A computer simulation study on the effects of input function measurement noise in tracer kinetic modeling with positron emission tomography (PET)

A Comparison of Arterial Input Function Interpolation Methods for Patlak Plot Analysis of 68Ga-PSMA-11 PET Prostate Cancer Studies

Positron emission tomography (PET) imaging enables quantitative assessment of tissue physiology. Dynamic pharmacokinetic analysis of PET images requires accurate estimation of the radiotracer plasma input function to derive meaningful parameter estimates, and small discrepancies in parameter estimation can mimic subtle physiologic tissue variation. This study evaluates the impact of input function interpolation method on the accuracy of Patlak kinetic parameter estimation through simulations modeling the pharmacokinetic properties of [68Ga]-PSMA-11. This study evaluated both trained and untrained methods. Although the mean kinetic parameter accuracy was similar across all interpolation models, the trained node weighting interpolation model estimated accurate kinetic parameters with reduced overall variability relative to standard linear interpolation. Trained node weighting interpolation reduced kinetic parameter estimation variance by a magnitude approximating the underlying physiologic differences between normal and diseased prostatic tissue. Overall, this analysis suggests that trained node weighting improves the reliability of Patlak kinetic parameter estimation for [68Ga]-PSMA-11 PET.

Whole-body dynamic imaging with continuous bed motion PET/CT

Most dynamic imaging protocols require long scan times that are beyond the range of what can be supported in a routine clinical environment and suffer from various difficulties related to step and shoot imaging techniques. In this short communication, we describe continuous bed motion (CBM) imaging techniques to create clinically relevant 15 min whole-body dynamic PET imaging protocols. We also present initial data that suggest that these CBM methods may be sufficient for quantitative analysis of uptake rates and rates of glucose metabolism. Multipass CBM PET was used in conjunction with a population-based input function to perform Patlak modeling of normal tissue. Net uptake rates were estimated and metabolic rates of glucose were calculated. Estimations of k₃ (K_i/V_d) were calculated along with modeling of liver regions of interest to assess model stability. Calculated values of metabolic rates of glucose were well within normal ranges found in the previous literature. CBM techniques can potentially be used clinically to obtain reliable, quantitative multipass whole-body dynamic PET data. Values calculated for normal brain were shown to be within previously published values for normal brain glucose metabolism.

Noninvasive image derived heart input function for CMRglc measurements in small animal slow infusion FDG PET studies

Absolute quantitation of the cerebral metabolic rate for glucose (CMRglc) can be obtained in positron emission tomography (PET) studies when serial measurements of the arterial [(18)F]-fluoro-deoxyglucose (FDG) input are available. Since this is not always practical in PET studies of rodents, there has been considerable interest in defining an image-derived input function (IDIF) by placing a volume of interest (VOI) within the left ventricle of the heart. However, spill-in arising from trapping of FDG in the myocardium often leads to progressive contamination of the IDIF, which propagates to underestimation of the magnitude of CMRglc. We therefore developed a novel, non-invasive method for correcting the IDIF without scaling to a blood sample. To this end, we first obtained serial arterial samples and dynamic FDG-PET data of the head and heart in a group of eight anaesthetized rats. We fitted a bi-exponential function to the serial measurements of the IDIF, and then used the linear graphical Gjedde-Patlak method to describe the accumulation in myocardium. We next estimated the magnitude of myocardial spill-in reaching the left ventricle VOI by assuming a Gaussian point-spread function, and corrected the measured IDIF for this estimated spill-in. Finally, we calculated parametric maps of CMRglc using the corrected IDIF, and for the sake of comparison, relative to serial blood sampling from the femoral artery. The uncorrected IDIF resulted in 20% underestimation of the magnitude of CMRglc relative to the gold standard arterial input method. However, there was no bias with the corrected IDIF, which was robust to the variable extent of myocardial tracer uptake, such that there was a very high correlation between individual CMRglc measurements using the corrected IDIF with gold-standard arterial input results. Based on simulation, we furthermore find that electrocardiogram-gating, i.e. ECG-gating is not necessary for IDIF quantitation using our approach.

Kinetic quantitation of cerebral PET-FDG studies without concurrent blood sampling: statistical recovery of the arterial input function

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 (18)F -Fluorodeoxyglucose (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.

A general algorithm for optimal sampling schedule design in nuclear medicine imaging

Optimal sampling schedule (OSS) is of great interest in biomedical experiment design, as it can improve the physiological parameter estimation precision and significantly reduce the samples required. A number of well designed algorithms and software packages have been developed, which deal with the instantaneous measurements at discrete times. However, in nuclear medicine tracer kinetic studies, the imaging systems, such as positron emission tomography (PET) and single photon emission computed tomography (SPECT), take measurements (images) based on continuous accumulation over time intervals. In this case, the existing algorithms cannot be used to design OSS so as to reduce the image frame numbers. In this paper, a general OSS design algorithm for the accumulative measurement is proposed. The potential usefulness of the algorithm is demonstrated by its designing OSS in [18F] fluoro-2-deoxy-D-glucose (FDG) studies with PET to estimate the local cerebral metabolic rate of glucose. The robustness of parameter estimation using the OSS with respect to intra-subject and inter-subject parameter variations is also presented.

