The simulation experiment description markup language (SED-ML): language specification for level 1 version 5

Modern biological research is increasingly informed by computational simulation experiments, which necessitate the development of methods for annotating, archiving, sharing, and reproducing the conducted experiments. These simulations increasingly require extensive collaboration among modelers, experimentalists, and engineers. The Minimum Information About a Simulation Experiment (MIASE) guidelines outline the information needed to share simulation experiments. SED-ML is a computer-readable format for the information outlined by MIASE, created as a community project and supported by many investigators and software tools. Level 1 Version 5 of SED-ML expands the ability of modelers to define simulations in SED-ML using the Kinetic Simulation Algorithm Onotoloy (KiSAO). While it was possible in Version 4 to define a simulation entirely using KiSAO, Version 5 now allows users to define tasks, model changes, ranges, and outputs using the ontology as well. SED-ML is supported by a growing ecosystem of investigators, model languages, and software tools, including various languages for constraint-based, kinetic, qualitative, rule-based, and spatial models, and many simulation tools, visual editors, model repositories, and validators. Additional information about SED-ML is available at https://sed-ml.org/.

CellML 2.0.1

We present here CellML 2.0.1, an XML-based language for describing and exchanging mathematical models of physiological systems. MathML embedded in CellML documents is used to define the underlying mathematics of models. Models consist of a network of reusable components, each with variables and equations giving relationships between those variables. Models may import other models to create systems of increasing complexity. CellML 2.0.1 is defined by the normative specification presented here, prescribing the CellML syntax and the rules by which it should be used. The normative specification is intended primarily for the developers of software tools which directly consume CellML syntax. Users of CellML models may prefer to browse the informative rendering of the specification (https://cellml.org/specifications/cellml_2.0/) which extends the normative specification with explanations of the rules combined with examples of their usage. This version improves the identification of rule statements and corrects errata present in the CellML 2.0 specification.

BioSimulators: a central registry of simulation engines and services for recommending specific tools

Computational models have great potential to accelerate bioscience, bioengineering, and medicine. However, it remains challenging to reproduce and reuse simulations, in part, because the numerous formats and methods for simulating various subsystems and scales remain siloed by different software tools. For example, each tool must be executed through a distinct interface. To help investigators find and use simulation tools, we developed BioSimulators (https://biosimulators.org), a central registry of the capabilities of simulation tools and consistent Python, command-line and containerized interfaces to each version of each tool. The foundation of BioSimulators is standards, such as CellML, SBML, SED-ML and the COMBINE archive format, and validation tools for simulation projects and simulation tools that ensure these standards are used consistently. To help modelers find tools for particular projects, we have also used the registry to develop recommendation services. We anticipate that BioSimulators will help modelers exchange, reproduce, and combine simulations.

The simulation experiment description markup language (SED-ML): language specification for level 1 version 4

Computational simulation experiments increasingly inform modern biological research, and bring with them the need to provide ways to annotate, archive, share and reproduce the experiments performed. These simulations increasingly require extensive collaboration among modelers, experimentalists, and engineers. The Minimum Information About a Simulation Experiment (MIASE) guidelines outline the information needed to share simulation experiments. SED-ML is a computer-readable format for the information outlined by MIASE, created as a community project and supported by many investigators and software tools. The first versions of SED-ML focused on deterministic and stochastic simulations of models. Level 1 Version 4 of SED-ML substantially expands these capabilities to cover additional types of models, model languages, parameter estimations, simulations and analyses of models, and analyses and visualizations of simulation results. To facilitate consistent practices across the community, Level 1 Version 4 also more clearly describes the use of SED-ML constructs, and includes numerous concrete validation rules. SED-ML is supported by a growing ecosystem of investigators, model languages, and software tools, including eight languages for constraint-based, kinetic, qualitative, rule-based, and spatial models, over 20 simulation tools, visual editors, model repositories, and validators. Additional information about SED-ML is available at https://sed-ml.org/.

