A5037754645- Advanced Numerical Methods in Computational Mathematics
- Inhalation and Respiratory Drug Delivery
- Advanced Mathematical Modeling in Engineering
- Chronic Obstructive Pulmonary Disease (COPD) Research
- Numerical methods in engineering
- Cardiac electrophysiology and arrhythmias
- Elasticity and Material Modeling
- Cardiovascular Function and Risk Factors
- Solidification and crystal growth phenomena
- Asthma and respiratory diseases
- Numerical methods for differential equations
- Computational Fluid Dynamics and Aerodynamics
- Respiratory Support and Mechanisms
- Fractional Differential Equations Solutions
- Matrix Theory and Algorithms
- Differential Equations and Numerical Methods
- Mechanical Circulatory Support Devices
- Gene Regulatory Network Analysis
- Mathematical Biology Tumor Growth
- Developmental Biology and Gene Regulation
- Cardiac Structural Anomalies and Repair
- stochastic dynamics and bifurcation
- Water resources management and optimization
- Atomic and Subatomic Physics Research
- Congenital heart defects research
University of Oxford
2011-2020
Science Oxford
2009-2017
Google (United States)
2009
University of Sussex
2000-2008
University of Manchester
2001
University of Leicester
1999
Beijing Research Institute of Uranium Geology
1993
Simon Fraser University
1989-1990
University of Wales Trinity Saint David
1986-1987
Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread key advancing our interpretation of dispersion repolarization. We propose fractional diffusion models as a novel mathematical description structurally heterogeneous excitable media, means representing the modulation total electric field secondary sources associated with tissue inhomogeneities. Our...
We present a new method for solving the sparse linear system of equations arising from discretization linearized steady-state Navier--Stokes (also known as Oseen equations). The solver is an iterative Krylov subspace type which we devise preconditioner through heuristic argument based on fundamental solution tensor operator. may also be conceived weaker involving differential operators. Computations indicate that convergence preconditioned discrete problem only mildly dependent viscosity...
Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of fractional operator causes memory (time fractional) nonlocality (space issues that impose number computational constraints. In this paper we develop efficient, scalable techniques solving fractional-in-space reaction using finite element method on both structured and unstructured grids via robust computing...
The visceral endoderm (VE) is a simple epithelium that forms the outer layer of egg-cylinder stage mouse embryo. anterior (AVE), specialised subset VE cells, responsible for specifying pattern. AVE cells show stereotypic migratory behaviour within VE, which correctly orientating anterior-posterior axis. epithelial integrity maintained during course migration, takes place by intercalation and other cells. Though continuous sheet, characterised two regions dramatically different behaviour, one...
ABSTRACT Neural crest (NC) cell migration is crucial to the formation of peripheral tissues during vertebrate development. However, how NC cells respond different microenvironments maintain persistence direction and cohesion in multicellular streams remains unclear. To address this, we profiled eight subregions a typical cranial migratory stream. Hierarchical clustering showed significant differences expression profiles lead three compared with newly emerged cells. Multiplexed imaging mRNA...
Rationale: Asthma is characterized by disease within the small airways. Several studies have suggested that forced oscillation technique–derived resistance at 5 Hz (R5) − 20 (R20) a measure of airway disease; however, there has been limited validation this measurement to date.Objectives: To validate use R5 R20 as narrowing in asthma, and investigate role plays asthma.Methods: Patient-based complete conducting models were generated from computed tomography scans simulate impact different...
Chaste (Cancer, Heart And Soft Tissue Environment) is an open source simulation package for the numerical solution of mathematical models arising in physiology and biology. To date, development has been driven primarily by applications that include continuum modelling cardiac electrophysiology ('Cardiac Chaste'), discrete cell-based soft tissues ('Cell-based ventilation lungs ('Lung Chaste'). Cardiac addresses need a high-performance, generic, verified framework freely available to...
We consider a semi-discrete and practical fully discrete finite element approximation of Cahn-Hilliard-Navier-Stokes system.This system arises in the modelling multiphase fluid systems.We show order h error estimate between solution semidiscrete approximation.We also convergence approximation.Finally, we present an efficient implementation scheme together with some numerical simulations.
