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

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

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

Improved derivation of input function in dynamic mouse [18F]FDG PET using bladder radioactivity kinetics

PURPOSE

Accurate determination of the plasma input function (IF) is essential for absolute quantification of physiological parameters in positron emission tomography (PET). However, it requires an invasive and tedious procedure of arterial blood sampling that is challenging in mice because of the limited blood volume. In this study, a hybrid modeling approach is proposed to estimate the plasma IF of 2-deoxy-2-[18F]fluoro-D-glucose ([18F]FDG) in mice using accumulated radioactivity in urinary bladder together with a single late-time blood sample measurement.

METHODS

Dynamic PET scans were performed on nine isoflurane-anesthetized male C57BL/6 mice after a bolus injection of [18F]FDG at the lateral caudal vein. During a 60- or 90-min scan, serial blood samples were taken from the femoral artery. Image data were reconstructed using filtered backprojection with computed tomography-based attenuation correction. Total accumulated radioactivity in the urinary bladder at late times was fitted to a renal compartmental model with the last blood sample and a one-exponential function that described the [18F]FDG clearance in blood. Multiple late-time blood sample estimates were calculated by the blood [18F]FDG clearance equation. A sum of four-exponentials was assumed for the plasma IF that served as a forcing function to all tissues. The estimated plasma IF was obtained by simultaneously fitting the [18F]FDG model to the time-activity curves (TACs) of liver and muscle and the forcing function to early (0-1 min) left-ventricle data (corrected for delay, dispersion, partial-volume effects, and erythrocyte uptake) and the late-time blood estimates. Using only the blood sample collected at the end of the study to estimate the IF and the use of liver TAC as an alternative IF were also investigated.

RESULTS

The area under the plasma IFs calculated for all studies using the hybrid approach was not significantly different from that using all blood samples. [18F]FDG uptake constants in brain, myocardium, skeletal muscle, and liver computed by the Patlak analysis using estimated and measured plasma IFs were in excellent agreement (slope∼1; R2>0.983). The IF estimated using only the last blood sample drawn at the end of the study and the use of liver TAC as the plasma IF provided less reliable results.

CONCLUSIONS

The estimated plasma IFs obtained with the hybrid method agreed well with those derived from arterial blood sampling. Importantly, the proposed method obviates the need of arterial catheterization, making it possible to perform repeated dynamic [18F]FDG PET studies on the same animal. Liver TAC is unsuitable as an input function for absolute quantification of [18F]FDG PET data.

Direct estimation of kinetic parametric images for dynamic PET

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

Measurement of radioactivity concentration in blood by using newly developed ToT LuAG-APD based small animal PET tomograph

In order to obtain plasma time activity curve (PTAC), input function for almost all quantitative PET studies, patient blood is sampled manually from the artery or vein which has various drawbacks. Recently a novel compact Time over Threshold (ToT) based Pr:LuAG-APD animal PET tomograph is developed in our laboratory which has 10% energy resolution, 4.2 ns time resolution and 1.76 mm spatial resolution. The measured value of spatial resolution shows much promise for imaging the blood vascular, i.e; artery of diameter 2.3-2.4mm, and hence, to measure PTAC for quantitative PET studies. To find the measurement time required to obtain reasonable counts for image reconstruction, the most important parameter is the sensitivity of the system. Usually small animal PET systems are characterized by using a point source in air. We used Electron Gamma Shower 5 (EGS5) code to simulate a point source at different positions inside the sensitive volume of tomograph and the axial and radial variations in the sensitivity are studied in air and phantom equivalent water cylinder. An average sensitivity difference of 34% in axial direction and 24.6% in radial direction is observed when point source is displaced inside water cylinder instead of air.

SAKE: a new quantification tool for positron emission tomography studies

In dynamic positron emission tomography (PET) studies, spectral analysis (SA) refers to a data-driven quantification method, based on a single-input single-output model for which the transfer function is described by a sum of exponential terms. SA allows to quantify numerosities, amplitudes and eigenvalues of the transfer function allowing, in this way, to separate kinetic components of the tissue tracer activity with minimal model assumptions. The SA model can be solved with a linear estimator alone or with numerical filters, resulting in different types of SA approaches. Once estimated the number, amplitudes and eigenvalues of the transfer function, one can distinguish the presence in the system of irreversible and/or reversible components as well as derive parameters of physiological significance. These characteristics make it an appealing alternative method to compartmental models which are widely used for the quantitative analysis of dynamic studies acquired with PET. However, despite its applicability to a large number of PET tracers, its implementation is not straightforward and its utilization in the nuclear medicine community has been limited especially by the lack of an user-friendly software application. In this paper we proposed SAKE, a computer program for the quantitative analysis of PET data through the main SA methods. SAKE offers a unified pipeline of analysis usable also by people with limited computer knowledge but with high interest in SA.