CellML 2.0

We present here CellML 2.0, an XML-based language for describing and exchanging mathematical models of physiological systems. MathML embedded in CellML documents is used to define the underlying mathematics of models. Models consist of a network of reusable components, each with variables and equations giving relationships between those variables. Models may import other models to create systems of increasing complexity. CellML 2.0 is defined by the normative specification presented here, prescribing the CellML syntax and the rules by which it should be used. The normative specification is intended primarily for the developers of software tools which directly consume CellML syntax. Users of CellML models may prefer to browse the informative rendering of the specification (https://cellml.org/specifications/cellml_2.0/) which extends the normative specification with explanations of the rules combined with examples of their usage.

Harmonizing semantic annotations for computational models in biology

Life science researchers use computational models to articulate and test hypotheses about the behavior of biological systems. Semantic annotation is a critical component for enhancing the interoperability and reusability of such models as well as for the integration of the data needed for model parameterization and validation. Encoded as machine-readable links to knowledge resource terms, semantic annotations describe the computational or biological meaning of what models and data represent. These annotations help researchers find and repurpose models, accelerate model composition and enable knowledge integration across model repositories and experimental data stores. However, realizing the potential benefits of semantic annotation requires the development of model annotation standards that adhere to a community-based annotation protocol. Without such standards, tool developers must account for a variety of annotation formats and approaches, a situation that can become prohibitively cumbersome and which can defeat the purpose of linking model elements to controlled knowledge resource terms. Currently, no consensus protocol for semantic annotation exists among the larger biological modeling community. Here, we report on the landscape of current annotation practices among the COmputational Modeling in BIology NEtwork community and provide a set of recommendations for building a consensus approach to semantic annotation.

Three-dimensional histology: tools and application to quantitative assessment of cell-type distribution in rabbit heart

Aims

Cardiac histo-anatomical organization is a major determinant of function. Changes in tissue structure are a relevant factor in normal and disease development, and form targets of therapeutic interventions. The purpose of this study was to test tools aimed to allow quantitative assessment of cell-type distribution from large histology and magnetic resonance imaging- (MRI) based datasets.

Methods and results

Rabbit heart fixation during cardioplegic arrest and MRI were followed by serial sectioning of the whole heart and light-microscopic imaging of trichrome-stained tissue. Segmentation techniques developed specifically for this project were applied to segment myocardial tissue in the MRI and histology datasets. In addition, histology slices were segmented into myocytes, connective tissue, and undefined. A bounding surface, containing the whole heart, was established for both MRI and histology. Volumes contained in the bounding surface (called ‘anatomical volume’), as well as that identified as containing any of the above tissue categories (called ‘morphological volume’), were calculated. The anatomical volume was 7.8 cm³ in MRI, and this reduced to 4.9 cm³ after histological processing, representing an ‘anatomical’ shrinkage by 37.2%. The morphological volume decreased by 48% between MRI and histology, highlighting the presence of additional tissue-level shrinkage (e.g. an increase in interstitial cleft space). The ratio of pixels classified as containing myocytes to pixels identified as non-myocytes was roughly 6:1 (61.6 vs. 9.8%; the remaining fraction of 28.6% was ‘undefined’).

Conclusion

Qualitative and quantitative differentiation between myocytes and connective tissue, using state-of-the-art high-resolution serial histology techniques, allows identification of cell-type distribution in whole-heart datasets. Comparison with MRI illustrates a pronounced reduction in anatomical and morphological volumes during histology processing.

Promoting Coordinated Development of Community-Based Information Standards for Modeling in Biology: The COMBINE Initiative

The Computational Modeling in Biology Network (COMBINE) is a consortium of groups involved in the development of open community standards and formats used in computational modeling in biology. COMBINE's aim is to act as a coordinator, facilitator, and resource for different standardization efforts whose domains of use cover related areas of the computational biology space. In this perspective article, we summarize COMBINE, its general organization, and the community standards and other efforts involved in it. Our goals are to help guide readers toward standards that may be suitable for their research activities, as well as to direct interested readers to relevant communities where they can best expect to receive assistance in how to develop interoperable computational models.

