title: Thin bio-artificial tissues in plane stress: the relationship between cell and tissue strain, and an improved constitutive model.
abstract: 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.
authors.affiliation: Department of Mechanical Engineering, Washington University, St. Louis, Missouri 63130, USA.
authors.forename: J Pablo
authors.initials: JP
authors.lastname: Marquez
authors.forename: Guy M
authors.initials: GM
authors.lastname: Genin
authors.forename: George I
authors.initials: GI
authors.lastname: Zahalak
authors.forename: Elliot L
authors.initials: EL
authors.lastname: Elson
mesh_terms: D000818:Animals; D021522:Bioartificial Organs; D002468:Cell Physiological Phenomena; D002478:Cells, Cultured; D003198:Computer Simulation; D004548:Elasticity; D005109:Extracellular Matrix / Q000502:physiology*; D006801:Humans; D040542:Mechanotransduction, Cellular / Q000502:physiology*; D008567:Membranes, Artificial; D008954:Models, Biological; D013314:Stress, Mechanical; D013718:Tensile Strength; D023822:Tissue Engineering / Q000379:methods*
chemical_list: D008567:Membranes, Artificial