期刊
BIOMECHANICS AND MODELING IN MECHANOBIOLOGY
卷 9, 期 6, 页码 689-702出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10237-010-0205-y
关键词
Biological growth; Mixture theory; Residual stress; Reference configuration; Cell division
资金
- National Institute of Arthritis and Musculoskeletal and Skin Diseases [AR46532]
- National Institute of General Medical Sciences, U.S. National Institutes of Health [GM083925]
- University of Duisberg-Essen
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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