OpenCOR: a modular and interoperable approach to computational biology

Computational biologists have been developing standards and formats for nearly two decades, with the aim of easing the description and exchange of experimental data, mathematical models, simulation experiments, etc. One of those efforts is CellML (cellml.org), an XML-based markup language for the encoding of mathematical models. Early CellML-based environments include COR and OpenCell. However, both of those tools have limitations and were eventually replaced with OpenCOR (opencor.ws). OpenCOR is an open source modeling environment that is supported on Windows, Linux and OS X. It relies on a modular approach, which means that all of its features come in the form of plugins. Those plugins can be used to organize, edit, simulate and analyze models encoded in the CellML format. We start with an introduction to CellML and two of its early adopters, which limitations eventually led to the development of OpenCOR. We then go onto describing the general philosophy behind OpenCOR, as well as describing its openness and its development process. Next, we illustrate various aspects of OpenCOR, such as its user interface and some of the plugins that come bundled with it (e.g., its editing and simulation plugins). Finally, we discuss some of the advantages and limitations of OpenCOR before drawing some concluding remarks.

Electrotonic suppression of early afterdepolarizations in the neonatal rat ventricular myocyte monolayer

Pathologies that result in early afterdepolarizations (EADs) are a known trigger for tachyarrhythmias, but the conditions that cause surrounding tissue to conduct or suppress EADs are poorly understood. Here we introduce a cell culture model of EAD propagation consisting of monolayers of cultured neonatal rat ventricular myocytes treated with anthopleurin-A (AP-A). AP-A-treated monolayers display a cycle length dependent prolongation of action potential duration (245 ms untreated, vs. 610 ms at 1 Hz and 1200 ms at 0.5 Hz for AP-A-treated monolayers). In contrast, isolated single cells treated with AP-A develop prominent irregular oscillations with a frequency of 2.5 Hz, and a variable prolongation of the action potential duration of up to several seconds. To investigate whether electrotonic interactions between coupled cells modulates EAD formation, cell connectivity was reduced by RNA silencing gap junction Cx43. In contrast to well-connected monolayers, gap junction silenced monolayers display bradycardia-dependent plateau oscillations consistent with EADs. Further, simulations of a cell displaying EADs electrically connected to a cell with normal action potentials show a coupling strength-dependent suppression of EADs consistent with the experimental results. These results suggest that electrotonic effects may play a critical role in EAD-mediated arrhythmogenesis.

Standards and tools supporting collaborative development of the virtual physiological human

The development of a virtual physiological human has an ambitious goal that requires the participation of a large and diverse community of scientists. To be successful in achieving this goal, members of this community must be able to share their work and easily collaborate on new developments and novel applications of existing work. To aid in this, various standardization projects have evolved as part of the Physiome community, as well as supporting computational tools and infrastructure. We present here an overview of the current state of these standardization efforts and key tools that support the collaborative development, integration, and exchange of computational physiology models under the Physiome umbrella.

How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project

Early modelling of cardiac cells (1960-1980) was based on extensions of the Hodgkin-Huxley nerve axon equations with additional channels incorporated, but after 1980 it became clear that processes other than ion channel gating were also critical in generating electrical activity. This article reviews the development of models representing almost all cell types in the heart, many different species, and the software tools that have been created to facilitate the cardiac Physiome Project.

Verification of cardiac tissue electrophysiology simulators using an N-version benchmark

Ongoing developments in cardiac modelling have resulted, in particular, in the development of advanced and increasingly complex computational frameworks for simulating cardiac tissue electrophysiology. The goal of these simulations is often to represent the detailed physiology and pathologies of the heart using codes that exploit the computational potential of high-performance computing architectures. These developments have rapidly progressed the simulation capacity of cardiac virtual physiological human style models; however, they have also made it increasingly challenging to verify that a given code provides a faithful representation of the purported governing equations and corresponding solution techniques. This study provides the first cardiac tissue electrophysiology simulation benchmark to allow these codes to be verified. The benchmark was successfully evaluated on 11 simulation platforms to generate a consensus gold-standard converged solution. The benchmark definition in combination with the gold-standard solution can now be used to verify new simulation codes and numerical methods in the future.

