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

Abstract

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.

Mathematical modeling of collagen turnover in biological tissue

“…We set the material parameters of the passive behavior of the tissue for the wormlike chain model (Garikipati et al, 2006;Kuhl et al, 2005;Alastrue et al, 2010) to L = 1.532, r 0 = 1.072, k = 1.381 × 10 −23 (J/K), N = 1.38 × 10 21 , θ = 310K and A = 1.107, as adapted from Alastrue et al (2010). The concentration parameters for the Bingham distribution are set to κ 1,2,3 = 0.0, 56.81, 58.70.…”

“…The worm-like chain model was initially used to model DNA (Bustamante et al, 2003), and was later used for different types of biological tissue. Buehler & Wong (2007) have used this approach to simulate the behavior of tropocollagen molecules and Kuhl et al (2005); Garikipati et al (2006); Alastrue et al (2010) have adopted it to simulate collagen fibers. Despite the mismatch between the different length scales, all these models have successfully characterized the behavior of the underlying hierarchical structure using the following free energy function of an individual worm-like chain,…”

Patches of Finite Elements for Singularly-Perturbed Diffusion Reaction Equations with Discontinuous Coefficients

“…Although very difficult to validate, they are much more bio-physical and allow checking different hypotheses and design new experiments useful for a better understanding of the specific problem analyzed. Multiphasic formulations are usually used, including complex interactions between Mechanics, cells and volume growth in the framework of open systems [30,31].…”

A theoretical model of the endothelial cell morphology due to different waveforms

“…In [28], a complete consistent linearization of the equations in an implicit finite element framework was performed. [25] presented an elegant energetic and stationary study of the remodeling problem from a thermodynamic point of view.…”