Attenuation of muscle damage by preconditioning with muscle hyperthermia

This study investigated the hypothesis that muscle damage would be attenuated in muscles subjected to passive hyperthermia 1 day prior to exercise. Fifteen male students performed 24 maximal eccentric actions of the elbow flexors with one arm; the opposite arm performed the same exercise 2-4 weeks later. The elbow flexors of one arm received a microwave diathermy treatment that increased muscle temperature to over 40°C, 16-20 h prior to the exercise. The contralateral arm acted as an untreated control. Maximal voluntary isometric contraction strength (MVC), range of motion (ROM), upper arm circumference, muscle soreness, plasma creatine kinase activity and myoglobin concentration were measured 1 day prior to exercise, immediately before and after exercise, and daily for 4 days following exercise. Changes in the criterion measures were compared between conditions (treatment vs. control) using a two-way repeated measures ANOVA with a significance level of P < 0.05. All measures changed significantly following exercise, but the treatment arm showed a significantly faster recovery of MVC, a smaller change in ROM, and less muscle soreness compared with the control arm. However, the protective effect conferred by the diathermy treatment was significantly less effective compared with that seen in the second bout performed 4-6 weeks after the initial bout by a subgroup of the subjects (n = 11) using the control arm. These results suggest that passive hyperthermia treatment 1 day prior to eccentric exercise-induced muscle damage has a prophylactic effect, but the effect is not as strong as the repeated bout effect. © Springer-Verlag 2006.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Provisional matrix deposition in hemostasis and venous insufficiency: Tissue preconditioning for nonhealing venous ulcers

Significance: Chronic wounds represent a major burden on global healthcare systems and reduce the quality of life of those affected. Significant advances have been made in our understanding of the biochemistry of wound healing progression. However, knowledge regarding the specific molecular processes influencing chronic wound formation and persistence remains limited. Recent Advances: Generally, healing of acute wounds begins with hemostasis and the deposition of a plasma-derived provisional matrix into the wound. The deposition of plasma matrix proteins is known to occur around the microvasculature of the lower limb as a result of venous insufficiency. This appears to alter limb cutaneous tissue physiology and consequently drives the tissue into a ‘preconditioned’ state that negatively influences the response to wounding. Critical Issues: Processes, such as oxygen and nutrient suppression, edema, inflammatory cell trapping/extravasation, diffuse inflammation, and tissue necrosis are thought to contribute to the advent of a chronic wound. Healing of the wound then becomes difficult in the context of an internally injured limb. Thus, interventions and therapies for promoting healing of the limb is a growing area of interest. For venous ulcers, treatment using compression bandaging encourages venous return and improves healing processes within the limb, critically however, once treatment concludes ulcers often reoccur. Future Directions: Improved understanding of the composition and role of pericapillary matrix deposits in facilitating internal limb injury and subsequent development of chronic wounds will be critical for informing and enhancing current best practice therapies and preventative action in the wound care field.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

How do supercontinents break up? — assessing the continental large igneous province (LIP) record of the break-up of Pangea

LIP emplacement is linked to the timing and evolution of supercontinental break-up. LIP-related break-up produces volcanic rifted margins, new and large (up to 108 km2) ocean basins, and new, smaller continents that undergo dispersal and potentially reassembly (e.g., India). However, not all continental LIPs lead to continental rupture. We analysed the <330 Ma continental LIP record(following final assembly of Pangea) to find relationships between LIP event attributes (e.g., igneous volume, extent, distance from pre-existing continental margin) and ocean basin attributes (e.g., length of new ocean basin/rifted margin) and how these varied during the progressive break up of Pangea. No correlation exists between LIP magnitude and size of the subsequent ocean basin or rifted margin. Our review suggests a three-phased break-up history of Pangea: 1) “Preconditioning” phase (∼330–200 Ma): LIP events (n=7) occurred largely around the supercontinental margin clustering today in Asia, with a low (<20%) rifting success rate. The Panjal Traps at ∼280 Ma may represent the first continental rupturing event of Pangea, resulting in continental ribboning along the Tethyan margin; 2) “Main Break-up” phase (∼200–100 Ma): numerous large LIP events(n=10) in the supercontinent interior, resulting in highly successful fragmentation (90%) and large, new ocean basins(e.g., Central/South Atlantic, Indian, >3000 km long); 3) “Waning” phase (∼100–0 Ma): Declining LIP magnitudes (n=6), greater proximity to continental margins (e.g., Madagascar, North Atlantic, Afro-Arabia, Sierra Madre) producing smaller ocean basins (<2600 km long). How Pangea broke up may thus have implications for earlier supercontinent reconstructions and LIP record.

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.

Computational strategies for surface fitting using thin plate spline finite element methods

Thin plate spline finite element methods are used to fit a surface to an irregularly scattered dataset [S. Roberts, M. Hegland, and I. Altas. Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions. SIAM, 1:208--234, 2003]. The computational bottleneck for this algorithm is the solution of large, ill-conditioned systems of linear equations at each step of a generalised cross validation algorithm. Preconditioning techniques are investigated to accelerate the convergence of the solution of these systems using Krylov subspace methods. The preconditioners under consideration are block diagonal, block triangular and constraint preconditioners [M. Benzi, G. H. Golub, and J. Liesen. Numerical solution of saddle point problems. Acta Numer., 14:1--137, 2005]. The effectiveness of each of these preconditioners is examined on a sample dataset taken from a known surface. From our numerical investigation, constraint preconditioners appear to provide improved convergence for this surface fitting problem compared to block preconditioners.

The development of virtual leaf surface models for interactive agrichemical spray applications

This project constructed virtual plant leaf surfaces from digitised data sets for use in droplet spray models. Digitisation techniques for obtaining data sets for cotton, chenopodium and wheat leaves are discussed and novel algorithms for the reconstruction of the leaves from these three plant species are developed. The reconstructed leaf surfaces are included into agricultural droplet spray models to investigate the effect of the nozzle and spray formulation combination on the proportion of spray retained by the plant. A numerical study of the post-impaction motion of large droplets that have formed on the leaf surface is also considered.

GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.