Toward a VPH/Physiome ToolKit

The Physiome Project was officially launched in 1997 and has since brought together teams from around the world to work on the development of a computational framework for the modeling of the human body. At the European level, this effort is focused around patient-specific solutions and is known as the Virtual Physiological Human (VPH) Initiative.Such modeling is both multiscale (in space and time) and multiphysics. This, therefore, requires careful interaction and collaboration between the teams involved in the VPH/Physiome effort, if we are to produce computer models that are not only quantitative, but also integrative and predictive.In that context, several technologies and solutions are already available, developed both by groups involved in the VPH/Physiome effort, and by others. They address areas such as data handling/fusion, markup languages, model repositories, ontologies, tools (for simulation, imaging, data fitting, etc.), as well as grid, middleware, and workflow.Here, we provide an overview of resources that should be considered for inclusion in the VPH/Physiome ToolKit (i.e., the set of tools that addresses the needs and requirements of the Physiome Project and VPH Initiative) and discuss some of the challenges that we are still facing.

Revision history aware repositories of computational models of biological systems

Background

Building repositories of computational models of biological systems ensures that published models are available for both education and further research, and can provide a source of smaller, previously verified models to integrate into a larger model.

One problem with earlier repositories has been the limitations in facilities to record the revision history of models. Often, these facilities are limited to a linear series of versions which were deposited in the repository. This is problematic for several reasons. Firstly, there are many instances in the history of biological systems modelling where an 'ancestral' model is modified by different groups to create many different models. With a linear series of versions, if the changes made to one model are merged into another model, the merge appears as a single item in the history. This hides useful revision history information, and also makes further merges much more difficult, as there is no record of which changes have or have not already been merged. In addition, a long series of individual changes made outside of the repository are also all merged into a single revision when they are put back into the repository, making it difficult to separate out individual changes. Furthermore, many earlier repositories only retain the revision history of individual files, rather than of a group of files. This is an important limitation to overcome, because some types of models, such as CellML 1.1 models, can be developed as a collection of modules, each in a separate file.

The need for revision history is widely recognised for computer software, and a lot of work has gone into developing version control systems and distributed version control systems (DVCSs) for tracking the revision history. However, to date, there has been no published research on how DVCSs can be applied to repositories of computational models of biological systems.

Results

We have extended the Physiome Model Repository software to be fully revision history aware, by building it on top of Mercurial, an existing DVCS. We have demonstrated the utility of this approach, when used in conjunction with the model composition facilities in CellML, to build and understand more complex models. We have also demonstrated the ability of the repository software to present version history to casual users over the web, and to highlight specific versions which are likely to be useful to users.

Conclusions

Providing facilities for maintaining and using revision history information is an important part of building a useful repository of computational models, as this information is useful both for understanding the source of and justification for parts of a model, and to facilitate automated processes such as merges. The availability of fully revision history aware repositories, and associated tools, will therefore be of significant benefit to the community.

An overview of the CellML API and its implementation

BACKGROUND

CellML is an XML based language for representing mathematical models, in a machine-independent form which is suitable for their exchange between different authors, and for archival in a model repository. Allowing for the exchange and archival of models in a computer readable form is a key strategic goal in bioinformatics, because of the associated improvements in scientific record accuracy, the faster iterative process of scientific development, and the ability to combine models into large integrative models.However, for CellML models to be useful, tools which can process them correctly are needed. Due to some of the more complex features present in CellML models, such as imports, developing code ab initio to correctly process models can be an onerous task. For this reason, there is a clear and pressing need for an application programming interface (API), and a good implementation of that API, upon which tools can base their support for CellML.

RESULTS

We developed an API which allows the information in CellML models to be retrieved and/or modified. We also developed a series of optional extension APIs, for tasks such as simplifying the handling of connections between variables, dealing with physical units, validating models, and translating models into different procedural languages.We have also provided a Free/Open Source implementation of this application programming interface, optimised to achieve good performance.

CONCLUSIONS

Tools have been developed using the API which are mature enough for widespread use. The API has the potential to accelerate the development of additional tools capable of processing CellML, and ultimately lead to an increased level of sharing of mathematical model descriptions.

