The mechanics of disc degeneration from an engineering and computational modelling viewpoint

The anatomy and microstructure of the spine and in particular the intervertebral disc are intimately linked to how they operate in vivo and how they distribute loads to the adjacent musculature and bony anatomy. The degeneration of the intervertebral discs may be characterised by a loss of hydration, loss of disc height, a granular texture and the presence of annular lesions. As such, degeneration of the intervertebral discs compromises the mechanical integrity of their components and results in adaption and modification in the mechanical means by which loads are distributed between adjacent spinal motion segments.

Two-scale computational modelling of unsaturated flow in soils exhibiting small scale heterogeneities

Unsaturated water flow in soil is commonly modelled using Richards’ equation, which requires the hydraulic properties of the soil (e.g., porosity, hydraulic conductivity, etc.) to be characterised. Naturally occurring soils, however, are heterogeneous in nature, that is, they are composed of a number of interwoven homogeneous soils each with their own set of hydraulic properties. When the length scale of these soil heterogeneities is small, numerical solution of Richards’ equation is computationally impractical due to the immense effort and refinement required to mesh the actual heterogeneous geometry. A classic way forward is to use a macroscopic model, where the heterogeneous medium is replaced with a fictitious homogeneous medium, which attempts to give the average flow behaviour at the macroscopic scale (i.e., at a scale much larger than the scale of the heterogeneities). Using the homogenisation theory, a macroscopic equation can be derived that takes the form of Richards’ equation with effective parameters. A disadvantage of the macroscopic approach, however, is that it fails in cases when the assumption of local equilibrium does not hold. This limitation has seen the introduction of two-scale models that include at each point in the macroscopic domain an additional flow equation at the scale of the heterogeneities (microscopic scale). This report outlines a well-known two-scale model and contributes to the literature a number of important advances in its numerical implementation. These include the use of an unstructured control volume finite element method and image-based meshing techniques, that allow for irregular micro-scale geometries to be treated, and the use of an exponential time integration scheme that permits both scales to be resolved simultaneously in a completely coupled manner. Numerical comparisons against a classical macroscopic model confirm that only the two-scale model correctly captures the important features of the flow for a range of parameter values.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Modelling of arc welding : the importance of including the arc plasma in the computational domain

We present results of computational simulations of tungsten-inert-gas and metal-inert-gas welding. The arc plasma and the electrodes (including the molten weld pool when necessary) are included self-consistently in the computational domain. It is shown, using three examples, that it would be impossible to accurately estimate the boundary conditions on the weld-pool surface without including the arc plasma in the computational domain. First, we show that the shielding gas composition strongly affects the properties of the arc that influence the weld pool: heat flux density, current density, shear stress and arc pressure at the weld-pool surface. Demixing is found to be important in some cases. Second, the vaporization of the weld-pool metal and the diffusion of the metal vapour into the arc plasma are found to decrease the heat flux density and current density to the weld pool. Finally, we show that the shape of the wire electrode in metal-inert-gas welding has a strong influence on flow velocities in the arc and the pressure and shear stress at the weld-pool surface. In each case, we present evidence that the geometry and depth of the weld pool depend strongly on the properties of the arc.

Feasibility of agent-based modelling of articular cartilage including a conceptual representation of its structure

