Phase-Field Modeling of Individual and Collective Cell Migration

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.

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Fig. 1

Adapted from [5]

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Adapted from [71]

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Adapted from [71]

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Reproduced from [116]. (Color figure online)

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Notes

  1. 1.

    The lipid molecules possess one end with hydrophilic properties and the other end with hydrophobic properties.

  2. 2.

    ATP hydrolysis is a molecular reaction that produces mechanical energy from chemical energy.

  3. 3.

    Chemokines are signaling proteins secreted by the cells.

  4. 4.

    The derivation of \(j_n\) and \({\mathbf {u}}_n\) is based on constitutive relations and energy dissipation’s principles; see [146, 200] for more details.

  5. 5.

    In a Hele-Shaw cell [160], viscous forces can be approximated by \(-\kappa {\mathbf {u}}\), where \(\kappa\) is a constant.

  6. 6.

    Eqs. (29) and (30) do not have any term that involves non-local computations associated to a single cell, such as, e.g., calculating integrals or distances.

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Moure, A., Gomez, H. Phase-Field Modeling of Individual and Collective Cell Migration. Arch Computat Methods Eng 28, 311–344 (2021). https://doi.org/10.1007/s11831-019-09377-1

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