Dynamic PET (dPET) with 18F-Deoxyglucose (FDG) provides quantitative information about distribution of the tracer in a predefined volume over time. A two-tissue compartment model can be used to obtain quantitative data regarding transport of FDG into and out of the cells, phosphorylation and dephosphorylation rate of intracellular FDG, and fractional blood volume in the target volume, also named vessel density. Aim of the study was the correlation of glucose transporters expression and hexokinases with the corresponding compartment parameters.Patients with colorectal tumors were examined with dynamic PET prior to surgery. Afterwards, tumor samples were obtained during surgery and gene expression was assessed using gene arrays. The dynamic PET data were evaluated to quantify the parameters of a two tissue compartment model for colorectal tumors using a Volume-of-Interest (VOI) technique. A multiple correlation/regression analysis was performed using glucose transporters as independent variables and k1 as the dependent variable. A correlation of r=0.7503 (p=0.03) was obtained for the transporters SLC2A1, SLC2A2, SLC2A4, SLC2A8, SLC2A9, SLC2A10 and k1. The correlation of r=0.7503 refers to an explained variance of data of 56.30 %, therefore more than 50 % of data changes are associated with the gene expression. An analysis of the hexokinases HK1-HK3 and k3 revealed a correlation coefficient of r=0.6093 (p=0.04), which is associated with an explained variance of 37.12 %. Therefore, parameters k1 and k3 reflect gene activity. The results demonstrate that k1 and k3 of the two-tissue compartment model are correlated with glucose transporters and hexokinases.
Dynamic PET; compartment model; glucose transporter; hexokinase
Introduction. The results obtained with dynamic PET (dPET) were compared to gene expression data obtained in patients with gastrointestinal stromal tumors (GIST). The primary aim was to assess the association of the dPET results and gene expression data. Material and Methods. dPET was performed following the injection of F-18-fluorodeoxyglucose (FDG) in 22 patients with GIST. All patients were examined prior to surgery for staging purpose. Compartment and noncompartment models were used for the quantitative evaluation of the dPET examinations. Gene array data were based on tumor specimen obtained by surgery after the PET examinations. Results. The data analysis revealed significant correlations for the dPET parameters and the expression of zinc finger genes (znf43, znf85, znf91, znf189). Furthermore, the transport of FDG (k1) was associated with VEGF-A. The cell cycle gene cyclin-dependent kinase inhibitor 1C was correlated with the maximum tracer uptake (SUVmax) in the tumors. Conclusions. The data demonstrate a dependency of the tracer kinetics on genes associated with prognosis in GIST. Furthermore, angiogenesis and cell proliferation have an impact on the tracer uptake.
Rats with osteoporosis were involved by combining ovariectomy (OVX) either with calcium and Vitamin D deficiency diet (Group D), or with glucocorticoid (dexamethasone) treatment (Group C). In the period of 1-12 months, dynamic PET-CT studies were performed in three groups of rats including Group D, Group C and the control Group K (sham-operated). Standardized uptake values (SUVs) were calculated, and a 2-tissue compartmental learning-machine model (calculation of K1-k4, VB and the plasma clearance of tracer to bone mineral (Ki) as well as a non-compartmental model based on the fractal dimension (FD) was used for quantitative analysis of both groups. The evaluation of PET data was performed over the lumbar spine. The correlation analysis revealed a significant linear correlation for certain dPET quantitative parameters and time up to 12 months after induction of osteoporosis. Based on the 18F-Fluoride data, we noted a significant negative correlation for K1 (the fluoride/hydroxyl exchange) in the Group C and a significant positive correlation for k3, SUV (bone metabolism) and FD in the Group K. The evaluation of the 18F-FDG data revealed a significant positive correlation for SUV (glucose metabolism) only in Group C. The correlation between the two tracers revealed significant results between K1 of 18F-Fluoride and SUV of FDG in Group K as well as between FD of 18F-Fluoride and FDG in Group D and C and between k3 of 18F-Fluoride and SUV of FDG in Group C.
dPET-CT; 18F-FDG; 18F-fluoride; osteoporosis
A new model for an input function for human [18F]-2-Deoxy-2-fluoro-D-glucose fluoro (FDG) positron emission tomography (PET) brain studies with bolus injection is presented.
