Estimation of the elastic parameters of human liver biomechanical models by means of medical images and evolutionary computation

This paper presents a method to computationally estimate the elastic parameters of two biomechanical models proposed for the human liver. The method is aimed at avoiding the invasive measurement of its mechanical response. The chosen models are a second order Mooney-Rivlin model and an Ogden model. A novel error function, the geometric similarity function (GSF), is formulated using similarity coefficients widely applied in the field of medical imaging (Jaccard coefficient and Hausdorff coefficient). This function is used to compare two 3D images. One of them corresponds to a reference deformation carried out over a finite element (FE) mesh of a human liver from a computer tomography image, whilst the other one corresponds to the FE simulation of that deformation in which variations in the values of the model parameters are introduced. Several search strategies, based on GSF as cost function, are developed to accurately find the elastics parameters of the models, namely: two evolutionary algorithms (scatter search and genetic algorithm) and an iterative local optimization. The results show that GSF is a very appropriate function to estimate the elastic parameters of the biomechanical models since the mean of the relative mean absolute errors committed by the three algorithms is lower than 4%.