CellML and associated tools and techniques

Ventricular Repolarization and Calcium Transient Show Resonant Behavior under Oscillatory Pacing Rate

Cardiac EC coupling is triggered by rhythmic depolarizing current fronts originating from the sino-atrial node, and the way variability in rhythm is associated with variability in action potential duration (APD) and, in turn, in the variability of calcium transient amplitude (CTA) and contraction is a key determinant of beating stability. Sinusoidal-varying pacing rate is adopted here in order to establish whether APD and CTA oscillations, elicited in a human ventricular AP model (OR) under oscillatory pacing, are consistent with the dynamics of two coupled harmonic oscillators, e.g., a two-degree-of-freedom system of mass and springs (MS model). I show evidence that this is the case, and that the MS model, preliminarily fitted to OR behavior, retains key features of the physiological system, such as the dependence of APD and CTA oscillation amplitudes from average value and from beat-to-beat changes in pacing rate, and the phase relationship between them. The bi-directionality of coupling between APD and CTA makes it difficult to discriminate which one leads EC coupling dynamics under variable pacing. The MS model suggests that the calcium cycling, with its greater inertia chiefly determined by the SR calcium release, is the leading mechanism. I propose the present approach to also be relevant at the whole organ level, where the need of compact representations of electromechanical interaction, particularly in clinical practice, remains urgent.

cellmlmanip and chaste_codegen: automatic CellML to C++ code generation with fixes for singularities and automatically generated Jacobians

Hundreds of different mathematical models have been proposed for describing electrophysiology of various cell types. These models are quite complex (nonlinear systems of typically tens of ODEs and sometimes hundreds of parameters) and software packages such as the Cancer, Heart and Soft Tissue Environment (Chaste) C++ library have been designed to run simulations with these models in isolation or coupled to form a tissue simulation. The complexity of many of these models makes sharing and translating them to new simulation environments difficult. CellML is an XML format that offers a widely-adopted solution to this problem. This paper specifically describes the capabilities of two new Python tools: the cellmlmanip library for reading and manipulating CellML models; and chaste_codegen, a CellML to C++ converter. These tools provide a Python 3 replacement for a previous Python 2 tool (called PyCML) and they also provide additional new features that this paper describes. Most notably, they can generate analytic Jacobians without the use of proprietary software, and also find singularities occurring in equations and automatically generate and apply linear approximations to prevent numerical problems at these points.

A Quantitative Systems Pharmacology Perspective on the Importance of Parameter Identifiability

There is an inherent tension in Quantitative Systems Pharmacology (QSP) between the need to incorporate mathematical descriptions of complex physiology and drug targets with the necessity of developing robust, predictive and well-constrained models. In addition to this, there is no “gold standard” for model development and assessment in QSP. Moreover, there can be confusion over terminology such as model and parameter identifiability; complex and simple models; virtual populations; and other concepts, which leads to potential miscommunication and misapplication of methodologies within modeling communities, both the QSP community and related disciplines. This perspective article highlights the pros and cons of using simple (often identifiable) vs. complex (more physiologically detailed but often non-identifiable) models, as well as aspects of parameter identifiability, sensitivity and inference methodologies for model development and analysis. The paper distills the central themes of the issue of identifiability and optimal model size and discusses open challenges.

chaste codegen: automatic CellML to C++ code generation with fixes for singularities and automatically generated Jacobians

Hundreds of different mathematical models have been proposed for describing electrophysiology of various cell types. These models are quite complex (nonlinear systems of typically tens of ODEs and sometimes hundreds of parameters) and software packages such as the Cancer, Heart and Soft Tissue Environment (Chaste) C++ library have been designed to run simulations with these models in isolation or coupled to form a tissue simulation. The complexity of many of these models makes sharing and translating them to new simulation environments difficult. CellML is an XML format that offers a solution to this problem and has been widely-adopted. This paper specifically describes the capabilities of chaste_codegen, a Python-based CellML to C++ converter based on the new cellmlmanip Python library for reading and manipulating CellML models. While chaste_codegen is a Python 3 redevelopment of a previous Python 2 tool (called PyCML) it has some additional new features that this paper describes. Most notably, chaste_codegen has the ability to generate analytic Jacobians without the use of proprietary software, and also to find singularities occurring in equations and automatically generate and apply linear approximations to prevent numerical problems at these points.