Articular cartilage is a complex structure with an architecture in which fluid-swollen proteoglycans constrained within a 3D network of collagen fibrils. Because of the complexity of the cartilage structure, the relationship between its mechanical behaviours at the macroscale level and its components at the micro-scale level are not completely understood. The research objective in this thesis is to create a new model of articular cartilage that can be used to simulate and obtain insight into the micro-macro-interaction and mechanisms underlying its mechanical responses during physiological function. The new model of articular cartilage has two characteristics, namely: i) not use fibre-reinforced composite material idealization ii) Provide a framework for that it does probing the micro mechanism of the fluid-solid interaction underlying the deformation of articular cartilage using simple rules of repartition instead of constitutive / physical laws and intuitive curve-fitting. Even though there are various microstructural and mechanical behaviours that can be studied, the scope of this thesis is limited to osmotic pressure formation and distribution and their influence on cartilage fluid diffusion and percolation, which in turn governs the deformation of the compression-loaded tissue. The study can be divided into two stages. In the first stage, the distributions and concentrations of proteoglycans, collagen and water were investigated using histological protocols. Based on this, the structure of cartilage was conceptualised as microscopic osmotic units that consist of these constituents that were distributed according to histological results. These units were repeated three-dimensionally to form the structural model of articular cartilage. In the second stage, cellular automata were incorporated into the resulting matrix (lattice) to simulate the osmotic pressure of the fluid and the movement of water within and out of the matrix; following the osmotic pressure gradient in accordance with the chosen rule of repartition of the pressure. The outcome of this study is the new model of articular cartilage that can be used to simulate and study the micromechanical behaviours of cartilage under different conditions of health and loading. These behaviours are illuminated at the microscale level using the socalled neighbourhood rules developed in the thesis in accordance with the typical requirements of cellular automata modelling. Using these rules and relevant Boundary Conditions to simulate pressure distribution and related fluid motion produced significant results that provided the following insight into the relationships between osmotic pressure gradient and associated fluid micromovement, and the deformation of the matrix. For example, it could be concluded that: 1. It is possible to model articular cartilage with the agent-based model of cellular automata and the Margolus neighbourhood rule. 2. The concept of 3D inter connected osmotic units is a viable structural model for the extracellular matrix of articular cartilage. 3. Different rules of osmotic pressure advection lead to different patterns of deformation in the cartilage matrix, enabling an insight into how this micromechanism influences macromechanical deformation. 4. When features such as transition coefficient were changed, permeability (representing change) is altered due to the change in concentrations of collagen, proteoglycans (i.e. degenerative conditions), the deformation process is impacted. 5. The boundary conditions also influence the relationship between osmotic pressure gradient and fluid movement at the micro-scale level. The outcomes are important to cartilage research since we can use these to study the microscale damage in the cartilage matrix. From this, we are able to monitor related diseases and their progression leading to potential insight into drug-cartilage interaction for treatment. This innovative model is an incremental progress on attempts at creating further computational modelling approaches to cartilage research and other fluid-saturated tissues and material systems.

Computational simulation of the early stage of bone healing under different configurations of locking compression plates

Flexible fixation or the so-called ‘biological fixation’ has been shown to encourage the formation of fracture callus, leading to better healing outcomes. However, the nature of the relationship between the degree of mechanical stability provided by a flexible fixation and the optimal healing outcomes has not been fully understood. In this study, we have developed a validated quantitative model to predict how cells in fracture callus might respond to change in their mechanical microenvironment due to different configurations of locking compression plate (LCP) in clinical practice, particularly in the early stage of healing. The model predicts that increasing flexibility of the LCP by changing the bone–plate distance (BPD) or the plate working length (WL) could enhance interfragmentary strain in the presence of a relatively large gap size (.3 mm). Furthermore, conventional LCP normally results in asymmetric tissue development during early stage of callus formation, and the increase of BPD or WL is insufficient to alleviate this problem.

Process modelling and simulation of tissue damage during mechanical peeling of pumpkin as a tough skinned vegetable

Food waste is a current challenge that both developing and developed countries face. This project applied a novel combination of available methods in Mechanical, agricultural and food engineering to address these challenges. A systematic approach was devised to investigate possibilities of reducing food waste and increasing the efficiency of industry by applying engineering concepts and theories including experimental, mathematical and computational modelling methods. This study highlights the impact of comprehensive understanding of agricultural and food material response to the mechanical operations and its direct relation to the volume of food wasted globally.