Input data for early time, roughly up to 0.6 minutes, are obtained non-invasively from the time activity curve measured from a carotid artery region of interest (CA-ROI). Representative tissue time activity curves are obtained by clustering the output curves to a limited number of dominant clusters. Three venous plasma samples at later time are used to fit the functional form of the input function in conjunction with obtaining kinetic rate parameters of the dominant clusters,K1, k2 and k3 using the compartmental model for FDG-PET. Experiments to test the approach use data from 18 healthy subjects.
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, yields highly correlated values of K =K1k3/(k2 + k3) for simulated data, correlation coefficient .99780, slope 1.019 and intercept almost zero. The estimates of K for real data by graphical Patlak analysis using the recovered input function are almost identical to those obtained using arterial plasma samples with correlation coefficients greater than 0.9976, regression slopes between .958 and 1.091 and intercepts that are virtually zero.
A reliable semi-automated alternative for input function estimation which uses image-derived data augmented with 3 plasma samples is presented and evaluated for FDG-PET human brain studies.
Input Function Estimation; FDG-PET; Quantification
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.
Reference tissue model (RTM) is a compartmental modeling approach that uses reference tissue time activity curve (TAC) as input for quantification of ligand-receptor dynamic PET without blood sampling. There are limitations in applying the RTM for kinetic analysis of PET studies using [11C]Pittsburgh compound B ([11C]PIB). For region of interest (ROI) based kinetic modeling, the low specific binding of [11C]PIB in a target ROI can result in a high linear relationship between the output and input. This condition may result in amplification of errors in estimates using RTM. For pixel-wise quantification, due to the high noise level of pixel kinetics, the parametric images generated by RTM with conventional linear or nonlinear regression may be too noisy for use in clinical studies.
We applied RTM with parameter coupling and a simultaneous fitting method as a spatial constraint for ROI kinetic analysis. Three RTMs with parameter coupling were derived from a classical compartment model with plasma input: a RTM of 4 parameters (R1, k′2R, k4, BP) (RTM4P); a RTM of 5 parameters (R1, k2R, NS, k6, BP) (RTM5P); and a simplified RTM (SRTM) of 3 parameters (R1, k′2R, BP) (RTM3P). The parameter sets [k′2R, k4], [k2R, NS, k6], and k′2R are coupled among ROIs for RTM4P, RTM5P, and RTM3P, respectively. A linear regression with spatial constraint (LRSC) algorithm was applied to the SRTM for parametric imaging. Logan plots were used to estimate the distribution volume ratio (DVR) (= 1 + BP (binding potential)) in ROI and pixel levels. Ninety-minute [11C]PIB dynamic PET was performed in 28 controls and 6 individuals with mild cognitive impairment (MCI) on a GE Advance scanner. ROIs of cerebellum (reference tissue) and 15 other regions were defined on coregistered MRI’s.
The coefficients of variation of DVR estimates from RTM3P obtained by the simultaneous fitting method were lower by 77 - 89% (in striatum, frontal, occipital, parietal, and cingulate cortex) as compared to that by conventional single ROI TAC fitting method. There were no significant differences in both TAC fitting and DVR estimates between the RTM3P and the RTM4P or RTM5P. The DVR in striatum, lateral temporal, frontal and cingulate cortex for MCI group was 25% to 38% higher compared to the control group (p ≤ 0.05), even in this group of individuals with generally low PIB retention. The DVR images generated by the SRTM with LRSC algorithm had high linear correlations with those from the Logan plot (R2 = 0.99). In conclusion, the RTM3P with simultaneous fitting method is shown to be a robust compartmental modeling approach that may be useful in [11C]PIB PET studies to detect early markers of Alzheimer’s disease where specific ROIs have been hypothesized. In addition, the SRTM with LRSC algorithm may be useful in generating R1 and DVR images for pixel-wise quantification of [11C]PIB dynamic PET.
