Advertisement

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

Abstract

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.

Keywords

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

Notes

Acknowledgements

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)

References

  1. Browning G, Kreiss HO, Oliger J (1973) Mesh refinement. Math Comput 27:29–39MathSciNetCrossRefzbMATHGoogle Scholar
  2. Chavali AK, Gianchandani EP, Tung KS, Lawrence MB, Peirce SM, Papin JA (2008) Characterizing emergent properties of immunological systems with multi-cellular rule-based computational modeling. Trends Immunol 29:589–599CrossRefGoogle Scholar
  3. Dobaczewski M, Gonzalez-Quesada C, Frangogiannis NG (2010) The extracellular matrix as a modulator of the inflammatory and reparative response following myocardial infarction. J Mol Cell Cardiol 48:504–511CrossRefGoogle Scholar
  4. Fomovsky G, Holmes J (2010) Evolution of scar structure, mechanics, and ventricular function after myocardial infarction in the rat. Am J Physiol Heart Circ Physiol 298:H221–H228CrossRefGoogle Scholar
  5. Groh A, Wagner M (2011) Biased three-dimensional cell migration and collagen matrix modification. Math Biosci 231:105–119MathSciNetCrossRefzbMATHGoogle Scholar
  6. Holmes JW, Yamashita H, Waldman LK, Covell JW (1994) Scar remodeling and transmural deformation after infarction in the pig. Circulation 90:411–420CrossRefGoogle Scholar
  7. Holmes JW, Borg TK, Covell JW (2005) Structure and mechanics of healing myocardial infarcts. Annu Rev Biomed Eng 7:223–253CrossRefGoogle Scholar
  8. Huang C, Yannas IV (1977) Mechanochemical studies of enzymatic degradation of insoluble collagen fibers. J Biomed Mater Res 11:137–154CrossRefGoogle Scholar
  9. Maas SA, Ellis BJ, Ateshian GA, Weiss JA (2012) FEBio: finite elements for biomechanics. Biomech Eng 134:011005CrossRefGoogle Scholar
  10. McDougall S, Dallon J, Sherratt J, Maini P (2006) Fibroblast migration and collagen deposition during dermal wound healing: mathematical modelling and clinical implications. Philos Trans A Math Phys Eng Sci 5:1385–1405MathSciNetCrossRefGoogle Scholar
  11. Moermana KM, Holtb CA, Evansb SL, Simmsa CK (2009) Digital image correlation and finite element modelling as a method to determine mechanical properties of human soft tissue in vivo. J Biomech 42:1150–1153CrossRefGoogle Scholar
  12. Ning J, Braxton VG, Wang Y, Sutton MA, Wang Y, Lessner SM (2011) Speckle patterning of soft tissues for strain field measurement using digital image correlation: preliminary quality assessment of patterns. Microsc Microanal 17:81–90CrossRefGoogle Scholar
  13. North MJ, Collier NT, Ozik J, Tatara ER, Macal CM, Bragen M, Sydelko P (2013) Complex adaptive systems modeling with Repast Simphony. Complex Adapt Syst Model 1:3CrossRefGoogle Scholar
  14. Pan B, Qian KM, Xie HM, Asundi A (2009) Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas Sci Technol 20:062001CrossRefGoogle Scholar
  15. Plank MJ, Simpson MJ (2012) Models of collective cell behaviour with crowding effects: comparing lattice-based and lattice-free approaches. J R Soc Interface 7:2983–2996CrossRefGoogle Scholar
  16. Rouillard AD, Holmes JW (2012) Mechanical regulation of fibroblast migration and collagen remodelling in healing myocardial infarcts. J Physiol 590:4585–4602CrossRefGoogle Scholar
  17. Rouillard AD, Holmes JW (2014) Coupled agent-based and finite-element models for predicting scar structure following myocardial infarction. Prog Biophys Mol Biol 115:235–243CrossRefGoogle Scholar
  18. Usyk TP, McCulloch AD (2003) Computational methods for soft tissue biomechanics, vol 441. Biomechanics of Soft Tissue in Cardiovascular Systems. International Centre for Mechanical Sciences (Courses and Lectures). Springer, ViennaGoogle Scholar
  19. Virgilio KM, Martin KS, Peirce SM, Blemker SS (2015) Multiscale models of skeletal muscle reveal the complex effects of muscular dystrophy on tissue mechanics and damage susceptibility. Interface Focus 5:20140080CrossRefGoogle Scholar
  20. Witzenburg CM, Barocas VH (2016) A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues. Comput Methods Biomech Biomed Eng 19:1630–1646CrossRefGoogle Scholar
  21. Zahedmanesh H, Lally C (2012) A multiscale mechanobiological modelling framework using agent-based models and finite element analysis: application to vascular tissue engineering. Biomech Model Mechanobiol 11:363–377CrossRefGoogle Scholar

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

Personalised recommendations