Objectives: The use of dynamic positron emission tomography/computed tomography (dPET/CT) studies with [18F]deoxyglucose (FDG) in oncological patients is limited and primarily confined to research protocols. A more widespread application is, however, desirable, and may help to assess small therapeutic effects early after therapy as well as to differentiate borderline differences between tumour and non-tumour lesions, e.g., lipomas versus low-grade liposarcomas. The aim is to present quantification approaches that can be used for the evaluation of dPET/CT series in combination with parametric imaging and to demonstrate the feasibility with regard to tumour diagnostics and therapy management. Methods: A 60-min data acquisition and short acquisition protocols (20-min dynamic series and a static image 60 min post injection) are discussed. A combination of a modified two-tissue compartment model and non-compartmental approaches from the chaos theory (fractal dimension of the time–activity curves) are presented. Fused PET/CT images as well as regression-based parametric images fused with CT or with PET/standardised uptake value images are demonstrated for the exact placement of volumes of interest. Results: The two-tissue compartmental method results in the calculation of 5 kinetic parameters, the fractional blood volume VB (known also as the distribution volume), and the transport rates k1 to k4. Furthermore, the influx according to Patlak can be calculated from the transport rates. The fractal dimension of the time–activity curves describes the heterogeneity of the tracer distribution. The use of the regression-based parametric images of FDG helps to visualise the transport/perfusion and the transport/phosphorylation-dependent FDG uptake, and adds a new dimension to the existing conventional PET or PET/CT images. Conclusions: More sophisticated quantification methods and dedicated software as well as high computational power and faster acquisition protocols can facilitate the assessment of dPET/CT, and may find use in clinical routine, in particular for the assessment of early therapeutic effects or new treatment protocols in combination with the new generation of PET/CT scanners.
Dynamic PET; oncology; compartment modelling; non-compartment modelling; parametric imaging; feature extraction
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
A single dynamic PET acquisition using multiple tracers administered closely in time could provide valuable complementary information about a tumor’s status under quasi-constant conditions. This study aims to investigate the utility of dual-tracer dynamic PET imaging with 18F-Alfatide II (18F-AlF-NOTA-E[PEG4-c(RGDfk)]2) and 18F-FDG for parametric monitoring of tumor responses to therapy.
We administered doxorubicin to one group of athymic nude mice with U87MG tumors and Abraxane to another group of mice with MDA-MB-435 tumors. To monitor therapeutic responses, we performed dual-tracer dynamic imaging, in sessions that lasted 90 min, starting by injecting the mice via tail vein catheters with 18F-Alfatide II, followed 40 minutes later by 18F-FDG. To achieve signal separation of the two tracers, we fit a three-compartment reversible model to the time activity curve (TAC) of 18F-Alfatide II for the 40 min prior to 18F-FDG injection, and then extrapolated to 90 min. The 18F-FDG tumor TAC was isolated from the 90 min dual tracer tumor TAC by subtracting the fitted 18F-Alfatide II tumor TAC. With separated tumor TACs, the 18F-Alfatide II binding potential (Bp=k3/k4) and volume of distribution (VD), and 18F-FDG influx rate ((K1×k3)/(k2 + k3)) based on the Patlak method were calculated to validate the signal recovery in a comparison with 60-min single tracer imaging and to monitor therapeutic response.
The transport and binding rate parameters K1-k3 of 18F-Alfatide II, calculated from the first 40 min of dual tracer dynamic scan, as well as Bp and VD, correlated well with the parameters from the 60 min single tracer scan (R2 > 0.95). Compared with the results of single tracer PET imaging, FDG tumor uptake and influx were recovered well from dual tracer imaging. Upon doxorubicin treatment, while no significant changes in static tracer uptake values of 18F-Alfatide II or 18F-FDG were observed, both 18F-Alfatide II Bp and 18F-FDG influx from kinetic analysis in tumors showed significant decreases. For Abraxane therapy of MDA-MB-435 tumors, significant decrease was only observed with 18F-Alfatide II Bp value from kinetic analysis but not 18F-FDG influx.
