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

Potencial alelopático de catequinas de Tachigali myrmecophyla (leguminosae).

Disponível também on-line

Isoflavona de Pueraria phaseoloides: efeitos alelopáticos sobre plantas daninhas.

PN-218

Eects of State of Charge on the Physical Characteristics of V(IV)/V(V) Electrolytes and Membrane for the All Vanadium Flow Battery

The VO2+/VO2+ redox couple commonly employed on the positive terminal of the all-vanadium redox flow battery was investigated at various states of charge (SOC) and H2SO4 supporting electrolyte concentrations. Electron paramagnetic resonance was used to investigate the VO2+ concentration and translational and rotational diffusion coefficient (DT, DR) in both bulk solution and Nafion membranes. Values of DT and DR were relatively unaffected by SOC and on the order of 10−10 m2s−1. Cyclic voltammetry measurements revealed that no significant changes to the redox mechanism were observed as the state of charge increased; however, the mechanism does appear to be affected by H2SO4 concentration. Electron transfer rate (k0) increased by an order of magnitude (10−6 ms−1 to 10−8 ms−1) for each H2SO4 concentrations investigated (1, 3 and 5 M). Analysis of cyclic voltammetry switching currents suggests that the technique might be suitable for fast determination of state of charge if the system is well calibrated. Membrane uptake and permeability measurements show that vanadium absorption and crossover is more dependent on both acid and vanadium concentration than state of charge. Vanadium diffusion in the membrane is about an order of magnitude slower (~10−11 m2s−1) than in solution (~10−10 m2s−1)