Optimal image sampling schedule for both image-derived input and output functions in PET cardiac studies

Optimal sampling schedule (OSS) design for both image-derived input and output functions in tracer kinetic modeling with positron emission tomography (PET) is investigated. This problem is very important in noninvasive PET dynamic cardiac studies where both the input function, i.e., the plasma time-activity curve (PTAC), and the output function, i.e., the tissue time-activity curve (TTAC), are obtained simultaneously from the same sequence of PET images. The integral PET measurement is used in this study. The spillover correction for the cross contaminations in cardiac studies is incorporated into the OSS design procedure. A new target function based on the D-optimal criterion involving both the input and output sensitivity functions is proposed. The fluorodeoxyglucose (FDG) model and a six-parameter PTAC model are used to illustrate the simultaneous OSS design for both the PTAC and TTAC. An OSS design consisting of six different scanning intervals is derived. Computer simulations are performed based on the estimated parameters from real studies to evaluate the effectiveness of the OSS. The double modeling approach is used in parameter estimation to simultaneously estimate the parameters involved. The results have shown that, for a wide range of parameter variations, the OSS is as effective as a conventional sampling schedule (CSS) and comparable parameter estimates can be obtained. Compared with the use of the CSS, the use of the OSS leads to an approximately 70% reduction in the storage space and data processing time.

Estimation of myocardial glucose utilisation with PET using the left ventricular time-activity curve as a non-invasive input function

The validation study is described of a new modelling method that has been developed, using tracer kinetic modelling with positron emission tomography (PET) to achieve non-invasive measurement of myocardial metabolic rate of glucose (MMRGlc). Eight data sets obtained from dynamic cardiac PET 2-[18F]fluoro-2-deoxy-D-glucose (FDG) studies on human subjects are employed, and the estimation of MMRGlc using both the new and traditional methods is compared. The results from all eight human FDG studies are consistent with those from previous computer simulations. With the new method, the estimated mean of K (a parameter directly proportional to MMRGlc) increases by about 8%, and that of k 4 (the rate constant of FDG dephosphorylation) decreases by about 48%. The approach should be more suitable for use in dynamic cardiac PET studies when non-invasive means are used to obtain the plasma time-activity curve from left-ventricle PET images.

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

Positron emission tomography (PET) is an important tool for enabling quantification of human brain function. However, quantitative studies using tracer kinetic modeling require the measurement of the tracer time-activity curve in plasma (PTAC) as the model input function. It is widely believed that the insertion of arterial lines and the subsequent collection and processing of the biomedical signal sampled from the arterial blood are not compatible with the practice of clinical PET, as it is invasive and exposes personnel to the risks associated with the handling of patient blood and radiation dose. Therefore, it is of interest to develop practical noninvasive measurement techniques for tracer kinetic modeling with PET. In this paper, a technique is proposed to extract the input function together with the physiological parameters from the brain dynamic images alone. The identifiability of this method is tested rigorously by using Monte Carlo simulation. The results show that the proposed method is able to quantify all the required parameters by using the information obtained from two or more regions of interest (ROI's) with very different dynamics in the PET dynamic images. There is no significant improvement in parameter estimation for the local cerebral metabolic rate of glucose (LCMRGlc) if the number of ROI's are more than three. The proposed method can provide very reliable estimation of LCMRGlc, which is our primary interest in this study.

Towards the reduction of dynamic image data in position emission tomography studies

In this study, we propose a method and investigate the reduction of dynamic image data with positron emission tomography (PET). The method is based upon the use of sampling schedules with a reduced number of scanning intervals and the use of an integral model in the cost function of nonlinear regression. The application of this method is illustrated by the problem of estimating the metabolic rate of glucose with the [18F]2-fluoro-2-deoxyglucose (FDG) model. Computer simulations were performed using various sampling schedules with scanning intervals of different lengths. The results were compared in terms of the accuracy and precision of the estimated parameters. It has been found that the use of sampling schedules with a reduced number of scanning intervals in conjunction with the integral model is very effective. The number of images in dynamic PET FDG studies can be reduced by a factor of 4.5 without losing the accuracy and precision of the parameter estimates.