The parameters fitted with compartmental modeling from the dual tracer dynamic imaging are consistent with those from single tracer imaging, substantiating the feasibility of this methodology. Even though no significant differences in tumor size were found until 5 days after doxorubicin treatment started, at day 3 there were already substantial differences in 18F-Alfatide II Bp and 18F-FDG influx rate. Dual tracer imaging can measure 18F-Alfatide II Bp value and 18F-FDG influx simultaneously to evaluate tumor angiogenesis and metabolism. Such changes are known to precede anatomical changes, and thus parametric imaging may offer the promise of early prediction of therapy response.
dual-tracer dynamic PET; parametric imaging; 18F-Alfatide II; 18F-FDG; therapy response
Derivation of the plasma time–activity curve in murine small-animal PET studies is a challenging task when tracers that are sequestered by the myocardium are used, because plasma time–activity curve estimation usually involves drawing a region of interest within the area of the reconstructed image that corresponds to the left ventricle (LV) of the heart. The small size of the LV relative to the resolution of the small-animal PET system, coupled with spillover effects from adjacent myocardial pixels, makes this method reliable only for the earliest frames of the scan. We sought to develop a method for plasma time–activity curve estimation based on a model of tracer kinetics in blood, muscle, and liver.
Sixteen C57BL/6 mice were injected with 18F-FDG, and approximately 15 serial blood samples were taken from the femoral artery via a surgically inserted catheter during 60-min small-animal PET scans. Image data were reconstructed by use of filtered backprojection with CT-based attenuation correction. We constructed a 5-compartment model designed to predict the plasma time–activity curve of 18F-FDG by use of data from a minimum of 2 blood samples and the dynamic small-animal PET scan. The plasma time–activity curve (TACp) was assumed to have 4 exponential components (TACP = A1eλ1t + A2eλ2t + A3eλ3t − (A1 + A2 + A3) eλ4t) based on the serial blood samples. Using Bayesian constraints, we fitted 2-compartment submodels of muscle and liver to small-animal PET data for these organs and simultaneously fitted the input (forcing) function to early small-animal PET LV data and 2 blood samples (~10 min and ~1 h).
The area under the estimated plasma time–activity curve had an overall Spearman correlation of 0.99 when compared with the area under the gold standard plasma time–activity curve calculated from multiple blood samples. Calculated organ uptake rates (Patlak Ki) based on the predicted plasma time–activity curve had a correlation of approximately 0.99 for liver, muscle, myocardium, and brain when compared with those based on the gold standard plasma time–activity curve. The model was also able to accurately predict the plasma time–activity curve under experimental conditions that resulted in different rates of clearance of the tracer from blood.
We have developed a robust method for accurately estimating the plasma time–activity curve of 18F-FDG by use of dynamic small-animal PET data and 2 blood samples.
mathematical model; mouse; pharmacokinetics; PET; 18F-FDG
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.
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 CT-based attenuation correction. Total accumulated radioactivity in the urinary bladder was fitted to a renal compartmental model with the last blood sample and a 1-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 4-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 erythrocytes uptake) and the late-time blood estimates. Using only the blood sample acquired at the end of the study to estimate the IF and the use of liver TAC as an alternative IF were also investigated.
The area under the plasma TACs 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 TACs were in excellent agreement (slope ~ 1; R2 > 0.938). The IF estimated using only the last blood sample acquired at the end of the study and the use of liver TAC as plasma IF provided less reliable results.
The estimated plasma IFs obtained with the hybrid model 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.
arterial input function; renal modeling; [18F]FDG; dynamic imaging; mouse; urinary bladder
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
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
The aim of this study was to evaluate various methods for estimating the metabolic rate of glucose utilization in the mouse brain (cMRglc) using small-animal PET and reliable blood curves derived by a microfluidic blood sampler. Typical values of 18F-FDG rate constants of normal mouse cerebral cortex were estimated and used for cMRglc calculations. The feasibility of using the image-derived liver time–activity curve as a surrogate input function in various quantification methods was also evaluated.
Thirteen normoglycemic C57BL/6 mice were studied. Eighteen blood samples were taken from the femoral artery by the microfluidic blood sampler. Tissue time–activity curves were derived from PET images. cMRglc values were calculated using 2 different input functions (one derived from the blood samples [IFblood] and the other from the liver time–activity curve [IFliver]) in various quantification methods, which included the 3-compartment 18F-FDG model (from which the 18F-FDG rate constants were derived), the Patlak analysis, and operational equations. The estimated cMRglc value based on IFblood and the 3-compartment model served as a standard for comparisons with the cMRglc values calculated by the other methods.