Restitution and adaptation measurements for the estimate of short-term cardiac action potential memory: comparison of five human ventricular models

AIMS

This computational study refines our recently published pacing protocol to measure short-term memory (STM) of cardiac action potential (AP), and apply it to five numerical models of human ventricular AP.

METHODS AND RESULTS

Several formulations of electrical restitution (ER) have been provided over the years, including standard, beat-to-beat, dynamic, steady-state, which make it difficult to compare results from different studies. We discuss here the notion of dynamic ER (dER) by relating it to its steady-state counterpart, and propose a pacing protocol based on dER to measure STM under periodically varying pacing cycle length (CL). Under high and highly variable-pacing rate, all models develop STM, which can be measured over the entire sequence by means of dER. Short-term memory can also be measured on a beat-to-beat basis by estimating action potential duration (APD) adaptation after clamping CL constant. We visualize STM as a phase shift between action potential (AP) parameters over consecutive cycles of CL oscillations, and show that delay between CL and APD oscillation is nearly constant (around 92 ms) in the five models, despite variability in their intrinsic AP properties.

CONCLUSION

dER, as we define it and together with other approaches described in the study, provides an univocal way to measure STM under extreme cardiac pacing conditions. Given the relevance of AP memory for repolarization dynamics and stability, STM should be considered, among other usual biomarkers, to validate and tune cardiac AP models. The possibility of extending the method to in vivo cellular and whole organ models can also be profitably explored.

Extrapolation for a pharmacokinetic model for acetaminophen from adults to neonates: A Latin Hypercube Sampling analysis

Physiological and drug-specific parameters need to be adjusted when extrapolating a pharmacokinetic (PK) model from adults to neonates, so as to reproduce the time profiles of the studied drug(s) consistent with clinical, in vivo data or in vitro cell line measurements. In this paper we present a parameter analysis method, i.e. the Latin Hypercube Sampling (LHS) method for an acetaminophen (APAP) PK model. The original model consists of two compartments (the blood and the urine) with Michaelis-Menten kinetic parameters determined for APAP and its metabolites. The physiological parameters are scaled through allometric laws from adults to neonates, and APAP-specific parameters are adjusted for enzymatic maturational changes. The LHS method is used to statistically investigate the interplay between these parameters. The results for the extrapolated APAP model are consistent with published APAP PK data in neonates. We found the sulphation clearance parameter played a crucial role in the neonatal PK model, but its influence was weakened if the volume of distribution parameters were included. We suggest that this kind of in silico experiment could be valuable as the first step in PK model extrapolation between different ages.

Assessing Cardiomyocyte Excitation-Contraction Coupling Site Detection From Live Cell Imaging Using a Structurally-Realistic Computational Model of Calcium Release

Calcium signaling plays a pivotal role in cardiomyocytes, coupling electrical excitation to mechanical contraction of the heart. Determining locations of active calcium release sites, and how their recruitment changes in response to stimuli and in disease states is therefore of central interest in cardiac physiology. Current algorithms for detecting release sites from live cell imaging data are however not easily validated against a known “ground truth,” which makes interpretation of the output of such algorithms, in particular the degree of confidence in site detection, a challenging task. Computational models are capable of integrating findings from multiple sources into a consistent, predictive framework. In cellular physiology, such models have the potential to reveal structure and function beyond the temporal and spatial resolution limitations of individual experimental measurements. Here, we create a spatially detailed computational model of calcium release in an eight sarcomere section of a ventricular cardiomyocyte, using electron tomography reconstruction of cardiac ultrastructure and confocal imaging of protein localization. This provides a high-resolution model of calcium diffusion from intracellular stores, which can be used as a platform to simulate confocal fluorescence imaging in the context of known ground truth structures from the higher resolution model. We use this capability to evaluate the performance of a recently proposed method for detecting the functional response of calcium release sites in live cells. Model permutations reveal how calcium release site density and mitochondria acting as diffusion barriers impact the detection performance of the algorithm. We demonstrate that site density has the greatest impact on detection precision and recall, in particular affecting the effective detectable depth of sites in confocal data. Our findings provide guidance on how such detection algorithms may best be applied to experimental data and give insights into limitations when using two-dimensional microscopy images to analyse three-dimensional cellular structures.

