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Originally published as Biophys J. BioFAST on December 13, 2004.
doi:10.1529/biophysj.104.040808
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Biophysical Journal 88:765-777 (2005)
© 2005 The Biophysical Society

Thin Bio-Artificial Tissues in Plane Stress: The Relationship between Cell and Tissue Strain, and an Improved Constitutive Model

J. Pablo Marquez *, Guy M. Genin *, George I. Zahalak * and Elliot L. Elson {dagger}

* Department of Mechanical Engineering, and {dagger} Department of Biochemistry and Molecular Biophysics, Washington University, St. Louis, Missouri 63130

Correspondence: Address reprint requests to Elliot L. Elson, E-mail: elson{at}wustl.edu.

Constitutive models are needed to relate the active and passive mechanical properties of cells to the overall mechanical response of bio-artificial tissues. The Zahalak model attempts to explicitly describe this link for a class of bio-artificial tissues. A fundamental assumption made by Zahalak is that cells stretch in perfect registry with a tissue. We show this assumption to be valid only for special cases, and we correct the Zahalak model accordingly. We focus on short-term and very long-term behavior, and therefore consider tissue constituents that are linear in their loading response (although not necessarily linear in unloading). In such cases, the average strain in a cell is related to the macroscopic tissue strain by a scalar we call the "strain factor". We incorporate a model predicting the strain factor into the Zahalak model, and then reinterpret experiments reported by Zahalak and co-workers to determine the in situ stiffness of cells in a tissue construct. We find that, without the modification in this article, the Zahalak model can underpredict cell stiffness by an order of magnitude.




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