The values of K1*,k2*,k3*,k4*, and KFDG* estimated by IFblood and the 3-compartment model were 0.22 ± 0.05 mL/min/g, 0.48 ± 0.09 min−1, 0.06 ± 0.02 min−1, 0.025 ± 0.010 min−1, and 0.024 ± 0.007 mL/min/g, respectively. The standard cMRglc value was, therefore, 40.6 ± 13.3 µmol/100 g/min (lumped constant = 0.6). No significant difference between the standard cMRglc and the cMRglc estimated by the operational equation that includes k4* was observed. The standard cMRglc was also found to have strong correlations (r > 0.8) with the cMRglc value estimated by the use of IFliver in the 3-compartment model and with those estimated by the Patlak analysis (using either IFblood or IFliver).
The 18F-FDG rate constants of normal mouse cerebral cortex were determined. These values can be used in the k4*-included operational equation to calculate cMRglc. IFliver can be used to estimate cMRglc in most methods included in this study, with proper linear corrections applied. The validity of using the Patlak analysis for estimating cMRglc in mouse PET studies was also confirmed.
18F-FDG rate constants of mouse brain; microfluidic blood sampler; noninvasive input function
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
Despite current advances in PET/CT systems, blood sampling still remains the standard method to obtain the radiotracer input function for tracer kinetic modelling. The purpose of this study was to validate the use of image-derived input functions (IDIF) of the carotid and femoral arteries to measure the arterial input function (AIF) in PET imaging. The data were obtained from two different research studies, one using 18F-FDG for brain imaging and the other using 11C-acetate and 18F-fluoro-6-thioheptadecanoic acid (18F-FTHA) in femoral muscles.
The method was validated with two phantom systems. First, a static phantom consisting of syringes of different diameters containing radioactivity was used to determine the recovery coefficient (RC) and spill-in factors. Second, a dynamic phantom built to model bolus injection and clearance of tracers was used to establish the correlation between blood sampling, AIF and IDIF. The RC was then applied to the femoral artery data from PET imaging studies with 11C-acetate and 18F-FTHA and to carotid artery data from brain imaging with 18F-FDG. These IDIF data were then compared to actual AIFs from patients.
With 11C-acetate, the perfusion index in the femoral muscle was 0.34±0.18 min−1 when estimated from the actual time–activity blood curve, 0.29±0.15 min−1 when estimated from the corrected IDIF, and 0.66±0.41 min−1 when the IDIF data were not corrected for RC. A one-way repeated measures (ANOVA) and Tukey’s test showed a statistically significant difference for the IDIF not corrected for RC (p<0.0001). With 18F-FTHA there was a strong correlation between Patlak slopes, the plasma to tissue transfer rate calculated using the true plasma radioactivity content and the corrected IDIF for the femoral muscles (vastus lateralis r=0.86, p=0.027; biceps femoris r=0.90, p=0.017). On the other hand, there was no correlation between the values derived using the AIF and those derived using the uncorrected IDIF. Finally, in the brain imaging study with 18F-FDG, the cerebral metabolic rate of glucose (CMRglc) measured using the uncorrected IDIF was consistently overestimated. The CMRglc obtained using blood sampling was 13.1±3.9 mg/100 g per minute and 14.0±5.7 mg/100 g per minute using the corrected IDIF (r2=0.90).
Correctly obtained, carotid and femoral artery IDIFs can be used as a substitute for AIFs to perform tracer kinetic modelling in skeletal femoral muscles and brain analyses.
Positron emission tomography; Tracer kinetic modelling; Image-derived input function
Radiolabeled arginine-glycine-aspartate (RGD) peptides are increasingly used in preclinical and clinical studies to assess the expression and function of the αvβ3 integrin, a cellular adhesion molecule involved in angiogenesis and tumor metastasis formation. To better understand the PET signal obtained with radiolabeled RGD peptides, we have constructed a compartmental model that can describe the time–activity curves in tumors after an intravenous injection.