The human heart beats as a result of multiscale nonlinear dynamics coupling subcellular to whole organ processes, achieving electrophysiologically-driven mechanical contraction. Computational cardiac modelling and simulation have achieved great degree maturity, both in terms mathematical models underlying biophysical processes the development software. In this study, we present detailed description human-based physiologically-based, fully-coupled ventricular electromechanical framework,...
We outline a new class of robust and efficient methods for solving the Navier–Stokes equations. describe general solution strategy that has two basic building blocks: an implicit time integrator using stabilized trapezoid rule with explicit Adams–Bashforth method error control, Krylov subspace solver spatially discretized system. present numerical experiments illustrating potential our approach.
The paper is concerned with the construction and convergence analysis of a discontinuous Galerkin finite element method for Cahn–Hilliard equation convection. Using piecewise polynomials degree $p\geq1$ backward Euler discretization in time, we show that order-parameter c approximated broken ${\rm L}^\infty({\rm H}^1)$ norm, optimal order ${\cal O}(h^p+\tau)$; associated chemical potential $w=\Phi'(c)-\gamma^2\Delta c$ shown to be approximated, O}(h^p+\tau)$ L}^2({\rm norm. Here...
Understanding the underlying feedback mechanisms of fluid/solid coupling and role it plays in heart function is crucial for characterizing normal its behavior disease. To improve this understanding, an anatomically accurate computational model fluid–solid mechanics left ventricle presented which assesses both passive diastolic active systolic phases heart. Integrating multiple data characterize hemodynamical tissue mechanical properties heart, a numerical approach was applied allows...
Summary We develop a lung ventilation model based on continuum poroelastic representation of parenchyma that is strongly coupled to pipe network the airway tree. The continuous system equations discretized using low‐order stabilised finite element method. framework applied realistic anatomical derived from computed tomography data and an artificially generated tree conducting region. Numerical simulations produce physiologically solutions demonstrate effect constriction reduced tissue...
The solution of Cahn--Hilliard variational inequalities is interest in many applications. We discuss the use them as a tool for binary image inpainting. This has been done before using double-well potentials but not nonsmooth considered here. existing bound constraints are incorporated via Moreau--Yosida regularization technique. develop effective preconditioners efficient Newton steps associated with fast regularized problem. Numerical results illustrate efficiency our approach. Moreover,...
The analysis of high-resolution computed tomography (CT) images the lung is dependent on inter-subject differences in airway geometry. application computational models understanding significance these has previously been shown to be a useful tool biomedical research. Studies using image-based geometries alone are limited central airways, down generation 6–10, as other airways not visible CT. However, distal this, often termed small known play crucial role common diseases such asthma and...
A stabilized conforming mixed finite element method for the three-field (displacement, fluid flux, and pressure) poroelasticity problem is developed analyzed. We use lowest possible approximation order, namely piecewise constant pressure linear continuous elements displacements flux. By applying a local jump stabilization term to mass conservation equation, we ensure stability avoid oscillations. Importantly, discretization leads symmetric system. For fully discretized prove existence...
The practical implementation of the lowest-order Pl - P0 (linear velocity, constant pressure) finite element method for steady-state incompressible (Navier--)Stokes equations is addressed in this work. Three different types a posteriori error indicator are introduced and each shown to be equivalent discretization error. Our numerical results show that these indicators can used drive an adaptive refinement process which specially tailored create grids conform requirements local stabilization....
A finite element discretization of the variable density Cahn–Hilliard–Navier–Stokes system is presented. This then decoupled with Cahn–Hilliard part solved via nonlinear multigrid method proposed by authors in [J. Comput. Phys., 212 (2006), pp. 288–304] and Navier–Stokes a preconditioned GMRES scheme. new solver examined numerically shown to be efficient respect mesh refinement robust problem parameters.
We present an efficient numerical solution of a PDE-driven model for color image segmentation and give examples the results. The method combines vector-valued Allen-Cahn phase field equation with initial data fitting terms prescribed interface width fidelity constants. Efficient is achieved using multigrid splitting finite element space, thereby producing robust large images. also use adaptive mesh refinement to further speed up process.
Ion channels are membrane proteins that open and close at random play a vital role in the electrical dynamics of excitable cells. The stochastic nature conformational changes these undergo can be significant, however current modeling methodologies limit ability to study such systems. Discrete-state Markov chain models seen as "gold standard," but computationally intensive, restricting investigation effects single-cell level. Continuous methods use differential equations (SDEs) model system...