Compartmental modelling for magnetic resonance renography

Abstract

A basic formalism is presented for generating and interpreting compartmental models for dynamic contrast-enhanced MRI data in the kidney. A graphical convention is introduced to represent and design compartmental models in a transparent and physically intuitive manner. A systematic system of notations and a simple set of rules allows direct translation of the graphical representation into a mathematical solution. The rules are derived from the physical principle of mass conservation, and the interpretation provided by the general tracer-kinetic theory of linear and stationary systems. The power of the formalism is illustrated using examples of models that have been proposed in the literature on perfusion MRI, and by generating a number of advanced models that may be of use in the kidney.