Spatial scaling in multiscale models: methods for coupling agent-based and finite-element models of wound healing

  • Jia-Jye Lee
  • Lee Talman
  • Shayn M. Peirce
  • Jeffrey W. HolmesEmail author
Original Paper


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.


Agent-based model Finite-element model Computational model Myocardial infarction Fibroblast Collagen 



This study was supported by NIH Grants R01 HL-116449 (JWH, JJL) and U01 HL-127654 (JWH, SPC, LT).

Supplementary material

10237_2019_1145_MOESM1_ESM.tiff (17.8 mb)
Supplementary material 1 (TIFF 18230 kb)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Jia-Jye Lee
    • 1
  • Lee Talman
    • 1
  • Shayn M. Peirce
    • 1
    • 2
  • Jeffrey W. Holmes
    • 1
    • 2
    • 3
    Email author
  1. 1.Department of Biomedical EngineeringUniversity of VirginiaCharlottesvilleUSA
  2. 2.Robert M. Berne Cardiovascular Research CenterUniversity of VirginiaCharlottesvilleUSA
  3. 3.Department of MedicineUniversity of VirginiaCharlottesvilleUSA

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