Amini Farsani Zahra, Schmid Volker J
Statistics Department, School of Science, Lorestan University, Khorramabad 68151-44316, Iran.
Bayesian Imaging and Spatial Statistics Group, Institute of Statistics, Ludwig-Maximilians-Universität München, Ludwigstraße 33, 80539 Munich, Germany.
Entropy (Basel). 2022 Jan 20;24(2):155. doi: 10.3390/e24020155.
: 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. : 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. : 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. : 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.
对于基于对比的医学成像中使用的动力学模型,名为动脉输入函数(AIF)的赋值对于通过解决优化问题来估计组织的生理参数至关重要。在当前研究中,我们基于改进的最大熵方法估计AIF。在无法获得足够关于AIF信息的情况下,评估了几种确定动力学参数和AIF的数值方法的有效性。本研究的目的是确定一种估计该函数的合适方法。改进算法是最大熵方法与一种名为教学学习方法的优化方法的混合。在此,我们在贝叶斯框架中应用此算法,通过最大熵方法指定AIF的唯一形式时估计动力学参数。当使用其他一些参数估计方法和标准固定AIF方法确定AIF时,我们评估了所提出方法在动态对比增强磁共振成像(DCE-MRI)中赋值动力学参数的熟练度。使用了一个先前分析过的数据集,该数据集包含组织和血浆中的造影剂浓度。我们将从MMEM获得的估计参数结果的准确性与经验方法、最大似然方法、矩匹配(“矩量法”)、最小二乘法、改进的最大似然方法以及我们之前工作的结果进行了比较。由于当前算法在参数估计阶段不存在起点问题,它可以找到与数据的经验模型最佳且最接近的模型,因此,结果表明威布尔分布是一种合适且稳健的AIF,并且还说明了所提出方法估计动力学参数的能力和有效性。