Biological remodelling: Stationary energy, configurational change, internal variables and dissipation

Details Biological remodelling: Stationary energy, configurational change, internal variables and dissipation Biological remodelling: Stationary energy, configurational change, internal variables and dissipation

2005-06-16

arxiv.org/abs/q-bio/0506023v2

Biology

Quantitative Biology

Tissues and Organs

24 pages, 4 figures. Replaced version has corrections to typos in equations, and the corresponding correct plot of the solutio

Scientific paper

10.1016/j.jmps.2005.11.011

Remodelling is defined as an evolution of microstructure or variations in the configuration of the underlying manifold. The manner in which a biological tissue and its subsystems remodel their structure is treated in a continuum mechanical setting. While some examples of remodelling are conveniently modelled as evolution of the reference configuration (Case I), others are more suited to an internal variable description (Case II). In this paper we explore the applicability of stationary energy states to remodelled systems. A variational treatment is introduced by assuming that stationary energy states are attained by changes in microstructure via one of the two mechanisms--Cases I and II. An example is presented to illustrate each case. The example illustrating Case II is further studied in the context of the thermodynamic dissipation inequality.

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