Optimized sampling and parameter estimation for quantification in whole body PET

Whole-body positron emission tomography (PET) has recently emerged as an important imaging tool for cancer detection and staging. Initial applications of the technique have been primarily qualitative. One of the major reasons is the limits imposed by kinetically undersampled data over the whole body, as opposed to the standard method of continuous dynamic sampling in one body location. In this paper, a new estimation method using weighted nonlinear least squares (WNLS) for the first bed position and Bayesian regression (BR) for subsequent positions is proposed. A general criterion for designing optimal sampling schedules which maximizes the measurement information with multiple bed positions is developed. The overall approach is illustrated with the problem of estimating the metabolic rate of glucose (MRGLu) in tumors at different axial positions (image bed positions) in the body by using computer simulations and patient data. The results show that estimates of MRGLu using sparse data and the optimized Bayesian approach are comparable with those obtained by standard methods and fully sampled data. This study demonstrates the potential of the technique described for quantification where several bed positions have to be used to image all the regions of interest (ROI).

Tracer kinetic modelling of receptor data with mathematical metabolite correction

Quantitation of metabolic processes with dynamic positron emission tomography (PET) and tracer kinetic modelling relies on the time course of authentic ligand in plasma, i.e. the input curve. The determination of the latter often requires the measurement of labelled metabolites, a laborious procedure. In this study we examined the possibility of mathematical metabolite correction, which might obviate the need for actual metabolite measurements. Mathematical metabolite correction was implemented by estimating the input curve together with kinetic tissue parameters. The general feasibility of the approach was evaluated in a Monte Carlo simulation using a two tissue compartment model. The method was then applied to a series of five human carbon-11 iomazenil PET studies. The measured cerebral tissue time-activity curves were fitted with a single tissue compartment model. For mathematical metabolite correction the input curve following the peak was approximated by a sum of three decaying exponentials, the amplitudes and characteristic half-times of which were then estimated by the fitting routine. In the simulation study the parameters used to generate synthetic tissue time-activity curves (K1-k4) were refitted with reasonable identifiability when using mathematical metabolite correction. Absolute quantitation of distribution volumes was found to be possible provided that the metabolite and the kinetic models are adequate. If the kinetic model is oversimplified, the linearity of the correlation between true and estimated distribution volumes is still maintained, although the linear regression becomes dependent on the input curve. These simulation results were confirmed when applying mathematical metabolite correction to the [11C]iomazenil study. Estimates of the distribution volume calculated with a measured input curve were linearly related to the estimates calculated using mathematical metabolite correction with correlation coefficients >0.990. However, the slope of the regression line displayed considerable variability among the subjects (0.33-0.95), demonstrating that absolute quantitation of the distribution volume was impaired. Mathematical metabolite correction is a feasible method and may prove useful in cases where actual metabolite data cannot be obtained. The potential for absolute quantitation seems limited, but the method allows the quantitative assessment of regional ratios of receptor measures.

A new double modeling approach for dynamic cardiac PET studies using noise and spillover contaminated LV measurements

A new double modeling approach for dynamic cardiac studies with positron emission tomography (PET) to estimate physiological parameters is proposed. This approach is exemplified by tracer fluorodeoxyglucose (FDG) studies and estimation of myocardial metabolic rate of glucose (MMRGlc). A separate input function model characterising the tracer kinetics in plasma is used to account for the measurement noise and spillover problems of the input curve obtained from the left ventricular region on the PET images. Measured left ventricle (LV) plasma time-activity and tissue time-activity curves are fitted simultaneously with cross contaminations by this input function model and the FDG model. The results indicate that the MMRGlc can be estimated much more accurately and reliably by this new approach. Compared with the traditional method, an improvement of about 20% in the estimated MMRGlc was achieved when the bidirectional spillover fractions are 20% at different noise levels studied. This new double modeling approach using two models fitting both the input and the output functions simultaneously is expected to be generally applicable to a broad range of system modeling.

Optimal image sampling schedule: a new effective way to reduce dynamic image storage space and functional image processing time

An optimal image sampling schedule for tracer dynamic studies with positron emission tomography (PET) is proposed. This schedule incorporates the characteristics of PET measurement and uses a new cost function and the D-optimal criterion. A detailed case study of the estimation of the local cerebral metabolic rate of glucose (LCMRGLc) using the tracer fluorodeoxyglucose (FDG) and the four-parameter FDG model is presented. As the sampling schedule designed requires only four dynamic images, the storage space and data processing time are greatly reduced, while the precision of the parameter estimates is almost the same as that achieved with a commonly used schedule. The effects of intersubject and intrasubject parameter variations on parameter estimation with the use of this optimal sampling schedule are investigated by computer simulation. The simulation results show that the estimation of parameters is sufficiently robust with respect to these intersubject and intrasubject variations. The optimal sampling schedule is quite suitable therefore for PET regional parameter estimation, as well as for image-wide parameter estimation, for different subjects.