Phase-Field Modeling of Individual and Collective Cell Migration
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ORIGINAL PAPER
Phase‑Field Modeling of Individual and Collective Cell Migration Adrian Moure1 · Hector Gomez1,2,3 Received: 14 June 2019 / Accepted: 13 November 2019 © CIMNE, Barcelona, Spain 2019
Abstract Cell motion is crucial in human health and development. Cells may migrate individually or in highly coordinated groups. Cell motion results from complex intra- and extra-cellular mechanochemical interactions. Computational models have become a powerful tool to shed light on the mechanisms that regulate cell migration. The phase-field method is an emerging modeling technique that permits a simple and direct formulation of the moving cell problem and the interaction between the cell and its environment. This paper intends to be a comprehensive review of phase-field models of individual and collective cell migration. We describe a numerical implementation, based on isogeometric analysis, which successfully deals with the challenges associated with phase-field problems. We present numerical simulations that illustrate the unique capabilities of the phase-field approach for cell migration. In particular, we show 2D and 3D simulations of individual cell migration in confined and fibrous environments that highlight the mechanochemical interplay between the cell and the extracellular environment. We also show 2D simulations of cell co-attraction in non-confluent multicellular systems, in which the use of the phase-field method is crucial to capture the dynamics of the multicellular system.
1 Introduction Cell motion occurs in many biological processes essential for life. While some cells move in a liquid medium by using cilia or flagella, most eukaryotic cells in the human body move through solid environments such as, e.g., the extracellular matrix or the basal lamina. Here we focus on the latter kind of cell migration. Thus, by cell migration we will refer to the crawling motion of cells on solid media. Cell migration is a highly coordinated process that results from complex interactions between the constituents of the cellular motile machinery and the extracellular environment. Cell motion manifests as individual motile cells or organized groups of cells that move as functional units. Both individual and collective cell migration regulate key biological
* Adrian Moure [email protected] 1
School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA
2
Weldon School of Biomedical Engineering, Purdue University, 206 S Martin Jischke Dr, West Lafayette, IN 47907, USA
3
Purdue University Center for Cancer Research, Purdue University, 201 S University St, West Lafayette, IN 47906, USA
functions such as tissue formation, wound healing, or cancer metastasis. Therefore, the biomechanics of cell migration has been, and continues to be, an active field of research. Computational modeling of cell migration is an emerging field in biomechanics and biophysics. Computational models can overcome the intrinsic limitations of the experimental setups and help to further underst
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