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SUMMARY A recent verification study compared 11 large-scale cardiac electrophysiology solvers on an unambiguously defined common problem. An unexpected amount of variation was observed between the codes, including significant error in conduction velocity in the majority of the codes at certain spatial resolutions. In particular, the results of the six finite element codes varied considerably despite each using the same order of interpolation. In this present study, we compare various algorithms for cardiac electrophysiological simulation, which allows us to fully explain the differences between the solvers. We identify the use of mass lumping as the fundamental cause of the largest variations, specifically the combination of the commonly used techniques of mass lumping and operator splitting, which results in a slightly different form of mass lumping to that supported by theory and leads to increased numerical error. Other variations are explained through the manner in which the ionic current is interpolated. We also investigate the effect of different forms of mass lumping in various types of simulation. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Models of cardiac electromechanics usually contain a contraction model determining the active tension induced at the cellular level and the equations of nonlinear elasticity to determine tissue deformation in response to this active tension. All contraction models are dependent on cardiac electrophysiology but can also be dependent on the stretch and stretch rate in the fibre direction. This fundamentally affects the mathematical problem being solved, through classification of the governing partial differential equations, which affects numerical schemes that can be used to solve the governing equations. We categorise contraction models into three types, and for each consider questions such as classification and the most appropriate choice from two numerical methods (the explicit and implicit schemes). In terms of mathematical classification, we consider the question of strong ellipticity of the total strain energy (important for precluding ‘unnatural’ material behaviour) for stretch-rate-independent contraction models; whereas for stretch-rate-dependent contraction models, we introduce a corresponding third-order problem and explain how certain choices of boundary condition could lead to constraints on allowable initial condition. In terms of suitable numerical methods, we show that an explicit approach (where the contraction model is integrated in the time step prior to the bulk deformation being computed) is (i) appropriate for stretch-independent contraction models; (ii) only conditionally stable, with the stability criterion independent of time step, for contractions models which just depend on stretch (but not stretch rate) and (iii) inappropriate for stretch-rate-dependent models. [ABSTRACT FROM PUBLISHER]

The inverse elasticity problem of determining the undeformed, deflated, configuration of a nonlinear elastic membrane, given the deformed configuration enclosing an incompressible fluid under known pressure, is considered. It is shown that, in practical cases, it is enough to determine only the undeformed metric tensor, and it is also shown how the two- and three-dimensional cases are fundamentally different. For the three-dimensional case, we set up and classify the partial differential equations to be solved, prove existence of an undeformed state given an undeformed metric and study the axisymmetric case in detail. [ABSTRACT FROM PUBLISHER]

Patient-specific cardiac models are now being used to guide therapies. The increased use of patientspecific cardiac simulations in clinical care will give rise to the development of virtual cohorts of cardiac models. These cohorts will allow cardiac simulations to capture and quantify inter-patient variability. However, the development of virtual cohorts of cardiac models will require the transformation of cardiac modelling from small numbers of bespoke models to robust and rapid workflows that can create large numbers of models. In this review, we describe the state of the art in virtual cohorts of cardiac models, the process of creating virtual cohorts of cardiac models, and how to generate the individual cohort member models, followed by a discussion of the potential and future applications of virtual cohorts of cardiac models. [ABSTRACT FROM AUTHOR]

Objectives: The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation. Methods: At the subcellular level, deterministic models characterise molecular networks, such as cell-cycle control and Wnt signalling. The output of these models determines the behaviour of each epithelial cell in response to intra-, inter- and extracellular cues. The modular nature of the model enables us to easily modify individual assumptions and analyse their effects on the system as a whole. Results: We perform virtual microdissection and labelling-index experiments, evaluate the impact of various model extensions, obtain new insight into clonal expansion in the crypt, and compare our predictions with recent mitochondrial DNA mutation data. Conclusions: We demonstrate that relaxing the assumption that stem-cell positions are fixed enables clonal expansion and niche succession to occur. We also predict that the presence of extracellular factors near the base of the crypt alone suffices to explain the observed spatial variation in nuclear beta-catenin levels along the crypt axis. [ABSTRACT FROM AUTHOR]