Generation of histo-anatomically representative models of the individual heart: tools and application

This paper presents methods to build histo-anatomically detailed individualized cardiac models. The models are based on high-resolution three-dimensional anatomical and/or diffusion tensor magnetic resonance images, combined with serial histological sectioning data, and are used to investigate individualized cardiac function. The current state of the art is reviewed, and its limitations are discussed. We assess the challenges associated with the generation of histo-anatomically representative individualized in silico models of the heart. The entire processing pipeline including image acquisition, image processing, mesh generation, model set-up and execution of computer simulations, and the underlying methods are described. The multifaceted challenges associated with these goals are highlighted, suitable solutions are proposed, and an important application of developed high-resolution structure-function models in elucidating the effect of individual structural heterogeneity upon wavefront dynamics is demonstrated.

CELLULAR OPEN RESOURCE (COR): current status and future directions

The need for tools to aid the description and sharing of biological models was highlighted at the launch of the International Union of Physiological Sciences Physiome Project in 1997. This has resulted in the release, in 2001, of the CellML specifications (http://www.cellml.org/specifications/). CELLULAR OPEN RESOURCE (COR) was among the early adopters of this standard, eventually forming the first publicly available CellML-based modelling and collaboration environment. From the onset, COR was designed to provide an environment that could not only be used by experienced modellers, but also by experimentalists, teachers and students. It therefore tries to combine a user-friendly interface with a computationally efficient numerical engine. In this paper, we introduce the philosophy behind COR, explain its user interface and current functionality, including the editing and running of CellML files, highlight lessons learned from user feedback and problems experienced during the development of COR and conclude by exploring future development potential.

CellML metadata standards, associated tools and repositories

The development of standards for encoding mathematical models is an important component of model building and model sharing among scientists interested in understanding multi-scale physiological processes. CellML provides such a standard, particularly for models based on biophysical mechanisms, and a substantial number of models are now available in the CellML Model Repository. However, there is an urgent need to extend the current CellML metadata standard to provide biological and biophysical annotation of the models in order to facilitate model sharing, automated model reduction and connection to biological databases. This paper gives a broad overview of a number of new developments on CellML metadata and provides links to further methodological details available from the CellML website.

CHASTE: incorporating a novel multi-scale spatial and temporal algorithm into a large-scale open source library

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.

Axial stretch of rat single ventricular cardiomyocytes causes an acute and transient increase in Ca2+ spark rate

We investigate acute effects of axial stretch, applied by carbon fibers (CFs), on diastolic Ca2+ spark rate in rat isolated cardiomyocytes. CFs were attached either to both cell ends (to maximize the stretched region), or to the center and one end of the cell (to compare responses in stretched and nonstretched half-cells). Sarcomere length was increased by 8.01+/-0.94% in the stretched cell fraction, and time series of XY confocal images were recorded to monitor diastolic Ca2+ spark frequency and dynamics. Whole-cell stretch causes an acute increase of Ca2+ spark rate (to 130.7+/-6.4%) within 5 seconds, followed by a return to near background levels (to 104.4+/-5.1%) within 1 minute of sustained distension. Spark rate increased only in the stretched cell region, without significant differences in spark amplitude, time to peak, and decay time constants of sparks in stretched and nonstretched areas. Block of stretch-activated ion channels (2 micromol/L GsMTx-4), perfusion with Na+/Ca2+-free solution, and block of nitric oxide synthesis (1 mmol/L L-NAME) all had no effect on the stretch-induced acute increase in Ca2+ spark rate. Conversely, interference with cytoskeletal integrity (2 hours of 10 micromol/L colchicine) abolished the response. Subsequent electron microscopic tomography confirmed the close approximation of microtubules with the T-tubular-sarcoplasmic reticulum complex (to within approximately 10(-8)m). In conclusion, axial stretch of rat cardiomyocytes acutely and transiently increases sarcoplasmic reticulum Ca2+ spark rate via a mechanism that is independent of sarcolemmal stretch-activated ion channels, nitric oxide synthesis, or availability of extracellular calcium but that requires cytoskeletal integrity. The potential of microtubule-mediated modulation of ryanodine receptor function warrants further investigation.

