Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA.
Robert M. Berne Cardiovascular Research Center, University of Virginia, Charlottesville, VA, USA.
Biomech Model Mechanobiol. 2019 Oct;18(5):1297-1309. doi: 10.1007/s10237-019-01145-1. Epub 2019 Apr 9.
Multiscale models that couple agent-based modeling (ABM) and finite-element modeling (FEM) allow the dynamic simulation of tissue remodeling and wound healing, with mechanical environment influencing cellular behaviors even as tissue remodeling modifies mechanics. One of the challenges in coupling ABM to FEM is that these two domains typically employ grid or element sizes that differ by several orders of magnitude. Here, we develop and demonstrate an interpolation-based method for mapping between ABM and FEM domains of different resolutions that is suitable for linear and nonlinear FEM meshes and balances accuracy with computational demands. We then explore the effects of refining the FEM mesh and the ABM grid in the setting of a fully coupled model. ABM grid refinement studies showed unexpected effects of grid size whenever cells were present at a high enough density for crowding to affect proliferation and migration. In contrast to an FE-only model, refining the FE mesh in the coupled model increased strain differences between adjacent finite elements. Allowing strain-dependent feedback on collagen turnover magnified the effects of regional heterogeneity, producing highly nonlinear spatial and temporal responses. Our results suggest that the choice of both ABM grid and FEM mesh density in coupled models must be guided by experimental data and accompanied by careful grid and mesh refinement studies in the individual domains as well as the fully coupled model.
多尺度模型将基于主体的建模（ABM）和有限元建模（FEM）耦合，允许对组织重塑和伤口愈合进行动态模拟，即使组织重塑改变力学特性，机械环境也会影响细胞行为。将 ABM 与 FEM 耦合的挑战之一在于，这两个领域通常采用网格或元素大小相差几个数量级。在这里，我们开发并展示了一种基于插值的方法，用于在不同分辨率的 ABM 和 FEM 域之间进行映射，该方法适用于线性和非线性 FEM 网格，并在准确性和计算需求之间取得平衡。然后，我们在完全耦合模型中探讨了细化 FEM 网格和 ABM 网格的效果。ABM 网格细化研究表明，只要细胞的密度足够高，以至于拥挤会影响增殖和迁移，那么网格大小就会产生意想不到的影响。与仅使用 FE 的模型相比，在耦合模型中细化 FE 网格会增加相邻有限元之间的应变差异。允许对胶原转化的应变依赖性反馈放大了区域异质性的影响，产生了高度非线性的时空响应。我们的结果表明，在耦合模型中，ABM 网格和 FEM 网格密度的选择都必须由实验数据来指导，并伴随着在单独的域以及完全耦合模型中进行仔细的网格和网格细化研究。
