A linear model for estimation of neurotransmitter response profiles from dynamic PET data

Abstract

The parametric ntPET model (p-ntPET) estimates the kinetics of neurotransmitter release from dynamic PET data with receptor-ligand radiotracers. Here we introduce a linearization (lp-ntPET) that is computationally efficient and can be applied to single scan data. lp-ntPET employs a non-invasive reference region input function and extends the LSRRM of Alpert et al. (2003) using basis functions to characterize the time course of neurotransmitter activation. In simulation studies, the temporal precision of neurotransmitter profiles estimated by lp-ntPET was similar to that of p-ntPET (standard deviation ~3 min for responses early in the scan) while computation time was reduced by several orders of magnitude. Violations of model assumptions such as activation-induced changes in regional blood flow or specific binding in the reference tissue have negligible effects on lp-ntPET performance. Application of the lp-ntPET method is demonstrated on [11C]raclopride data acquired in rats receiving methamphetamine, which yielded estimated response functions that were in good agreement with simultaneous microdialysis measurements of extracellular dopamine concentration. These results demonstrate that lp-ntPET is a computationally efficient, linear variant of ntPET that can be applied to PET data from single or multiple scan designs to estimate the time course of neurotransmitter activation.

Figure 1. Example response and basis functions

(A) Family of activation responses and (B) basis functions generated from them. To aid visualization, a small subset of functions is displayed and the basis functions are normalized by the integral of the corresponding response function in order to yield bases of a similar scale. Also note that the response curves in this subset all have the same onset time (t=0), whereas the entire set of functions includes profiles with a variety of start times.

Figure 2. Unconstrained fits of dual-scan data

Responses estimated using non-negative (NNLS; panels A–C) or weighted (WLS; panels D–F) least squares from dual-scan data with early (A,D), late (B,E), or no (C,F) NT response. Data were generated without model violations. Solid red curve: average of the estimated responses from 1000 simulated data sets expressed as percentage of the estimated baseline k_2a. Dashed red curves: envelope of ±1 standard deviation about the mean. Black curve: true neurotransmitter response. Agreement between true and estimated responses for late activation is good, but degraded compared to data sets with early activation. Responses estimated from null data sets lacking activation are temporally incoherent with the zero magnitude level enclosed within the ±1 s.d. interval.

Figure 3. Constrained fits of single- and dual-scan data

Comparison of responses estimated by lp-ntPET with WLS from dual-scan (A,B) or single-scan (C,D) data sets for late activation task. Data in upper panels include neurotransmitter release, while those in lower panels are null data sets. Responses were constrained to begin no earlier than five minutes before the challenge initiation. Results are presented as described in Figure 2. Note the strong correspondence between true and estimated responses, and between the performance of the model applied to dual-scan versus single-scan data sets.

Figure 4. Activation-induced change in blood flow

Responses estimated from dual-scan data with concomitant increased blood flow in the target region and decreased blood flow in reference region during activation. Data shown in upper panels include neurotransmitter release, while those in lower panels are null data sets. Results are presented as described in Figure 2. Changes in blood flow had little impact on the performance of lp-ntPET (compare to results in Figure 2 and Table 1). Outcomes with decreased flow in the reference region (and no effect on the target region) were similar.

Figure 5. Simultaneous PET-microdialysis experiments

Measured data and modeling results obtained from a rat that received intra-cranial infusion of methamphetamine (upper panels, A–C) and a control animal that received a sham infusion (lower panels, D–F). Baseline PET data from left striatum are shown in left panels (A,D) and activation data from right striatum are shown in middle column (B,E). Open circles: striatal PET data. Filled black circles: cerebellar PET data. Solid black curve: model fit obtained by lp-ntPET with WLS optimization. Dashed black curve: MRTM model fit. Neurotransmitter responses measured by microdialysis (left vertical axis) and estimated by lp-ntPET (right vertical axis) are plotted in the right panels (C,F). Filled gray circles: measured microdialysis data. Dashed gray curves: gamma variate function fitted to microdialysis data. Solid black curve: responses estimated by lp-ntPET. In the control animal, lp-ntPET and MRTM provide nearly identical fits (D,E); the response (F) estimated by lp-ntPET is not significant (p > 0.98 in all tests). In the animal that received drug, the fit from the MRTM model (no activation term) is poor while lp-ntPET provides a good fit to the data (A,B); the response estimated by lp-ntPET is significant (p < 10⁻⁷ in all tests) and in good agreement with microdialysis measurements of dopamine (C).