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

Fano resonances in plasmonic core-shell particles and the Purcell effect

Despite a long history, light scattering by particles with size comparable with the light wavelength still unveils surprising optical phenomena, and many of them are related to the Fano effect. Originally described in the context of atomic physics, the Fano resonance in light scattering arises from the interference between a narrow subradiant mode and a spectrally broad radiation line. Here, we present an overview of Fano resonances in coated spherical scatterers within the framework of the Lorenz-Mie theory. We briefly introduce the concept of conventional and unconventional Fano resonances in light scattering. These resonances are associated with the interference between electromagnetic modes excited in the particle with different or the same multipole moment, respectively. In addition, we investigate the modification of the spontaneous-emission rate of an optical emitter at the presence of a plasmonic nanoshell. This modification of decay rate due to electromagnetic environment is referred to as the Purcell effect. We analytically show that the Purcell factor related to a dipole emitter oriented orthogonal or tangential to the spherical surface can exhibit Fano or Lorentzian line shapes in the near field, respectively.Comment: 28 pages, 10 figures; invited book chapter to appear in "Fano Resonances in Optics and Microwaves: Physics and Application", Springer Series in Optical Sciences (2018), edited by E. O. Kamenetskii, A. Sadreev, and A. Miroshnichenk

Evaluation of ripening Vitis vinifera grown in Northeastern Brazil.

This study aimed to determine physical characteristics and chemical composition of grapes cvs. Syrah and Tempranillo, during maturation

The Non-Equilibrium Thermodynamics and Kinetics of Focal Adhesion Dynamics

BACKGROUND: We consider a focal adhesion to be made up of molecular complexes, each consisting of a ligand, an integrin molecule, and associated plaque proteins. Free energy changes drive the binding and unbinding of these complexes and thereby controls the focal adhesion's dynamic modes of growth, treadmilling and resorption. PRINCIPAL FINDINGS: We have identified a competition among four thermodynamic driving forces for focal adhesion dynamics: (i) the work done during the addition of a single molecular complex of a certain size, (ii) the chemical free energy change associated with the addition of a molecular complex, (iii) the elastic free energy change associated with deformation of focal adhesions and the cell membrane, and (iv) the work done on a molecular conformational change. We have developed a theoretical treatment of focal adhesion dynamics as a nonlinear rate process governed by a classical kinetic model. We also express the rates as being driven by out-of-equilibrium thermodynamic driving forces, and modulated by kinetics. The mechanisms governed by the above four effects allow focal adhesions to exhibit a rich variety of behavior without the need to introduce special constitutive assumptions for their response. For the reaction-limited case growth, treadmilling and resorption are all predicted by a very simple chemo-mechanical model. Treadmilling requires symmetry breaking between the ends of the focal adhesion, and is achieved by driving force (i) above. In contrast, depending on its numerical value (ii) causes symmetric growth, resorption or is neutral, (iii) causes symmetric resorption, and (iv) causes symmetric growth. These findings hold for a range of conditions: temporally-constant force or stress, and for spatially-uniform and non-uniform stress distribution over the FA. The symmetric growth mode dominates for temporally-constant stress, with a reduced treadmilling regime. SIGNIFICANCE: In addition to explaining focal adhesion dynamics, this treatment can be coupled with models of cytoskeleton dynamics and contribute to the understanding of cell motility