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ABSTRACT: INTRODUCTION: Unwanted drug interactions with ionic currents in the heart can lead to an increased pro-arrhythmic risk to patients in the clinic. It is therefore a priority for pharmaceutical safety pharmacology teams to detect block of cardiac ion channels, and new technologies have enabled the development of automated and high-throughput screening assays using cell lines. As a result of screening multiple ion-channels there is a need to integrate information, particularly for compounds affecting more than one current, and mathematical electrophysiology in-silico action potential models are beginning to be used for this. METHODS: We quantified the variability associated with concentration-effect curves fitted to recordings from high-throughput Molecular Devices IonWorks® Quattro™ screens when detecting block of trmIKr (hERG), INa (NaV1.5), ICaL (CaV1.2), IKs (KCNQ1/minK) and Ito (Kv4.3/KChIP2.2), and the Molecular Devices FLIPR® Tetra fluorescence screen for ICaL (CaV1.2), for control compounds used at AstraZeneca and GlaxoSmithKline. We examined how screening variability propagates through in-silico action potential models for whole cell electrical behaviour, and how confidence intervals on model predictions can be estimated with repeated simulations. RESULTS: There are significant levels of variability associated with high-throughput ion channel electrophysiology screens. This variability is of a similar magnitude for different cardiac ion currents and different compounds. Uncertainty in the Hill coefficients of reported concentration-effect curves is particularly high. Depending on a compound's ion channel blocking profile, the uncertainty introduced into whole-cell predictions can become significant. DISCUSSION: Our technique allows confidence intervals to be placed on computational model predictions that are based on high-throughput ion channel screens. This allows us to suggest when repeated screens should be performed to reduce uncertainty in a compound's action to acceptable levels, to allow a meaningful interpretation of the data.
Journal of pharmacological and toxicological methods 05/2013; · 2.32 Impact Factor
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ABSTRACT: INTRODUCTION: Drugs that prolong the QT interval on the electrocardiogram present a major safety concern for pharmaceutical companies and regulatory agencies. Despite a range of assays performed to assess compound effects on the QT interval, QTprolongation remains a major cause of attrition during compound development. In silico assays could alleviate such problems. In this study we evaluated an in silico method of predicting the results of a rabbit left-ventricular wedge assay. METHODS: Concentration-effect data were acquired from either: the high-throughput IonWorks/FLIPR; the medium-throughput PatchXpress ion channel assays; or QSAR, a statistical IC50 value prediction model, for hERG, fast sodium, L-type calcium and KCNQ1/minK channels. Drug block of channels was incorporated into a mathematical differential equation model of rabbit ventricular myocyte electrophysiology through modification of the maximal conductance of each channel by a factor dependent on the IC50 value, Hill coefficient and concentration of each compound tested. Simulations were performed and agreement with experimental results, based upon input data from the different assays, was evaluated. RESULTS: The assay was found to be 78% accurate, 72% sensitive and 81% specific when predicting QT prolongation (>10%) using PatchXpress assay data (77 compounds). Similar levels of predictivity were demonstrated using IonWorks/FLIPR data (121 compounds) with 78% accuracy, 73% sensitivity and 80% specificity. QT Shortening (<-10%) was predicted with 77% accuracy, 33% sensitivity and 90% specificity using PatchXpress data and 71% accuracy, 42% sensitivity and 81% specificity using IonWorks/FLIPR data. Strong quantitative agreement between simulation and experimental results was also evident. DISCUSSION: The in silico action potential assay demonstrates good predictive ability, and is suitable for very high-throughput use in early drug development. Adoption of such an assay into cardiovascular safety assessment, integrating ion channel data from routine screens to infer results of animal-based tests, could provide a cost- and time-effective cardiac safety screen.
