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.
Highlights
Determining the probability density function of a random variable based on observations is a major and old issue in statistics
Various parametric and non-parametric methods have been introduced for the estimation of the probability density function for a random variable based on observations, but there is very limited work reported on the optimization methods
To better evaluate the desired method (MMEM), we considered the data of 12 more patients in total
Summary
Determining the probability density function of a random variable based on observations is a major and old issue in statistics. Various parametric and non-parametric methods have been introduced for the estimation of the probability density function for a random variable based on observations, but there is very limited work reported on the optimization methods. The principle of maximum entropy, as a method of statistical inference, is due to Jaynes [1] His idea is that this principle leads to the selection of a probability density function that is consistent with our knowledge and introduces no unwarranted information. 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. 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 the results indicated the Weibull distribution as an appropriate and robust AIF and illustrated the power and effectiveness of the proposed method to estimate the kinetic parameters
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