Noninvasive estimation of the arterial input function in positron emission tomography imaging of cerebral blood flow

Positron emission tomography (PET) with (15)O-labeled water can provide reliable measurement of cerebral blood flow (CBF). Quantification of CBF requires knowledge of the arterial input function (AIF), which is usually provided by arterial blood sampling. However, arterial sampling is invasive. Moreover, the blood generally is sampled at the wrist, which does not perfectly represent the AIF of the brain, because of the effects of delay and dispersion. We developed and validated a new noninvasive method to obtain the AIF directly by PET imaging of the internal carotid artery in a region of interest (ROI) defined by coregistered high-resolution magnetic resonance angiography. An ROI centered at the petrous portion of the internal carotid artery was defined, and the AIF was estimated simultaneously with whole brain blood flow. The image-derived AIF (IDAIF) method was validated against conventional arterial sampling. The IDAIF generated highly reproducible CBF estimations, generally in good agreement with the conventional technique.

Parametric imaging via kinetics-induced filter for dynamic positron emission tomography

Due to the noisy measurement of the voxel-wise time activity curve (TAC), parametric imaging for dynamic positron emission tomography (PET) is a challenging task. To address this problem, some spatial filters, such as Gaussian filter, bilateral filter, wavelet-based filter, and so on, are often performed to reduce the noise of each frame. However, these filters usually just consider local properties of each frame without exploring the kinetic information. In this paper, aiming to improve the quantitative accuracy of parametric imaging, we present a kinetics-induced filter to lower the noise of dynamic PET images by incorporating the kinetic information. The present kinetics-induced filter is designed via the similarity between voxel-wise TACs under the framework of bilateral filter. Experimental results with a simulation study demonstrate that the present kinetics-induced filter can achieve noticeable gains than other existing methods for parametric images in terms of quantitative accuracy measures.

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

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

A study of non-invasive Patlak quantification for whole-body dynamic FDG-PET studies of mice

Physiological changes in dynamic PET images can be quantitatively estimated by kinetic modeling technique. The process of PET quantification usually requires an input function in the form of a plasma-time activity curve (PTAC), which is generally obtained by invasive arterial blood sampling. However, invasive arterial blood sampling poses many challenges especially for small animal studies, due to the subjects' limited blood volume and small blood vessels. A simple non-invasive quantification method based on Patlak graphical analysis (PGA) has been recently proposed to use a reference region to derive the relative influx rate for a target region without invasive blood sampling, and evaluated by using the simulation data of human brain FDG-PET studies. In this study, the non-invasive Patlak (nPGA) method was extended to whole-body dynamic small animal FDG-PET studies. The performance of nPGA was systematically investigated by using experimental mouse studies and computer simulations. The mouse studies showed high linearity of relative influx rates between the nPGA and PGA for most pairs of reference and target regions, when an appropriate underlying kinetic model was used. The simulation results demonstrated that the accuracy of the nPGA method was comparable to that of the PGA method, with a higher reliability for most pairs of reference and target regions. The results proved that the nPGA method could provide a non-invasive and indirect way for quantifying the FDG kinetics of tumor in small animal studies.

Image-derived input function for brain PET studies: many challenges and few opportunities

Quantitative positron emission tomography (PET) brain studies often require that the input function be measured, typically via arterial cannulation. Image-derived input function (IDIF) is an elegant and attractive noninvasive alternative to arterial sampling. However, IDIF is also a very challenging technique associated with several problems that must be overcome before it can be successfully implemented in clinical practice. As a result, IDIF is rarely used as a tool to reduce invasiveness in patients. The aim of the present review was to identify the methodological problems that hinder widespread use of IDIF in PET brain studies. We conclude that IDIF can be successfully implemented only with a minority of PET tracers. Even in those cases, it only rarely translates into a less-invasive procedure for the patient. Finally, we discuss some possible alternative methods for obtaining less-invasive input function.

Quantification of the glycine transporter 1 in rhesus monkey brain using [18F]MK-6577 and a model-based input function

BACKGROUND

Glycine transporter 1 (GlyT1) inhibitors have emerged as potential treatments for schizophrenia due to their potentiation of NMDA receptor activity by modulating the local concentrations of the NMDA co-agonist glycine. [18F]MK-6577 is a potent and selective GlyT1 inhibitor PET tracer. Although differences in ligand kinetics can be expected between non-human primates and humans, the tracer pre-clinical evaluation can provide valuable information supporting protocol design and quantification in the clinical space. The main objective of this work was to evaluate the in vivo kinetics of [18F]MK-6577 in rhesus monkey brain. Additionally, a method for estimating the tracer input function from the tracer brain tissue kinetics and venous sampling was validated. This technique was applied for determination of the dose-occupancy relationship of a GlyT1 inhibitor in monkey brain.

METHODS

Compartmental and Logan graphical analysis were utilized for quantification of the [18F]MK-6577 binding using the measured tracer arterial input function. The stability of the tracer volume of distribution relative to scan length was assessed. The proposed model-based input function method takes advantage of the agreement between the tracer concentration in arterial and venous plasma from ~5 min. The approach estimates the initial peak of the input curve by adding a gamma like function term to the measured venous curve. The parameters of the model function were estimated by simultaneously fitting several brain time activity curves to a compartmental model.

RESULTS

Good agreement was found between the model-based and the measured arterial plasma curve and the corresponding distribution volumes. The Logan analysis was the preferred method of analysis providing reliable and stable volume of distribution and occupancy results using a 90 and possibly 60 min scan length.

CONCLUSION

The model-based input function method and Logan analysis are well suited for quantification of [18F]MK-6577 binding and GlyT1 occupancy in monkey brain.