We analyzed 60-min dynamic PET scans obtained with 64Cu-1,4,7,10-tetraazacyclododecane-N,N′,N″,N′′-tetraacetic acid (DOTA)-RGD in 20 tumor-bearing severe combined immunodeficient (SCID) mice after a bolus dose (18,500 kBq [500 μCi]), using variations of the standard 2-compartment (4k) tissue model augmented with a compartment for irreversible tracer internalization. αvβ3 binding sites were blocked in 5 studies with a coinjection of cold peptide. In addition, 20 h after injection, static PET was performed on 9 of 20 mice. We fitted 2k (k3 = k4 = 0), 3k (k4 = 0), 4k, and 4kc (k4 = constant) models to the PET data and used several criteria to determine the best model structure for describing 64Cu-DOTA-RGD kinetics in mice. Akaike information criteria (AIC), calculated from model fits and the ability of each model to predict tumor concentration 20 h after tracer injection, were considered.
The 4kc model has the best profile in terms of AIC values and predictive ability, and a constant k4 is further supported by Logan–Patlak analysis and results from iterative Bayesian parameter estimation. The internalization compartment allows quantification of the putative tracer internalization rate for each study, which is estimated here to be approximately an order of magnitude less than k3 and thus does not confound the apparent specific binding of the tracer to the tumor integrin during the first 60 min of the scan. Analysis of specific (S) and nonspecific or nondisplaceable (ND) binding using fitted parameter values showed that the 4kc model provided expected results when comparing αvβ3 blocked and nonblocked studies. That is, specific volume of distribution, [VS = (K1k3)/(k2k4)], is much higher than is nondisplaceable volume of distribution, [VND = (K1/k2)], in nonblocking studies (2.2 ± 0.6 vs. 0.85 ± 0.14); VS and VND are about the same in the blocking studies (0.46 ± 1.6 vs. 0.56 ± 0.09). Also, the ratio of static tumor and plasma measurements at 60 and 10 min [CT(60)/CP(10)] is highly correlated (RS = 0.92) to tumor VS.
We have developed and tested a compartmental model for use with the 64Cu-DOTA-RGD PET tracer and demonstrated its potential as a tool for analysis and design of preclinical and clinical imaging studies.
compartmental model; pharmacokinetics; small-animal PET; RGD peptide; αvβ3 integrin
The Langendorff perfused heart is a physiologically relevant and controllable model with potential for assessing the pharmacokinetics of new radiotracers under a range of pathophysiological conditions.. We assess the feasibility of extending the methods validated for in vivo PET data analysis to the characterisation of PET tracer kinetics applied to Langendorff perfused hearts.
Monte Carlo simulations were used to study the accuracy and reproducibility of linear and non-linear spectral analysis (SA/NLSA), the Patlak graphical method and normalised tissue activity (NA). The methods were used to analyse time-activity curves of two widely used PET tracers, [18 F]-FDG and [18 F]-FMISO, acquired ex vivo from Langendorff perfused rat hearts under normoxic and hypoxic conditions.
Monte Carlo simulations showed NLSA to be superior to SA in identifying and quantifying the presence of irreversible trapping component (αo), for low values of αo. The performance of NLSA and SA for high values of trapping was comparable. NLSA was also more precise than SA in determining the absence of trapping over the range of simulated kinetics and SNR. Simulations also suggest that the semi-quantitative method NA is adequate for the evaluation of trapping, and it was found to be more accurate than Patlak. The values of α0 estimated with NLSA from the time series of both [18 F]-FDG and [18 F]-FMISO increased significantly from normoxia to hypoxia in agreement with previous studies. The values of trapping derived using SA increased but not significantly, reflecting the larger error associate with this method. Patlak estimated from the experimental datasets increased from normoxia to hypoxia but was not significant. NA estimated from the [18 F]-FDG data increased from normoxia to hypoxia, but was not significant, whilst NA calculated for [18 F]-FMISO time-activity curves increased significantly.
Monte Carlo simulations suggested that spectral-based quantitative analysis methods are adequate for the kinetic characterisation of time-activity curves acquired ex vivo from perfused hearts. The uptake rate Patlak and the index NA also represent a good alternative to the SA and NLSA algorithms when the aim of the kinetic analysis is to measure changes in the amount of tracer trapped in the irreversible compartment in response to external stimuli. For low levels of trapping, NLSA and NA were subject to lower errors than SA and Patlak, respectively.
