The value of mathematical modelling in understanding contrast enhancement in CT with particular reference to the detection of hypovascular liver metastases

Abstract

Objective: Few subjects in body imaging have generated such intensive debate as that surrounding the optimising of strategies for the detection of liver metastases using contrast-enhanced Computed Tomography (CT). Despite this, research on the subject has been almost entirely focused on experimental studies, little attention having been paid to the value of theoretical analyses. The authors’ aim was to develop a relatively simple and robust mathematical model which could be implemented on a personal computer. Methods: Simple differential equations describing the distribution of contrast agent between intra- and extra-vascular spaces during an infusion are set up. An analytic solution is obtained for the plasma/blood concentrations as a fraction of time and a solution for the interstitial concentrations as a fraction of time is obtained by converting the differential equations to difference equations which are solved in a stepwise manner. Results: Vascular and hepatic parenchymal enhancement–time curves are generated which are in close agreement with expectations. The model may be used to compare different infusion regimes, e.g. lower versus higher dose, faster versus slower infusions, monophasic versus biphasic infusions and scan start delay. The implications of the results of the model for clinical protocol design are discussed and the special value of spiral/helical technology indicated. Conclusion: A simple mathematical model has been developed to model blood and tissue contrast enhancement in CT during contrast infusion. The model clarifies a number of issues related to contrast enhancement regimes for the study of the liver and these have been discussed.