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Biomedical subjects

David J Gavaghan

Publications and source records attributed to David J Gavaghan.

12 recordsLinked to original sources
PubMed2006

Adaptive finite element methods in electrochemistry.

In this article, we review some of our previous work that considers the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the edge effect. Our approach to overcoming this problem has involved the derivation of an a posteriori bound on the error in the numerical approximation for the current that can be used to drive an adaptive mesh-generation algorithm, allowing calculation of the quantity of interest (the current) to within a prescribed tolerance. We illustrate the generic applicability of the approach by considering a broad range of steady-state applications of the technique.

Journal Article↗
PubMed2006

Metabolic changes during carcinogenesis: potential impact on invasiveness.

Successful adaptation to varying microenvironmental constraints plays a crucial role during carcinogenesis. We develop a hybrid cellular automation approach to investigate the cell-microenvironmental interactions that mediate somatic evolution of cancer cells. This allows investigation of the hypothesis that regions of premalignant lesions develop a substrate-limited environment as proliferation carries cells away from blood vessels which remain separated by the intact basement membrane. We find that selective forces in tumoural regions furthest from the blood supply act to favour cells whose metabolism is best suited to respond to local changes in oxygen, glucose and pH levels. The model predicts three phases of somatic evolution. Initially, cell survival and proliferation is limited due to diminished oxygen levels. This promotes adaptation to a second phase of growth dominated by cells with constitutively up-regulated glycolysis, less reliant on oxygen for ATP production. Increased glycolysis induces acidification of the local environment, limiting proliferation and inducing cell death through necrosis and apoptosis. This promotes a third phase of cellular evolution, with emergence of phenotypes resistant to acid-induced toxicity. This emergent cellular phenotype has a significant proliferative advantage because it will consistently acidify the local environment in a way that is toxic to its competitors but harmless to itself. The model's results suggest this sequence is essential in the transition from self-limited premalignant growth to invasive cancer, and, therefore, that this transition may be delayed or prevented through novel strategies directed towards interrupting the hypoxia-glycolysis-acidosis cycle.

Adenosine Triphosphate↗
PubMed2006

Synthesis of voltage-sensitive optical signals: application to panoramic optical mapping.

Fluorescent photon scattering is known to distort optical recordings of cardiac transmembrane potentials; however, this process is not well quantified, hampering interpretation of experimental data. This study presents a novel model, which accurately synthesizes fluorescent recordings over the irregular geometry of the rabbit ventricles. Using the model, the study aims to provide quantification of fluorescent signal distortion for different optical characteristics of the preparation and of the surrounding medium. A bi-domain representation of electrical activity is combined with finite element solutions to the photon diffusion equation simulating both the excitation and emission processes, along with physically realistic boundary conditions at the epicardium, which allow simulation of different experimental setups. We demonstrate that distortion in the optical signal as a result of fluorescent photon scattering is truly a three-dimensional phenomenon and depends critically upon the geometry of the preparation, the scattering properties of the tissue, the direction of wavefront propagation, and the specifics of the experimental setup. Importantly, we show that in an anatomically accurate model of ventricular geometry and fiber orientation, the morphology of the optical signal does not provide reliable information regarding the intramural direction of wavefront propagation. These findings underscore the potential of the new model in interpreting experimental data.

Animals↗
PubMed2005

The role of acidity in solid tumour growth and invasion.

Acidic pH is a common characteristic of human tumours. It has a significant impact on tumour progression and response to therapies. In this paper, we develop a simple model of three-dimensional tumour growth to examine the role of acidosis in the interaction between normal and tumour cell populations. Both vascular and avascular tumour dynamics are investigated, and a number of different behaviours are observed. Whilst an avascular tumour always proceeds to a benign steady state, a vascular tumour may display either benign or invasive dynamics, depending on the value of a critical parameter. Analysis of the model allows us to assess novel therapies directed towards changing the level of acidity within the tumour.

Cell Proliferation↗
PubMed2004

Resistance, capacitance, and electrode kinetic effects in Fourier-transformed large-amplitude sinusoidal voltammetry: emergence of powerful and intuitively obvious tools for recognition of patterns of behavior.

Large-amplitude sinusoidal ac voltammetric techniques, when analyzed in the frequency domain using the Fourier transform-inverse Fourier transform sequence, produce the expected dc and fundamental harmonic ac responses in addition to very substantial second, third, and higher ac harmonics that arise from the presence of significant nonlinearity. A full numerical simulation of the process, Red right arrow over left arrow Ox + e(-), incorporates terms for the uncompensated resistance (R(u)), capacitance of the double layer (C(dl)), and slow electron transfer kinetics (in particular, the reversible potential (E degrees ), rate constant (k(0)), and charge transfer coefficient (alpha) from the Butler-Volmer model). Identification of intuitively obvious patterns of behavior (with characteristically different sensitivity regimes) in dc, fundamental, and higher harmonic terms enables simple protocols to be developed to estimate R(u), C(dl), E degrees , k(0), and alpha. Thus, if large-amplitude sinusoidal cyclic voltammograms are obtained for two concentrations of the reduced species, data obtained from analysis of the recovered signals provide initial estimates of parameters as follows: (a) the dc cyclic component provides an estimate of E degrees (because the R(u) and k(0) effects are minimized); (b) the fundamental harmonic provides an estimate of C(dl) (because it has a high capacitance-to-faradaic current ratio); and (c) the second harmonic provides an estimate of R(u), k(0), and alpha (because the C(dl) effect is minimized). Methods of refining the initial estimates are then implemented. As a check on the fidelity of the parameters (estimated on the basis of an essentially heuristic approach that solely utilizes the dc, fundamental, and second harmonic voltammograms), comparison of the predicted simulated and experimental third (or higher) harmonic voltammograms can be made to verify that agreement between theory and experiment has been achieved at a predetermined level. The use of the heuristic pattern recognition approach to evaluate the oxidation of ferrocene at a platinum electrode (a reversible process) in the very high resistance solvent dichloromethane (0.1 M Bu(4)NPF(6)) and the reduction of [Fe(CN(6))](3)(-) at a glassy carbon electrode (a quasi-reversible process) in much lower resistance but higher capacitance conditions found in aqueous (0.5 M KCl) media is described and verifies the inherent advantages of employing large-amplitude sinusoidal techniques in quantitative studies of electrode processes.

