Multigenerational interstitial growth of biological tissues.
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.
Ateshian
Gerard A
GA
Columbia University, New York, NY, USA. ateshian@columbia.edu
Ricken
Tim
T
D002455:Cell Division; D020342:Finite Element Analysis; D008954:Models, Biological; D038081:Organogenesis / Q000502:physiology*; D013314:Stress, Mechanical