Using Numerical Simulations and Experiments to Compare Different Pure Mathematical Models for Analyzing Dynamic Contrast Enhanced MRI Data

Objective: Numerical simulations and experiments were performed to compare eight pure mathematical models for fitting the contrast agent concentration curves (C(t)) obtained from dynamic contrast enhanced (DCE) MRI data. Methods: For simulations, randomly generated pharmacokinetic parameters (Ktrans and ve) were used to calculate the C(t) using the standard Tofts model of DCE-MRI. For experiments, DCE-MRI data of the Copenhagen rats with implanted prostate tumors on the hind limb were acquired with a temporal resolution of ~5 sec at 4.7 Tesla small animal scanner. A total of eight pure mathematical models, including empirical mathematical models with three (EMM3), four (EMM4), and five parameters (EMM), a modified logistic model (MLM), a modified sigmoidal function (MSF), the Weibull model, an extended phenomenological universalities (EU1) and a 5th order of polynomial (POLY5) were compared to fitting the C(t). The normalized root mean square errors (NRMSEs) were calculated to measure the goodness of fits. Results: The results showed that the EMM provided the best fitting to C(t) among eight models. For most of the experiment cases, the four-parameter models had significantly smaller errors (p < 0.05) than the three-parameter models. Conclusion: The pure mathematical models were not equal even if they had the same number of parameters. The EMM model could be used to accurately fit a variety of C(t).