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

[ Vol. 14 , Issue. 3 ]

Author(s):

Dianning He, Wei Qian, Lisheng Xu, Marta Zamora, Gregory S. Karczmar and Xiaobing Fan*   Pages 468 - 476 ( 9 )

Abstract:


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).

Keywords:

DCE-MRI, pharmacokinetic model, pure mathematical model, numerical simulations, contrast agent concentration curves, MLM.

Affiliation:

Sino-Dutch Biomedical and Information Engineering School, Northeastern University, Shenyang, Sino-Dutch Biomedical and Information Engineering School, Northeastern University, Shenyang, Sino-Dutch Biomedical and Information Engineering School, Northeastern University, Shenyang, Department of Radiology, The University of Chicago, Chicago, IL 60637, Department of Radiology, The University of Chicago, Chicago, IL 60637, Department of Radiology, The University of Chicago, Chicago, IL 60637

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