Pulmonary uptake of 18F-FDG assessed with PET has been used to quantify the metabolic activity of inflammatory cells in the lung. This assessment involves modeling of tracer kinetics and knowledge of a time–activity curve in pulmonary artery plasma as an input function, usually acquired by manual blood sampling. This paper presents and validates a method to accurately derive an input function from a blood-pool region of interest (ROI) defined in dynamic PET images.
The method is based on a 2-parameter model describing the activity of blood and that from spillover into the time–activity curve for the ROI. The model parameters are determined using an iterative algorithm, with 2 blood samples used to calibrate the raw PET-derived activity data. We validated both the 2-parameter model and the method to derive a quantitative input function from ROIs defined for the cavities of the right and left heart and for the descending aorta by comparing them against the time–activity curve obtained by manual blood sampling from the pulmonary artery in lungs with acute inflammation.
The model accurately described the time–activity curve from sampled blood. The 2-sample calibration method provided an efficient algorithm to derive input functions that were virtually identical to those sampled manually, including the fast kinetics of the early phase. The 18F-FDG uptake rates in acutely injured lungs obtained using this method correlated well with those obtained exclusively using manual blood sampling (R2 > 0.993). Within some bounds, the model was found quite insensitive to the timing of calibration blood samples or the exact definition of the blood-pool ROIs.
Using 2 mixed venous blood samples, the method accurately assesses the entire time course of the pulmonary 18F-FDG input function and does not require the precise geometry of a specific blood-pool ROI or a population-based input function. This method may substantially facilitate studies involving modeling of pulmonary 18F-FDG in patients with viral or bacterial infections, pulmonary fibrosis, and chronic obstructive pulmonary disease.
PET; Massachusetts General Hospital; 18F-FDG; acute lung injury; inflammation
The purpose of this study was to detect the physiological process of FDG's filtration from blood to urine and to establish a mathematical model to describe the process. Dynamic positron emission tomography scan for FDG was performed on seven normal volunteers. The filtration process in kidney can be seen in the sequential images of each study. Variational distribution of FDG in kidney can be detected in dynamic data. According to the structure and function, kidney is divided into parenchyma and pelvis. A unidirectional three-compartment model is proposed to describe the renal function in FDG excretion. The time-activity curves that were picked up from the parenchyma, pelvis, and abdominal aorta were used to estimate the parameter of the model. The output of the model has fitted well with the original curve from dynamic data.
Dynamic FDG-PET imaging was used to study inflammation in lungs of mice following administration of a virulent strain of Klebsiella (K.) pneumoniae. Net whole-lung FDG influx constant (Ki) was determined in a compartment model using an image-derived blood input function. Methods. K. pneumoniae (~3 x 105 CFU) was intratracheally administered to six mice with 6 other mice serving as controls. Dynamic FDG-PET and X-Ray CT scans were acquired 24 hr after K. pneumoniae administration. The experimental lung time activity curves were fitted to a 3-compartment FDG model to obtain Ki. Following imaging, lungs were excised and immunohistochemistry analysis was done to assess the relative presence of neutrophils and macrophages. Results. Mean Ki for control and K. pneumoniae infected mice were (5.1 ± 1.2) ×10−3 versus (11.4 ± 2.0) ×10−3 min−1, respectively, revealing a 2.24 fold significant increase (P = 0.0003) in the rate of FDG uptake in the infected lung. Immunohistochemistry revealed that cellular lung infiltrate was almost exclusively neutrophils. Parametric Ki maps by Patlak analysis revealed heterogeneous inflammatory foci within infected lungs. Conclusion. The kinetics of FDG uptake in the lungs of mice can be noninvasively quantified by PET with a 3-compartment model approach based on an image-derived input function.