Journal Article↗
PubMed2003

Mathematical modelling of pulmonary gas transport.

Equations governing the transport of the gases oxygen and carbon dioxide inside the pulmonary capillaries are written down. By analysing these equations it is predicted that there will be negligible limitation to the transport of oxygen when oxygen concentration takes a normal physiological or higher value. For low values of oxygen concentration, there may be limitation to oxygen transport. It is predicted further that the quantity of carbon dioxide excreted from blood into alveolar gas is dependent on oxygen concentration, with low oxygen concentrations inhibiting the carbon dioxide transport process. The relatively slow reaction involving carbon dioxide in plasma also inhibits the excretion of carbon dioxide. These predictions are verified by solving the whole system of governing equations numerically.

Biological Transport↗
PubMed2003

Efficient computations of gas transport in the respiratory tree.

The equation governing the transport of an inert gas in the respiratory tree is a linear PDE. There are several clinical situations where the PDE must be solved on a large number of consecutive breaths and, on each breath, a very small number of linear functionals of this solution evaluated. In this study we show how the solution of a relatively small number of adjoint problems may be used to calculate these linear functionals, thus reducing the volume of computation significantly. This technique may be used with other physical problems.

Carbon Dioxide↗
PubMed2002

Pooling data for number needed to treat: no problems for apples.

OBJECTIVE: To consider the problem of the calculation of number needed to treat (NNT) derived from risk difference, odds ratio, and raw pooled events shown to give different results using data from a review of nursing interventions for smoking cessation. DISCUSSION: A review of nursing interventions for smoking cessation from the Cochrane Library provided different values for NNT depending on how NNTs were calculated. The Cochrane review was evaluated for clinical heterogeneity using L'Abbé plot and subsequent analysis by secondary and primary care settings.Three studies in primary care had low (4%) baseline quit rates, and nursing interventions were without effect. Seven trials in hospital settings with patients after cardiac surgery, or heart attack, or even with cancer, had high baseline quit rates (25%). Nursing intervention to stop smoking in the hospital setting was effective, with an NNT of 14 (95% confidence interval 9 to 26). The assumptions involved in using risk difference and odds ratio scales for calculating NNTs are discussed. SUMMARY: Clinical common sense and concentration on raw data helps to detect clinical heterogeneity. Once robust statistical tests have told us that an intervention works, we then need to know how well it works. The number needed to treat or harm is just one way of showing that, and when used sensibly can be a useful tool.

Bias↗
PubMed2002

Mathematical modelling of oxygen transport to tissue.

The equations governing oxygen transport from blood to tissue are presented for a cylindrical tissue compartment, with blood flowing along a co-axial cylindrical capillary inside the tissue. These governing equations take account of: (i) the non-linear reactions between oxygen and haemoglobin in blood and between oxygen and myoglobin in tissue; (ii) diffusion of oxygen in both the axial and radial directions; and (iii) convection of haemoglobin and plasma in the capillary. A non-dimensional analysis is carried out to assess some assumptions made in previous studies. It is predicted that: (i) there is a boundary layer for oxygen partial pressure but not for haemoglobin or myoglobin oxygen saturation close to the inflow boundary in the capillary; (ii) axial diffusion may not be neglected everywhere in the model; (iii) the reaction between oxygen and both haemoglobin and myoglobin may be assumed to be instantaneous in nearly all cases; and (iv) the effect of myoglobin is only significant for tissue with a low oxygen partial pressure. These predictions are validated by solving the full equations numerically and are then interpreted physically.

Capillaries↗
PubMed2002

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.

Animals↗
PubMed2000

An evaluation of homogeneity tests in meta-analyses in pain using simulations of individual patient data.

In this paper we consider the validity and power of some commonly used statistics for assessing the degree of homogeneity between trials in a meta-analysis. We show, using simulated individual patient data typical of that occurring in randomized controlled trials in pain, that the most commonly used statistics do not give the expected levels of statistical significance (i.e. the proportion of trials giving a significant result is not equal to the proportion expected due to random chance) when used with truly homogeneous data. In addition, all such statistics are shown to have extremely low power to detect true heterogeneity even when that heterogeneity is very large. Since, in most practical situations, failure to detect heterogeneity does not allow us to say with any helpful degree of certainty that the data is truly homogeneous, we advocate the quantitative combination of results only where the trials contained in a meta-analysis can be shown to be clinically homogeneous. We propose as a definition of clinical homogeneity that all trials have (i) fixed and clearly defined inclusion criteria and (ii) fixed and clearly defined outcomes or outcome measures. In pain relief, for example, the first of these would be satisfied by all patients having moderate or severe pain, whilst the second would be satisfied by using at least 50% pain relief as the successful outcome measure.

Algorithms↗