Analysis Of Mathematical Model For The Pharmacokinetic Process Of [18f]-2flouro-Deoxyglucose

Abstract

Parametric imaging is a compartmental approach that processes nuclear imaging data to estimate the spatial distribution of the kinetic parameters governing tracer flow. The aim of this thesis is to analyzed the Mathematical model for the pharmacokinetic process of radiopharmaceutic in the tissue, using Laplace transform method. When the tracer is administered intravenously absorption is complete and it is available in the bloodstream to be distributed throughout the whole body in all tissues and fluids, then eliminated. This kinetic mathematical model define a relation ship between the concentration of the radioactive tracer in a given tissue and the concentration of radioactive tracer in the plasma. This analysis of compartmental model is described by a system of two differential equations, where each equation represents the sum of all the transfer rates to and from a specific compartments. The transport of [18F] FDG across the arterial blood is very fast in the first ten minutes and then decreases slowly. The thesis show actual uptake of [18F]FDG in arterial tissue. The model is stable, positive and well posed. We have introduced a quantitative analysis method that provides a direct estimate of the metabolic rate of [18F]FDG in arterial tissue. Key words: Derivative, Laplace transform, Heaviside function,[18F]FDG.