The production of images of kinetic parameters is often the ultimate goal of positron emission tomography (PET) imaging. The indirect method of PET parametric imaging, also called the frame-based method (FM), is performed by fitting the time-activity curve (TAC) for each voxel with an appropriate compartment model after image reconstruction. The indirect method is simple and easily implemented, however, it usually leads to some loss of accuracy or precision, due to the use of two separate steps. This paper presents a direct 4-D method for producing 3-D images of kinetic parameters from list mode PET data. In this application, the TAC for each voxel is described by a one-tissue compartment model (1T). Extending previous EM algorithms, a new spatiotemporal complete data space was introduced to optimize the maximum likelihood function. This leads to a straightforward closed-form parametric image update equation. This method was implemented by extending the current list mode platform MOLAR to produce a parametric algorithm PMOLAR-1T. Using an ordered subset approach, qualitative and quantitative evaluations were performed using 2-D (x, t) and 4-D (x, y, z, t) simulated list mode data based on brain receptor tracers and also with a human brain study. Comparisons with the indirect method showed that the proposed direct method can lead to accurate estimation of the parametric image values with reduced variance, especially at low count levels. In the 2-D test, the direct method showed similar bias to the frame-based method but with variance reduction of 23%–60%. In the 4-D test, bias values of both methods were no more than 4% and the direct method had lower variability (coefficient of variation reduction of 0%–64% compared to the frame-based method) at the normal count level. The direct method had a larger reduction in variability (27%–81%) and lower bias (1%–5% for 4-D and 1%–19% for FM) at low count levels. The results in the human brain study are similar with PMOLAR-1T showing lower noise than FM.
Expectation maximization; image reconstruction; one-tissue compartment model; parametric imaging
Kinetic modeling of brain glucose metabolism in small rodents from positron emission tomography (PET) data using 2-deoxy-2-[18 F]fluoro-d-glucose (FDG) has been highly inconsistent, due to different modeling parameter settings and underestimation of the impact of methodological flaws in experimentation. This article aims to contribute toward improved experimental standards. As solutions for arterial input function (IF) acquisition of satisfactory quality are becoming available for small rodents, reliable two-tissue compartment modeling and the determination of transport and phosphorylation rate constants of FDG in rodent brain are within reach.
Data from mouse brain FDG PET with IFs determined with a coincidence counter on an arterio-venous shunt were analyzed with the two-tissue compartment model. We assessed the influence of several factors on the modeling results: the value for the fractional blood volume in tissue, precision of timing and calibration, smoothing of data, correction for blood cell uptake of FDG, and protocol for FDG administration. Kinetic modeling with experimental and simulated data was performed under systematic variation of these parameters.
Blood volume fitting was unreliable and affected the estimation of rate constants. Even small sample timing errors of a few seconds lead to significant deviations of the fit parameters. Data smoothing did not increase model fit precision. Accurate correction for the kinetics of blood cell uptake of FDG rather than constant scaling of the blood time-activity curve is mandatory for kinetic modeling. FDG infusion over 4 to 5 min instead of bolus injection revealed well-defined experimental input functions and allowed for longer blood sampling intervals at similar fit precisions in simulations.
FDG infusion over a few minutes instead of bolus injection allows for longer blood sampling intervals in kinetic modeling with the two-tissue compartment model at a similar precision of fit parameters. The fractional blood volume in the tissue of interest should be entered as a fixed value and kinetics of blood cell uptake of FDG should be included in the model. Data smoothing does not improve the results, and timing errors should be avoided by precise temporal matching of blood and tissue time-activity curves and by replacing manual with automated blood sampling.
CMRglc; FDG; Fractional blood volume; Kinetic modeling; Reliability; Positron emission tomography; Infusion
This paper systematically evaluates a pharmacokinetic compartmental model for identifying tumor hypoxia using dynamic positron-emission-tomography (PET) imaging with 18F-fluoromisonidazole (FMISO). A generic irreversible one-plasma two-tissue compartmental model was used. A dynamic PET image dataset was simulated with 3 tumor regions -- normoxic, hypoxic and necrotic, embedded in a normal-tissue background, and with an image-based arterial input function. Each voxelized tissue’s time-activity-curve (TAC) was simulated with typical values of kinetic parameters, as deduced from FMISO-PET data from 9 head-and-neck cancer patients. The dynamic dataset was first produced without any statistical noise to ensure that correct kinetic parameters were reproducible. Next, to investigate the stability of kinetic parameter estimation in the presence of noise, 1000 noisy samples of the dynamic dataset were generated, from which 1000 noisy estimates of kinetic parameters were calculated and used to estimate the sample mean and covariance matrix. It is found that a more peaked input function gave less variation in various kinetic parameters, and the variation of kinetic parameters could also be reduced by two region-of-interest averaging techniques. To further investigate how bias in the arterial input function affected the kinetic parameter estimation, a shift error was introduced in the peak-amplitude and peak-location of the input TAC, and the bias of various kinetic parameters calculated. In summary, mathematical phantom studies have been used to determine the statistical accuracy and precision of model-based kinetic analysis, which helps to validate this analysis and provides guidance in planning clinical dynamic FMISO-PET studies.