CellML and associated tools and techniques

We have, in the last few years, witnessed the development and availability of an ever increasing number of computer models that describe complex biological structures and processes. The multi-scale and multi-physics nature of these models makes their development particularly challenging, not only from a biological or biophysical viewpoint but also from a mathematical and computational perspective. In addition, the issue of sharing and reusing such models has proved to be particularly problematic, with the published models often lacking information that is required to accurately reproduce the published results. The International Union of Physiological Sciences Physiome Project was launched in 1997 with the aim of tackling the aforementioned issues by providing a framework for the modelling of the human body. As part of this initiative, the specifications of the CellML mark-up language were released in 2001. Now, more than 7 years later, the time has come to assess the situation, in particular with regard to the tools and techniques that are now available to the modelling community. Thus, after introducing CellML, we review and discuss existing editors, validators, online repository, code generators and simulation environments, as well as the CellML Application Program Interface. We also address possible future directions including the need for additional mark-up languages.

Chaste: using agile programming techniques to develop computational biology software

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.

Enabling computer models of the heart for high-performance computers and the grid

Although it is now feasible to compute multi-cellular models of the heart on a personal desktop or laptop computer, it is not feasible to undertake the detailed sweeps of high-dimensional parameter spaces required if we are to undertake in silico experimentation of the complex processes that constitute heart disease. For this research, modelling requirements move rapidly beyond the limit of commodity computers' resource both in terms of their memory footprint and the speed of calculation, so that multi-processor architectures must be considered. In addition, as such models have become more mature and have been validated against experimental data, there is increasing pressure for experimentalists to be able to make use of these models themselves as a key tool for hypothesis formulation and in planning future experimental studies to test those hypotheses. This paper discusses our initial experiences in a large-scale project (the Integrative Biology (IB) e-Science project) aimed at meeting these dual aims. We begin by putting the research in context by describing in outline the overall aims of the IB project, in particular focusing on the challenge of enabling novice users to make full use of high-performance resources without the need to gain detailed technical expertise in computing. We then discuss our experience of adapting one particular heart modelling package, Cellular Open Resource, and show how the solving engine of this code was dissected from the rest of the package, ported to C++ and parallelized using the Message-Passing Interface. We show that good parallel efficiency and realistic memory reduction can be achieved on simple geometries. We conclude by discussing lessons learnt in this process.

Mathematical models in physiology

Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with more than 34000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5-6 years, compared to only about one-third in the preceding 5-6 decades. The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function-the Physiome. The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations.

Effects of mechanosensitive ion channels on ventricular electrophysiology: experimental and theoretical models

The heart is an electrically driven mechanical pump, somewhat like an electric motor. Interestingly, like an electric motor in 'dynamo mode', the heart can also convert mechanical stimuli into electrical signals. This feedback from cardiac mechanics to electrical activity involves mechanosensitive ion channels, whose properties and pathophysiological relevance are reviewed in the context of experimental and theoretical modelling of ventricular beat-by-beat electromechanical function.

Dimensionality in cardiac modelling

The development of mathematical models of the heart has been an ongoing concern for many decades. The initial focus of this work was on single cell models that incorporate varyingly detailed descriptions of the mechanisms that give rise to experimentally observed action potential shapes. Clinically relevant heart rhythm disturbances, however, are multicellular phenomena, and there have been many initiatives to develop multidimensional representations of cardiac electromechanical activity. Here, we discuss the merits of dimensionality, from 0D single cell models, to 1D cell strands, 2D planes and 3D volumes, for the simulation of normal and disturbed rhythmicity. We specifically look at models of: (i) the origin and spread of cardiac excitation from the sino-atrial node into atrial tissue, and (ii) stretch-activated channel effects on ventricular cell and tissue activity. Simulation of the spread of normal and disturbed cardiac excitation requires multicellular models. 1D architectures suffer from limitations in neighbouring tissue effects on individual cells, but they can (with some modification) be applied to the simulation of normal spread of excitation or, in ring-like structures, re-entry simulation (colliding wave fronts, tachycardia). 2D models overcome many of the limitations imposed by models of lower dimensionality, and can be applied to the study of complex co-existing re-entry patterns or even fibrillation. 3D implementations are closest to reality, as they allow investigation of scroll waves. Our results suggest that 2D models offer a good compromise between computational resources, complexity of electrophysiological models, and applicability to basic research, and that they should be considered as an important stepping-stone towards anatomically detailed simulations. This highlights the need to identify and use the most appropriate model for any given task. The notion of a single and ultimate model is as useful as the idea of a universal mechanical tool for all possible repairs and servicing requirements in daily life. The ideal model will be as simple as possible and as complex as necessary for the particular question raised.

