Multiscale Kinematic Growth Coupled With Mechanosensitive Systems Biology in Open-Source Software

Multiscale coupling between cell-scale biology and tissue-scale mechanics is a promising approach for modeling disease growth. In such models, tissue-level growth and remodeling (G&R) are driven by cell-level signaling pathways and systems biology models, where each model operates at different scales. Herein, we generate multiscale G&R models to capture the associated multiscale connections. At the cell-scale, we consider systems biology models in the form of systems of ordinary differential equations (ODEs) and partial differential equations (PDEs) representing the reactions between the biochemicals causing the growth based on mass-action or logic-based Hill-type kinetics. At the tissue-scale, we employ kinematic growth in continuum frameworks. Two illustrative test problems (a tissue graft and aneurysm growth) are examined with various chemical signaling networks, boundary conditions, and mechano-chemical coupling strategies. We extend two open-source software frameworks-febio and fenics-to disseminate examples of multiscale growth and remodeling simulations. One-way and two-way coupling between the systems biology and the growth models are compared and the effect of biochemical diffusivity and ODE versus PDE-based systems biology modeling on the G&R results are studied. The results show that growth patterns emerge from reactions between biochemicals, the choice between ODEs and PDEs systems biology modeling, and the coupling strategy. Cross-verification confirms that results for febio and fenics are nearly identical. We hope that these open-source tools will support reproducibility and education within the biomechanics community.