hypoxia; pharmacokinetics; compartmental modeling; positron emission tomography; 18F-FMISO
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.
The purpose of this research was to develop a novel numerical procedure to deconvolute arterial input function from contrast concentration vs. time curves and to obtain the impulse response functions from dynamic contrast enhanced MRI data. Numerical simulations were performed to study variations of contrast concentration vs. time curves and the corresponding impulse response functions. The simulated contrast media concentration curves were generated by varying the parameters of an empirical mathematical model within reasonable ranges based on a previous experimental study. The arterial input function was calculated from plots of contrast media concentration vs. time in muscle under assumption that they are well approximated by the two-compartment model. A general simple mathematical model of the impulse response function was developed and the physiological meaning of the model parameters was determined by comparing them with the widely accepted ‘two compartment model’. The results demonstrate that the deconvolution procedure developed in this research is a simple, robust, and useful technique. In addition, ‘impulse response analysis’ leads to the derivation of novel parameters relating to tumor vascular architecture, and these new parameters may have clinical utility.
Deconvolution; impulse response function; perfusion; DCE-MRI; arterial input function
The objective of this study is the implementation of a kinetic model for 11C-desmethylloperamide (11C-dLop) and the determination of a typical parameter for P-glycoprotein (P-gp) functionality in mice. Since arterial blood sampling in mice is difficult, an alternative method to obtain the arterial plasma input curve used in the kinetic model is proposed.
Wild-type (WT) mice (pre-injected with saline or cyclosporine) and P-gp knock-out (KO) mice were injected with 20 MBq of 11C-dLop, and a dynamic μPET scan was initiated. Afterwards, 18.5 MBq of 18F-FDG was injected, and a static μPET scan was started. An arterial input and brain tissue curve was obtained by delineation of an ROI on the left heart ventricle and the brain, respectively based on the 18F-FDG scan.
A comparison between the arterial input curves obtained by the alternative and the blood sampling method showed an acceptable agreement. The one-tissue compartment model gives the best results for the brain. In WT mice, the K1/k2 ratio was 0.4 ± 0.1, while in KO mice and cyclosporine-pretreated mice the ratio was much higher (2.0 ± 0.4 and 1.9 ± 0.2, respectively). K1 can be considered as a pseudo value K1, representing a combination of passive influx of 11C-desmethylloperamide and a rapid washout by P-glycoprotein, while k2 corresponds to slow passive efflux out of the brain.
An easy to implement kinetic modeling for imaging P-glycoprotein function is presented in mice without arterial blood sampling. The ratio of K1/k2 obtained from a one-tissue compartment model can be considered as a good value for P-glycoprotein functionality.
Rationale and objectives
Dynamic positron-emission tomography (PET) imaging of the radiotracer 2-deoxy-2-[18F]fluoro-D-glucose (18F-FDG) is increasingly used to assess metabolic activity of lung inflammatory cells. To analyze the kinetics of 18F-FDG in brain and tumor tissues the ‘Sokoloff’ model has been typically used. In the lungs, however, a high blood-to-parenchymal volume ratio and 18F-FDG distribution in edematous injured tissue could require a modified model to properly describe 18F-FDG kinetics.
