Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Preface to special issue on digital human modelling for vehicle design and manufacturing

The automotive industry has been the focus of digital human modeling (DHM) research and application for many years. In the highly competitive marketplace for personal transportation, the desire to improve the customer’s experience has driven extensive research in both the physical and cognitive interaction between the vehicle and its occupants. Human models provide vehicle designers with tools to view and analyze product interactions before the first prototypes are built, potentially improving the design while reducing cost and development time. The focus of DHM research and applications began with prediction and representation of static postures for purposes of driver workstation layout, including assessments of seat adjustment ranges and exterior vision. Now DHMs are used for seat design and assessment of driver reach and ingress/egress. DHMs and related simulation tools are expanding into the cognitive domain, with computational models of perception and motion, and into the dynamic domain with models of physical responses to ride and vibration. Moreover, DHMs are now widely used to analyze the ergonomics of vehicle assembly tasks. In this case, the analysis aims to determine whether workers can be expected to complete the tasks safely and with good quality. This preface provides a review of the literature to provide context for the nine new papers presented in this special issue.

Contribution to single-point closure Reynolds-stress modelling of inhomogeneous flow

This paper is concerned with recent advances in the development of near wall-normal-free Reynolds-stress models, whose single point closure formulation, based on the inhomogeneity direction concept, is completely independent of the distance from the wall, and of the normal to the wall direction. In the present approach the direction of the inhomogeneity unit vector is decoupled from the coefficient functions of the inhomogeneous terms. A study of the relative influence of the particular closures used for the rapid redistribution terms and for the turbulent diffusion is undertaken, through comparison with measurements, and with a baseline Reynolds-stress model (RSM) using geometric wall normals. It is shown that wall-normal-free rsms can be reformulated as a projection on a tensorial basis that includes the inhomogeneity direction unit vector, suggesting that the theory of the redistribution tensor closure should be revised by taking into account inhomogeneity effects in the tensorial integrity basis used for its representation.

Growth of confined cancer spheroids : a combined experimental marker, critical modelling approach

A critical step in the dissemination of ovarian cancer is the formation of multicellular spheroids from cells shed from the primary tumour. The objectives of this study were to apply bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer spheroids in vitro and simultaneously to build on a mathematical model describing the growth of multicellular spheroids in these biomimetic matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and grown for up to 4 weeks. Immunohistochemistry, imaging and growth analyses were used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel. The mathematical model was formulated as a free boundary problem in which each spheroid was treated as an incompressible porous medium. The functional forms used to describe the rates of cell proliferation and apoptosis were motivated by the experimental work and predictions of the mathematical model compared with the experimental output. This work aimed to establish whether it is possible to simulate solid tumour growth on the basis of data on spheroid size, cell proliferation and cell death within these spheroids. The mathematical model predictions were in agreement with the experimental data set and simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture duration and administration of a chemotherapeutic drug. Our computational model provides new perspectives on experimental results and has informed the design of new 3D studies of chemoresistance of multicellular cancer spheroids.

Continuum mechanics modelling of microfilament networks with different architectures based on molecular investigation of single F-actin

The actin microfilament plays a critical role in many cellular processes including embryonic development, wound healing, immune response, and tissue development. It is commonly organized in the form of networks whose mechanical properties change with changes in their architecture due to cell evolution processes. This paper presents a new nonlinear continuum mechanics model of single filamentous actin (F-actin) that is based on nanoscale molecular simulations. Following this continuum model of the single F-actin, mechanical properties of differently architected lamellipodia are studied. The results provide insight that can contribute to the understanding of the cell edge motions of living cells.

Cohesive zone modelling of mineralized collagen fibril arrays in bending

Hard biological materials such as bone possess superior material properties of high stiffness and toughness. Two unique characteristics of bone microstructure are a large aspect ratio of mineralized collagen fibrils (MCF), and an extremely thin and large area of extrafibrillar protein matrix located between the MCF. The objective of this study is to investigate the effects of: (1) MCF aspect ratio, and (2) energy dissipation in extrafibrillar protein matrix on the mechanical behaviour of MCF arrays. In this study, notched specimens of MCF arrays in extrafibrillar protein matrix are subjected to bending. Cohesive zone model was implemented to simulate the failure of extrafibrillar protein matrix. The study reveals that the MCF array with a higher MCF aspect ratio and the MCF array with a higher protein energy dissipation in the interface direction are able to sustain a higher bending force and dissipate higher energy.

