Two Non-linear Parametric Models of Contrast Enhancement for DCE-MRI of the Breast Amenable to Fitting Using Linear Least Squares

Abstract

This paper proffers two non-linear empirical parametric models—linear slope and Ricker—for use in characterising contrast enhancement in dynamic contrast enhanced (DCE) MRI. The advantage of these models over existing empirical parametric and pharmacokinetic models is that they can be fitted using linear least squares (LS). This means that fitting is quick, there is no need to specify initial parameter estimates, and there are no convergence issues. Furthermore the LS fit can itself be used to provide initial parameter estimates for a subsequent NLS fit (self-starting models). The results of an empirical evaluation of the goodness of fit (GoF) of these two models, measured in terms of both MSE and R^2, relative to a two-compartment pharmacokinetic model and the Hayton model are also presented. The GoF was evaluated using both routine clinical breast MRI data and a single high temporal resolution breast MRI data set. The results demonstrate that the linear slope model fits the routine clinical data better than any of the other models and that the two parameter self-starting Ricker model fits the data nearly as well as the three parameter Hayton model. This is also demonstrated by the results for the high temporal data and for several temporally sub-sampled versions of this data.