Constructing growth evolution laws of arteries via reinforcement learning

Abstract

Growth evolution laws, which mathematically describe how living tissues change their shape and properties in response to external stimuli, are required for modeling arterial growth. Traditionally, specific forms of growth laws are devised by domain experts. Since in vivo animal studies usually provide limited experimental data, generalization and inference are often employed to prescribe the functional form of growth laws. In this work, we employed the finite growth theory and developed a reinforcement learning (RL) approach to construct growth evolution laws by formulating the arterial growth problem under the framework of the Markov decision process (MDP). To maintain homeostatic stress levels in an optimal manner, RL agents were employed to determine stress-modulated anisotropic growth evolution at each time step. We illustrate the capabilities of the RL-based growth laws in two representative applications: 1) predicting homogenous growth of a thin-walled artery in response to hypertensive blood pressure, and 2) generating residual stress with heterogeneous growth in a thick-walled bi-layer aorta via distributed growth policies. Experimental data, where available, were used to compare expert-prescribed and RL-based growth laws. Our results demonstrated the capabilities of RL to effectively control the growth processes in response to hypertension, and the predictions are in good agreement with experimental observations. In particular, the RL growth laws captured the reduction of in vivo axial stretch without using experimental data for training. Moreover, the distributed RL growth policies achieved residual stress generation in a collaborative manner, which may pave the way for implementation in a finite element setting. This study sheds light on a new avenue to uncover growth evolution laws via RL, perhaps reducing the need for large experimental datasets and expert intelligence during growth law construction.