Rapid Characterization of hERG Channel Kinetics II: Temperature Dependence

Ion channel behavior can depend strongly on temperature, with faster kinetics at physiological temperatures leading to considerable changes in currents relative to room temperature. These temperature-dependent changes in voltage-dependent ion channel kinetics (rates of opening, closing, inactivating, and recovery) are commonly represented with Q₁₀ coefficients or an Eyring relationship. In this article, we assess the validity of these representations by characterizing channel kinetics at multiple temperatures. We focus on the human Ether-à-go-go-Related Gene (hERG) channel, which is important in drug safety assessment and commonly screened at room temperature so that results require extrapolation to physiological temperature. In Part I of this study, we established a reliable method for high-throughput characterization of hERG1a (Kv11.1) kinetics, using a 15-second information-rich optimized protocol. In this Part II, we use this protocol to study the temperature dependence of hERG kinetics using Chinese hamster ovary cells overexpressing hERG1a on the Nanion SyncroPatch 384PE, a 384-well automated patch-clamp platform, with temperature control. We characterize the temperature dependence of hERG gating by fitting the parameters of a mathematical model of hERG kinetics to data obtained at five distinct temperatures between 25 and 37°C and validate the models using different protocols. Our models reveal that activation is far more temperature sensitive than inactivation, and we observe that the temperature dependency of the kinetic parameters is not represented well by Q₁₀ coefficients; it broadly follows a generalized, but not the standardly-used, Eyring relationship. We also demonstrate that experimental estimations of Q₁₀ coefficients are protocol dependent. Our results show that a direct fit using our 15-s protocol best represents hERG kinetics at any given temperature and suggests that using the Generalized Eyring theory is preferable if no experimental data are available to derive model parameters at a given temperature.

Mapping Tyrosine Kinase Receptor Dimerization to Receptor Expression and Ligand Affinities

Tyrosine kinase receptor (RTK) ligation and dimerization is a key mechanism for translating external cell stimuli into internal signaling events. This process is critical to several key cell and physiological processes, such as in angiogenesis and embryogenesis, among others. While modulating RTK activation is a promising therapeutic target, RTK signaling axes have been shown to involve complicated interactions between ligands and receptors both within and across different protein families. In angiogenesis, for example, several signaling protein families, including vascular endothelial growth factors and platelet-derived growth factors, exhibit significant cross-family interactions that can influence pathway activation. Computational approaches can provide key insight to detangle these signaling pathways but have been limited by the sparse knowledge of these cross-family interactions. Here, we present a framework for studying known and potential non-canonical interactions. We constructed generalized models of RTK ligation and dimerization for systems of two, three and four receptor types and different degrees of cross-family ligation. Across each model, we developed parameter-space maps that fully determine relative pathway activation for any set of ligand-receptor binding constants, ligand concentrations and receptor concentrations. Therefore, our generalized models serve as a powerful reference tool for predicting not only known ligand: Receptor axes but also how unknown interactions could alter signaling dimerization patterns. Accordingly, it will drive the exploration of cross-family interactions and help guide therapeutic developments across processes like cancer and cardiovascular diseases, which depend on RTK-mediated signaling.

Multiscale computing for science and engineering in the era of exascale performance

In this position paper, we discuss two relevant topics: (i) generic multiscale computing on emerging exascale high-performing computing environments, and (ii) the scaling of such applications towards the exascale. We will introduce the different phases when developing a multiscale model and simulating it on available computing infrastructure, and argue that we could rely on it both on the conceptual modelling level and also when actually executing the multiscale simulation, and maybe should further develop generic frameworks and software tools to facilitate multiscale computing. Next, we focus on simulating multiscale models on high-end computing resources in the face of emerging exascale performance levels. We will argue that although applications could scale to exascale performance relying on weak scaling and maybe even on strong scaling, there are also clear arguments that such scaling may no longer apply for many applications on these emerging exascale machines and that we need to resort to what we would call multi-scaling. This article is part of the theme issue 'Multiscale modelling, simulation and computing: from the desktop to the exascale'.

