Browsing by Author "McBride, Andrew Trevor"

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    Open Access
    Computational simulation of bone remodelling post reverse total shoulder arthroplasty
    (2017) Liedtke, Helen; McBride, Andrew Trevor; Reddy, B Daya
    Bone is a living material. It adapts, in an optimal sense, to loading by changing its density and trabeculae architecture - a process termed remodelling. Implanted orthopaedic devices can significantly alter the loading on the surrounding bone. In addition, these devices rely on bone ingrowth to ensure secure implant fixation. In this project, a computational model that accounts for bone remodelling is developed and used to elucidate the response of bone following a reverse shoulder procedure. The reverse shoulder procedure investigated here is for rotary cuff deficient patients. In this procedure up to 75 % complications are reported in some clinical series. It is therefore necessary, for the design of successful implants, to understand the loading environment to promote bone growth in the correct areas. The physical process of remodelling is modelled using continuum scale, open system thermodynamics whereby the density of bone evolves isotropically in response to the loading it experiences. The fully-nonlinear continuum theory is solved approximately using the finite element method. The finite element library AceGEN forms the basis for the implementation. Several benchmark problems were implemented to validate the code and demonstrate features of the theory. These include several one-dimensional problems, the classical two-dimensional femur benchmark, and a series of three-dimensional examples. The three-dimensional examples include different loading scenarios on a rectangular block, as well as the investigation of the ASTM testing procedure of the glenoid side prosthesis implanted in a polyurethane foam block. The results clearly demonstrate the adaptive behaviour of the bone density in response to the magnitude and duration of the loading. The numerical implementation is also shown to be robust. The remodelling of the scapula post reverse shoulder arthroplasty is then investigated. A statistical shape model of the scapula was obtained from collaborators in the Division of Biomedical Engineering at the University of Cape Town. The finite element model was used to determine the density distribution in the scapula prior to surgery. A virtual surgery was then performed. The resulting geometry provides the input for the pre-processing phase of the post reverse shoulder arthroplasty model. The loading conditions for the reverse shoulder were provided by collaborators in the Division of Biomedical Engineering and the Leon Root Motion Analysis Laboratory at the Hospital for Special Surgery in New York City. The maximal loading condition at 90° abduction is used as the input for the simulation. It was found that the density increases in the vicinity of the screws, where the maximum stresses are concentrated, however, bone resorption is observed directly below and adjacent to the implant. No conclusive statement can be made, however, as only one loading scenario is considered and calibration of the model against experimental results is still outstanding. A unique feature of the code is that the upper and lower bounds of the density do not have to be enforced directly, as done in most bone remodelling theories in the literature. Rather, the bounds of the density are naturally enforced by calibrating the mass flux for the problem at hand. This project lays out the groundwork for a sound remodelling code, which can serve as a predictive tool in the field of orthopaedics.