Modelling client puzzles and denial-of-service resistant protocols

Denial-of-service (DoS) attacks are a growing concern to networked services like the Internet. In recent years, major Internet e-commerce and government sites have been disabled due to various DoS attacks. A common form of DoS attack is a resource depletion attack, in which an attacker tries to overload the server's resources, such as memory or computational power, rendering the server unable to service honest clients. A promising way to deal with this problem is for a defending server to identify and segregate malicious traffic as earlier as possible. Client puzzles, also known as proofs of work, have been shown to be a promising tool to thwart DoS attacks in network protocols, particularly in authentication protocols. In this thesis, we design efficient client puzzles and propose a stronger security model to analyse client puzzles. We revisit a few key establishment protocols to analyse their DoS resilient properties and strengthen them using existing and novel techniques. Our contributions in the thesis are manifold. We propose an efficient client puzzle that enjoys its security in the standard model under new computational assumptions. Assuming the presence of powerful DoS attackers, we find a weakness in the most recent security model proposed to analyse client puzzles and this study leads us to introduce a better security model for analysing client puzzles. We demonstrate the utility of our new security definitions by including two hash based stronger client puzzles. We also show that using stronger client puzzles any protocol can be converted into a provably secure DoS resilient key exchange protocol. In other contributions, we analyse DoS resilient properties of network protocols such as Just Fast Keying (JFK) and Transport Layer Security (TLS). In the JFK protocol, we identify a new DoS attack by applying Meadows' cost based framework to analyse DoS resilient properties. We also prove that the original security claim of JFK does not hold. Then we combine an existing technique to reduce the server cost and prove that the new variant of JFK achieves perfect forward secrecy (the property not achieved by original JFK protocol) and secure under the original security assumptions of JFK. Finally, we introduce a novel cost shifting technique which reduces the computation cost of the server significantly and employ the technique in the most important network protocol, TLS, to analyse the security of the resultant protocol. We also observe that the cost shifting technique can be incorporated in any Diffine{Hellman based key exchange protocol to reduce the Diffie{Hellman exponential cost of a party by one multiplication and one addition.

Modelling sea water intrusion in coastal aquifers using heterogeneous computing

The objective of this PhD research program is to investigate numerical methods for simulating variably-saturated flow and sea water intrusion in coastal aquifers in a high-performance computing environment. The work is divided into three overlapping tasks: to develop an accurate and stable finite volume discretisation and numerical solution strategy for the variably-saturated flow and salt transport equations; to implement the chosen approach in a high performance computing environment that may have multiple GPUs or CPU cores; and to verify and test the implementation. The geological description of aquifers is often complex, with porous materials possessing highly variable properties, that are best described using unstructured meshes. The finite volume method is a popular method for the solution of the conservation laws that describe sea water intrusion, and is well-suited to unstructured meshes. In this work we apply a control volume-finite element (CV-FE) method to an extension of a recently proposed formulation (Kees and Miller, 2002) for variably saturated groundwater flow. The CV-FE method evaluates fluxes at points where material properties and gradients in pressure and concentration are consistently defined, making it both suitable for heterogeneous media and mass conservative. Using the method of lines, the CV-FE discretisation gives a set of differential algebraic equations (DAEs) amenable to solution using higher-order implicit solvers. Heterogeneous computer systems that use a combination of computational hardware such as CPUs and GPUs, are attractive for scientific computing due to the potential advantages offered by GPUs for accelerating data-parallel operations. We present a C++ library that implements data-parallel methods on both CPU and GPUs. The finite volume discretisation is expressed in terms of these data-parallel operations, which gives an efficient implementation of the nonlinear residual function. This makes the implicit solution of the DAE system possible on the GPU, because the inexact Newton-Krylov method used by the implicit time stepping scheme can approximate the action of a matrix on a vector using residual evaluations. We also propose preconditioning strategies that are amenable to GPU implementation, so that all computationally-intensive aspects of the implicit time stepping scheme are implemented on the GPU. Results are presented that demonstrate the efficiency and accuracy of the proposed numeric methods and formulation. The formulation offers excellent conservation of mass, and higher-order temporal integration increases both numeric efficiency and accuracy of the solutions. Flux limiting produces accurate, oscillation-free solutions on coarse meshes, where much finer meshes are required to obtain solutions with equivalent accuracy using upstream weighting. The computational efficiency of the software is investigated using CPUs and GPUs on a high-performance workstation. The GPU version offers considerable speedup over the CPU version, with one GPU giving speedup factor of 3 over the eight-core CPU implementation.

Mechanical testing and modelling of a bone-implant construct

Finite Element modelling of bone fracture fixation systems allows computational investigation of the deformation response of the bone to load. Once validated, these models can be easily adapted to explore changes in design or configuration of a fixator. The deformation of the tissue within the fracture gap determines its healing and is often summarised as the stiffness of the construct. FE models capable of reproducing this behaviour would provide valuable insight into the healing potential of different fixation systems. Current model validation techniques lack depth in 6D load and deformation measurements. Other aspects of the FE model creation such as the definition of interfaces between components have also not been explored. This project investigated the mechanical testing and FE modelling of a bone– plate construct for the determination of stiffness. In depth 6D measurement and analysis of the generated forces, moments and movements showed large out of plane behaviours which had not previously been characterised. Stiffness calculated from the interfragmentary movement was found to be an unsuitable summary parameter as the error propagation is too large. Current FE modelling techniques were applied in compression and torsion mimicking the experimental setup. Compressive stiffness was well replicated, though torsional stiffness was not. The out of plane behaviours prevalent in the experimental work were not replicated in the model. The interfaces between the components were investigated experimentally and through modification to the FE model. Incorporation of the interface modelling techniques into the full construct models had no effect in compression but did act to reduce torsional stiffness bringing it closer to that of the experiment. The interface definitions had no effect on out of plane behaviours, which were still not replicated. Neither current nor novel FE modelling techniques were able to replicate the out of plane behaviours evident in the experimental work. New techniques for modelling loads and boundary conditions need to be developed to mimic the effects of the entire experimental system.

