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. 2009 Oct;131(10):101001.
doi: 10.1115/1.3192138.

Continuum modeling of biological tissue growth by cell division, and alteration of intracellular osmolytes and extracellular fixed charge density

Gerard A Ateshian  1 , Kevin D Costa, Evren U Azeloglu, Barclay Morrison 3rd, Clark T Hung
Affiliations

Continuum modeling of biological tissue growth by cell division, and alteration of intracellular osmolytes and extracellular fixed charge density

Gerard A Ateshian et al. J Biomech Eng. 2009 Oct.

Abstract

A framework is formulated within the theory of mixtures for continuum modeling of biological tissue growth that explicitly addresses cell division, using a homogenized representation of cells and their extracellular matrix (ECM). The model relies on the description of the cell as containing a solution of water and osmolytes, and having a porous solid matrix. The division of a cell into two nearly identical daughter cells is modeled as the doubling of the cell solid matrix and osmolyte content, producing an increase in water uptake via osmotic effects. This framework is also generalized to account for the growth of ECM-bound molecular species that impart a fixed charge density (FCD) to the tissue, such as proteoglycans. This FCD similarly induces osmotic effects, resulting in extracellular water uptake and osmotic pressurization of the ECM interstitial fluid, with concomitant swelling of its solid matrix. Applications of this growth model are illustrated in several examples.

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Figures

FIGURE 1
FIGURE 1
Effect of growth of fixed charge density on opening angle of rat aorta. Due to symmetry, only one-quarter of a cut ring is displayed. The opening angle increases from 13° to 95° as c˜mrF increases from 40 mEq/L to 120 mEq/L in the intima and media.
FIGURE 2
FIGURE 2
Effect of growth of intracellular membrane-impermeant solute concentration on opening angle of rat aorta. Due to symmetry, only one-quarter of a cut ring is displayed. The opening angle decreases from 13° to −37° as c˜cri decreases from 210 mEq/L to 175 mEq/L in the intima and media.
FIGURE 3
FIGURE 3
Growth of hyaline cartilage model in long bone morphogenesis. Due to symmetry, only one octant of the model is shown. In this analysis growth occurs by cell division. Sixfold increases in φcrsandc˜cri lead to a sixfold increase in tissue volume (χ = 1).
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References

    1. Hsu FH. The influences of mechanical loads on the form of a growing elastic body. J Biomech. 1968;1(4):303–311. - PubMed
    1. Cowin SC, Hegedus DH. Bone remodeling - 1. theory of adaptive elasticity. J Elasticity. 1976;6(3):313–326.
    1. Skalak R, Dasgupta G, Moss M, Otten E, Dullumeijer P, Vilmann H. Analytical description of growth. J Theor Biol. 1982;94(3):555–577. - PubMed
    1. Rodriguez EK, Hoger A, McCulloch AD. Stress-dependent finite growth in soft elastic tissues. J Biomech. 1994;27(4):455–467. - PubMed
    1. Epstein M, Maugin GA. Thermomechanics of volumetric growth in uniform bodies. Int J Plasticity. 2000;16(7–8):951–978.

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