Application of hpDGFEM to mechanisms at channel microband electrodes

We extend our earlier work (Harriman et al., Oxford University Computing Laboratory Technical Report NA04/19) on hp-DGFEM for disc electrodes to the case of reaction mechanisms to the increasingly popular channel microband electrode configuration. We present results for the simple E reaction mechanism (convection-diffusion equation), for the ECE and EC2E reaction mechanisms (linear and nonlinear systems of reaction-convection- diffusion equations, respectively) and for the DISP1 and DISP2 reaction mechanisms (linear and nonlinear coupled systems of reaction-convection-diffusion equations, respectively). In all cases we demonstrate excellent agreement with previous results using relatively coarse meshes and without the need for streamline-diffusion stabilisation, even at high flow rates

Models for pattern formation in somitogenesis: a marriage of cellular and molecular biology

Somitogenesis, the process by which a bilaterally symmetric pattern of cell aggregations is laid down in a cranio-caudal sequence in early vertebrate development, provides an excellent model study for the coupling of interactions at the molecular and cellular level. Here, we review some of the key experimental results and theoretical models related to this process. We extend a recent chemical pre-pattern model based on the cell cycle Journal of Theoretical Biology 207 (2000) 305-316, by including cell movement and show that the resultant model exhibits the correct spatio-temporal dynamics of cell aggregation. We also postulate a model to account for the recently observed spatio-temporal dynamics at the molecular level

Approximation of linear functionals using an hp-adaptive discontinuous Galerkin finite element method

We consider the problem of computing a linear functional of the solution of an elliptic partial differential equation to within a given tolerance. We drive an a posteriori error bound for the linear functional and use this as the basis of an hp-adaptive discontinuous Galerkin finite element algorithm to deliver the functional to within a prescribed error tolerance

A Comparison of Numerical Methods used for\ud Finite Element Modelling of Soft Tissue\ud Deformation

Soft tissue deformation is often modelled using incompressible nonlinear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular, the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. We investigate the effect of these choices on the accuracy of the computed solution, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. We set up model problems with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). We find that the choice of pressure basis functions are vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general that it is important to take the expected regularity of the solution into account when choosing a numerical scheme

Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues

The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to PDE-based continuum methods, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for non-crystalline materials, it may still be used as a first order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to 2-D cellular-scale models by assessing the mechanical behaviour of model biological tissues, including crystalline (honeycomb) and non-crystalline reference states. The numerical procedure consists in precribing an affine deformation on the boundary cells and computing the position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For centre-based models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete/continuous modelling, adaptation of atom-to-continuum (AtC) techniques to biological tissues and model classification

The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method

We describe how a discontinuous Galerkin finite element method with interior penalty can be used to compute the solution to an elliptic partial differential equation and a linear functional of this solution can be evaluated. We show that, in order to have an adjoint consistent method and thus obtain optimal rates of convergence of the functional, a symmetric interior penalty Galerkin method must be used and, when the functional depends on the derivative of the solution of the PDE, an equivalent formulation of the functional must be used

Challenges of ultra large scale integration of biomedical computing systems

The NCRI Informatics Initiative is overseeing the implementation of an informatics framework for the UK cancer research community. The framework advocates an integrated multidisciplinary method of working between scientific and medical communities. Key to this process is community adoption of high quality acquisition, storage, sharing and integration of diverse data elements to improve knowledge of the causes, prevention and treatment of cancer. The integration of the complex data and meta-data used by these multiple communities is a significant challenge and there are technical, resource-based and sociological issues to be addressed. In this paper we review progress aimed at establishing the framework and outline key challenges in ultra large scale integration of biomedical computing systems

Clinical and economic consequences of hospital-acquired resistant and multidrug-resistant Pseudomonas aeruginosa infections: a systematic review and meta-analysis

Background Increasing rates of resistant and multidrug-resistant (MDR) P. aeruginosa in hospitalized patients constitute a major public health threat. We present a systematic review of the clinical and economic impact of this resistant pathogen. Methods Studies indexed in MEDLINE and Cochrane databases between January 2000-February 2013, and reported all-cause mortality, length of stay, hospital costs, readmission, or recurrence in at least 20 hospitalized patients with laboratory confirmed resistant P. aeruginosa infection were included. We accepted individual study definitions of MDR, and assessed study methodological quality. Results The most common definition of MDR was resistance to more than one agent in three or more categories of antibiotics. Twenty-three studies (7,881 patients with susceptible P. aeruginosa, 1,653 with resistant P. aeruginosa, 559 with MDR P. aeruginosa, 387 non-infected patients without P. aeruginosa) were analyzed. A random effects model meta-analysis was feasible for the endpoint of all-cause in-hospital mortality. All-cause mortality was 34% (95% confidence interval (CI) 27% – 41%) in patients with any resistant P. aeruginosa compared to 22% (95% CI 14% – 29%) with susceptible P. aeruginosa. The meta-analysis demonstrated a > 2-fold increased risk of mortality with MDR P. aeruginosa (relative risk (RR) 2.34, 95% CI 1.53 – 3.57) and a 24% increased risk with resistant P. aeruginosa (RR 1.24, 95% CI 1.11 – 1.38), compared to susceptible P. aeruginosa. An adjusted meta-analysis of data from seven studies demonstrated a statistically non-significant increased risk of mortality in patients with any resistant P. aeruginosa (adjusted RR 1.24, 95% CI 0.98 – 1.57). All three studies that reported infection-related mortality found a statistically significantly increased risk in patients with MDR P. aeruginosa compared to those with susceptible P. aeruginosa. Across studies, hospital length of stay (LOS) was higher in patients with resistant and MDR P. aeruginosa infections, compared to susceptible P. aeruginosa and control patients. Limitations included heterogeneity in MDR definition, restriction to nosocomial infections, and potential confounding in analyses. Conclusions Hospitalized patients with resistant and MDR P. aeruginosa infections appear to have increased all-cause mortality and LOS. The negative clinical and economic impact of these pathogens warrants in-depth evaluation of optimal infection prevention and stewardship strategies

Finite element solution of a membrane covered electrode problem

Membrane covered oxygen sensors, or Clark electrodes, are used for monitoring the concentration of oxygen in blood. The operation of such sensors is governed by the diffusion equation with different diffusion coefficients in different sub-domains. The form of the boundary conditions and the material interface conditions means that the derivative of the solution has discontinuities which restrict the convergence of standard numerical methods on regular meshes. We describe and computationally compare adaptive finite element methods based on continuous and discontinuous basis functions to overcome this problem

Explaining rain forest diversity

This group, which is concerned with the applications of mathematics to agricultural science, was formed in 1970 and has since met at approximately yearly intervals in London for one-day meetings. The thirty-third meeting of the group, chaired by Professor P. K. Maini of the Mathematical Institute, University of Oxford, was held in the Kohn Centre at the Royal Society, 6 Carlton House Terrace, London on Friday, 6 April 2001 when the following papers were read