Kinetic modeling, parameter estimation and model comparison in PET: Functional images of neurotransmitter dynamics and drug affinity
Positron Emission Tomography (PET) makes it possible to image molecular targets, in vivo, with high specificity. Kinetic models are used to fit PET data to quantify pertinent physiological properties of the target and to describe tracer-target dynamics. Traditional models estimate time-invariant parameters that reflect steady-state characteristics of binding of the tracer at the target. However, advances in modeling techniques have made it possible to detect transient time-varying interactions of the tracer and target. Our group has developed a suite of ‘ntPET’ models specifically tailored to detect and characterize brief drug-induced dopamine (DA) release (on the order of minutes), which has broad applications for studying drug addiction. The operational equations that describe the PET signal contain a term that models the effect of transient competitive binding between the tracer and endogenous DA molecules, at the DA receptor. Linear parametric ntPET (lp-ntPET) is the linearized version of the ntPET model. Thanks to linearization, lp-ntPET can be implemented to perform voxel-level parameter estimation with high computational efficiency. To implement linear estimation, parameters that describe the timing of the DA signal are discretized, and explicitly defined by a set of basis functions. The implementation of the model using discretized basis functions poses unique challenges for significance testing. Significance testing employs model comparison metrics to determine the significance of the improvement of the fit accomplished by including a basis function. The number of parameters in a model is crucial for the calculation of model selection metrics and controlling the false positive rate (FPR). We demonstrated the dependence of FPR on the number of bases and proposed a correction to the number of parameters in the model p^eff, which adapts to the number of bases used. Implementing model selection with p^effmaintained a stable FPR independent of number of bases. lp-ntPET may be used with the next generation brain PET scanner, the NeuroEXPLORER (NX), to classify DA signals based on their timing and amplitude. The NX will offer an order-of-magnitude improvement in detection sensitivity to counts compared to the current state-of-the-art, Siemens HRRT. We simulated [C-11]raclopride PET data acquired on the NX and HRRT in the presence of DA signals that varied in start-times, peak-times, and amplitudes. We assessed the detection sensitivity of lp-ntPET to each DA signal and evaluated classification thresholds for their ability to separate “early”- vs. “late”-peaking, and “low”- vs. “high”-amplitude events. To further refine the characterization of DA signals, we developed a weighted k-nearest neighbors algorithm to incorporate information from the neighborhood around each voxel to reclassify it, with a resulting level of certainty. We implemented a version of lp-ntPET incorporating a single basis function to detect cigarette smoking-induced DA responses in smokers, while treated with a nicotine (NIC) patch versus a placebo (PBO) patch. The effect of the NIC patch on DA release was highly localized, i.e., it was enhanced in some areas while diminished in others. In addition, nicotine metabolism ratio and pack-years affected the probability of DA activation in any voxel. These insights may inform the development of more targeted smoking cessation treatments. In a separate exploration of modeling in brain PET, we developed a method create images of target-occupancy binding parameters. Our group recently developed a novel method to obtain occupancy estimates at every voxel of the brain. Given a set of occupancy images and drug plasma concentrations, we applied the Emax model, voxel-by-voxel, to create images of EC50, maximum occupancy, and Hill coefficient. We applied the method to a [C-11]flumazenil data set to estimate binding parameters for candidate ligand CVL-865. We evaluated the stability of the Emax model when 1, 2, or all 3 binding parameters were estimated. We explored the bias-variance tradeoff and the goodness-of-fit with three implementations of the Emax model, using model selection criteria. Finally, we discussed the implications of spatially varying EC¬50 and how dose ranges should be selected in target-occupancy PET studies in order to account for this phenomenon.