Dynamic mechanical finite element model of biological cells for studying cellular pattern formation

Abstract

Understanding the geometric, topologic, and mechanical properties of cells and their interactions is critical for studying tissue pattern formation and organ development. Computational model and tools for simulating cell pattern formation have broad implications in studying embryogenesis, blood-vessel development, tissue regeneration, and tumor growth. Although a number of cell modeling methods exist, they do not simultaneously account for detailed cellular shapes as well as dynamic changes in cell geometry and topology. Here we describe a dynamic finite element cell model (dFEMC) for studying populations of cells and tissue development. By incorporating details of cell shape, cell growth and shrinkage, cell birth and death, cell division and fusion, our method can model realistically a variety problems of cell pattern formation. We give two examples of applying our method to the study of cell fusion and cell apoptosis. The dFEMC model developed here provides a general computational framework for studying dynamics pattern formation of tissue.

Multiscale Modeling of Cellular Epigenetic States: Stochasticity in Molecular Networks, Chromatin Folding in Cell Nuclei, and Tissue Pattern Formation of Cells

“…We count every 9 cells as one colony. The colony number ratio between the two treatments, 12 against 7, is consistent with the colony number ratio between the two treatments found in experiment studies [108] (see reference [104] for details).…”

“…(b) Each cell is tiled by a triangular mesh generated using the farthest point sampling method based on Delaunay triangulation. [107] (c) Cell grows incrementally, with volume change attributed to individual boundary element that sum to Δ V (adapted from references [81,104] ).…”

“…[104] We were able to reproduce suppression of tumor tissue growth under the treatment of curcumin and DMSO which influences the growth rate of cancer cells, as observed in clinical experiment. [104,110,111] Differential suppression effects of curcumin and DMSO treatments from our simulation were consistent with experimental observations, [108] where curcumin exhibited stronger suppression effect on cancer cells than DMSO agent (Figure 12). …”

Cell–substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model

“…Recently, computational models have become increasingly useful to complement experimental observations towards understanding the mechanisms of collective cell migration. A number of computational cell models have been developed to study the mechanical interactions between cells or between cell and ECM (Albert and Schwarz, 2016;Basan et al, 2013;Checa et al, 2015;Drasdo and Hoehme, 2012;Hoehme and Drasdo, 2010;Hutson et al, 2009;Kabla, 2012;Kachalo et al, 2015;Kim et al, 2018Kim et al, , 2015Lee and Wolgemuth, 2011;Lee et al, 2017;Marée et al, 2007;Merchant et al, 2018;Nagai and Honda, 2009;Nematbakhsh et al, 2017;Sandersius et al, 2011;Van Liedekerke et al, 2019;Vermolen and Gefen, 2015;Vitorino et al, 2011;Zhao et al, 2013). However, these models have limitations.…”

“…However, the contribution of specific cell shape to the mechanical energy of cell interior is not well considered (Kabla, 2012;Kachalo et al, 2015;Vitorino et al, 2011). Finite element models have also been developed, but they only allowed limited changes in cell shape and limited flexibility in cell movement (Hutson et al, 2009;Vermolen and Gefen, 2015;Zhao et al, 2013). Other models mimic the cellular mechanics using arbitrarily imposed Morse potential which is unrealistic at cellular level (Nematbakhsh et al, 2017;Sandersius et al, 2011).…”