Two non-linear parametric models of enhancement for breast DCE-MRI that can be fitted using linear least squares
Paper in proceeding, 2011
The interpretation of dynamic contrast enhanced (DCE) MR images of the breast is predicated on the assessment of tissue enhancement kinetics. Both pharmacokinetic (PK) and empirical parametric (EP) models have been developed to quantify this change in enhancement. The former aim to measure physiologically meaningful parameters while the latter seek to measure the shape of the enhancement curve. Given that different PK models can yield markedly different estimates of the same physiological parameter (because of model assumptions) and that such models need to be fitted using non-linear least squares (NLS) which is in itself problematic (need to specify starting values, convergence issues), EP models remain of interest. Herein we propose two such models—linear-slope  and Ricker —which have the advantage that they can be fitted using linear least squares (LS) meaning that fitting is quick and that there is no need to specify initial parameter estimates. Furthermore, if desired, the LS fit can be used to provide parameter estimates for a subsequent NLS fit. The results of an empirical evaluation of the goodness-of-fit (GoF) of these two models relative to the pharmacokinetically-inspired Hayton model , and the simplified gamma-variate model  are also presented.