Forecasting the Pharmacokinetics With Limited Early Frames in Dynamic Brain PET Imaging Using Neural Ordinary Differential Equation

Abstract

In dynamic brain positron emission tomography (PET) studies, acquiring a time series of images, typically lasting more than an hour, is necessary to derive pharmacokinetic parameters. Analytically, these parameters are estimated by establishing kinetic models such as compartment models that consist of sets of ordinary differential equations (ODE), and by fitting the sparse time-activity curve (TAC) of the tracer. Yet, these models are simplified approximations of highly complex underlying processes, and sufficient samples of TAC are required throughout the entire acquisition, which is not only impractical but also hindered by patient involuntary motion and intrinsic noise. Therefore, recovering samples in missing timeframes is often required, which, in practice, is achieved by interpolation or extrapolation. Here, we introduce a novel deep-learning-based method that utilizes neural ODE (N-ODE) to predict TAC in the extended timeframes by mimicking analytical method in a datadriven manner. By training N-ODE to solve and fit sets of ODE such that the solution replicates the observed TAC, the N-ODE converges to the functional shapes that best describe the underlying pharmacokinetic processes. We customized N-ODE to predict the full-dynamic images (12 frames, 60min), hence pharmacokinetic parameters, given limited early-frame images (7 to 9 frames, 20 to 30min). For proof of concept, the proposed N-ODE was applied to simulated and clinical 18 F-PI-2620 brain PET. We demonstrated that the proposed N-ODE delivered promising performance, indicated by bias, variance, and mean absolute error as well as pharmacokinetic parameters such as rate constants, standardized uptake value ratio (SUVr), and binding potential (BPND).

On the Applications of Neural Ordinary Differential Equations in Medical Image Analysis

“…Recent endeavors [82][83][84] have attempted to incorporate NODE into the medical data generation domain. Since NODE is time-continuous, it allows for smooth interpolation between observed data points.…”

“…Since NODE is time-continuous, it allows for smooth interpolation between observed data points. Hong et al [82] present a NODE-based method for forecasting pharmacokinetic parameters in dynamic brain positron emission tomography (PET) imaging. Compared with traditional methods, such as interpolation or extrapolation require sufficient samples of the time-activity curve (TAC) throughout the entire acquisition, which is not always practical due to patient motion and noise.…”