence from inconsistent, as well as insufficient and truncated, cone beam single photon emission computed tomography (SPECT) projection data acquired by a slowly rotating gantry. The artifacts can lead to biases in kinetic model parameters estimated from time-activity curves generated by overlaying volumes of interest on the images. However, the biases in time-activity curve estimates and subsequent kinetic parameter estimates can be reduced significantly by first modeling the spatial and temporal distribution of the radiopharmaceutical throughout the projected field of view, and then estimating the time-activity curves directly from the projections. This approach is potentially useful for clinical SPECT studies involving slowly rotating gantries, particularly those using a single-detector system or body contouring orbits with a multidetector system. We have implemented computationally efficient methods for fully four-dimensional (4-D) direct estimation of spatiotemporal distributions from dynamic SPECT projection data. Temporal B-splines providing various orders of temporal continuity, as well as various time samplings, were used to model the time-activity curves for segmented blood pool and tissue volumes in simulated cone beam and parallel beam cardiac data acquisitions. Least-squares estimates of time-activity curves were obtained quickly using a workstation. Given faithful spatial modeling, accurate curve estimates were obtained using cubic, quadratic, or linear B-splines and a relatively rapid time sampling during initial tracer uptake. From these curves, kinetic parameters were estimated accurately for noiseless data and with some bias for noisy data. A preliminary study of spatial segmentation errors showed that spatial model mismatch adversely affected quantitative accuracy, but also resulted in structured errors (projected model versus raw data) that were easily detected in our simulations. This suggests iterative refinement of the spatial model to reduce structured errors as an area of future research.

Characterizing tumors using metabolic imaging: PET imaging of cellular proliferation and steroid receptors

Treatment decisions in oncology are increasingly guided by information on the biologic characteristics of tumors. Currently, patient-specific information on tumor biology is obtained from the analysis of biopsy material. Positron emission tomography (PET) provides quantitative estimates of regional biochemistry and receptor status and can overcome the sampling error and difficulty in performing serial studies inherent with biopsy. Imaging using the glucose metabolism tracer, 2 -deoxy-2- fluoro-D-glucose (FDG), has demonstrated PET's ability to guide therapy in clinical oncology. In this review, we highlight PET approaches to imaging two other aspects of tumor biology: cellular proliferation and tumor steroid receptors. We review the biochemical and biologic processes underlying the imaging, positron-emitting radiopharmaceuticals that have been developed, quantitative image-analysis considerations, and clinical studies to date. This provides a basis for evaluating future developments in these promising applications of PET metabolic imaging.

Use of ridge regression for improved estimation of kinetic constants from PET data

The estimation of parameters in radio-tracer models from positron emission tomography (PET) data by nonlinear least squares (NLS) often leads to results with unacceptable mean square error (ME) characteristics. The introduction of constraints on parameters has the potential to address this problem. We examine a ridge-regression technique that augments the standard NLS criterion by the addition of a term which penalizes estimates which deviate from physiologically reasonable values. A variation on a plug-in methodology of Hoerl et al. [7] is examined for data-dependent selection of the degree of reliance to place on the penalizing term. A simulation study is carried out to evaluate the performance of this approach in the context of estimation of kinetic constants in the three-compartment model used to analyze data from PET studies with fluoro-deoxyglucose (FDG). Results show that over a range of realistic noise levels, the ridge-regression procedure can be expected to reduce the root ME of parameter estimates by 60%. This result is not found to be substantially dependent on the precise formulation of the penalty function used. Thus, the use of ridge regression for estimation of kinetic parameters in PET studies is considered to be a promising tool.

New method for the analysis of multiple positron emission tomography dynamic datasets: an example applied to the estimation of the cerebral metabolic rate of oxygen

Positron emission tomography (PET) provides the ability to extract useful quantitative information not available through other radiological techniques. In certain studies, the physiological parameters of interest cannot be determined from the data obtained from a single PET experiment alone. In this case, multiple experiments are required. At present, the methods used to analyse measurements acquired from multiple experiments often involve considering them separately during the modelling procedures. These methods of analysis may cause errors to be propagated through successive modelling procedures and do not fully utilise the information content provided by the PET measurements. A new method is presented, based on linear least squares for the analysis of PET dynamic data acquired from multiple experiments. This method simultaneously considers the complete set of measurements obtained and provides reliable parameter estimates. The efficient use of the information content provided by multiple experiments is considered and the propagation of errors is discussed. To facilitate our discussion, we apply this new method to the estimation of the cerebral metabolic rate of oxygen and the parameters of the oxygen utilisation model as a practical example. The results demonstrate a significant improvement in the reliability and estimation accuracy of the estimates for this new method. Furthermore, this method reduced the likelihood of errors being propagated. Therefore, the proposed method is suitable for the analysis of multiple PET dynamic datasets.

A clinical perspective of accelerated statistical reconstruction

Although the potential benefits of maximum likelihood reconstruction have been recognised for many years, the technique has only recently found widespread popularity in clinical practice. Factors which have contributed to the wider acceptance include improved models for the emission process, better understanding of the properties of the algorithm and, not least, the practicality of application with the development of acceleration schemes and the improved speed of computers. The objective in this article is to present a framework for applying maximum likelihood reconstruction for a wide range of clinically based problems. The article draws particularly on the experience of the three authors in applying an acceleration scheme involving use of ordered subsets to a range of applications. The potential advantages of statistical reconstruction techniques include: (a) the ability to better model the emission and detection process, in order to make the reconstruction converge to a quantitative image, (b) the inclusion of a statistical noise model which results in better noise characteristics, and (c) the possibility to incorporate prior knowledge about the distribution being imaged. The great flexibility in adapting the reconstruction for a specific model results in these techniques having wide applicability to problems in clinical nuclear medicine.

Metabolic images from dynamic positron emission tomography studies

A dynamic sequence of positron emission tomography (PET) images gives rise to the possibility of creating images of in vivo tissue metabolism. For this reason PET is potentially a valuable instrument in the study of human biology and medicine. The analysis of dynamic PET data to produce metabolic images is a challenging problem from a statistical point of view. For example, a typical data set arising in the study of cerebral glucose utilization has on the order of 30 time-binned images per cross-sectional slice of tissue under examination, each of dimension 128 x 128 pixels. Metabolic imaging requires that the time series at each pixel, known as the time activity curve (TAC), be analysed to produce an estimate of local metabolism. This paper describes a mixture analysis approach to the construction of such metabolic images. In the approach the TAC at a given pixel is expressed as a weighted sum of sub-TACs corresponding to homogeneous tissues represented at the pixel. Estimates of tissue metabolism at the pixel are then constructed as a weighted sum of the metabolism associated with the individual sub-TACs. The procedure is illustrated by application to a [F-18]-labelled deoxyglucose study in a patient with a brain tumour. The ability to map simultaneously a range of parameters related to the transport and biochemical transformation of the radio-tracer, demonstrates the potential power of dynamic PET.