A novel model for one-dimensional morphoelasticity. Part I - Theoretical foundations

While classical continuum theories of elasticity and viscoelasticity have long been used to describe the mechanical behaviour of solid biological tissues, they are of limited use for the description of biological tissues that undergo continuous remodelling. The structural changes to a soft tissue associated with growth and remodelling require a mathematical theory of ‘morphoelasticity’ that is more akin to plasticity than elasticity. However, previously-derived mathematical models for plasticity are difficult to apply and interpret in the context of growth and remodelling: many important concepts from the theory of plasticity do not have simple analogues in biomechanics.\ud \ud In this work, we describe a novel mathematical model that combines the simplicity and interpretability of classical viscoelastic models with the versatility of plasticity theory. While our focus here is on one-dimensional problems, our model builds on earlier work based on the multiplicative decomposition of the deformation gradient and can be adapted to develop a three-dimensional theory. The foundation of this work is the concept of ‘effective strain’, a measure of the difference between the current state and a hypothetical state where the tissue is mechanically relaxed. We develop one-dimensional equations for the evolution of effective strain, and discuss a number of potential applications of this theory. One significant application is the description of a contracting fibroblast-populated collagen lattice, which we further investigate in Part II

A novel model for one-dimensional morphoelasticity. Part II - Application to the contraction of fibroblast-populated collagen lattices

Fibroblast-populated collagen lattices are commonly used in experiments to study the interplay between fibroblasts and their pliable environment. Depending on the method by which\ud they are set, these lattices can contract significantly, in some cases contracting to as little as 10% of their initial lateral (or vertical) extent. When the reorganisation of such lattices by fibroblasts is interrupted, it has been observed that the gels re-expand slightly but do not return to their original size. In order to describe these phenomena, we apply our theory of one-dimensional morphoelasticity derived in Part I to obtain a system of coupled ordinary differential equations, which we use to describe the behaviour of a fibroblast-populated collagen lattice that is tethered by a spring of known stiffness. We obtain approximate solutions that describe the behaviour of the system at short times as well as those that are valid for long times. We also obtain an exact description of the behaviour of the system in the case where the lattice reorganisation is interrupted. In addition, we perform a perturbation analysis in the limit of large spring stiffness to obtain inner and outer asymptotic expansions for the solution, and examine the relation between force and traction stress in this limit. Finally, we compare predicted numerical values for the initial stiffness and viscosity of the gel with corresponding values for previously obtained sets of experimental data and also compare the qualitative behaviour with that of our model in each case. We find that our model captures many features of the observed behaviour of fibroblast-populated collagen lattices

A two-compartment mechanochemical model of the roles of\ud transforming growth factor β and tissue tension in dermal wound healing

The repair of dermal tissue is a complex process of interconnected phenomena, where cellular, chemical and mechanical aspects all play a role, both in an autocrine and in a paracrine fashion. Recent experimental results have shown that transforming growth factor−β (TGFβ) and tissue mechanics play roles in regulating cell proliferation, differentiation and the production of extracellular materials. We have developed a 1D mathematical model that considers the interaction between the cellular, chemical and mechanical phenomena, allowing the combination of TGFβ and tissue stress to inform the activation of fibroblasts to myofibroblasts. Additionally, our model incorporates the observed feature of residual stress by considering the changing zero-stress state in the formulation for effective strain. Using this model, we predict that the continued presence of TGFβ in dermal wounds will produce contractures due to the persistence of myofibroblasts; in contrast, early elimination of TGFβ significantly reduces the myofibroblast numbers resulting in an increase in wound size. Similar results were obtained by varying the rate at which fibroblasts differentiate to myofibroblasts and by changing the myofibroblast apoptotic rate. Taken together, the implication is that elevated levels of myofibroblasts is the key factor behind wounds healing with excessive contraction, suggesting that clinical strategies which aim to reduce the myofibroblast density may reduce the appearance of contractures

A fibrocontractive mechanochemical model of dermal wound\ud closure incorporating realistic growth factor kinetics

Fibroblasts and their activated phenotype, myofibroblasts, are the primary cell types involved in the contraction associated with dermal wound healing. Recent experimental evidence indicates that the transformation from fibroblasts to myofibroblasts involves two distinct processes: the cells are stimulated to change phenotype by the combined actions of transforming growth factor β (TGFβ) and mechanical tension. This observation indicates a need for a detailed exploration of the effect of the strong interactions between the mechanical changes and growth factors in dermal wound healing. We review the experimental findings in detail and develop a model of dermal wound healing that incorporates these phenomena. Our model includes the interactions between TGFβ and collagenase, providing a more biologically realistic form for the growth factor kinetics than those included in previous mechanochemical descriptions. A comparison is made between the model predictions and experimental data on human dermal wound healing and all the essential features are well matched

