Modelling of some biological materials using continuum mechanics

Continuum mechanics provides a mathematical framework for modelling the physical stresses experienced by a material. Recent studies show that physical stresses play an important role in a wide variety of biological processes, including dermal wound healing, soft tissue growth and morphogenesis. Thus, continuum mechanics is a useful mathematical tool for modelling a range of biological phenomena. Unfortunately, classical continuum mechanics is of limited use in biomechanical problems. As cells refashion the �bres that make up a soft tissue, they sometimes alter the tissue's fundamental mechanical structure. Advanced mathematical techniques are needed in order to accurately describe this sort of biological `plasticity'. A number of such techniques have been proposed by previous researchers. However, models that incorporate biological plasticity tend to be very complicated. Furthermore, these models are often di�cult to apply and/or interpret, making them of limited practical use. One alternative approach is to ignore biological plasticity and use classical continuum mechanics. For example, most mechanochemical models of dermal wound healing assume that the skin behaves as a linear viscoelastic solid. Our analysis indicates that this assumption leads to physically unrealistic results. In this thesis we present a novel and practical approach to modelling biological plasticity. Our principal aim is to combine the simplicity of classical linear models with the sophistication of plasticity theory. To achieve this, we perform a careful mathematical analysis of the concept of a `zero stress state'. This leads us to a formal de�nition of strain that is appropriate for materials that undergo internal remodelling. Next, we consider the evolution of the zero stress state over time. We develop a novel theory of `morphoelasticity' that can be used to describe how the zero stress state changes in response to growth and remodelling. Importantly, our work yields an intuitive and internally consistent way of modelling anisotropic growth. Furthermore, we are able to use our theory of morphoelasticity to develop evolution equations for elastic strain. We also present some applications of our theory. For example, we show that morphoelasticity can be used to obtain a constitutive law for a Maxwell viscoelastic uid that is valid at large deformation gradients. Similarly, we analyse a morphoelastic model of the stress-dependent growth of a tumour spheroid. This work leads to the prediction that a tumour spheroid will always be in a state of radial compression and circumferential tension. Finally, we conclude by presenting a novel mechanochemical model of dermal wound healing that takes into account the plasticity of the healing skin.

Load compensation for systems with non-stiff source using state feedback

Various load compensation schemes proposed in literature assume that voltage source at point of common coupling (PCC) is stiff. In practice, however, the load is remote from a distribution substation and is supplied by a feeder. In the presence of feeder impedance, the PWM inverter switchings distort both the PCC voltage and the source currents. In this paper load compensation with such a non-stiff source is considered. A switching control of the voltage source inverter (VSI) based on state feedback is used for load compensation with non-stiff source. The design of the state feedback controller requires careful considerations in choosing a gain matrix and in the generation of reference quantities. These aspects are considered in this paper. Detailed simulation and experimental results are given to support the control design.

Relaxin stimulates leukocyte adhesion and migration through a relaxin receptor LGR7-dependent mechanism

Leukocytes are critical effectors of inflammation and tumor biology. Chemokine-like factors produced by such inflammatory sites are key mediators of tumor growth that activate leukocytic recruitment and tumor infiltration and suppress immune surveillance. Here we report that the endocrine peptide hormone, relaxin, is a regulator of leukocyte biology with properties important in recruitment to sites of inflammation. This study uses the human monocytic cell line THP-1 and normal human peripheral blood mononuclear cells to define a novel role for relaxin in regulation of leukocyte adhesion and migration. Our studies indicate that relaxin promotes adenylate cyclase activation, substrate adhesion, and migratory capacity of mononuclear leukocytes through a relaxin receptor LGR7-dependent mechanism. Relaxin-stimulated cAMP accumulation was observed to occur primarily in non-adherent cells. Relaxin stimulation results in increased substrate adhesion and increased migratory activity of leukocytes. In addition, relaxin-stimulated substrate adhesion resulted in enhanced chemotaxis to monocyte chemoattractant protein-1. These responses in THP-1 and peripheral blood mononuclear cells are relaxin dose-dependent and proportional to cAMP accumulation. We further demonstrate that LGR7 is critical for mediating these biological responses by use of RNA interference lentiviral short hairpin constructs. In summary, we provide evidence that relaxin is a novel leukocyte stimulatory agent with properties affecting adhesion and chemomigration