PET; Spectral analysis; Kinetic modelling; [18 F]-FDG; [18 F]-FMISO; Perfused heart
Kinetic quantitation of dynamic positron emission tomography (PET) studies via compartmental modeling usually requires the time-course of the radio-tracer concentration in the arterial blood as an arterial input function (AIF). For human and animal imaging applications, significant practical difficulties are associated with direct arterial sampling and as a result there is substantial interest in alternative methods that require no blood sampling at the time of the study. A fixed population template input function derived from prior experience with directly sampled arterial curves is one possibility. Image-based extraction, including requisite adjustment for spillover and recovery, is another approach. The present work considers a hybrid statistical approach based on a penalty formulation in which the information derived from a priori studies is combined in a Bayesian manner with information contained in the sampled image data in order to obtain an input function estimate. The absolute scaling of the input is achieved by an empirical calibration equation involving the injected dose together with the subject’s weight, height and gender. The technique is illustrated in the context of 18F-Flu-orodeoxyglucose (FDG) PET studies in humans. A collection of 79 arterially sampled FDG blood curves are used as a basis for a priori characterization of input function variability, including scaling characteristics. Data from a series of 12 dynamic cerebral FDG PET studies in normal subjects are used to evaluate the performance of the penalty-based AIF estimation technique. The focus of evaluations is on quantitation of FDG kinetics over a set of 10 regional brain structures. As well as the new method, a fixed population template AIF and a direct AIF estimate based on segmentation are also considered. Kinetics analyses resulting from these three AIFs are compared with those resulting from radially sampled AIFs. The proposed penalty-based AIF extraction method is found to achieve significant improvements over the fixed template and the segmentation methods. As well as achieving acceptable kinetic parameter accuracy, the quality of fit of the region of interest (ROI) time-course data based on the extracted AIF, matches results based on arterially sampled AIFs. In comparison, significant deviation in the estimation of FDG flux and degradation in ROI data fit are found with the template and segmentation methods. The proposed AIF extraction method is recommended for practical use.
Blood curve representation; image segmentation; kinetics; mixture modeling; no blood sampling; penalty method
To quantify the post-radiotherapy 2-[18F]-fluoro-2-deoxyglucose (FDG) pulmonary uptake dose-response in lung cancer patients and determine its relationship with radiation pneumonitis symptoms.
Methods and Materials
The data from 24 patients treated for lung cancer with thoracic radiotherapy who received restaging PET/CT imaging between 4 and 12 weeks after radiotherapy completion were evaluated. Their radiation dose distribution was registered with the post-treatment restaging PET/CT. Using histogram analysis, the voxel average FDG-PET uptake versus radiation dose was obtained for each case and linear regression was performed. The resulting slope, the pulmonary metabolic radiation response (PMRR), was used to characterize the dose-response. The Common Toxicity Criteria version 3 was used to score clinical pulmonary toxicity symptoms. Receiver operating characteristic (ROC) curves were used to determine the level of FDG uptake v. dose, MLD, V5, V10, V20, and V30 that can best predict symptomatic and asymptomatic patients.
The median time between radiotherapy completion and FDG-PET imaging was 59 days (range, 26–70 days). The median of the mean SUV from lung that received 0–5 Gy was 1.00 (range, 0.37–1.48), 5–10 Gy was 1.01 (range, 0.37–1.77), 10 –20 Gy was 1.04 (0.42–1.53), and > 20 Gy was 1.29 (range, 0.41–8.01). Using the dose range of 0 Gy to the maximum dose minus 10 Gy, hierarchical linear regression model of the radiation dose and normalized FDG uptake per case found an adequate fit with the linear model. Pneumonitis scores were: Grade 0 for 13, Grade 1 for 5, Grade 2 for 6, and Grade 3, 4 or 5 for none. Using a PMRR threshold of 0.017 yields an associated true positive rate of 0.67 and false positive rate of 0.15 with average error of 30%. A V5 threshold of 57.6 gives an associated true positive rate of 0.67 and false positive rate of 0.05 with a 20% average error.
The metabolic radiation pneumonitis dose response was evaluated from post-treatment FDG-PET/CT imaging. Statistical modeling found a linear relationship. The FDG uptake dose response and V5 correlated with symptomatic radiation pneumonitis.