Extended Bidomain Modeling of Defibrillation: Quantifying Virtual Electrode Strengths in Fibrotic Myocardium

Defibrillation is a well-established therapy for atrial and ventricular arrhythmia. Here, we shed light on defibrillation in the fibrotic heart. Using the extended bidomain model of electrical conduction in cardiac tissue, we assessed the influence of fibrosis on the strength of virtual electrodes caused by extracellular electrical current. We created one-dimensional models of rabbit ventricular tissue with a central patch of fibrosis. The fibrosis was incorporated by altering volume fractions for extracellular, myocyte and fibroblast domains. In our prior work, we calculated these volume fractions from microscopic images at the infarct border zone of rabbit hearts. An average and a large degree of fibrosis were modeled. We simulated defibrillation by application of an extracellular current for a short duration (5 ms). We explored the effects of myocyte-fibroblast coupling, intra-fibroblast conductivity and patch length on the strength of the virtual electrodes present at the borders of the normal and fibrotic tissue. We discriminated between effects on myocyte and fibroblast membranes at both borders of the patch. Similarly, we studied defibrillation in two-dimensional models of fibrotic tissue. Square and disk-like patches of fibrotic tissue were embedded in control tissue. We quantified the influence of the geometry and fibrosis composition on virtual electrode strength. We compared the results obtained with a square and disk shape of the fibrotic patch with results from the one-dimensional simulations. Both, one- and two-dimensional simulations indicate that extracellular current application causes virtual electrodes at boundaries of fibrotic patches. A higher degree of fibrosis and larger patch size were associated with an increased strength of the virtual electrodes. Also, patch geometry affected the strength of the virtual electrodes. Our simulations suggest that increased fibroblast-myocyte coupling and intra-fibroblast conductivity reduce virtual electrode strength. However, experimental data to constrain these modeling parameters are limited and thus pinpointing the magnitude of the reduction will require further understanding of electrical coupling of fibroblasts in native cardiac tissues. We propose that the findings from our computational studies are important for development of patient-specific protocols for internal defibrillators.

Construction of lumped-parameter cardiovascular models using the CellML language

Lumped-parameter models are widely used by cardiovascular researchers in the analysis of the circulatory dynamics. However, portability and model exchange have always been a problem, with different researchers implement the model differently. To improve the situation, in this study, a group of lumped-parameter cardiovascular system models with different levels of complexity have been implemented using the CellML mark-up language. The models have been curated and made publicly available in the CellML model repository, and the purpose of this paper is to provide further technical details to support the usage of these models by the research community. The developed models are validated and tested under the OpenCell environment as part of the curation process. Simulation results agree well with typical published data on cardiovascular system response.

Data Management in Computational Systems Biology: Exploring Standards, Tools, Databases, and Packaging Best Practices

Computational systems biology involves integrating heterogeneous datasets in order to generate models. These models can assist with understanding and prediction of biological phenomena. Generating datasets and integrating them into models involves a wide range of scientific expertise. As a result these datasets are often collected by one set of researchers, and exchanged with others researchers for constructing the models. For this process to run smoothly the data and models must be FAIR-findable, accessible, interoperable, and reusable. In order for data and models to be FAIR they must be structured in consistent and predictable ways, and described sufficiently for other researchers to understand them. Furthermore, these data and models must be shared with other researchers, with appropriately controlled sharing permissions, before and after publication. In this chapter we explore the different data and model standards that assist with structuring, describing, and sharing. We also highlight the popular standards and sharing databases within computational systems biology.

Insights on the impact of mitochondrial organisation on bioenergetics in high-resolution computational models of cardiac cell architecture

Recent electron microscopy data have revealed that cardiac mitochondria are not arranged in crystalline columns but are organised with several mitochondria aggregated into columns of varying sizes spanning the cell cross-section. This raises the question—how does the mitochondrial arrangement affect the metabolite distributions within cardiomyocytes and what is its impact on force dynamics? Here, we address this question by employing finite element modeling of cardiac bioenergetics on computational meshes derived from electron microscope images. Our results indicate that heterogeneous mitochondrial distributions can lead to significant spatial variation across the cell in concentrations of inorganic phosphate, creatine (Cr) and creatine phosphate (PCr). However, our model predicts that sufficient activity of the creatine kinase (CK) system, coupled with rapid diffusion of Cr and PCr, maintains near uniform ATP and ADP ratios across the cell cross sections. This homogenous distribution of ATP and ADP should also evenly distribute force production and twitch duration with contraction. These results suggest that the PCr shuttle and associated enzymatic reactions act to maintain uniform force dynamics in the cell despite the heterogeneous mitochondrial organization. However, our model also predicts that under hypoxia activity of mitochondrial CK enzymes and diffusion of high-energy phosphate compounds may be insufficient to sustain uniform ATP/ADP distribution and hence force generation.