Journal of pharmacological and toxicological methods 04/2013; · 2.32 Impact Factor
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Gary R Mirams,
Christopher J Arthurs,
Miguel O Bernabeu,
Rafel Bordas,
Jonathan Cooper,
Alberto Corrias,
Yohan Davit,
Sara-Jane Dunn,
Alexander G Fletcher,
Daniel G Harvey,
Megan E Marsh,
James M Osborne,
Pras Pathmanathan,
Joe Pitt-Francis,
James Southern,
Nejib Zemzemi, David J Gavaghan
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ABSTRACT: Chaste - Cancer, Heart And Soft Tissue Environment - is an open source C++ library for the computational simulation of mathematical models developed for physiology and biology. Code development has been driven by two initial applications: cardiac electrophysiology and cancer development. A large number of cardiac electrophysiology studies have been enabled and performed, including high-performance computational investigations of defibrillation on realistic human cardiac geometries. New models for the initiation and growth of tumours have been developed. In particular, cell-based simulations have provided novel insight into the role of stem cells in the colorectal crypt. Chaste is constantly evolving and is now being applied to a far wider range of problems. The code provides modules for handling common scientific computing components, such as meshes and solvers for ordinary and partial differential equations (ODEs/PDEs). Re-use of these components avoids the need for researchers to 're-invent the wheel' with each new project, accelerating the rate of progress in new applications. Chaste is developed using industrially-derived techniques, in particular test-driven development, to ensure code quality, re-use and reliability. In this article we provide examples that illustrate the types of problems Chaste can be used to solve, which can be run on a desktop computer. We highlight some scientific studies that have used or are using Chaste, and the insights they have provided. The source code, both for specific releases and the development version, is available to download under an open source Berkeley Software Distribution (BSD) licence at http://www.cs.ox.ac.uk/chaste, together with details of a mailing list and links to documentation and tutorials.
PLoS Computational Biology 03/2013; 9(3):e1002970. · 5.22 Impact Factor
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ABSTRACT: The potential-dependences of the rate constants associated with heterogeneous electron transfer predicted by the empirically based Butler-Volmer and fundamentally based Marcus-Hush formalisms are well documented for dc cyclic voltammetry. However, differences are often subtle, so, presumably on the basis of simplicity, the Butler-Volmer method is generally employed in theoretical-experimental comparisons. In this study, the ability of Large Amplitude Fourier Transform AC Cyclic Voltammetry to distinguish the difference in behaviour predicted by the two formalisms has been investigated. The focus of this investigation is on the difference in the profiles of the first to sixth harmonics, which are readily accessible when a large amplitude of the applied ac potential is employed. In particular, it is demonstrated that systematic analysis of the higher order harmonic responses in suitable kinetic regimes provides predicted deviations of Marcus-Hush from Butler-Volmer behaviour to be established from a single experiment under conditions where the background charging current is minimal.
Physical Chemistry Chemical Physics 12/2012; · 3.57 Impact Factor
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ABSTRACT: A detailed analysis of the cooperative two-electron transfer of surface-confined cytochrome c peroxidase (CcP) in contact with pH 6.0 phosphate buffer solution has been undertaken. This investigation is prompted by the prospect of achieving a richer understanding of this biologically important system via the employment of kinetically sensitive, but background devoid, higher harmonic components available in the large-amplitude Fourier transform ac voltammetric method. Data obtained from the conventional dc cyclic voltammetric method are also provided for comparison. Theoretical considerations based on both ac and dc approaches are presented for cases where reversible or quasi-reversible cooperative two-electron transfer involves variation in the separation of their reversible potentials, including potential inversion (as described previously for solution phase studies), and reversibility of the electrode processes. Comparison is also made with respect to the case of a simultaneous two-electron transfer process that is unlikely to occur in the physiological situation. Theoretical analysis confirms that the ac higher harmonic components provide greater sensitivity to the various mechanistic nuances that can arise in two-electron surface-confined processes. Experimentally, the ac perturbation with amplitude and frequency of 200 mV and 3.88 Hz, respectively, was employed to detect the electron transfer when CcP is confined to the surface of a graphite electrode. Simulations based on cooperative two-electron transfer with the employment of reversible potentials of 0.745 ± 0.010 V, heterogeneous electron transfer rate constants of between 3 and 10 s(-1) and charge transfer coefficients of 0.5 for both processes fitted experimental data for the fifth to eighth ac harmonics. Imperfections in theory-experiment comparison are consistent with kinetic and thermodynamic dispersion and other nonidealities not included in the theory used to model the voltammetry of surface-confined CcP.
Langmuir 05/2012; 28(25):9864-77. · 4.19 Impact Factor
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ABSTRACT: The bidomain framework has been extensively used to model tissue electrophysiology in a variety of applications. One limitation of the bidomain model is that it describes the activity of only one cell type interacting with the extracellular space. If more than one cell type contributes to the tissue electrophysiology, then the bidomain model is not sufficient. Recently, evidence has suggested that this is the case for at least two important applications: cardiac and gastrointestinal tissue electrophysiology. In the heart, fibroblasts ubiquitously interact with myocytes and are believed to play an important role in the organ electrophysiology. Along the GI tract, interstitial cells of Cajal (ICC) generate electrical waves that are passed on to surrounding smooth muscle cells (SMC), which are interconnected with the ICC and with each other. Because of the contribution of more than one cell type to the overall organ electrophysiology, investigators in different fields have independently proposed similar extensions of the bidomain model to incorporate multiple cell types and tested it on simplified geometries. In this paper, we provide a general derivation of such an extended bidomain framework applicable to any tissue and provide a generic and efficient implementation applicable to any geometry. Proof-of-concept results of tissue electrophysiology on realistic 3D organ geometries using the extended bidomain framework are presented for the heart and the stomach.