Radiation pneumonitis; Pulmonary injury; Computed tomography; Positron emission tomography
Static whole body PET/CT, employing the standardized uptake value (SUV), is considered the standard clinical approach to diagnosis and treatment response monitoring for a wide range of oncologic malignancies. Alternative PET protocols involving dynamic acquisition of temporal images have been implemented in the research setting, allowing quantification of tracer dynamics, an important capability for tumor characterization and treatment response monitoring. Nonetheless, dynamic protocols have been confined to single bed-coverage limiting the axial field-of-view to ~15–20 cm, and have not been translated to the routine clinical context of whole-body PET imaging for the inspection of disseminated disease. Here, we pursue a transition to dynamic whole body PET parametric imaging, by presenting, within a unified framework, clinically feasible multi-bed dynamic PET acquisition protocols and parametric imaging methods. We investigate solutions to address the challenges of: (i) long acquisitions, (ii) small number of dynamic frames per bed, and (iii) non-invasive quantification of kinetics in the plasma. In the present study, a novel dynamic (4D) whole body PET acquisition protocol of ~45min total length is presented, composed of (i) an initial 6-min dynamic PET scan (24 frames) over the heart, followed by (ii) a sequence of multi-pass multi-bed PET scans (6 passes x 7 bed positions, each scanned for 45sec). Standard Patlak linear graphical analysis modeling was employed, coupled with image-derived plasma input function measurements. Ordinary least squares (OLS) Patlak estimation was used as the baseline regression method to quantify the physiological parameters of tracer uptake rate Ki and total blood distribution volume V on an individual voxel basis. Extensive Monte Carlo simulation studies, using a wide set of published kinetic FDG parameters and GATE and XCAT platforms, were conducted to optimize the acquisition protocol from a range of 10 different clinically acceptable sampling schedules examined. The framework was also applied to six FDG PET patient studies, demonstrating clinical feasibility. Both simulated and clinical results indicated enhanced contrast-to-noise ratios (CNRs) for Ki images in tumor regions with notable background FDG concentration, such as the liver, where SUV performed relatively poorly. Overall, the proposed framework enables enhanced quantification of physiological parameters across the whole-body. In addition, the total acquisition length can be reduced from 45min to ~35min and still achieve improved or equivalent CNR compared to SUV, provided the true Ki contrast is sufficiently high. In the follow-up companion paper, a set of advanced linear regression schemes is presented to particularly address the presence of noise, and attempt to achieve a better trade-off between the mean-squared error (MSE) and the CNR metrics, resulting in enhanced task-based imaging.
The impulse response function of a radioligand is the most fundamental way to describe its pharmacokinetics and to assess its tissue uptake and retention pattern. This study investigates the impulse response function of [11C](+)McN5652, a radioligand used for positron emission tomography (PET) imaging of the serotonin transporter (SERT) in the brain. Dynamic PET studies were performed in eight healthy volunteers injected with [11C](+)McN5652 and subsequently with its pharmacologically inactive enantiomer [11C](−)McN5652. The impulse response function was calculated by deconvolution analysis of regional time-activity curves, and its peak value (fmax), its retention value at 75 minutes (fT), and its normalized retention (frel = fr/fmax) were obtained. Alternatively, compartmental models were applied to calculate the apparent total distribution volume (DVT) and its specific binding component (DVS). Both the noncompartmental (fT, frel) and the compartmental parameters (DV) were investigated with and without correction for nonspecific binding by simple subtraction of the corresponding value obtained with [11C](−)McN5652. The impulse response function obtained by deconvolution analysis demonstrated high tracer extraction followed by a slow decline in the form of a monoexponential function. Statistical analysis revealed that the best compartmental model in terms of analysis of variance F and condition number of the parameter variance-covariance matrix was the one that was based on a single tissue compartment with parameters k1and k2 and that also included the parameter of regional cerebral blood volume (BV). The parameter frel demonstrated low between-subject variance (coefficient of variation [CV] = 19%), a midbrain to cerebellum ratio of 1.85, and high correlation with the known density of SERT (r = 0.787 where r is the coefficient of linear correlation between the parameter and the known density of SERT). After correction for nonspecific binding, frel demonstrated further improvement in correlation (r = 0.814) and midbrain to cerebellum ratio (3.09). The variance of the distribution volumes was acceptable when the logarithmic transform lnDV was used instead of DV (17% for the three-parameter model), but correlation of this compartmental parameter was slightly less (r = 0.652 for the three-parameter model) than the correlation of the noncompartmental frel with the known density of SERT, and the midbrain to cerebellum ratio was only 1.5 (uncorrected) and 1.8 (corrected). At the expense of increasing variance, the correlation was increased after correction for nonspecific binding using the inactive enantiomer (r = 0.694; CV = 22%). These results indicate that the kinetics of [11C](+)McN5652 can best be described by a one-tissue compartment model with three parameters (k1, k2, and BV), and that both the noncompartmental parameter frel and the compartmental distribution volumes have the potential for quantitative estimation of the density of SERT. Further validation of the radioligand in experimental and clinical situations is warranted.
