A continuum treatment of growth in biological tissue: The coupling of mass transport and mechanics

Growth (and resorption) of biological tissue is formulated in the continuum setting. The treatment is macroscopic, rather than cellular or sub-cellular. Certain assumptions that are central to classical continuum mechanics are revisited, the theory is reformulated, and consequences for balance laws and constitutive relations are deduced. The treatment incorporates multiple species. Sources and fluxes of mass, and terms for momentum and energy transfer between species are introduced to enhance the classical balance laws. The transported species include: (\romannumeral 1) a fluid phase, and (\romannumeral 2) the precursors and byproducts of the reactions that create and break down tissue. A notable feature is that the full extent of coupling between mass transport and mechanics emerges from the thermodynamics. Contributions to fluxes from the concentration gradient, chemical potential gradient, stress gradient, body force and inertia have not emerged in a unified fashion from previous formulations of the problem. The present work demonstrates these effects via a physically-consistent treatment. The presence of multiple, interacting species requires that the formulation be consistent with mixture theory. This requirement has far-reaching consequences. A preliminary numerical example is included to demonstrate some aspects of the coupled formulation.Comment: 29 pages, 11 figures, accepted for publication in Journal of the Mechanics and Physics of Solids. See journal for final versio

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

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.Comment: 24 pages, 4 figures. Replaced version has corrections to typos in equations, and the corresponding correct plot of the solution--all in Section

Fractura frisaria y desplazamiento de la epífisis distal del radio

Se presenta el caso clínico de un perro de 9 meses de edad. Tiene una fractura con luxación y desplazamiento del radio. Se decide colocar, unas agujas Kirschner de 1,5 mm en posición oblicua.Clinical case of a dog nine months oId with a fracture luxation of the ulna radius (tipe salter 1). We obtain a good stabtlisation and growing using two pins Kirschner (1.5 mm)

Ecrasement d'une goutte en projection plasma : application au revêtement de matériaux thermiquement dégradables

6 pagesDuring plasma spray process hot droplet of melted metal or ceramic inpinge cold target. In some processes this target should be destroyed by the thermal flux. It is why in this report the freezing and layering of the droplet on the cold substrate is studied with a special interest on the thermal penetration in the sustrate