Mechanics of Cell Growth

Abstract

Cell growth describes an essential feature of biological tissues. This growth process may be modeled by using a set of relatively simple governing equations based on the axioms of mass and momentum balance, and using a continuum framework that describes cells and tissues as mixtures of a solid matrix, a solvent and multiple solutes. In this model the mechanics of cell growth is driven by osmotic effects, regulated by the cells' active uptake of solutes and passive uptake of solvent. By accounting for the anisotropy of the cells' cytoskeletal structures or extracellular matrix, as well as external constraints, a wide variety of growing shapes may be produced as illustrated in various examples.

Figure 4.1

Unconstrained growth of a tubular cellularized tissue with isotropic solid matrix. Growth is induced by increasing the cell solute and solid content fivefold. (a) Initial configuration. (b) Final configuration.

Figure 4.2

Unconstrained growth of a tubular cellularized tissue with orthotropic solid matrix. Growth is induced by increasing the cell solute and solid content fivefold. (a) Initial configuration. (b) Final configuration when axial stiffness is negligible, ${\mu }_Z^s\ll {\mu }_R^s,{\mu }_{ϴ}^s$. (c) Final configuration when radial and circumferential stiffnesses are negligible, ${\mu }_R^s={\mu }_{ϴ}^s\ll {\mu }_Z^s$.

Figure 4.3

Constrained growth of an initially round cell abutting against rigid platens. Growth is induced by increasing the cell solute and solid content fivefold. (a) Initial configuration. (b) Final configuration.

Figure 4.4

Growth and buckling of a tissue layer constrained at lateral ends. Growth is induced by increasing the cell solute and solid content fivefold. The solid matrix is isotropic, with an elastic modulus of 10⁻³ MPa. (a) Layer in initial configuration. (b) Layer in final configuration. Buckling is induced by nudging the structure with a small, transient vertical force at the center of the layer at the start of the growth process.

Figure 4.5

Inhomogeneous growth in a bilayered strip. Growth is induced only in the top layer, by increasing the cell solute and solid content by a factor of 2.5. Both strips have a compressible neo-Hookean isotropic solid matrix with a Young's modulus of 10⁻¹ MPa and Poisson's ratio of 0. (a) Initial configuration. (b) Final configuration.