Understanding the relationship between interfragmentary movement and callus growth in fracture healing: A novel computational approach

Introduction & Aims Optimising fracture treatments requires a sound understanding of relationships between stability, callus development and healing outcomes. This has been the goal of computational modelling, but discrepancies remain between simulations and experimental results. We compared healing patterns vs fixation stiffness between a novel computational callus growth model and corresponding experimental data. Hypothesis We hypothesised that callus growth is stimulated by diffusible signals, whose production is in turn regulated by mechanical conditions at the fracture site. We proposed that introducing this scheme into computational models would better replicate the observed tissue patterns and the inverse relationship between callus size and fixation stiffness. Method Finite element models of bone healing under stiff and flexible fixation were constructed, based on the parameters of a parallel rat femoral osteotomy study. An iterative procedure was implemented, to simulate the development of callus and its mechanical regulation. Tissue changes were regulated according to published mechano-biological criteria. Predictions of healing patterns were compared between standard models, with a pre-defined domain for callus development, and a novel approach, in which periosteal callus growth is driven by a diffusible signal. Production of this signal was driven by local mechanical conditions. Finally, each model’s predictions were compared to the corresponding histological data. Results Models in which healing progressed within a prescribed callus domain predicted that greater interfragmentary movements would displace early periosteal bone formation further from the fracture. This results from artificially large distortional strains predicted near the fracture edge. While experiments showed increased hard callus size under flexible fixation, this was not reflected in the standard models. Allowing the callus to grow from a thin soft tissue layer, in response to a mechanically stimulated diffusible signal, results in a callus shape and tissue distribution closer to those observed histologically. Importantly, the callus volume increased with increasing interfragmentary movement. Conclusions A novel method to incorporate callus growth into computational models of fracture healing allowed us to successfully capture the relationship between callus size and fixation stability observed in our rat experiments. This approach expands our toolkit for understanding the influence of different fixation strategies on healing outcomes.

Study of industrially relevant boundary layer and axisymmetric flows, including swirl and turbulence

Micropolar and RNG-based modelling of industrially relevant boundary layer and recirculating swirling flows is described. Both models contain a number of adjustable parameters and auxiliary conditions that must be either modelled or experimentally determined, and the effects of varying these on the resulting flow solutions is quantified. To these ends, the behaviour of the micropolar model for self-similar flow over a surface that is both stretching and transpiring is explored in depth. The simplified governing equations permit both analytic and numerical approaches to be adopted, and a number of closed form solutions (both exact and approximate) are obtained using perturbation and order of magnitude analyses. Results are compared with the corresponding Newtonian flow solution in order to highlight the differences between the micropolar and classical models, and significant new insights into the behaviour of the micropolar model are revealed for this flow. The behaviour of the RNG-bas based models for swirling flow with vortex breakdown zones is explored in depth via computational modelling of two experimental data sets and an idealised breakdown flow configuration. Meticulous modeling of upstream auxillary conditions is required to correctly assess the behavior of the models studied in this work. The novel concept of using the results to infer the role of turbulence in the onset and topology of the breakdown zone is employed.

Structural characterisation and environmental application of organoclays for the removal of phenolic compounds

Modified montmorillonite was prepared at different surfactant (HDTMA) loadings through ion exchange. The conformational arrangement of the loaded surfactants within the interlayer space of MMT was obtained by computational modelling. The conformational change of surfactant molecules enhance the visual understanding of the results obtained from characterization methods such as XRD and surface analysis of the organoclays. Batch experiments were carried out for the adsorption of p-chlorophenol (PCP) and different conditions (pH and temperature) were used in order to determine the optimum sorption. For comparison purpose, the experiments were repeated under the same conditions for p-nitrophenol (PNP). Langmuir and Freundlich equations were applied to the adsorption isotherm of PCP and PNP. The Freundlich isotherm model was found to be the best fit for both of the phenolic compounds. This involved multilayer adsorptions in the adsorption process. In particular, the binding affinity value of PNP was higher than that of PCP and this is attributable to their hydrophobicities. The adsorption of the phenolic compounds by organoclays intercalated with highly loaded surfactants was markedly improved possibly due to the fact that the intercalated surfactant molecules within the interlayer space contribute to the partition phases, which result in greater adsorption of the organic pollutants.