Clustering-based linear least square fitting method for generation of parametric images in dynamic FDG PET studies

Parametric images generated from dynamic positron emission tomography (PET) studies are useful for presenting functional/biological information in the 3-dimensional space, but usually suffer from their high sensitivity to image noise. To improve the quality of these images, we proposed in this study a modified linear least square (LLS) fitting method named cLLS that incorporates a clustering-based spatial constraint for generation of parametric images from dynamic PET data of high noise levels. In this method, the combination of K-means and hierarchical cluster analysis was used to classify dynamic PET data. Compared with conventional LLS, cLLS can achieve high statistical reliability in the generated parametric images without incurring a high computational burden. The effectiveness of the method was demonstrated both with computer simulation and with a human brain dynamic FDG PET study. The cLLS method is expected to be useful for generation of parametric images from dynamic FDG PET study.

Constrained estimation of the arterial input function for myocardial perfusion cardiovascular magnetic resonance

Accurate quantification of myocardial perfusion remains challenging due to saturation of the arterial input function at high contrast concentrations. A method for estimating the arterial input function directly from tissue curves in the myocardium that avoids these difficulties is presented. In this constrained alternating minimization with model (CAMM) algorithm, a portion of the left ventricular blood pool signal is also used to constrain the estimation process. Extensive computer simulations assessing the accuracy of kinetic parameter estimation were performed. In 5000 noise realizations, the use of the AIF given by the estimation method returned kinetic parameters with mean Ktrans error of -2% and mean kep error of 0.4%. Twenty in vivo resting perfusion datasets were also processed with this method, and pharmacokinetic parameter values derived from the blind AIF were compared with those derived from a dual-bolus measured AIF. For 17 of the 20 datasets, there were no statistically significant differences in Ktrans estimates, and in aggregate the kinetic parameters were not significantly different from the dual-bolus method. The cardiac constrained alternating minimization with model method presented here provides a promising approach to quantifying perfusion of myocardial tissue with a single injection of contrast agent and without a special pulse sequence though further work is needed to validate the approach in a clinical setting.

Propagation of Blood Function Errors to the Estimates of Kinetic Parameters with Dynamic PET

Dynamic PET, in contrast to static PET, can identify temporal variations in the radiotracer concentration. Mathematical modeling of the tissue of interest in dynamic PET can be simplified using compartment models as a linear system where the time activity curve of a specific tissue is the convolution of the tracer concentration in the plasma and the impulse response of the tissue containing kinetic parameters. Since the arterial sampling of blood to acquire the value of tracer concentration is invasive, blind methods to estimate both blood input function and kinetic parameters have recently drawn attention. Several methods have been developed, but the effect of accuracy of the estimated blood function on the estimation of the kinetic parameters is not studied. In this paper, we present a method to compute the error in the kinetic parameter estimates caused by the error in the blood input function. Computer simulations show that analytical expressions we derive are sufficiently close to results obtained from numerical methods. Our findings are important to observe the effect of the blood function on kinetic parameter estimation, but also useful to evaluate various blind methods and observe the dependence of kinetic parameter estimates to certain parts of the blood function.

Sensitivity analysis for biomedical models

This article discusses the application of sensitivity analysis (SA) in biomedical models. Sensitivity analysis is widely applied in physics, chemistry, economics, social sciences and other areas where models are developed. By assigning a prior probability distribution to each model variable, the SA framework appeals to the posterior probabilities of the model to evaluate the relative importance of these variables on the output distribution based on the principle of general variance decomposition. Within this framework, the SA paradigm serves as an objective platform to quantify the contributions of each model factor relative to their empirical range. We present statistical derivations of variance-based SA in this context and discuss its detailed properties through some practical examples. Our emphasis is on the application of SA in the biomedical field. As we show, it may provide a useful tool for model quality assessment, model reduction and factor prioritization, and improve our understanding of the model structure and underlying mechanisms. When usual approaches for calculating sensitivity index involve the employment of Monte Carlo analysis, which is computationally expensive in the large-sampling paradigm, we develop two effective numerical approximate methods for quick SA evaluations based on the unscented transformation (UT) that utilize a deterministic sampling approach in place of random sampling to calculate posterior statistics. We show that these methods achieve an excellent compromise between computational burden and calculation precision. In addition, a clear guideline is absent to evaluate the importance of variable for model reduction, we also present an objective statistical criterion to quantitatively decide whether or not a descriptive parameter is nominal and may be discarded in ensuing model-based analysis without significant loss of information on model behavior.

A hybrid clustering method for ROI delineation in small-animal dynamic PET images: application to the automatic estimation of FDG input functions

Tracer kinetic modeling with dynamic positron emission tomography (PET) requires a plasma time-activity curve (PTAC) as an input function. Several image-derived input function (IDIF) methods that rely on drawing the region of interest (ROI) in large vascular structures have been proposed to overcome the problems caused by the invasive approach for obtaining the PTAC, especially for small-animal studies. However, the manual placement of ROIs for estimating IDIF is subjective and labor-intensive, making it an undesirable and unreliable process. In this paper, we propose a novel hybrid clustering method (HCM) that objectively delineates ROIs in dynamic PET images for the estimation of IDIFs, and demonstrate its application to the mouse PET studies acquired with [ (18)F]Fluoro-2-deoxy-2-D-glucose (FDG). We begin our HCM using k-means clustering for background removal. We then model the time-activity curves using polynomial regression mixture models in curve clustering for heart structure detection. The hierarchical clustering is finally applied for ROI refinements. The HCM achieved accurate ROI delineation in both computer simulations and experimental mouse studies. In the mouse studies, the predicted IDIF had a high correlation with the gold standard, the PTAC derived from the invasive blood samples. The results indicate that the proposed HCM has a great potential in ROI delineation for automatic estimation of IDIF in dynamic FDG-PET studies.