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    Constitutive modelling of the skin accounting for chronological ageing
    (2017) Pond, Damien; McBride, Andrew Trevor
    The skin is the largest organ in the human body. It is the first line of contact with the outside world, being subject to a harsh array of physical loads and environmental factors. In addition to this, the skin performs numerous physiological tasks such as thermo-regualtion, vitamin D synthesis and neurotransduction. The skin, as with all biological tissue, is subject to chronological ageing, whereby there is a general breakdown of tissue function and a decline in mechanical properties. In addition to this, skin undergoes extrinsic forms of ageing through exposure to external factors such as ultraviolet radiation, air pollution and cigarette smoking. Skin modelling is an area of biomechanics that, although medical in nature, has expanded into areas such as cosmetics, military, sports equipment and computer graphics. Skin can be approximated at the macroscopic continuum scale as an anisotropic, nearly-incompressible, viscoelastic and non-linear material whose material properties are highly dependent on the ageing process. Through the literature, several phenomenologically based models have been satisfactorily employed to capture the behaviour inherent to the skin, but despite the intrinsic link to age, to date no constitutive model for the UV-induced ageing/damage of skin has been developed that is both capable of capturing the material and structural effects, and is embedded in the rigorous framework of non-linear continuum mechanics. Such a mechanistic model is proposed here. The macroscopic response of the skin is due to microscopic components such as collagen, elastin and the surrounding ground substance and the interaction between them. An overview on the structure of the skin helps motivate the form of the continuum model and identifies which aspects of the skin need to be captured in order to replicate the macroscopic response. Furthermore, the ageing process is explored and a firm understanding of the influence of ageing on the substructures is established. Over time, elastin levels tend to decrease which results in a loss of skin elasticity. Collagen levels drop with age, but tend to flatten out which results in an overall increase in skin stiffness and loss of anisotropy. A worm-like chain constitutive model, arranged in an 8-chain configuration, is employed to capture the mechanical response of the skin. The use of such a micro-structurally-motivated model attempts to connect the underlying substructures (collagen, elastin and ground substance) present in the skin to the overall mechanical response. The constitutive model is implemented within a finite element scheme. Simple uniaxial tests are employed to ascertain the validity of the model, whereby skin samples are stretched to elicit the typical anisotropic locking response. A more complex loading condition is applied through bulge tests where a pressure is applied to an in vitro skin specimen. This more complex test is subsequently used to conduct a series of ageing numerical experiments to ascertain the response of the model to changes in material properties associated with ageing. A modified model is then proposed to capture the ageing response of the skin. The key microscopic biophysical processes that underpin ageing are identified, approximated and adapted sufficiently to be of use in the macroscopic continuum model. Aspects of open-system thermodynamics and mixture theory are adapted to the context of ageing in order to capture a continuous ageing response.
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    Fluid-structure interaction modelling of a patient-specific arteriovenous access fistula
    (2016) Guess, Winston; Reddy, B Daya; McBride, Andrew Trevor
    This research forms part of an interdisciplinary project that aims to improve the detailed understanding of the haemodynamics and vascular mechanics in arteriovenous shunts that are required for haemodialysis treatments. A combination of new PCMRA imaging and computational modelling of in vivo blood flow aims to determine the haemodynamic conditions that may lead to the high failure rate of vascular access in these circumstances. This thesis focuses on developing a patient-specific fluid-structure interaction (FSI) model of a PC-MRA imaged arteriovenous fistula. The numerical FSI model is developed and simulated within the commercial multiphysics simulation package ANSYS® Academic Research, Release 16. The blood flow is modelled as a Newtonian fluid with the finite-volume method solver ANSYS® Fluent®. A pulsatile mass-flow boundary condition is applied at the artery inlet and a three-element Windkessel model at the artery and vein outlets. ANSYS® Mechanical™, a finite element method solver, is used to model the nonlinear behaviour of the vessel walls. The artery and vein walls are assumed to follow a third-order Yeoh model, and are differentiated by thickness and by material strength characteristics. The staggered FSI model is configured and executed in ANSYS® Workbench™, forming a semi-implicit coupling of the blood flow and vessel wall models. This work shows the effectiveness of combining a number of stabilisation techniques to simultaneously overcome the added-mass effect and optimise the efficiency of the overall model. The PC-MRA data, fluid model, and FSI model show almost identical flow features in the fistula; this applies in particular to a flow recirculation region in the vein that could potentially lead to fistula failure.