Reactions of simple and peptidic alpha-carboxylate radical anions with dioxygen in the gas phase

alpha-Carboxylate radical anions are potential reactive intermediates in the free radical oxidation of biological molecules (e. g., fatty acids, peptides and proteins). We have synthesised well-defined alpha-carboxylate radical anions in the gas phase by UV laser photolysis of halogenated precursors in an ion-trap mass spectrometer. Reactions of isolated acetate ((center dot)CH(2)CO(2)) and 1-carboxylatobutyl (CH(3)CH(2)CH(2)(center dot)CHCO(2)(-)) radical anions with dioxygen yield carbonate (CO(3)(center dot-)) radical anions and this chemistry is shown to be a hallmark of oxidation in simple and alkyl-substituted cross-conjugated species. Previous solution phase studies have shown that C(alpha)-radicals in peptides, formed from free radical damage, combine with dioxygen to form peroxyl radicals that subsequently decompose into imine and keto acid products. Here, we demonstrate that a novel alternative pathway exists for two alpha-carboxylate C(alpha)-radical anions: the acetylglycinate radical anion (CH(3)C(O)NH(center dot)CHCO(2)(-)) and the model peptide radical anion, YGGFG(center dot-). Reaction of these radical anions with dioxygen results in concerted loss of carbon dioxide and hydroxyl radical. The reaction of the acetylglycinate radical anion with dioxygen reveals a two-stage process involving a slow, followed by a fast kinetic regime. Computational modelling suggests the reversible formation of the C(alpha) peroxyl radical facilitates proton transfer from the amide to the carboxylate group, a process reminiscent of, but distinctive from, classical proton-transfer catalysis. Interestingly, inclusion of this isomerization step in the RRKM/ME modelling of a G3SX level potential energy surface enables recapitulation of the experimentally observed two-stage kinetics.

STI-GMaS : an open-source environment for simulation of sexually-transmitted infections

Background Sexually-transmitted pathogens often have severe reproductive health implications if treatment is delayed or absent, especially in females. The complex processes of disease progression, namely replication and ascension of the infection through the genital tract, span both extracellular and intracellular physiological scales, and in females can vary over the distinct phases of the menstrual cycle. The complexity of these processes, coupled with the common impossibility of obtaining comprehensive and sequential clinical data from individual human patients, makes mathematical and computational modelling valuable tools in developing our understanding of the infection, with a view to identifying new interventions. While many within-host models of sexually-transmitted infections (STIs) are available in existing literature, these models are difficult to deploy in clinical/experimental settings since simulations often require complex computational approaches. Results We present STI-GMaS (Sexually-Transmitted Infections – Graphical Modelling and Simulation), an environment for simulation of STI models, with a view to stimulating the uptake of these models within the laboratory or clinic. The software currently focuses upon the representative case-study of Chlamydia trachomatis, the most common sexually-transmitted bacterial pathogen of humans. Here, we demonstrate the use of a hybrid PDE–cellular automata model for simulation of a hypothetical Chlamydia vaccination, demonstrating the effect of a vaccine-induced antibody in preventing the infection from ascending to above the cervix. This example illustrates the ease with which existing models can be adapted to describe new studies, and its careful parameterisation within STI-GMaS facilitates future tuning to experimental data as they arise. Conclusions STI-GMaS represents the first software designed explicitly for in-silico simulation of STI models by non-theoreticians, thus presenting a novel route to bridging the gap between computational and clinical/experimental disciplines. With the propensity for model reuse and extension, there is much scope within STI-GMaS to allow clinical and experimental studies to inform model inputs and drive future model development. Many of the modelling paradigms and software design principles deployed to date transfer readily to other STIs, both bacterial and viral; forthcoming releases of STI-GMaS will extend the software to incorporate a more diverse range of infections.