Minimizing Computational Time for Long-Term Three-Dimensional Dynamic Simulation of Stem Cell Adipogenesis

Abstract This paper presents a high-speed approach to simulating the long-term mechanobiological development of stem cells during the adipogenesis process. A novel three-dimensional model of human bone marrow-derived mesenchymal stem cells (hMSCs) undergoing adipogenic differentiation is presented herein. The elements of the cellular model have minute masses in femtograms and dimensions in nanometers. The disproportionality between the force and mass terms of the system, yielding a multiscale dynamic model, requires the solution to be calculated in femto- and picosecond time-steps. This makes producing the two-week time history of the adipogenic differentiation process computationally infeasible with conventional methods, even with the aid of supercomputers. The scaling method, based on the method of multiple scales proposed in authors' previous works, has been shown to address these imbalances and yield fast computational time for long-term simulation of cell processes. Herein, a novel approach to the scaling formulation is proposed, and methods for choosing scaling factors are presented and examined. Employing the new formulation results in a computational time of less than 1 h and 9 min on a normal desktop computer for the simulation of the 3D cellular model for the two-week time history of the adipogenic differentiation process. This is faster than previous efforts, which modeled the cell in two dimensions.