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    Formulation, analysis and solution algorithms for a model of gradient plasticity within a discontinuous Galerkin framework
    (2008) McBride, Andrew Trevor; Reddy, B Daya
    An investigation of a model of gradient plasticity in which the classical von Mises yield function is augmented by a term involving the Laplacian of the equivalent plastic strain is presented. The theory is developed within the framework of non-smooth convex analysis by exploiting the equivalence between the primal and dual expressions of the plastic deformation evolution relations. The nonlocal plastic evolution relations for the case of gradient plasticity are approximated using a discontinuous Galerkin finite element formulation. Both the small- and finite-strain theories are investigated. Considerable attention is focused on developing a firm mathematical foundation for the model of gradient plasticity restricted to the infinitesimal-strain regime. The key contributions arising from the analysis of the classical plasticity problem and the model of gradient plasticity include demonstrating the consistency of the variational formulation, and analyses of both the continuous-in-time and fully-discrete approximations; the error estimates obtained correspond to those for the conventional Galerkin approximations of the classical problem. The focus of the analysis is on those properties of the problem that would ensure existence of a unique solution for both hardening and softening problems. It is well known that classical finite element method simulations of softening problems are pathologically dependent on the discretisation.
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    Multiple particle tracking in PEPT using Voronoi tessellations
    (2016) Blakemore, Dylan; Govender, Indresan; McBride, Andrew Trevor
    An algorithm is presented which makes use of three-dimensional Voronoi tessellations to track up to 20 tracers using a PET scanner. The lines of response generated by the PET scanner are discretized into sets of equidistant points, and these are used as the input seeds to the Voronoi tessellation. For each line of response, the point with the smallest Voronoi region is located; this point is assumed to be the origin of the corresponding line of response. Once these origin points have been determined, any outliers are removed, and the remaining points are clustered using the DBSCAN algorithm. The centroid of each cluster is classified as a tracer location. Once the tracer locations are determined for each time frame in the experimental data set, a custom multiple target tracking algorithm is used to associate identical tracers from frame to frame. Since there are no physical properties to distinguish the tracers from one another, the tracking algorithm uses velocity and position to extrapolate the locations of existing tracers and match the next frame's tracers to the trajectories. A series of experiments were conducted in order to test the robustness, accuracy and computational performance of the algorithm. A measure of robustness is the chance of track loss, which occurs when the algorithm fails to match a tracer location with its trajectory, and the track is terminated. The chance of track loss increases with the number of tracers; the acceleration of the tracers; the time interval between successive frames; and the proximity of tracers to each other. In the case of two tracers colliding, the two tracks merge for a short period of time, before separating and become distinguishable again. Track loss also occurs when a tracer leaves the field of view of the scanner; on return it is treated as a new object. The accuracy of location of the algorithm was found to be slightly affected by tracer velocity, but is much more dependent on the distance between consecutive points on a line of response, and the number of lines of response used per time frame. A single tracer was located to within 1.26mm. This was compared to the widely accepted Birmingham algorithm, which located the same tracer to within 0.92mm. Precisions of between 1.5 and 2.0mm were easily achieved for multiple tracers. The memory usage and processing time of the algorithm are dependent on the number of tracers used in the experiment. It was found that the processing time per frame for 20 tracers was about 15s, and the memory usage was 400MB. Because of the high processing times, the algorithm as is is not feasible for practical use. However, the location phase of the algorithm is massively parallel, so the code can be adapted to significantly increase the efficiency.
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    A patient-specific FSI model for vascular access in haemodialysis
    (2017) De Villiers, Anna Magdalena; Reddy, B Daya; McBride, Andrew Trevor
    This research forms part of an interdisciplinary project that aims to improve the understanding of haemodynamics and vascular mechanics in arteriovenous shunting. To achieve the high flow rates that enable patients with renal disease to receive haemodialysis, a fistula is created between an artery and a vein. The patency rate of fistulas, especially those located in the upper arm, is low. The approach adopted here makes use of new magnetic resonance image (MRI) technology and computational modelling of blood flow, with a view to improving therapeutic strategies of disease requiring vascular interventions. This thesis presents the construction and development of a 3D finite element model of the fluid-structure interaction in a brachial–cephalic patient–specific fistula. An overview of the mathematical models that describe the vessel wall and fluid behaviour as well their interaction with each other is given. An Arbitrary Lagrangian- Eulerian (ALE) framework is used together with a transversely isotropic hyperelastic constitutive model for the vessel walls, while blood flow is modelled as a Newtonian fluid. A three-element Windkessel model is used to allow the fluid to move through the outlets of the computational domain without causing non–physical reflections. Flow data acquired from MRI is used to prescribe the flow at the inlet. The parameters of the Windkessel-model at the two outlets are calibrated to resemble the flow acquired from the 2D MRI. The model is validated against the flow patterns acquired from the 4D MRI. The flow patterns of the blood, and stress present in the vessel are investigated. Of special significance are the flow and wall shear stress at the anastomosis. An area of very high velocity in the anastomosis is followed by an area of recirculation and low velocity. The propagation of pressure waves and their reflection at the anastomosis are studied. Areas that are subjected to low wall shear stress, high oscillatory wall shear stress or flow circulation are identified as areas where intimal hyperplasia may develop. The flow results from the simulation show good qualitative agreement with the MRI data.