A model-constrained Monte Carlo method for blind arterial input function estimation in dynamic contrast-enhanced MRI: I. Simulations

Widespread adoption of quantitative pharmacokinetic modeling methods in conjunction with dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) has led to increased recognition of the importance of obtaining accurate patient-specific arterial input function (AIF) measurements. Ideally, DCE-MRI studies use an AIF directly measured in an artery local to the tissue of interest, along with measured tissue concentration curves, to quantitatively determine pharmacokinetic parameters. However, the numerous technical and practical difficulties associated with AIF measurement have made the use of population-averaged AIF data a popular, if sub-optimal, alternative to AIF measurement. In this work, we present and characterize a new algorithm for determining the AIF solely from the measured tissue concentration curves. This Monte Carlo blind estimation (MCBE) algorithm estimates the AIF from the subsets of D concentration-time curves drawn from a larger pool of M candidate curves via nonlinear optimization, doing so for multiple (Q) subsets and statistically averaging these repeated estimates. The MCBE algorithm can be viewed as a generalization of previously published methods that employ clustering of concentration-time curves and only estimate the AIF once. Extensive computer simulations were performed over physiologically and experimentally realistic ranges of imaging and tissue parameters, and the impact of choosing different values of D and Q was investigated. We found the algorithm to be robust, computationally efficient and capable of accurately estimating the AIF even for relatively high noise levels, long sampling intervals and low diversity of tissue curves. With the incorporation of bootstrapping initialization, we further demonstrated the ability to blindly estimate AIFs that deviate substantially in shape from the population-averaged initial guess. Pharmacokinetic parameter estimates for K(trans), k(ep), v(p) and v(e) all showed relative biases and uncertainties of less than 10% for measurements having a temporal sampling rate of 4 s and a concentration measurement noise level of sigma = 0.04 mM. A companion paper discusses the application of the MCBE algorithm to DCE-MRI data acquired in eight patients with malignant brain tumors.

Model-based blind estimation of kinetic parameters in dynamic contrast enhanced (DCE)-MRI

A method to simultaneously estimate the arterial input function (AIF) and pharmacokinetic model parameters from dynamic contrast-enhanced (DCE)-MRI data was developed. This algorithm uses a parameterized functional form to model the AIF and k-means clustering to classify tissue time-concentration measurements into a set of characteristic curves. An iterative blind estimation algorithm alternately estimated parameters for the input function and the pharmacokinetic model. Computer simulations were used to investigate the algorithm's sensitivity to noise and initial estimates. In 12 patients with sarcomas, pharmacokinetic parameter estimates were compared with "truth" obtained from model regression using a measured AIF. When arterial voxels were included in the blind estimation algorithm, the resulting AIF was similar to the measured input function. The "true" K(trans) values in tumor regions were not significantly different than the estimated values, 0.99 +/- 0.41 and 0.86 +/- 0.40 min(-1), respectively, P = 0.27. "True" k(ep) values also matched closely, 0.70 +/- 0.24 and 0.65 +/- 0.25 min(-1), P = 0.08. When only tissue curves free of significant vascular contribution are used (v(p) < 0.05), the resulting AIF showed substantial delay and dispersion consistent with a more local AIF such as has been observed in dynamic susceptibility contrast imaging in the brain.

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

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

Single-input-dual-output modeling of image-based input function estimation

PURPOSE

Quantification of small-animal positron emission tomography (PET) images necessitates knowledge of the plasma input function (PIF). We propose and validate a simplified hybrid single-input-dual-output (HSIDO) algorithm to estimate the PIF.

PROCEDURES

The HSIDO algorithm integrates the peak of the input function from two region-of-interest time-activity curves with a tail segment expressed by a sum of two exponentials. Partial volume parameters are optimized simultaneously. The algorithm is validated using both simulated and real small-animal PET images. In addition, the algorithm is compared to existing techniques in terms of area under curve (AUC) error, bias, and precision of compartmental model micro-parameters.

RESULTS

In general, the HSIDO method generated PIF with significantly (P < 0.05) less AUC error, lower bias, and improved precision of kinetic estimates in comparison to the reference method.

CONCLUSIONS

HSIDO is an improved modeling-based PIF estimation method. This method can be applied for quantitative analysis of small-animal dynamic PET studies.

