Real-time biomechanical modeling of the liver using Machine Learning models trained on Finite Element Method simulations

[EN] The development of accurate real-time models of the biomechanical behavior of different organs and tissues still poses a challenge in the field of biomechanical engineering. In the case of the liver, specifically, such a model would constitute a great leap forward in the implementation of complex applications such as surgical simulators, computed-assisted surgery or guided tumor irradiation. In this work, a relatively novel approach for developing such a model is presented. It consists in the use of a machine learning algorithm, which provides real-time inference, trained on tens of thousands of simulations of the biomechanical behavior of the liver carried out by the finite element method on more than 100 different liver geometries. Considering a target accuracy threshold of 3 mm for the Euclidean Error, four different scenarios were modeled and assessed: a single liver with an arbitrary force applied (99.96% of samples within the accepted error range), a single liver with two simultaneous forces applied (99.84% samples in range), a single liver with different material properties and an arbitrary force applied (98.46% samples in range), and a much more general model capable of modeling the behavior of any liver with an arbitrary force applied (99.01% samples in range for the median liver). The results show that the Machine Learning models perform extremely well on all the scenarios, managing to keep the Mean Euclidean Error under 1 mm in all cases. Furthermore, the proposed model achieves working frequencies above 100Hz on modest hardware (with frequencies above 1000Hz being easily achievable on more powerful GPUs) thus fulfilling the real-time requirements. 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