The Relationship between Cell and Tissue Strain in Three-dimensional Bio-artificial Tissues

¹ Washington University in St. Louis

^* To whom correspondence should be addressed. E-mail: pablo{at}me.wustl.edu.

Submitted on February 25, 2004
Revised on July 1, 2004
Accepted on 22 November 2004

	Abstract

Continuum constitutive laws are needed to ensure that bio-artificial tissue constructs replicate the mechanical response of the tissues they replace, and to understand how the constituents of these constructs contribute to their overall mechanical response. One model designed to achieve both of these aims is the Zahalak (2000) model, which was modified by Marquez et al. (2004) to incorporate inhomogeneous strain fields within very thin tissues. When applied to re-interpret previous measurements, the modified Zahalak model predicted higher values of the continuum stiffness of fibroblasts than earlier estimates. In this work, we further modify the Zahalak model to account for inhomogeneous strain fields in constructs whose cell orientations have a significant out-of-plane component. When applied to re-interpret results from the literature, the new model shows that estimates of continuum cell stiffness might need to be revised upwards. As in this paper's companion, we updated the average cell strain by defining a correction factor ("strain factor"), based upon the elastic response. Three different cell orientation distributions were studied. We derived an approximate scaling model for the strain factor, and validated it against exact and self-consistent (mean-field) solutions from the literature for dilute cell concentrations, and Monte Carlo simulations involving three-dimensional finite element analyses for high cell concentrations.

Key Words: bio-artificial tissues, cell-mechanics, constitutive modeling

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