Integrative Biology 02/2012; 4(2):192-201. · 4.51 Impact Factor
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ABSTRACT: As in many scientific disciplines, modern chemistry involves a mix of experimentation and computer-supported theory. Historically, these skills have been provided by different groups, and range from traditional 'wet' laboratory science to advanced numerical simulation. Increasingly, progress is made by global collaborations, in which new theory may be developed in one part of the world and applied and tested in the laboratory elsewhere. e-Science, or cyber-infrastructure, underpins such collaborations by providing a unified platform for accessing scientific instruments, computers and data archives, and collaboration tools. In this paper we discuss the application of advanced e-Science software tools to electrochemistry research performed in three different laboratories--two at Monash University in Australia and one at the University of Oxford in the UK. We show that software tools that were originally developed for a range of application domains can be applied to electrochemical problems, in particular Fourier voltammetry. Moreover, we show that, by replacing ad-hoc manual processes with e-Science tools, we obtain more accurate solutions automatically.
Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 08/2011; 369(1949):3336-52. · 2.77 Impact Factor
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ABSTRACT: Recent optical mapping studies of cardiac tissue suggest that membrane voltage (V(m)) and intracellular calcium concentrations (Ca) become dissociated during ventricular fibrillation (VF), generating a proarrhythmic substrate. However, experimental methods used in these studies may accentuate measured dissociation due to differences in fluorescent emission wavelengths of optical voltage/calcium (V(opt)/Ca(opt)) signals. Here, we simulate dual voltage-calcium optical mapping experiments using a monodomain-Luo-Rudy ventricular-tissue model coupled to a photon-diffusion model. Dissociation of both electrical, V(m)/Ca, and optical, V(opt)/Ca(opt), signals is quantified by calculating mutual information (MI) for VF and rapid pacing protocols. We find that photon scattering decreases MI of V(opt)/Ca(opt) signals by 23% compared to unscattered V(m)/Ca signals during VF. Scattering effects are amplified by increasing wavelength separation between fluorescent voltage/calcium signals and respective measurement-location misalignment. In contrast, photon scattering does not affect MI during rapid pacing, but high calcium dye affinity can decrease MI by attenuating alternans in Ca(opt) but not in V(opt). We conclude that some dissociation exists between voltage and calcium at the cellular level during VF, but MI differences are amplified by current optical mapping methods.
Biophysical Journal 07/2011; 101(2):307-18. · 3.65 Impact Factor
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ABSTRACT: The level of inhibition of the human Ether-à-go-go-related gene (hERG) channel is one of the earliest preclinical markers used to predict the risk of a compound causing Torsade-de-Pointes (TdP) arrhythmias. While avoiding the use of drugs with maximum therapeutic concentrations within 30-fold of their hERG inhibitory concentration 50% (IC(50)) values has been suggested, there are drugs that are exceptions to this rule: hERG inhibitors that do not cause TdP, and drugs that can cause TdP but are not strong hERG inhibitors. In this study, we investigate whether a simulated evaluation of multi-channel effects could be used to improve this early prediction of TdP risk.
We collected multiple ion channel data (hERG, Na, L-type Ca) on 31 drugs associated with varied risks of TdP. To integrate the information on multi-channel block, we have performed simulations with a variety of mathematical models of cardiac cells (for rabbit, dog, and human ventricular myocyte models). Drug action is modelled using IC(50) values, and therapeutic drug concentrations to calculate the proportion of blocked channels and the channel conductances are modified accordingly. Various pacing protocols are simulated, and classification analysis is performed to evaluate the predictive power of the models for TdP risk. We find that simulation of action potential duration prolongation, at therapeutic concentrations, provides improved prediction of the TdP risk associated with a compound, above that provided by existing markers.
The suggested calculations improve the reliability of early cardiac safety assessments, beyond those based solely on a hERG block effect.