Serotonin transporter; Brain; Positron emission tomography; [11C](+)McN5652; Kinetic model; Impulse response function; Deconvolution analysis
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.
There is an unmet clinical need for an imaging method for quantification of hepatic blood perfusion. The purpose of the present study was to develop and validate a PET method using blood-to-cell clearance (K1) of 2-[18F]fluoro-2-deoxy-D-glucose (18F-FDG), 3-O-[11C]-methylglucose (11C-MG) or 2-[18F]fluoro-2-deoxy-D-galactose (18F-FDGal) as a measure of hepatic blood perfusion without the need of portal venous blood samples. We aimed to make the method as simple as possible with the perspective of future application to clinical studies. For this purpose, we examined the possibility of using 3-min data acquisition and a model-derived dual-input calculated from measurements of radioactivity concentrations in a peripheral artery.
Pigs (40 kg) underwent dynamic PET of the liver with 18F-FDG, 11C-MG or 18F-FDGal with simultaneous measurements of time-activity curves (TAC) in blood sampled from a femoral artery and the portal vein (PV); blood flow rates were measured in the hepatic artery (HA) and portal vein (PV) by transit-time flow-meters. Two input functions were compared: A measured dual-input and a model-derived dual-input, the latter with the PV TAC estimated from the measured arterial TAC and a previously validated one-parametric PV-model. K1 was estimated for each tracer by fitting compartmental models to the data comparing 3-min and 60-min data acquisitions and the two dual-input TACs.
Agreement between K1 estimated using the measured and the model-derived dual-input was good for all 3 tracers. For 18F-FDG and 11C-MG, K1 (3-min data acquisition, model-derived dual-input and one-tissue compartmental model) correlated to the measured blood perfusion (P = 0.01 and P = 0.07, respectively). For 18F-FDGal the correlation was not significant.
A simplified method for quantification of hepatic blood perfusion using 3-min dynamic 18F-FDG PET or 11C-MG PET with blood sampling from only a peripheral artery was developed. Parametric K1 images were constructed and showed homogeneous blood perfusion in these normal livers.
PET kinetics; molecular imaging; pharmacokinetics; liver PET; liver hemodynamics
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.
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
Positron emission tomography (PET) allows for the measurement of cerebral blood flow (CBF; based on [15O]H2O) and cerebral metabolic rate of glucose utilization (CMRglu; based on [18 F]-2-fluoro-2-deoxy-d-glucose ([18 F]FDG)). By using kinetic modeling, quantitative CBF and CMRglu values can be obtained. However, hardware limitations led to the development of semiquantitive calculation schemes which are still widely used. In this paper, the analysis of CMRglu and CBF scans, acquired on a current state-of-the-art PET brain scanner, is presented. In particular, the correspondence between nonlinear as well as linearized methods for the determination of CBF and CMRglu is investigated. As a further step towards widespread clinical applicability, the use of an image-derived input function (IDIF) is investigated.
Thirteen healthy male volunteers were included in this study. Each subject had one scanning session in the fasting state, consisting of a dynamic [15O]H2O scan and a dynamic [18 F]FDG PET scan, acquired at a high-resolution research tomograph. Time-activity curves (TACs) were generated for automatically delineated and for manually drawn gray matter (GM) and white matter regions. Input functions were derived using on-line arterial blood sampling (blood sampler derived input function (BSIF)). Additionally, the possibility of using carotid artery IDIFs was investigated. Data were analyzed using nonlinear regression (NLR) of regional TACs and parametric methods.