Material and Methods
We developed and validated a new model of lung 18F-FDG kinetics that includes an extravascular/non-cellular compartment in addition to blood and 18F-FDG precursor pools for phosphorylation. Parameters obtained from this model were compared with those obtained using the Sokoloff model. We analyzed dynamic PET data from 15 sheep with smoke or ventilator-induced lung injury.
In the majority of injured lungs, the new model provided better fit to the data than the Sokoloff model. Rate of pulmonary 18F-FDG net uptake and distribution volume in the precursor pool for phosphorylation correlated between the two models (R2 = 0.98, 0.78), but were overestimated with the Sokoloff model by 17% (p < 0.05) and 16% (p < 0.0005) as compared to the new one. The range of the extravascular/non-cellular 18F-FDG distribution volumes was up to 13% and 49% of lung tissue volume in smoke and ventilator-induced lung injury, respectively.
The lung-specific model predicted 18F-FDG kinetics during acute lung injury more accurately than the Sokoloff model and may provide new insights in the pathophysiology of lung injury.
radionuclide imaging; 18F-FDG; positron-emission tomography
Changes in tumor metabolism from PET in locally advanced breast cancer (LABC) patients treated with neoadjuvant chemotherapy (NC) are predictive of pathologic response. Serial dynamic [18F]-FDG PET scans were used to compare kinetic parameters to the standardized uptake value (SUV) as predictors of pathologic response, disease-free survival (DFS) and overall survival (OS).
Seventy-five LABC patients underwent FDG PET prior to and at midpoint of NC. FDG delivery (K1), FDG flux (Ki), and SUV measures were calculated and compared by clinical and pathological tumor characteristics using regression methods and area under the receiver operating characteristic curve (AUC). Associations between K1, Ki, and SUV and DFS and OS were evaluated using the Cox proportional hazards model.
Tumors that were hormone receptor negative, high grade, highly proliferative, or of ductal histology had higher FDG Ki and SUV values; on average, FDG K1 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 compared to SUV (AUC = 0.84, P = 0.005). Changes in K1 and Ki predicted both DFS and OS, while changes in SUV predicted OS only. In multivariate modeling, only changes in K1 remained an independent prognosticator of DFS and OS.
Kinetic measures of FDG PET for LABC patients treated with NC accurately measured treatment response and predicted outcome compared to static SUV measures, suggesting kinetic analysis may hold advantage of static uptake measures for response assessment.
PET; FDG kinetics; SUV; breast cancer; neoadjuvant
We present a direct method for producing images of kinetic parameters from list mode PET data. The time-activity curve for each voxel is described by a one-tissue compartment, 2-parameter model. Extending previous EM algorithms, a new spatiotemporal complete data space was introduced to optimize the maximum likelihood function. This leads to a straightforward parametric image update equation with moderate additional computation requirements compared to the conventional algorithm. Qualitative and quantitative evaluations were performed using 2D (x,t) and 4D (x,y,z,t) simulated list mode data for a brain receptor study. Comparisons with the two-step approach (frame-based reconstruction followed by voxel-by-voxel parameter estimation) show that the proposed method can lead to accurate estimation of the parametric image values with reduced variance, especially for the volume of distribution (VT).
Previously, we presented a direct EM method for producing kinetic parameter images from list mode PET data, where the time-activity curve for each voxel is described by a one-tissue compartment model (1T). The initial evaluations were performed with simulations, without motion, randoms, or scatter effects included. By extension of our previous frame-based physics correction methods, a practical direct 4D parametric reconstruction algorithm is now proposed and implemented for human data. Initial evaluations were performed using 3 human subjects with the serotonin transporter tracer [11C]AFM. Comparisons with the 2-step approach (frame-based reconstruction followed by voxel-by-voxel parameter estimation) provided encouraging initial results. Regional analysis showed that the 2-step and 4D methods have similar K1 and VT values, but with a consistent difference. Visual analysis showed some noise reduction in 4D. These initial results suggest that direct 4D parametric reconstruction can be performed with real data, and offers the potential for improved accuracy and precision over the 2-step frame method.
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.