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

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

Analysis of penalized likelihood image reconstruction for dynamic PET quantification

Quantification of tracer kinetics using dynamic positron emission tomography (PET) provides important information for understanding the physiological and biochemical processes in humans and animals. A common procedure is to reconstruct a sequence of dynamic images first, and then apply kinetic analysis to the time activity curve of a region of interest derived from the reconstructed images. Obviously, the choice of image reconstruction method and its parameters affect the accuracy of the time activity curve and hence the estimated kinetic parameters. This paper analyzes the effects of penalized likelihood image reconstruction on tracer kinetic parameter estimation. Approximate theoretical expressions are derived to study the bias, variance, and ensemble mean squared error of the estimated kinetic parameters. Computer simulations show that these formulae predict correctly the changes of these statistics as functions of the regularization parameter. It is found that the choice of the regularization parameter has a significant impact on kinetic parameter estimation, indicating proper selection of image reconstruction parameters is important for dynamic PET. A practical method has been developed to use the theoretical formulae to guide the selection of the regularization parameter in dynamic PET image reconstruction.

Model-Based receptor quantization analysis for PET parametric imaging

Dynamic PET (positron emission tomography) imaging technique allows image-wide quantification of physiologic and biochemical parameters. Compartment modeling is the most popular approach for receptor binding studies. However, current compartment-model based methods often either require the accurate arterial blood measurements as the input function or assume the existence of a reference region. To obviate the need for the input function or a reference region, in this paper, we propose to estimate the input function and the kinetic parameters simultaneously. The initial estimate of the input functions is obtained by the analysis of space intersections. Then both the input function and the receptor parameters, thus the underlying distribution volume (DV) parametric image, are estimated iteratively. The performance of the proposed scheme is examined by both simulations and real brain PET data in obtaining the underlying parametric images.

A Factor-Image Framework to Quantification of Brain Receptor Dynamic PET Studies

The positron emission tomography (PET) imaging technique enables the measurement of receptor distribution or neurotransmitter release in the living brain and the changes of the distribution with time and thus allows quantification of binding sites as well as the affinity of a radioligand. However, quantification of receptor binding studies obtained with PET is complicated by tissue heterogeneity in the sampling image elements (i.e., voxels, pixels). This effect is caused by a limited spatial resolution of the PET scanner. Spatial heterogeneity is often essential in understanding the underlying receptor binding process. Tracer kinetic modeling also often requires an intrusive collection of arterial blood samples. In this paper, we propose a likelihood-based framework in the voxel domain for quantitative imaging with or without the blood sampling of the input function. Radioligand kinetic parameters are estimated together with the input function. The parameters are initialized by a subspace-based algorithm and further refined by an iterative likelihood-based estimation procedure. The performance of the proposed scheme is examined by simulations. The results show that the proposed scheme provides reliable estimation of factor time-activity curves (TACs) and the underlying parametric images. A good match is noted between the result of the proposed approach and that of the Logan plot. Real brain PET data are also examined, and good performance is observed in determining the TACs and the underlying factor images.

Segmentation of rodent whole-body dynamic PET images: an unsupervised method based on voxel dynamics

Positron emission tomography (PET) is a useful tool for pharmacokinetics studies in rodents during the preclinical phase of drug and tracer development. However, rodent organs are small as compared to the scanner's intrinsic resolution and are affected by physiological movements. We present a new method for the segmentation of rodent whole-body PET images that takes these two difficulties into account by estimating the pharmacokinetics far from organ borders. The segmentation method proved efficient on whole-body numerical rat phantom simulations, including 3-14 organs, together with physiological movements (heart beating, breathing, and bladder filling). The method was resistant to spillover and physiological movements, while other methods failed to obtain a correct segmentation. The radioactivity concentrations calculated with this method also showed an excellent correlation with the manual delineation of organs in a large set of preclinical images. In addition, it was faster, detected more organs, and extracted organs' mean time activity curves with a better confidence on the measure than manual delineation.

Noninvasive estimation of normalized distribution volume: application to the muscarinic-2 ligand [(18)F]FP-TZTP

Reference tissue methods to estimate neuroreceptor binding are not applicable to [(18)F]FP-TZTP (a muscarinic-2 cholinergic receptor ligand), because there is no suitable receptor-free reference region. We evaluated a new method to estimate, without using arterial data or a receptor-free reference region, a receptor parameter called the normalized distribution volume, V(T)(*), using a region containing receptors as the input tissue. V(T)(*) is defined as V(T)/K'(1) (distribution volume (V(T)) normalized by K'(1) of the input region). We used a two-parameter multilinear reference tissue model (MRTM2) to generate parametric images of V(T)(*) and R(1) (R(1)=K(1)/K'(1)) from [(18)F]FP-TZTP PET data of healthy aged subjects (10 with apolipoprotein E-epsilon4 alleles (APOE-epsilon4(+)) and nine without (APOE-epsilon4(-)). V(T)(*) and V(T) were normalized by plasma-free fraction, f(P). By one-tissue kinetic analysis (1TKA) with metabolite-corrected plasma data, V(T) was previously reported as higher in the APOE-epsilon4(+) group. The noise magnitude of MRTM2 V(T)(*) and R(1) images were nearly identical to those of 1TKA V(T) and K(1) images. K'(1) or f(P) was not different between the two groups. V(T)(*) (mins) (1,659+/-497) and V(T) (mL/cm(3)) (701+/-99) in APOE-epsilon4(+) were higher by 38 and 22% than those (1,209+/-233 and 577+/-112) in APOE-epsilon4(-), respectively. The statistical significance for V(T)(*) (0.041) was lower than that for V(T) (0.025), due to the higher intersubject variability of V(T)(*) (25%) than that of V(T) (17%). We conclude that MRTM2 V(T)(*) allows detection of group differences in receptor binding without arterial blood or a receptor-free reference region.

