Reducing Computational Cost in Long-Term Simulations of Multiscale Cellular Mechanobiology

The long-term simulation of biological systems at the cellular level presents a significant computational challenge due to pronounced multiscale behavior and severe numerical stiffness. While implicit solvers offer improved stability in solving stiff systems, they can incur prohibitively high computational costs. Alternative conventional methods, such as mass scaling or unit transformation, are often inadequate because model stiffness may arise from multiple causes beyond inertial effects. To address these limitations, this study proposes a model-reduction technique integrated with an adaptive Runge-Kutta solver, which substantially reduces computational time. The effectiveness of the proposed approach is demonstrated by successfully simulating a 14-day adipogenic differentiation process in less than 1 hour and 9 minutes of computational time on a typical desktop computer. Numerical evaluations conducted on a linear spring-mass-damper benchmark, a nonlinear Duffing oscillator, and a detailed human mesenchymal stem cell model show that the proposed approach substantially outperforms conventional scaling techniques and stiff solvers, establishing it as a robust and efficient tool for the long-term simulation of large, multiscale, stiff systems.