Non-invasive; Patlak graphical analysis; Parameter estimation; FDG-PET
Voxelwise quantification of hepatic perfusion parameters from dynamic contrast enhanced (DCE) imaging greatly contributes to assessment of liver function in response to radiation therapy. However, the efficiency of the estimation of hepatic perfusion parameters voxel-by-voxel in the whole liver using a dual-input single-compartment model requires substantial improvement for routine clinical applications. In this paper, we utilize the parallel computation power of a graphics processing unit (GPU) to accelerate the computation, while maintaining the same accuracy as the conventional method. Using CUDA-GPU, the hepatic perfusion computations over multiple voxels are run across the GPU blocks concurrently but independently. At each voxel, non-linear least squares fitting the time series of the liver DCE data to the compartmental model is distributed to multiple threads in a block, and the computations of different time points are performed simultaneously and synchronically. An efficient fast Fourier transform in a block is also developed for the convolution computation in the model. The GPU computations of the voxel-by-voxel hepatic perfusion images are compared with ones by the CPU using the simulated DCE data and the experimental DCE MR images from patients. The computation speed is improved by 30 times using a NVIDIA Tesla C2050 GPU compared to a 2.67 GHz Intel Xeon CPU processor. To obtain liver perfusion maps with 626400 voxels in a patient’s liver, it takes 0.9 min with the GPU-accelerated voxelwise computation, compared to 110 min with the CPU, while both methods result in perfusion parameters differences less than 10−6. The method will be useful for generating liver perfusion images in clinical settings.
dynamic contrast enhanced imaging; hepatic perfusion; compartmental model; nonlinear least squares fitting; GPU; convolution
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.
A three-compartment model is proposed for analyzing magnetic resonance renography (MRR) and computed tomography renography (CTR) data to derive clinically useful parameters such as glomerular filtration rate (GFR) and renal plasma flow (RPF). The model fits the convolution of the measured input and the predefined impulse retention functions to the measured tissue curves. A MRR study of 10 patients showed that relative root mean square errors by the model were significantly lower than errors for a previously reported three-compartmental model (11.6% ± 4.9 vs 15.5% ± 4.1; P < 0.001). GFR estimates correlated well with reference values by 99mTc-DTPA scintigraphy (correlation coefficient r = 0.82), and for RPF, r = 0.80. Parameter-sensitivity analysis and Monte Carlo simulation indicated that model parameters could be reliably identified. When the model was applied to CTR in five pigs, expected increases in RPF and GFR due to acetylcholine were detected with greater consistency than with the previous model. These results support the reliability and validity of the new model in computing GFR, RPF, and renal mean transit times from MR and CT data.
computed tomography; glomerular filtration rate; impulse retention function; magnetic resonance renography; renal plasma flow
The novel PET radioligand 11C-N,N-dimethyl-2-(2′-amino-4′-hydroxymethylphenylthio)benzylamine (11C-HOMADAM) binds with high affinity and selectively to the serotonin transporter (SERT). The purpose of this study was to develop a reliable kinetic model to describe the uptake of 11C-HOMADAM in the healthy human brain.
Eight volunteers participated in the study; 5 of them were fitted with arterial catheters for blood sampling and all were scanned on a high-resolution research tomograph after the injection of 11C-HOMADAM. Regional distribution volumes and binding potentials were calculated with 2- and 4-parameter arterial-input compartment models, a 3-parameter reference tissue compartment model, and the Logan graphic approach.
The 2-parameter arterial-input compartment model was statistically superior to the 4-parameter model and described all brain regions. Calculated binding potentials agreed well between the arterial-input model and the reference tissue model when the cerebellum was used as the reference tissue. The Logan graphic approach was not able to estimate the higher concentration of SERT in the dorsal raphe than in the midbrain.
11C-HOMADAM is a highly promising radioligand with high ratios of specific binding to nonspecific binding in known SERT-rich structures, such as the raphe nuclei. The 3-parameter reference tissue model approach permits a simplified quantitatively accurate method for estimating SERT binding potentials.
PET; serotonin transporter; kinetic modeling
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.
Deconvolution; Functional inference; Kinetic analysis; Regularization