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.

Bioavailability of soil organic carbon and Fe as influenced by forestry practices in a subtropical coastal catchment

Potential impacts of plantation forestry practices on soil organic carbon and Fe available to microorganisms were investigated in a subtropical coastal catchment. The impacts of harvesting or replanting were largely limited to the soil top layer (0–10 cm depth). The thirty-year-old Pinus plantation showed low soil moisture content (Wc) and relatively high levels of soil total organic carbon (TOC). Harvesting and replanting increased soil Wc but reduced TOC levels. Mean dissolved organic carbon (DOC) and microbial biomass carbon (MBC) increased in harvested or replanted soils, but such changes were not statistically significant (P > 0.05). Total dithionite-citrate and aqua regia-extractable Fe did not respond to forestry practices, but acid ammonium oxalate and pyrophosphate-extractable, bioavailable Fe decreased markedly after harvesting or replanting. Numbers of heterotrophic bacteria were significantly correlated with DOC levels (P < 0.05), whereas Fe-reducing bacteria and S-bacteria detected using laboratory cultivation techniques did not show strong correlation with either soil DOC or Fe content.

Does physical protection of soil organic matter attenuate temperature sensitivity?

Global climate change may induce accelerated soil organic matter (SOM) decomposition through increased soil temperature, and thus impact the C balance in soils. We hypothesized that compartmentalization of substrates and decomposers in the soil matrix would decrease SOM sensitivity to temperature. We tested our hypothesis with three short-term laboratory incubations with differing physical protection treatments conducted at different temperatures. Overall, CO2 efflux increased with temperature, but responses among physical protection treatments were not consistently different. Similar respiration quotient (Q(10)) values across physical protection treatments did not support our original hypothesis that the largest Q(10) values would be observed in the treatment with the least physical protection. Compartmentalization of substrates and decomposers is known to reduce the decomposability of otherwise labile material, but the hypothesized attenuation of temperature sensitivity was not detected, and thus the sensitivity is probably driven by the thermodynamics of biochemical reactions as expressed by Arrhenius-type equations.

Experimental warming shows that decomposition temperature sensitivity increases with soil organic matter recalcitrance

Soil C decomposition is sensitive to changes in temperature, and even small increases in temperature may prompt large releases of C from soils. But much of what we know about soil C responses to global change is based on short-term incubation data and model output that implicitly assumes soil C pools are composed of organic matter fractions with uniform temperature sensitivities. In contrast, kinetic theory based on chemical reactions suggests that older, more-resistant C fractions may be more temperature sensitive. Recent research on the subject is inconclusive, indicating that the temperature sensitivity of labile soil organic matter (OM) decomposition could either be greater than, less than, or equivalent to that of resistant soil OM. We incubated soils at constant temperature to deplete them of labile soil OM and then successively assessed the CO2-C efflux in response to warming. We found that the decomposition response to experimental warming early during soil incubation (when more labile C remained) was less than that later when labile C was depleted. These results suggest that the temperature sensitivity of resistant soil OM pools is greater than that for labile soil OM and that global change-driven soil C losses may be greater than previously estimated.