An input function estimation method for FDG-PET human brain studies

BACKGROUND

A new model of an input function for human [(18)F]-2-Deoxy-2-fluoro-d-glucose fluoro (FDG) positron emission tomography (PET) brain studies with bolus injection is presented.

METHODS

Input data for early time, roughly up to 0.6 min, were obtained noninvasively from the time-activity curve (TAC) measured from a carotid artery region of interest. Representative tissue TACs were obtained by clustering the output curves to a limited number of dominant clusters. Three venous plasma samples at a later time were used to fit the functional form of the input function in conjunction with obtaining kinetic rate parameters of the dominant clusters, K(1), k(2) and k(3), using the compartmental model for FDG-PET. Experiments to test the approach used data from 18 healthy subjects.

RESULTS

The model provides an effective means to recover the input function in FDG-PET studies. Weighted nonlinear least squares parameter estimation using the recovered input function, as contrasted with use of plasma samples, yielded highly correlated values of K=K(1)k(3)/(k(2)+k(3)) for simulated data, a correlation coefficient of 0.99780, a slope of 1.019 and an intercept of almost zero. The estimates of K for real data by graphical Patlak analysis using the recovered input function were almost identical to those obtained using arterial plasma samples, with correlation coefficients greater than 0.9976, regression slopes between 0.958 and 1.091 and intercepts that are virtually zero.

CONCLUSIONS

A reliable semiautomated alternative for input function estimation that uses image-derived data augmented with three plasma samples is presented and evaluated for FDG-PET human brain studies.

Analysis and interpretation of dynamic FDG PET oncological studies using data reduction techniques

Background

Dynamic positron emission tomography studies produce a large amount of image data, from which clinically useful parametric information can be extracted using tracer kinetic methods. Data reduction methods can facilitate the initial interpretation and visual analysis of these large image sequences and at the same time can preserve important information and allow for basic feature characterization.

Methods

We have applied principal component analysis to provide high-contrast parametric image sets of lower dimensions than the original data set separating structures based on their kinetic characteristics. Our method has the potential to constitute an alternative quantification method, independent of any kinetic model, and is particularly useful when the retrieval of the arterial input function is complicated. In independent component analysis images, structures that have different kinetic characteristics are assigned opposite values, and are readily discriminated. Furthermore, novel similarity mapping techniques are proposed, which can summarize in a single image the temporal properties of the entire image sequence according to a reference region.

Results

Using our new cubed sum coefficient similarity measure, we have shown that structures with similar time activity curves can be identified, thus facilitating the detection of lesions that are not easily discriminated using the conventional method employing standardized uptake values.

Simplifications in analyzing positron emission tomography data: effects on outcome measures

Initial validation studies of new radiotracers generally involve kinetic models that require a measured arterial input function. This allows for the separation of tissue binding from delivery and blood flow effects. However, when using a tracer in a clinical setting, it is necessary to eliminate arterial blood sampling due to its invasiveness and the extra burden of counting and analyzing the blood samples for metabolites. In some cases, it may also be necessary to replace dynamic scanning with a shortened scanning period some time after tracer injection, as is done with FDG (F-18 fluorodeoxyglucose). These approximations represent loss of information. In this work, we considered several questions related to this: (1) Do differences in experimental conditions (drug treatments) or populations affect the input function, and what effect, if any, does this have on the final outcome measure? (2) How do errors in metabolite measurements enter into results? (3) What errors are incurred if the uptake ratio is used in place of the distribution volume ratio? (4) Is one- or two-point blood sampling any better for FDG data than the standardized uptake value? and (5) If blood sampling is necessary, what alternatives are there to arterial blood sampling? The first three questions were considered in terms of data from human dynamic positron emission tomography (PET) studies under conditions of baseline and drug pretreatment. Data from [11C]raclopride studies and those from the norepinephrine transporter tracer (S,S)-[11C]O-methyl reboxetine were used. Calculation of a metabolic rate for FDG using the operational equation requires a measured input function. We tested a procedure based on two blood samples to estimate the plasma integral and convolution that occur in the operational equation. There are some tracers for which blood sampling is necessary. Strategies for brain studies involve using the internal carotids in estimating the radioactivity after correcting for partial volume and spillover in order to eliminate arterial sampling. Some venous blood samples are still required for metabolite measurements. The ultimate solution to the problem of arterial sampling may be a wrist scanner, which acts as a small PET camera for imaging the arteries in the wrist. This is currently under development.

