A novel machine learning based computational framework for homogenization of heterogeneous soft materials: application to liver tissue.

Real-time simulation of organs increases comfort and safety for patients during the surgery. Proper generalized decomposition (PGD) is an efficient numerical method with coordinate errors below 1 mm and response time below 0.1 s that can be used for simulated surgery. For input of this approach, nonlinear mechanical properties of each segment of the liver need to be calculated based on the geometries of the patient's liver extracted using medical imaging techniques. In this research work, a map of the mechanical properties of the liver tissue has been estimated with a novel combined method of the finite element (FE) optimization. Due to the existence of major-size vessels in the liver that makes the surrounding tissue anisotropic, the simulation of hyperelastic material with two different sections is computationally expensive. Thus, a homogenized, anisotropic, and hyperelastic model with the nearest response to the real heterogeneous model was developed and presented. Because of various possibilities of the vessel orientation, position, and size, homogenization has been carried out for adequate samples of heterogeneous models to train artificial neural networks (ANNs) as machine learning tools. Then, an unknown sample of heterogeneous material was categorized and mapped to its homogenized material parameters with the trained networks for the fast and low-cost generalization of our combined FE optimization method. The results showed the efficiency of the proposed novel machine learning based technique for the prediction of effective material properties of unknown heterogeneous tissues.