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    Stable algorithms for generalized thermoelasticity based on operator-splitting and time-discontinuous Galerkin finite element methods
    (2016) Wakeni, Mebratu Fenta; Reddy, B Daya; McBride, Andrew Trevor
    This thesis deals with the theoretical and numerical analysis of coupled problems in thermoelasticity. Of particular interest are models that support propagation of thermal energy as waves, rather than the usual mechanism by diffusion. The thesis consists of two parts. The first deals with the non-classical, linear thermoelastic model first proposed and developed by Green and Naghdi in the years between 1991 and 1995, as a possible alternative that potentially removes the shortcomings of the standard Fourier based model. The non-classical theory incorporates three models: the classical model based on Fourier's law of heat conduction, resulting in a hyperbolic-parabolic coupled system; a non-classical theory of a fully-hyperbolic extension; and a combination of the two. An efficient staggered time-stepping algorithm is proposed based on operator-splitting and the time-discontinuous Galerkin finite element method for the non-classical, linear thermoelastic model. The coupled problem is split into two contractive sub-problems, namely, the mechanical phase and thermal phase, on the basis of an entropy controlling mechanism. In the mechanical phase temperature is allowed to vary so as to ensure the entropy remains constant, while the thermal phase is a purely non-classical heat conduction problem in a fixed configuration. Each sub-problem is discretized using the time-discontinuous Galerkin finite element method, resulting in stable time-stepping sub-algorithms. A global stable algorithm is obtained by combining the algorithms for the sub-problems by way of a product method. A number of numerical examples are presented to demonstrate the performance and capability of the method. The second part of this work concerns the formulation of a thermodynamically consistent generalized model of nonlinear thermoelasticity, whose linearization about a natural reference configuration includes the theory of Green and Naghdi. The generalized model is based on the fundamental laws of continuum mechanics and thermodynamics, and is realized through two basic assumptions: The first is the inclusion into the state space of a vector field, which is known as the thermal displacement, and is a time primitive of the absolute temperature. The second is that the heat flux vector is additively split into two parts, which are referred to as the energetic and dissipative components of the heat flux vector. The application of the Coleman-Noll procedure leads to find constitutive relations for the stress, entropy, and energetic component of the heat flux as derivatives of the free energy function. Furthermore, a Clausius-Duhem-type inequality is assumed on a constitutive relation for the dissipative component of the heat flux vector to ensure thermodynamic consistency. A Lyapunov function is obtained for the generalized problem with finite strains; this serves as the basis for the stability analysis of the numerical methods designed for generalized thermoelasticity at finite strains. Due to the lack of convexity of the elastic potential in the finite strain case, a direct extension of the time-discontinuous formulation from the linear to the finite strain case does not guarantee stability. For this reason, various numerical formulations both in monolithic and staggered approaches with fully or partially time-discontinuity assumptions are presented in the framework of the space-time methods. The stability of each of the numerical algorithms is thoroughly analysed. The capability of the newly formulated generalized model of thermoelasticity in predicting various expected features of non-Fourier response is illustrated by a number of numerical examples. These also serve to demonstrate the performance of the space-time Galerkin method in capturing fine solution features.