Modified Maximum Entropy Method and Estimating the AIF via DCE-MRI Data Analysis

Abstract

Background: For the kinetic models used in contrast-based medical imaging, the assignment of the arterial input function named AIF is essential for the estimation of the physiological parameters of the tissue via solving an optimization problem. Objective: In the current study, we estimate the AIF relayed on the modified maximum entropy method. The effectiveness of several numerical methods to determine kinetic parameters and the AIF is evaluated—in situations where enough information about the AIF is not available. The purpose of this study is to identify an appropriate method for estimating this function. Materials and Methods: The modified algorithm is a mixture of the maximum entropy approach with an optimization method, named the teaching-learning method. In here, we applied this algorithm in a Bayesian framework to estimate the kinetic parameters when specifying the unique form of the AIF by the maximum entropy method. We assessed the proficiency of the proposed method for assigning the kinetic parameters in the dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), when determining AIF with some other parameter-estimation methods and a standard fixed AIF method. A previously analyzed dataset consisting of contrast agent concentrations in tissue and plasma was used. Results and Conclusions: We compared the accuracy of the results for the estimated parameters obtained from the MMEM with those of the empirical method, maximum likelihood method, moment matching (“method of moments”), the least-square method, the modified maximum likelihood approach, and our previous work. Since the current algorithm does not have the problem of starting point in the parameter estimation phase, it could find the best and nearest model to the empirical model of data, and therefore, the results indicated the Weibull distribution as an appropriate and robust AIF and also illustrated the power and effectiveness of the proposed method to estimate the kinetic parameters.

Maximum Entropy Technique and Regularization Functional for Determining the Pharmacokinetic Parameters in DCE-MRI

“…In the previous work [ 76 , 77 ], the MET/MAP and MET/TLBO have been applied to estimate the ME distribution of the AIF along with the pharmacokinetic parameters. In the following a brief description of the MET/TLBO is provided.…”

“…In another study, we proposed two enhanced algorithms to estimate the AIF as a combination of Bayesian inference and optimization techniques. The first algorithm combines MET, teaching–learning-based optimization (TLBO) to assess the performance of observer in the classification tasks with existing data, and Bayesian methods to estimate the pharmacokinetic parameters [ 77 ]. Similar to other algorithms inspired by nature, TLBO is also a population-based approach and employs a population of solutions to obtain a global result [ 31 , 78 ].…”