How to increase the accuracy of analysis and reduce the computational time in ANSYS in the case of deformation study of orthopedic bone plates

Currently, finite element analyses are usually done by means of commercial software tools. Accuracy of analysis and computational time are two important factors in efficiency of these tools. This paper studies the effective parameters in computational time and accuracy of finite element analyses performed by ANSYS and provides the guidelines for the users of this software whenever they us this software for study on deformation of orthopedic bone plates or study on similar cases. It is not a fundamental scientific study and only shares the findings of the authors about structural analysis by means of ANSYS workbench. It gives an idea to the readers about improving the performance of the software and avoiding the traps. The solutions provided in this paper are not the only possible solutions of the problems and in similar cases there are other solutions which are not given in this paper. The parameters of solution method, material model, geometric model, mesh configuration, number of the analysis steps, program controlled parameters and computer settings are discussed through thoroughly in this paper.

Correlating flow induced shear stress and chondrocytes activity in micro-porous scaffold using computational fluid dynamics and rapid prototyping

Flow induced shear stress plays an important role in regulating cell growth and distribution in scaffolds. This study sought to correlate wall shear stress and chondrocytes activity for engineering design of micro-porous osteochondral grafts based on the hypothesis that it is possible to capture and discriminate between the transmitted force and cell response at the inner irregularities. Unlike common tissue engineering therapies with perfusion bioreactors in which flow-mediated stress is the controlling parameter, this work assigned the associated stress as a function of porosity to influence in vitro proliferation of chondrocytes. D-optimality criterion was used to accommodate three pore characteristics for appraisal in a mixed level fractional design of experiment (DOE); namely, pore size (4 levels), distribution pattern (2 levels) and density (3 levels). Micro-porous scaffolds (n=12) were fabricated according to the DOE using rapid prototyping of an acrylic-based bio-photopolymer. Computational fluid dynamics (CFD) models were created correspondingly and used on an idealized boundary condition with a Newtonian fluid domain to simulate the dynamic microenvironment inside the pores. In vitro condition was reproduced for the 3D printed constructs seeded by high pellet densities of human chondrocytes and cultured for 72 hours. The results showed that cell proliferation was significantly different in the constructs (p<0.05). Inlet fluid velocity of 3×10-2mms-1 and average shear stress of 5.65×10-2 Pa corresponded with increased cell proliferation for scaffolds with smaller pores in hexagonal pattern and lower densities. Although the analytical solution of a Poiseuille flow inside the pores was found insufficient for the description of the flow profile probably due to the outside flow induced turbulence, it showed that the shear stress would increase with cell growth and decrease with pore size. This correlation demonstrated the basis for determining the relation between the induced stress and chondrocyte activity to optimize microfabrication of engineered cartilaginous constructs.

A multiscale road map of cancer spheroids : incorporating experimental and mathematical modelling to understand cancer progression

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.

GPU accelerated MCMC for modelling terrorist activity

The use of graphical processing unit (GPU) parallel processing is becoming a part of mainstream statistical practice. The reliance of Bayesian statistics on Markov Chain Monte Carlo (MCMC) methods makes the applicability of parallel processing not immediately obvious. It is illustrated that there are substantial gains in improved computational time for MCMC and other methods of evaluation by computing the likelihood using GPU parallel processing. Examples use data from the Global Terrorism Database to model terrorist activity in Colombia from 2000 through 2010 and a likelihood based on the explicit convolution of two negative-binomial processes. Results show decreases in computational time by a factor of over 200. Factors influencing these improvements and guidelines for programming parallel implementations of the likelihood are discussed.

Numerical modelling of porous injection in a radical farming scramjet

A numerical investigation of the behaviour of fuel injection through a porous surface in an inlet-fuelled, radial-farming scramjet is presented. The performance of porous fuel injection is compared to discrete port hole injection at an equivalence ratio of φ ≈ 0.4 for both cases. The comparison is performed at a Mach 6.5 flow condition with a total specific enthalpy of 4.3 MJ/kg. The numerical results are compared to experiments performed in the T4 shock tunnel where available. The presented results demonstrate for the first time, that porous fuel injection has the potential to outperform port hole injectors in scramjet engines in terms of fuel-air mixing, ignition delays and achievable combustion efficiencies despite reduced fuel penetration heights.

Computation of ECG signal features using MCMC modelling in software and FPGA reconfigurable hardware

Computational optimisation of clinically important electrocardiogram signal features, within a single heart beat, using a Markov-chain Monte Carlo (MCMC) method is undertaken. A detailed, efficient data-driven software implementation of an MCMC algorithm has been shown. Initially software parallelisation is explored and has been shown that despite the large amount of model parameter inter-dependency that parallelisation is possible. Also, an initial reconfigurable hardware approach is explored for future applicability to real-time computation on a portable ECG device, under continuous extended use.