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Multigenerational interstitial growth of biological tissues

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Abstract

This study formulates a theory for multigenerational interstitial growth of biological tissues whereby each generation has a distinct reference configuration determined at the time of its deposition. In this model, the solid matrix of a growing tissue consists of a multiplicity of intermingled porous permeable bodies, each of which represents a generation, all of which are constrained to move together in the current configuration. Each generation’s reference configuration has a one-to-one mapping with the master reference configuration, which is typically that of the first generation. This mapping is postulated based on a constitutive assumption with regard to that generations’ state of stress at the time of its deposition. For example, the newly deposited generation may be assumed to be in a stress-free state, even though the underlying tissue is in a loaded configuration. The mass content of each generation may vary over time as a result of growth or degradation, thereby altering the material properties of the tissue. A finite element implementation of this framework is used to provide several illustrative examples, including interstitial growth by cell division followed by matrix turnover.

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Authors and Affiliations

  1. Columbia University, New York, NY, USA

    Gerard A. Ateshian

  2. University of Duisburg-Essen, Essen, Germany

    Tim Ricken

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  1. Gerard A. Ateshian
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  2. Tim Ricken
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Correspondence to Gerard A. Ateshian.

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Ateshian, G.A., Ricken, T. Multigenerational interstitial growth of biological tissues. Biomech Model Mechanobiol 9, 689–702 (2010). https://doi.org/10.1007/s10237-010-0205-y

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  • DOI: https://doi.org/10.1007/s10237-010-0205-y

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