Multigenerational interstitial growth of biological tissues

作者：Ateshian Gerard A^*; Ricken Tim

来源：Biomechanics and Modeling in Mechanobiology, 2010, 9(6): 689-702.

DOI：10.1007/s10237-010-0205-y

• Biological growth
• Mixture theory
• Residual stress
• Reference configuration
• Cell division

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.

• 出版日期2010-12