Elastica-based strain energy functions for soft biological tissue

Continuum strain energy functions are developed for soft biological tissues that possess long fibrillar components. The treatment is based on the model of an elastica, which is our fine scale model, and is homogenized in a simple fashion to obtain a continuum strain energy function. Notably, we avoid solving the full fourth-order, nonlinear, partial differential equation for the elastica by resorting to other assumptions, kinematic and energetic, on the response of the individual, elastica-like fibrils.Comment: To appear in J. Mech. Phys. Solid

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

Beliefs and Trust: An Experiment

In this paper, we address the concept of trust by combining (i) the self-reported trust and belief in trustworthiness of others from a general unpaid questionnaire, (ii) choices made in a social valuation task designed to measure subjects' distributional preferences, (iii) strategies submitted in the trust game in both roles of the game, and (iv) subjects' beliefs about the strategies of their co-player submitted in the form of probability distributions nad incentivized by the quadratic scoring rule.We show that trust can be expressed as a belief in positive reciprocity of the trustee, and answers to general questionnaire lack predictive power.Distributional preferences also play a role in the decision to trust in that they affect the subjects' beliefs about the positive reciprocity of others.Cooperative subjects are more optimistic in their beliefs and therefore trust more.experimental economics;trust;beliefs;distributional preferences

In silico estimates of the free energy rates in growing tumor spheroids

The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of eventually developing a system-level understanding of the progression of cancer. At this scale, cell populations and chemical species are best treated as concentration fields that vary with time and space. The cells have chemo-mechanical interactions with each other and with the ECM, consume glucose and oxygen that are transported through the tumor, and create chemical byproducts. We present a continuum mathematical model for the biochemical dynamics and mechanics that govern tumor growth. The biochemical dynamics and mechanics also engender free energy changes that serve as universal measures for comparison of these processes. Within our mathematical framework we therefore consider the free energy inequality, which arises from the first and second laws of thermodynamics. With the model we compute preliminary estimates of the free energy rates of a growing tumor in its pre-vascular stage by using currently available data from single cells and multicellular tumor spheroids.Comment: 27 pages with 5 figures and 2 tables. Figures and tables appear at the end of the pape

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

The Cost of Empowerment: Multiple Sources of Women’s Debt in Rural India

Poor women borrow from multiple sources. This study examines whether the source of debt matters for women’s role in household financial decisions. Drawing on a household survey from rural Tamil Nadu, we categorise women’s loans along the lines of accessibility and formality into ‘planned loans’ and ‘instant loans’. We find that ‘instant loans’ support women’s bargaining power in various types of household financial decisions, whereas ‘planned loans’ have no impact. This surprising result is better understood when the nature of ‘instant loans’ is examined – these are frequently usurious, involve coercive enforcement methods and are considered socially debasing. Hence women who use them perform a convenient role for their households and in return gain some negotiating power