Fast parametric imaging algorithm for dual-input biomedical system parameter estimation

Medical parametric imaging with dynamic positron emission tomography (PET) plays an increasingly potential role in modern biomedical research and clinical diagnosis. The key issue in parametric imaging is to estimate parameters based on sampled data at the pixel-by-pixel level from certain dynamic processes described by valid mathematical models. Classic nonlinear least squares (NLS) algorithm requires a "good" initial guess and the computational time-complexity is high, which is impractical for image-wide parameter estimation. Although a variety of fast parametric imaging techniques have been developed, most of them focus on single input systems, which do not provide an optimal solution for dual-input biomedical system parameter estimation, which is the case of liver metabolism. In this study, a dual-input-generalized linear least squares (D-I-GLLS) algorithm was proposed to identify the model parameters including the parameter in the dual-input function. Monte Carlo simulation was conducted to examine this novel fast algorithm. The results of the quantitative analysis suggested that the proposed technique could provide comparable reliability of the parameter estimation with NLS fitting and accurately identify the parameter in the dual-input function. This method may be potentially applicable to other dual-input biomedical system parameter estimation as well.

Direct reconstruction of kinetic parameter images from dynamic PET data

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

Tracer kinetic modeling of 11C-acetate applied in the liver with positron emission tomography

It is well known that 40%-50% of hepatocellular carcinoma (HCC) do not show increased 18F-fluorodeoxyglucose (FDG) uptake. Recent research studies have demonstrated that 11C-acetate may be a complementary tracer to FDG in positron emission tomography (PET) imaging of HCC in the liver. Quantitative dynamic modeling is, therefore, conducted to evaluate the kinetic characteristics of this tracer in HCC and nontumor liver tissue. A three-compartment model consisting of four parameters with dual inputs is proposed and compared with that of five parameters. Twelve regions of dynamic datasets of the liver extracted from six patients are used to test the models. Estimation of the adequacy of these models is based on Akaike Information Criteria (AIC) and Schwarz Criteria (SC) by statistical study. The forward clearance K = K1 * k3/(k2 + k3) is estimated and defined as a new parameter called the local hepatic metabolic rate-constant of acetate (LHMRAct) using both the weighted nonlinear least squares (NLS) and the linear Patlak methods. Preliminary results show that the LHMRAct of the HCC is significantly higher than that of the nontumor liver tissue. These model parameters provide quantitative evidence and understanding on the kinetic basis of C-acetate for its potential role in the imaging of HCC using PET.

Blind identification of the kinetic parameters in three-compartment models

Quantified knowledge of tissue kinetic parameters in the regions of the brain and other organs can offer information useful in clinical and research applications. Dynamic medical imaging with injection of radioactive or paramagnetic tracer can be used for this measurement. The kinetics of some widely used tracers such as [18F]2-fluoro-2-deoxy-D-glucose can be described by a three-compartment physiological model. The kinetic parameters of the tissue can be estimated from dynamically acquired images. Feasibility of estimation by blind identification, which does not require knowledge of the blood input, is considered analytically and numerically in this work for the three-compartment type of tissue response. The non-uniqueness of the two-region case for blind identification of kinetic parameters in three-compartment model is shown; at least three regions are needed for the blind identification to be unique. Numerical results for the accuracy of these blind identification methods in different conditions were considered. Both a separable variables least-squares (SLS) approach and an eigenvector-based algorithm for multichannel blind deconvolution approach were used. The latter showed poor accuracy. Modifications for non-uniform time sampling were also developed. Also, another method which uses a model for the blood input was compared. Results for the macroparameter K, which reflects the metabolic rate of glucose usage, using three regions with noise showed comparable accuracy for the separable variables least squares method and for the input model-based method, and slightly worse accuracy for SLS with the non-uniform sampling modification.

Cluster analysis in kinetic modelling of the brain: a noninvasive alternative to arterial sampling

In emission tomography, quantification of brain tracer uptake, metabolism or binding requires knowledge of the cerebral input function. Traditionally, this is achieved with arterial blood sampling. We propose a noninvasive alternative via the use of a blood vessel time-activity curve (TAC) extracted directly from dynamic positron emission tomography (PET) scans by cluster analysis. Five healthy subjects were injected with the 5HT(2A)-receptor ligand [(18)F]-altanserin and blood samples were subsequently taken from the radial artery and cubital vein. Eight regions-of-interest (ROI) TACs were extracted from the PET data set. Hierarchical K-means cluster analysis was performed on the PET time series to extract a cerebral vasculature ROI. The number of clusters was varied from K = 1 to 10 for the second of the two-stage method. Determination of the correct number of clusters was performed by the 'within-variance' measure and by 3D visual inspection of the homogeneity of the determined clusters. The cluster-determined input curve was then used in Logan plot analysis and compared with the arterial and venous blood samples, and additionally with one of the currently used alternatives to arterial blood sampling, the Simplified Reference Tissue Model (SRTM) and Logan analysis with cerebellar TAC as an input. There was a good agreement (P < 0.05) between the values of Distribution Volume (DV) obtained from the K-means-clustered input function and those from the arterial blood samples. This work acts as a proof-of-principle that the use of cluster analysis on a PET data set could obviate the requirement for arterial cannulation when determining the input function for kinetic modelling of ligand binding, and that this may be a superior approach as compared to the other noninvasive alternatives.