Cardiovascular research 02/2011; 91(1):53-61. · 5.80 Impact Factor
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ABSTRACT: The fourth and higher harmonic components available in large-amplitude Fourier transformed ac voltammetry have been employed in a study involving surface-confined redox proteins having multiple electron-transfer centers. Ferredoxin I from Azotobacter vinelandii (AvFdI) and two variants exhibit significant differences in the reversible reduction potentials (Eo′) of their two non-interacting FeS clusters which are located at a fixed distance 1.2 nm apart. At pH 9.0 in aqueous buffered medium, FdI adsorbed on a pyrolytic graphite edge electrode displays two one-electron-transfer processes that are not complicated by coupled proton transfer. Ac voltammetric faradaic currents devoid of significant background, are detected and analyzed for the fourth to seventh harmonics of the [4Fe–4S]2+/+ and [3Fe–4S]+/0 processes. The absence of a non-faradaic background in these, but not in the dc or initial three ac harmonics, facilitates the experimental analysis. In potential regions where overlay of the [4Fe–4S]2+/+ and [3Fe–4S]+/0 processes occur, the alternating currents are not always additive because each process may exhibit different phases. The level of resolution of the two processes is governed by the separation of the Eo′ values, with the higher harmonic components giving enhanced resolution in the regimes of the reversible potentials. Simulation–experimental data comparisons have been used to determine the rate constants for each electron-transfer process. Theory–experiment comparisons are generally in satisfactory agreement, but some imperfections are consistent with the kinetic or/and thermodynamic dispersion associated with films of surface-confined proteins adhered to a heterogeneous edge plane graphite electrode.
Journal of Electroanalytical Chemistry. 09/2010;
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Anna A Sher,
Michael T Cooling,
Blair Bethwaite,
Jefferson Tan,
Tom Peachey,
Colin Enticott,
Slavisa Garic, David J Gavaghan,
Denis Noble,
David Abramson,
Edmund J Crampin
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ABSTRACT: Cardiovascular diseases are the major cause of death in the developed countries. Identifying key cellular processes involved in generation of the electrical signal and in regulation of signal transduction pathways is essential for unraveling the underlying mechanisms of heart rhythm behavior. Computational cardiac models provide important insights into cardiovascular function and disease. Sensitivity analysis presents a key tool for exploring the large parameter space of such models, in order to determine the key factors determining and controlling the underlying physiological processes. We developed a new global sensitivity analysis tool which implements the Morris method, a global sensitivity screening algorithm, onto a Nimrod platform, which is a distributed resources software toolkit. The newly developed tool has been validated using the model of IP3-calcineurin signal transduction pathway model which has 30 parameters. The key driving factors of the IP3 transient behaviour have been calculated and confirmed to agree with previously published data. We next demonstrated the use of this method as an assessment tool for characterizing the structure of cardiac ionic models. In three latest human ventricular myocyte models, we examined the contribution of transmembrane currents to the shape of the electrical signal (i.e. on the action potential duration). The resulting profiles of the ionic current balance demonstrated the highly nonlinear nature of cardiac ionic models and identified key players in different models. Such profiling suggests new avenues for development of methodologies to predict drug action effects in cardiac cells.
Conference proceedings: ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference 01/2010; 2010:1498-502.
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ABSTRACT: Recent advances in magnetic resonance (MR) imaging technology have unveiled a wealth of information regarding cardiac histoanatomical complexity. However, methods to faithfully translate this level of fine-scale structural detail into computational whole ventricular models are still in their infancy, and, thus, the relevance of this additional complexity for simulations of cardiac function has yet to be elucidated. Here, we describe the development of a highly detailed finite-element computational model (resolution: approximately 125 microm) of rabbit ventricles constructed from high-resolution MR data (raw data resolution: 43 x 43 x 36 microm), including the processes of segmentation (using a combination of level-set approaches), identification of relevant anatomical features, mesh generation, and myocyte orientation representation (using a rule-based approach). Full access is provided to the completed model and MR data. Simulation results were compared with those from a simplified model built from the same images but excluding finer anatomical features (vessels/endocardial structures). Initial simulations showed that the presence of trabeculations can provide shortcut paths for excitation, causing regional differences in activation after pacing between models. Endocardial structures gave rise to small-scale virtual electrodes upon the application of external field stimulation, which appeared to protect parts of the endocardium in the complex model from strong polarizations, whereas intramural virtual electrodes caused by blood vessels and extracellular cleft spaces appeared to reduce polarization of the epicardium. Postshock, these differences resulted in the genesis of new excitation wavefronts that were not observed in more simplified models. Furthermore, global differences in the stimulus recovery rates of apex/base regions were observed, causing differences in the ensuing arrhythmogenic episodes. In conclusion, structurally simplified models are well suited for a large range of cardiac modeling applications. However, important differences are seen when behavior at microscales is relevant, particularly when examining the effects of external electrical stimulation on tissue electrophysiology and arrhythmia induction. This highlights the utility of histoanatomically detailed models for investigations of cardiac function, in particular for future patient-specific modeling.
