A new technique for solving nonlinear differential equations encountered in modeling of neuroreceptor-binding ligands

Abstract

For assessing neuroreceptor density with positron-emission tomography (PET), nonlinear differential equations consisting of products of the tracer concentrations are needed to describe the tracer kinetics of receptor-binding ligands. The authors have investigated an iterative solution technique for this type of nonlinear differential equation. The technique involves solving iteratively a sequence of linear differential equations that is related to the original nonlinear differential equation. The sequence of solution of these linear differential equations converges to the solution of the nonlinear differential equation. The technique is faster and more accurate than Runge-Kutta numerical integration technique. The solution technique can facilitate the investigation of the tracer kinetic characteristics of neuroreceptor-binding ligands and the estimation of neuroreceptor density from PET-collected kinetics of receptor-binding ligands.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>