Mammalian cardiomyocytes contain a high volume of mitochondria, which maintains the continuous and bulk supply of ATP to sustain normal heart function. Previously, cardiac mitochondria were understood to be distributed in a regular, crystalline pattern, which facilitated a steady supply of ATP at different workloads. Using electron microscopy images of cell cross sections, we recently found that they are not regularly distributed inside cardiomyocytes. We created new spatially accurate computational models of cardiac cell bioenergetics and tested whether this heterogeneous distribution of mitochondria causes non-uniform energy supply and contractile force production in the cardiomyocyte. We found that ATP and ADP concentrations remain uniform throughout the cell because of the activity of creatine kinase (CK) enzymes that convert ATP produced in the mitochondria into creatine phosphate. Creatine phosphate rapidly diffuses to the myofibril region where it can be converted back to ATP for the contraction cycle in a timely manner. This mechanism is called the phosphocreatine shuttle (PCr shuttle). The PCr shuttle ensures that different areas of the cell produce the same amount of force regardless of the mitochondrial distribution. However, our model also shows that when the cellular oxygen supply is limited—as can be the case in conditions such as heart failure—the PCr shuttle cannot maintain uniform ATP and ADP concentrations across the cell. This causes a non-uniform acto-myosin force distribution and non-uniform twitch duration across the cell cross section. Our study suggests that mechanisms other than the PCr shuttle may be necessary to maintain uniform supply of ATP in a hypoxic environment.

Reproducible model development in the cardiac electrophysiology Web Lab

The modelling of the electrophysiology of cardiac cells is one of the most mature areas of systems biology. This extended concentration of research effort brings with it new challenges, foremost among which is that of choosing which of these models is most suitable for addressing a particular scientific question. In a previous paper, we presented our initial work in developing an online resource for the characterisation and comparison of electrophysiological cell models in a wide range of experimental scenarios. In that work, we described how we had developed a novel protocol language that allowed us to separate the details of the mathematical model (the majority of cardiac cell models take the form of ordinary differential equations) from the experimental protocol being simulated. We developed a fully-open online repository (which we termed the Cardiac Electrophysiology Web Lab) which allows users to store and compare the results of applying the same experimental protocol to competing models. In the current paper we describe the most recent and planned extensions of this work, focused on supporting the process of model building from experimental data. We outline the necessary work to develop a machine-readable language to describe the process of inferring parameters from wet lab datasets, and illustrate our approach through a detailed example of fitting a model of the hERG channel using experimental data. We conclude by discussing the future challenges in making further progress in this domain towards our goal of facilitating a fully reproducible approach to the development of cardiac cell models.

Short-term action potential memory and electrical restitution: A cellular computational study on the stability of cardiac repolarization under dynamic pacing

Electrical restitution (ER) is a major determinant of repolarization stability and, under fast pacing rate, it reveals memory properties of the cardiac action potential (AP), whose dynamics have never been fully elucidated, nor their ionic mechanisms. Previous studies have looked at ER mainly in terms of changes in AP duration (APD) when the preceding diastolic interval (DI) changes and described dynamic conditions where this relationship shows hysteresis which, in turn, has been proposed as a marker of short-term AP memory and repolarization stability. By means of numerical simulations of a non-propagated human ventricular AP, we show here that measuring ER as APD versus the preceding cycle length (CL) provides additional information on repolarization dynamics which is not contained in the companion formulation. We focus particularly on fast pacing rate conditions with a beat-to-beat variable CL, where memory properties emerge from APD vs CL and not from APD vs DI and should thus be stored in APD and not in DI. We provide an ion-currents characterization of such conditions under periodic and random CL variability, and show that the memory stored in APD plays a stabilizing role on AP repolarization under pacing rate perturbations. The gating kinetics of L-type calcium current seems to be the main determinant of this safety mechanism. We also show that, at fast pacing rate and under otherwise identical pacing conditions, a periodically beat-to-beat changing CL is more effective than a random one in stabilizing repolarization. In summary, we propose a novel view of short-term AP memory, differentially stored between systole and diastole, which opens a number of methodological and theoretical implications for the understanding of arrhythmia development.