AJP Heart and Circulatory Physiology 11/2009; 298(2):H699-718. · 3.71 Impact Factor
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ABSTRACT: Recent work has described the software engineering and computational infrastructure that has been set up as part of the Cancer, Heart and Soft Tissue Environment (CHASTE) project. CHASTE is an open source software package that currently has heart and cancer modelling functionality. This software has been written using a programming paradigm imported from the commercial sector and has resulted in a code that has been subject to a far more rigorous testing procedure than that is usual in this field. In this paper, we explain how new functionality may be incorporated into CHASTE. Whiteley has developed a numerical algorithm for solving the bidomain equations that uses the multi-scale (MS) nature of the physiology modelled to enhance computational efficiency. Using a simple geometry in two dimensions and a purpose-built code, this algorithm was reported to give an increase in computational efficiency of more than two orders of magnitude. In this paper, we begin by reviewing numerical methods currently in use for solving the bidomain equations, explaining how these methods may be developed to use the MS algorithm discussed above. We then demonstrate the use of this algorithm within the CHASTE framework for solving the monodomain and bidomain equations in a three-dimensional realistic heart geometry. Finally, we discuss how CHASTE may be developed to include new physiological functionality--such as modelling a beating heart and fluid flow in the heart--and how new algorithms aimed at increasing the efficiency of the code may be incorporated.
Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 06/2009; 367(1895):1907-30. · 2.77 Impact Factor
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ABSTRACT: Breast cancer is one of the biggest killers in the western world, and early diagnosis is essential for improved prognosis. The shape of the breast varies hugely between the scenarios of magnetic resonance (MR) imaging (patient lies prone, breast hanging down under gravity), X-ray mammography (breast strongly compressed) and ultrasound or biopsy/surgery (patient lies supine), rendering image fusion an extremely difficult task. This paper is concerned with the use of the finite-element method and nonlinear elasticity to build a 3-D, patient-specific, anatomically accurate model of the breast. The model is constructed from MR images and can be deformed to simulate breast shape and predict tumor location during mammography or biopsy/surgery. Two extensions of the standard elasticity problem need to be solved: an inverse elasticity problem (arising from the fact that only a deformed, stressed, state is known initially), and the contact problem of modeling compression. The model is used for craniocaudal mediolateral oblique mammographic image matching, and a number of numerical experiments are performed.
IEEE transactions on bio-medical engineering 11/2008; 55(10):2471-80. · 2.15 Impact Factor
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ABSTRACT: Cardiac modelling is the area of physiome modelling where the available simulation software is perhaps most mature, and it therefore provides an excellent starting point for considering the software requirements for the wider physiome community. In this paper, we will begin by introducing some of the most advanced existing software packages for simulating cardiac electrical activity. We consider the software development methods used in producing codes of this type, and discuss their use of numerical algorithms, relative computational efficiency, usability, robustness and extensibility. We then go on to describe a class of software development methodologies known as test-driven agile methods and argue that such methods are more suitable for scientific software development than the traditional academic approaches. A case study is a project of our own, Cancer, Heart and Soft Tissue Environment, which is a library of computational biology software that began as an experiment in the use of agile programming methods. We present our experiences with a review of our progress thus far, focusing on the advantages and disadvantages of this new approach compared with the development methods used in some existing packages. We conclude by considering whether the likely wider needs of the cardiac modelling community are currently being met and suggest that, in order to respond effectively to changing requirements, it is essential that these codes should be more malleable. Such codes will allow for reliable extensions to include both detailed mathematical models--of the heart and other organs--and more efficient numerical techniques that are currently being developed by many research groups worldwide.
Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 07/2008; 366(1878):3111-36. · 2.77 Impact Factor
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ABSTRACT: Optical mapping of arrhythmias and defibrillation provides important insights; however, a limitation of the technique is signal distortion due to photon scattering. The goal of this experimental/simulation study is to investigate the role of three-dimensional photon scattering in optical signal distortion during ventricular tachycardia (VT) and defibrillation. A three-dimensional realistic bidomain rabbit ventricular model was combined with a model of photon transport. Shocks were applied via external electrodes to induce sustained VT, and transmembrane potentials (V(m)) were compared with synthesized optical signals (V(opt)). Fluorescent recordings were conducted in isolated rabbit hearts to validate simulation results. Results demonstrate that shock-induced membrane polarization magnitude is smaller in V(opt) and in experimental signals as compared to V(m). This is due to transduction of potentials from weakly polarized midmyocardium to the epicardium. During shock-induced reentry and in sustained VT, photon scattering, combined with complex wavefront dynamics, results in optical action potentials near a filament exhibiting i), elevated resting potential, ii), reduced amplitude relative to pacing, and iii), dual-humped morphologies. A shift of up to 4 mm in the phase singularity location was observed in V(opt) maps when compared to V(m). This combined experimental/simulation study provides an interpretation of optical recordings during VT and defibrillation.
Biophysical Journal 12/2007; 93(10):3714-26. · 3.65 Impact Factor
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ABSTRACT: Tumour tissue characteristically experiences fluctuations in substrate supply. This unstable microenvironment drives constitutive metabolic changes within cellular populations and, ultimately, leads to a more aggressive phenotype. Previously, variations in substrate levels were assumed to occur through oscillations in the haemodynamics of nearby and distant blood vessels. In this paper we examine an alternative hypothesis, that cycles of metabolite concentrations are also driven by cycles of cellular quiescence and proliferation. Using a mathematical modelling approach, we show that the interdependence between cell cycle and the microenvironment will induce typical cycles with the period of order hours in tumour acidity and oxygenation. As a corollary, this means that the standard assumption of metabolites entering diffusive equilibrium around the tumour is not valid; instead temporal dynamics must be considered.
Journal of Mathematical Biology 12/2007; 55(5-6):767-79. · 2.96 Impact Factor
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ABSTRACT: The numerical solution of the coupled system of partial differential and ordinary differential equations that model the whole heart in three dimensions is a considerable computational challenge. As a consequence, it is not computationally practical--either in terms of memory or time--to repeat simulations on a finer computational mesh to ensure that convergence of the solution has been attained. In an attempt to avoid this problem while retaining mathematical rigour, we derive a one dimensional model of a cardiac fibre that takes account of elasticity properties in three structurally defined axes within the myocardial tissue. This model of a cardiac fibre is then coupled with an electrophysiological cell model and a model of cellular electromechanics to allow us to simulate the coupling of the electrical and mechanical activity of the heart. We demonstrate that currently used numerical methods for coupling electrical and mechanical activity do not work in this case, and identify appropriate numerical techniques that may be used when solving the governing equations. This allows us to perform a series of simulations that: (i) investigate the effect of some of the assumptions inherent in other models; and (ii) reproduce qualitatively some experimental observations.
Bulletin of Mathematical Biology 11/2007; 69(7):2199-225. · 1.85 Impact Factor
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ABSTRACT: Previous approaches to modelling the large deformation of breast tissue, as occurs, e.g. in imaging using magnetic resonance imaging or mammography, include using linear elasticity and pseudo-non-linear elasticity, in which case the non-linear deformation is approximated by a series of small linear isotropic deformations, with the (constant) Young's modulus of each linear deformation an exponential function of the total non-linear strain. In this paper, these two approaches are compared to the solution of the full non-linear elastic problem for tissue with an exponential relationship between stress and strain. Having formulated each model and related the coefficients between the models, numerical simulations are performed on a block of incompressible material. These demonstrate that the simpler models may not be appropriate even in the case of modelling deformations of the human breast under gravity.
Mathematical Medicine and Biology 10/2007; 24(3):327-45. · 1.82 Impact Factor
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ABSTRACT: Co-localization of Na+/Ca2+ exchangers (NCX) with ryanodine receptors (RyRs) is debated. We incorporate local NCX current in a biophysically detailed model of L-type Ca2+ channels (LCCs) and RyRs and study the effect of NCX on the regulation of Ca2+-induced Ca2+ release and the shape of the action potential. In canine ventricular cells, under pathological conditions, e.g., impaired LCCs, local NCXs become an enhancer of sarcoplasmic reticulum release. Under such conditions incorporation of local NCXs is critical to accurately capture mechanisms of excitation-contraction coupling.
Annals of the New York Academy of Sciences 04/2007; 1099:215-20. · 3.15 Impact Factor