Mechanical induction of arrhythmias during ventricular repolarization: modeling cellular mechanisms and their interaction in two dimensions

Nonpenetrating mechanical stimulation of the precordial chest is particularly likely to instantaneously induce sustained rhythm disturbances if timed to coincide with ventricular repolarization. A number of possible mechanisms have been proposed, including mechanoelectric feedback acting via stretch-activated ion channels. The cellular effects of such channel activation have been studied and mathematically modeled in great detail. In this study, we investigate their dynamic interaction with the trailing wave of action potential repolarization in a two-dimensional model of ventricular tissue. The model identifies how stretch activation of cation-nonselective ion channels causes ectopic excitation in fully repolarized tissue and functional block of conduction at the intersection of the mechanical stimulus and the repolarization wave end, which may give rise to both trigger and sustaining mechanisms of ventricular arrhythmia. Simulation of stretch activation of K(+)-selective ion channels alone is insufficient in causing instantaneous arrhythmia, although it may, via action potential shortening, contribute to its sustenance.

One‐Dimensional Rabbit Sinoatrial Node Models:

INTRODUCTION

Cardiac multicellular modeling has traditionally focused on ventricular electromechanics. More recently, models of the atria have started to emerge, and there is much interest in addressing sinoatrial node structure and function.

METHODS AND RESULTS

We implemented a variety of one-dimensional sinoatrial models consisting of descriptions of central, transitional, and peripheral sinoatrial node cells, as well as rabbit or human atrial cells. These one-dimensional models were implemented using CMISS on an SGI Origin 2000 supercomputer. Intercellular coupling parameters recorded in experimental studies on sinoatrial node and atrial cell-pairs under-represent the electrotonic interactions that any cardiomyocyte would have in a multidimensional setting. Unsurprisingly, cell-to-cell coupling had to be scaled-up (by a factor of 5) in order to obtain a stable leading pacemaker site in the sinoatrial node center. Further critical parameters include the gradual increase in intercellular coupling from sinoatrial node center to periphery, and the presence of electrotonic interaction with atrial cells. Interestingly, the electrotonic effect of the atrium on sinoatrial node periphery is best described as opposing depolarization, rather than necessarily hyperpolarizing, as often assumed.

CONCLUSION

Multicellular one-dimensional models of sinoatrial node and atrium can provide useful insight into the origin and spread of normal cardiac excitation. They require larger than "physiologic" intercellular conductivities in order to make up for a lack of "anatomical" spatial scaling. Multicellular models for more in-depth quantitative studies will require more realistic anatomico-physiologic properties.

Cardiac electrophysiology: theoretical considerations of a potential target for weak electromagnetic field effects

With the widespread introduction of extra high voltage power transmission lines in the 1960s, and subsequent to early reports from Soviet Union scientists about health risks for transformer station personnel, public concern regarding the effects of electromagnetic fields (EMFs) on biological function has given rise to a large number of investigations and legislation to limit domestic and occupational exposure to EMFs. The underlying rationale for concern is related to the fact that living cells are electrically active, which makes them potentially vulnerable to electromagnetic interference. In the heart, electrical activity is crucial in coordinating the contraction of millions of cardiac cells, and disturbances in cardiac electrical activity, also known as arrhythmias, are often life threatening. Electrical fields induced in the heart by weak external EMFs (such as those encountered in a domestic setting) are understood to be at least 2 orders of magnitude smaller (< 1%) than those that occur naturally as an intrinsic consequence of cardiac activity. Using quantitative models of cardiac cellular electrophysiology, the effect of weak (1%) manipulation of key current mechanisms that give rise to the electrical activity of the heart is therefore assessed.