Real Estate Returns and the Macroeconomy: Some Empirical Evidence from Real Estate Investment Trust

This paper explores the relationship between the macroeconomy and real estate returns. Equity REIT data are used as a proxy for real estate returns; however, the equity REIT returns are regressed against returns from the Standard and Poor's 500 Stock Index, saving the residuals. These residuals, known as extra-market covariance, are used in the analysis since this technique controls for the covariance between equity REIT returns and the overall stock market. Thus, the residuals represent pure industry effects. The residuals are then employed in an unrestricted vector autoregressive model with the macroeconomic variables to test for relationships. The results show that prices, nominal rates, output, and investment all directly influence the real estate series. Nominal interest rates, moreover, explain the majority of the variation in the real estate series.

Propranolol blocks ventricular refractory period changes with orthostatic stress in humans

The purpose of this study was to test the hypothesis that orthostatic stress shortens the right ventricular effective refractory period by reflex activation of beta-adrenergic receptors. Twelve patients undergoing electrophysiologic testing for standard clinical indications were studied. After a full electrophysiologic study, patients underwent graded lower body negative pressure before and after administration of either propranolol (0.2 mg/kg intravenously) in Group I or atropine (0.035 mg/kg intravenously) in Group II.Before the addition of drugs, lower body negative pressure produced decreases in systolic blood pressure and significant increases in sinus rate. The effective refractory period shortened from 214 ± 8 (mean ± SEM) to 206 ± 7 ms at −40 cm H2O and to 197 ± 4 ms at −60 cm H2O lower body negative pressure. After propranolol, Group I patients had no change in right ventricular effective refractory period despite similar changes in sinus rate and systolic blood pressure. In Group II patients, atropine did not alter effective refractory period responses to lower body negative pressure.Thus, reflex adjustments to orthostatic stress result in shortening of right ventricular effective refractory period mediated by way of beta-adrenergic mechanisms. These findings constitute the first evidence that sympathetic influences mobilized by the body can directly modulate ventricular electrophysiologic changes

Beaten into Submissiveness? An Investigation into the Protective Strategies used by Survivors of Domestic Abuse

This is a pre-copyedited, author-produced pdf of an article accepted for publication in Journal of Interpersonal Violence following peer review. Laura Irving & Ben Chi-pun Liu, 'Beaten into Submissiveness? An investigation Into the Protective Strategies Used by Survivors of Domestic Abuse', Journal of Interpersonal Violence, first published online 14 December 2016, available online at doi: 10.1177/0886260516682520 © The Author(s) 2016 Published by SAGEThe aim of the study was to identify the prevalence and perceived helpfulness of a variety of protective strategies that were used by female survivors of domestic abuse and to explore factors that may have influenced strategy usage. Forty participants were recruited from a voluntary sector domestic abuse service, commissioned by an outer London local authority in the UK. The measurement tools used were the Intimate Partner Violence Strategies Index and the CAADA Domestic Abuse, Stalking and ‘Honour’-Based Violence (DASH) Risk Assessment Checklist. The average age was 33 (SD=7.9, range: 20-57), half reported to be of Asian ethnicity, 37.5% White and 12.5% Black or Mixed ethnicity. The average DASH score was 9.8 (SD=13.2, range: 0-18) and an average of 18 (SD=6.7, range: 1-29) protective strategies were utilised by each participant. All of the most commonly used strategies were from the Placating category. Though Safety Planning strategies were rated as the most helpful by all participants, Placating strategies were also rated as helpful by two-thirds of participants. Stepwise multiple regression showed that Placating was the only significant predictor of DASH score (β=0.375, p<0.05) and accounted for 14% of the variance of DASH score. Findings showed that women utilized a diverse range of protective strategies with placating strategies being most intensely used and rated as helpful. However, placating strategy usage could be a risk factor as opposed to a protective factor. This study has also demonstrated that greater placating strategies were used by White than South Asian women, and women who were employed used more formal strategies. This research has extended the knowledge base of protective strategies that professionals can draw from to underpin decisions and interventions when working with domestic abuse survivors.Peer reviewedFinal Accepted Versio