Tissue growth and remodeling (G&R) has been modeled in a continuum mechanics framework with an approach similar to plasticity named 'finite growth model'. Computationally, G&R has been simulated with custom finite element implementations. However, these computational implementations are computationally expensive and require an expert modeler to setup for any new set of parameters, boundary or initial conditions. Thus, current models capture the overall trends of G&R in different applications but are difficult to calibrate, cannot be evaluated easily, and ignore mechanical and biological uncertainty. To address these limitations, we leverage machine learning tools to replace the finite element simulations with an inexpensive surrogate with quantified epistemic uncertainty. Specifically, we look at skin growth during tissue expansion and propose a multi-fidelity Gaussian process surrogate to replace the finite element solver. The methodology can be extended to other applications of G&R. We have published one article and the code is available through Bitbucket (link below).
Lee, Taeksang, Ilias Bilionis, and Adrian Buganza Tepole. "Propagation of uncertainty in the mechanical and biological response of growing tissues using multi-fidelity Gaussian process regression." Computer Methods in Applied Mechanics and Engineering 359 (2020): 112724.