Estimating the input function non-invasively for FDG-PET quantification with multiple linear regression analysis: simulation and verification with in vivo data

A novel statistical method, namely Regression-Estimated Input Function (REIF), is proposed in this study for the purpose of non-invasive estimation of the input function for fluorine-18 2-fluoro-2-deoxy- d-glucose positron emission tomography (FDG-PET) quantitative analysis. We collected 44 patients who had undergone a blood sampling procedure during their FDG-PET scans. First, we generated tissue time-activity curves of the grey matter and the whole brain with a segmentation technique for every subject. Summations of different intervals of these two curves were used as a feature vector, which also included the net injection dose. Multiple linear regression analysis was then applied to find the correlation between the input function and the feature vector. After a simulation study with in vivo data, the data of 29 patients were applied to calculate the regression coefficients, which were then used to estimate the input functions of the other 15 subjects. Comparing the estimated input functions with the corresponding real input functions, the averaged error percentages of the area under the curve and the cerebral metabolic rate of glucose (CMRGlc) were 12.13+/-8.85 and 16.60+/-9.61, respectively. Regression analysis of the CMRGlc values derived from the real and estimated input functions revealed a high correlation (r=0.91). No significant difference was found between the real CMRGlc and that derived from our regression-estimated input function (Student's t test, P>0.05). The proposed REIF method demonstrated good abilities for input function and CMRGlc estimation, and represents a reliable replacement for the blood sampling procedures in FDG-PET quantification.

Estimation of kinetic parameters without input functions: analysis of three methods for multichannel blind identification

Compartment modeling of dynamic medical image data implies that the concentration of the tracer over time in a particular region of the organ of interest is well modeled as a convolution of the tissue response with the tracer concentration in the blood stream. The tissue response is different for different tissues while the blood input is assumed to be the same for different tissues. The kinetic parameters characterizing the tissue responses can be estimated by multichannel blind identification methods. These algorithms use the simultaneous measurements of concentration in separate regions of the organ; if the regions have different responses, the measurement of the blood input function may not be required. Three blind identification algorithms are analyzed here to assess their utility in medical imaging: eigenvector-based algorithm for multichannel blind deconvolution; cross relations; and iterative quadratic maximum-likelihood (IQML). Comparisons of accuracy with conventional (not blind) identification techniques where the blood input is known are made as well. Tissue responses corresponding to a physiological two-compartment model are primarily considered. The statistical accuracies of estimation for the three methods are evaluated and compared for multiple parameter sets. The results show that IQML gives more accurate estimates than the other two blind identification methods.

Simultaneous estimation of physiological parameters and the input function--in vivo PET data

Dynamic imaging with positron emission tomography (PET) is widely used for the in vivo measurement of regional cerebral metabolic rate for glucose (rCMRGlc) with [18F]fluorodeoxy-D-glucose (FDG) and is used for the clinical evaluation of neurological disease. However, in addition to the acquisition of dynamic images, continuous arterial blood sampling is the conventional method to obtain the tracer time-activity curve in blood (or plasma) for the numeric estimation of rCMRGlc in mg glucose/100-g tissue/min. The insertion of arterial lines and the subsequent collection and processing of multiple blood samples are impractical for clinical PET studies because it is invasive, has the remote, but real potential for producing limb ischemia, and it exposes personnel to additional radiation and risks associated with handling blood. In this paper, based on our previously proposed method for extracting kinetic parameters from dynamic PET images, we developed a modified version (post-estimation method) to improve the numerical identifiability of the parameter estimates when we deal with data obtained from clinical studies. We applied both methods to dynamic neurologic FDG PET studies in three adults. We found that the input function and parameter estimates obtained with our noninvasive methods agreed well with those estimated from the gold standard method of arterial blood sampling and that rCMRGlc estimates were highly correlated (r = 0.973). More importantly, no significant difference was found between rCMRGlc estimated by our methods and the gold standard method (P > 0.16). We suggest that our proposed noninvasive methods may offer an advance over existing methods.

Content-based retrieval of dynamic PET functional images

The recent information explosion has led to massively increased demand for multimedia data storage in integrated database systems. Content-based retrieval is an important alternative and complement to traditional keyword-based searching for multimedia data and can greatly enhance information management. However, current content-based image retrieval techniques have some deficiencies when applied in the biomedical functional imaging domain. In this paper, we presented a prototype design for a content-based functional image retrieval database system for dynamic positron emission tomography. The system supports efficient content-based retrieval based on physiological kinetic features and reduces image storage requirements. This design makes it possible to maintain a large number of patient data sets online and to rapidly retrieve dynamic functional image sequences for interpretation and generation of physiological parametric images, and offers potential advantages in medical image data management and telemedicine, as well as providing possible opportunities in the statistical and comparative analysis of functional image data.

Information technology applications in biomedical functional imaging

In parallel with rapid advances in computer technology, biomedical functional imaging is having an ever-increasing impact on healthcare. Functional imaging allows us to see dynamic processes quantitatively in the living human body. However, as we need to deal with four-dimensional time-varying images, space requirements and computational complexity are extremely high. This makes information management, processing, and communication difficult. Using the minimum amount of data to represent the required information, developing fast algorithms to process the data, organizing the data in such a way as to facilitate information management, and extracting the maximum amount of useful information from the recorded data have become important research tasks in biomedical information technology. For the last ten years, the Biomedical and Multimedia Information Technology (BMIT) Group and, recently, the Center for Multimedia Signal Processing have conducted systematic studies on these topics. Some of the results relating to functional imaging data acquisition, compression, storage, management, processing, modeling, and simulation are briefly reported in this paper.