After quality control, 9 CMRglu and 11 CBF scans were available for analysis. Average GM CMRglu values were 0.33 ± 0.04 μmol/cm3 per minute, and average CBF values were 0.43 ± 0.09 mL/cm3 per minute. Good correlation between NLR and parametric CMRglu measurements was obtained as well as between NLR and parametric CBF values. For CMRglu Patlak linearization, BSIF and IDIF derived results were similar. The use of an IDIF, however, did not provide reliable CBF estimates.
Nonlinear regression analysis, allowing for the derivation of regional CBF and CMRglu values, can be applied to data acquired with high-spatial resolution current state-of-the-art PET brain scanners. Linearized models, applied to the voxel level, resulted in comparable values. CMRglu measurements do not require invasive arterial sampling to define the input function.
Cerebral blood flow; Cerebral metabolic rate of glucose consumption; [18 F]FDG; Full kinetic analysis; [15O]H2O; High-resolution research tomograph; Image-derived input function; Parametric images
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
We present a method for extracting arterial input functions from dynamic
[18F]FLT PET images of the head and neck, directly accounting for
the partial volume effect. The method uses two blood samples, for which the
optimum collection times are assessed.
Six datasets comprising dynamic PET images, co-registered computed tomography (CT)
scans and blood-sampled input functions were collected from four patients with
head and neck tumours. In each PET image set, a region was identified that
comprised the carotid artery (outlined on CT images) and surrounding tissue within
the voxels containing the artery. The time course of activity in the region was
modelled as the sum of the blood-sampled input function and a compartmental model
of tracer uptake in the surrounding tissue.
The time course of arterial activity was described by a mathematical function with
seven parameters. The parameters of the function and the compartmental model were
simultaneously estimated, aiming to achieve the best match between the modelled
and imaged time course of regional activity and the best match of the estimated
blood activity to between 0 and 3 samples. The normalised root-mean-square
(RMSnorm) differences and errors in areas under the curves (AUCs)
between the measured and estimated input functions were assessed.
A one-compartment model of tracer movement to and from the artery best described
uptake in the tissue surrounding the artery, so the final model of the input
function and tissue kinetics has nine parameters to be estimated. The estimated
and blood-sampled input functions agreed well when two blood samples, obtained at
times between 2 and 8 min and between 8 and 60 min, were used in the estimation
process (RMSnorm values of 1.1 ± 0.5 and AUC errors for the peak
and tail region of the curves of 15% ± 9% and 10% ± 8%, respectively). A
third blood sample did not significantly improve the accuracy of the estimated
Input functions for FLT-PET studies of the head and neck can be estimated well
using a one-compartment model of tracer movement and TWO blood samples obtained
after the peak in arterial activity.
Input function; Partial volume effect; Simultaneous estimation
We report on two cases of patients with fat-equivalent masses in computed tomography (CT), referred to our department for dynamic positron emission tomography/CT (dPET/CT) with 18F-fluorodeoxyglucose (18F-FDG) in order to investigate their dignity. Both qualitative and quantitative information, as derived from dPET/CTs, couldn’t exclude a high-grade liposarcoma: Visual evaluation, revealed a large hypermetabolic focus of intense 18F-FDG uptake in each patient (average SUVs 8.3 and 11.3). Regression-based parametric imaging demonstrated an enhanced distribution volume, which correlates to perfusion, and a high phosphorylation rate that correlates to cell viability. Kinetic analysis, based on a two-tissue compartment model demonstrated an enhanced FDG transport k1 and an enhanced phosphorylation rate k3. A non-compartmental approach based on fractal dimension revealed also enhanced values. However, final diagnosis was based on biopsy, which revealed hibernoma, a benign brown fat tumor. Brown adipose contains increased numbers of mitochondria and a high-rate of glucose metabolism. Therefore, they have increased FDG uptake. The evaluation of lipomatous lesions on CT, with high FDG uptake, should include the possibility of hibernoma as a differential diagnosis.
Hibernoma; Dynamic positron emission tomography/CT; 18F-fluorodeoxyglucose; Kinetic Modeling; Parametric imaging