Computation of variance in compartment model parameter estimates from dynamic PET data

Towards Improved Pharmacokinetic Models for the Analysis of Transporter-Mediated Hepatic Disposition of Drug Molecules with Positron Emission Tomography

Positron emission tomography (PET) imaging with radiolabeled drugs holds great promise to assess the influence of membrane transporters on hepatobiliary clearance of drugs. To exploit the full potential of PET, quantitative pharmacokinetic models are required. In this study, we evaluated the suitability of different compartment models to describe the hepatic disposition of [11C]erlotinib as a small-molecule model drug which undergoes transporter-mediated hepatobiliary excretion. We analyzed two different, previously published data sets in healthy volunteers, in which a baseline [11C]erlotinib PET scan was followed by a second PET scan either after oral intake of unlabeled erlotinib (300 mg) or after intravenous infusion of the prototypical organic anion-transporting polypeptide inhibitor rifampicin (600 mg). We assessed a three-compartment (3C) and a four-compartment (4C) model, in which either a sampled arterial blood input function or a mathematically derived dual input function (DIF), which takes the contribution of the portal vein to the liver blood supply into account, was used. Both models provided acceptable fits of the observed PET data in the liver and extrahepatic bile duct and gall bladder. Changes in model outcome parameters between scans were consistent with the involvement of basolateral hepatocyte uptake and canalicular efflux transporters in the hepatobiliary clearance of [11C]erlotinib. Our results demonstrated that inclusion of a DIF did not lead to substantial improvements in model fits. The models developed in this work represent a step forward in applying PET as a tool to assess the impact of hepatic transporters on drug disposition and their involvement in drug-drug interactions.

Rapid computation of single PET scan rest-stress myocardial blood flow parametric images by table look up

PURPOSE

We have recently reported a method for measuring rest-stress myocardial blood flow (MBF) using a single, relatively short, PET scan session. The method requires two IV tracer injections, one to initiate rest imaging and one at peak stress. We previously validated absolute flow quantitation in ml/min/cc for standard bull's eye, segmental analysis. In this work, we extend the method for fast computation of rest-stress MBF parametric images.

METHODS

We provide an analytic solution to the single-scan rest-stress flow model which is then solved using a two-dimensional table lookup method (LM). Simulations were performed to compare the accuracy and precision of the lookup method with the original nonlinear method (NLM). Then the method was applied to 16 single scan rest/stress measurements made in 12 pigs: seven studied after infarction of the left anterior descending artery (LAD) territory, and nine imaged in the native state. Parametric maps of rest and stress MBF as well as maps of left (f_LV ) and right (f_RV ) ventricular spill-over fractions were generated. Regions of interest (ROIs) for 17 myocardial segments were defined in bull's eye fashion on the parametric maps. The mean of each ROI was then compared to the rest (K_1r ) and stress (K_1s ) MBF estimates obtained from fitting the 17 regional TACs with the NLM.

RESULTS

In simulation, the LM performed as well as the NLM in terms of precision and accuracy. The simulation did not show that bias was introduced by the use of a predefined two-dimensional lookup table. In experimental data, parametric maps demonstrated good statistical quality and the LM was computationally much more efficient than the original NLM. Very good agreement was obtained between the mean MBF calculated on the parametric maps for each of the 17 ROIs and the regional MBF values estimated by the NLM (K_1mapLM  = 1.019 × K_1ROINLM  + 0.019, R²  = 0.986; mean difference = 0.034 ± 0.036 mL/min/cc).

CONCLUSIONS

We developed a table lookup method for fast computation of parametric imaging of rest and stress MBF. Our results show the feasibility of obtaining good quality MBF maps using modest computational resources, thus demonstrating that the method can be applied in a clinical environment to obtain full quantitative MBF information.

Dynamic PET simulator via tomographic emission projection for kinetic modeling and parametric image studies

PURPOSE

To develop and evaluate a fast and simple tool called dpetstep (Dynamic PET Simulator of Tracers via Emission Projection), for dynamic PET simulations as an alternative to Monte Carlo (MC), useful for educational purposes and evaluation of the effects of the clinical environment, postprocessing choices, etc., on dynamic and parametric images.

METHODS

The tool was developed in matlab using both new and previously reported modules of petstep (PET Simulator of Tracers via Emission Projection). Time activity curves are generated for each voxel of the input parametric image, whereby effects of imaging system blurring, counting noise, scatters, randoms, and attenuation are simulated for each frame. Each frame is then reconstructed into images according to the user specified method, settings, and corrections. Reconstructed images were compared to MC data, and simple Gaussian noised time activity curves (GAUSS).

RESULTS

dpetstep was 8000 times faster than MC. Dynamic images from dpetstep had a root mean square error that was within 4% on average of that of MC images, whereas the GAUSS images were within 11%. The average bias in dpetstep and MC images was the same, while GAUSS differed by 3% points. Noise profiles in dpetstep images conformed well to MC images, confirmed visually by scatter plot histograms, and statistically by tumor region of interest histogram comparisons that showed no significant differences (p < 0.01). Compared to GAUSS, dpetstep images and noise properties agreed better with MC.

CONCLUSIONS

The authors have developed a fast and easy one-stop solution for simulations of dynamic PET and parametric images, and demonstrated that it generates both images and subsequent parametric images with very similar noise properties to those of MC images, in a fraction of the time. They believe dpetstep to be very useful for generating fast, simple, and realistic results, however since it uses simple scatter and random models it may not be suitable for studies investigating these phenomena. dpetstep can be downloaded free of cost from https://github.com/CRossSchmidtlein/dPETSTEP.

Quality and precision of parametric images created from PET sinogram data by direct reconstruction: proof of concept

We have previously implemented the direct reconstruction of dense kinetic model parameter images ("parametric images") from sinogram data, and compared it to conventional image domain kinetic parameter estimation methods . Although it has been shown that the direct reconstruction algorithm estimates the kinetic model parameters with lower root mean squared error than the conventional image domain techniques, some theoretical obstacles remain. These obstacles include the difficulty of evaluating the accuracy and precision of the estimated parameters. In image domain techniques, the reconstructed time activity curve (TAC) and the model predicted TAC are compared, and the goodness-of-fit is evaluated as a measure of the accuracy and precision of the estimated parameters. This approach cannot be applied to the direct reconstruction technique as there are no reconstructed TACs. In this paper, we propose ways of evaluating the precision and goodness-of-fit of the kinetic model parameters estimated by the direct reconstruction algorithm. Specifically, precision of the estimates requires the calculation of variance images for each parameter, and goodness-of-fit is addressed by reconstructing the difference between the measured and the fitted sinograms. We demonstrate that backprojecting the difference from sinogram space to image space creates error images that can be examined for goodness-of-fit and model selection purposes. The presence of nonrandom structures in the error images may indicate an inadequacy of the kinetic model that has been incorporated into the direct reconstruction algorithm. We introduce three types of goodness-of-fit images. We propose and demonstrate a number-of-runs image as a means of quantifying the adequacy or deficiency of the model. We further propose and demonstrate images of the F statistic and the change in the Akaike Information Criterion as devices for identifying the statistical advantage of one model over another at each voxel. As direct reconstruction to parametric images proliferates, it will be essential for imagers to adopt methods such as those proposed herein to assess the accuracy and precision of their parametric images.