Next-generation, personalised, model-based critical care medicine: a state-of-the art review of in silico virtual patient models, methods, and cohorts, and how to validation them

Critical care, like many healthcare areas, is under a dual assault from significantly increasing demographic and economic pressures. Intensive care unit (ICU) patients are highly variable in response to treatment, and increasingly aging populations mean ICUs are under increasing demand and their cohorts are increasingly ill. Equally, patient expectations are growing, while the economic ability to deliver care to all is declining. Better, more productive care is thus the big challenge. One means to that end is personalised care designed to manage the significant inter- and intra-patient variability that makes the ICU patient difficult. Thus, moving from current "one size fits all" protocolised care to adaptive, model-based "one method fits all" personalised care could deliver the required step change in the quality, and simultaneously the productivity and cost, of care. Computer models of human physiology are a unique tool to personalise care, as they can couple clinical data with mathematical methods to create subject-specific models and virtual patients to design new, personalised and more optimal protocols, as well as to guide care in real-time. They rely on identifying time varying patient-specific parameters in the model that capture inter- and intra-patient variability, the difference between patients and the evolution of patient condition. Properly validated, virtual patients represent the real patients, and can be used in silico to test different protocols or interventions, or in real-time to guide care. Hence, the underlying models and methods create the foundation for next generation care, as well as a tool for safely and rapidly developing personalised treatment protocols over large virtual cohorts using virtual trials. This review examines the models and methods used to create virtual patients. Specifically, it presents the models types and structures used and the data required. It then covers how to validate the resulting virtual patients and trials, and how these virtual trials can help design and optimise clinical trial. Links between these models and higher order, more complex physiome models are also discussed. In each section, it explores the progress reported up to date, especially on core ICU therapies in glycemic, circulatory and mechanical ventilation management, where high cost and frequency of occurrence provide a significant opportunity for model-based methods to have measurable clinical and economic impact. The outcomes are readily generalised to other areas of medical care.

MarkoLAB: A simulator to study ionic channel's stochastic behavior

Mathematical models of the cardiac cell have started to include markovian representations of the ionic channels instead of the traditional Hodgkin & Huxley formulations. There are many reasons for this: Markov models are not restricted to the idea of independent gates defining the channel, they allow more complex description with specific transitions between open, closed or inactivated states, and more importantly those states can be closely related to the underlying channel structure and conformational changes.

METHODS

We used the LabVIEW^® and MATLAB^® programs to implement the simulator MarkoLAB that allow a dynamical 3D representation of the markovian model of the channel. The Monte Carlo simulation was used to implement the stochastic transitions among states. The user can specify the voltage protocol by setting the holding potential, the step-to voltage and the duration of the stimuli.

RESULTS

The most studied feature of a channel is the current flowing through it. This happens when the channel stays in the open state, but most of the time, as revealed by the low open probability values, the channel remains on the inactive or closed states. By focusing only when the channel enters or leaves the open state we are missing most of its activity. MarkoLAB proved to be quite useful to visualize the whole behavior of the channel and not only when the channel produces a current. Such dynamic representation provides more complete information about channel kinetics and will be a powerful tool to demonstrate the effect of gene mutations or drugs on the channel function.

CONCLUSIONS

MarkoLAB provides an original way of visualizing the stochastic behavior of a channel. It clarifies concepts, such as recovery from inactivation, calcium- versus voltage-dependent inactivation, and tail currents. It is not restricted to ionic channels only but it can be extended to other transporters, such as exchangers and pumps. This program is intended as a didactical tool to illustrate the dynamical behavior of a channel. It has been implemented in two platforms MATLAB^® and LabVIEW^® to enhance the target users of this new didactical tool. The computational cost of implementing a stochastic simulation is within the range of a personal computer performance; making MarkoLAB suitable to be run during a lecture or presentation.

LongQt: A cardiac electrophysiology simulation platform

Mathematical modeling has been used for over half a century to advance our understanding of cardiac electrophysiology and arrhythmia mechanisms. Notably, computational studies using mathematical models of the cardiac action potential (AP) have provided important insight into the fundamental nature of cell excitability, mechanisms underlying both acquired and inherited arrhythmia, and potential therapies. Ultimately, an approach that tightly integrates mathematical modeling and experimental techniques has great potential to accelerate discovery. Despite the increasing acceptance of mathematical modeling as a powerful tool in cardiac electrophysiology research, there remain significant barriers to its more widespread use in the field, due in part to the increasing complexity of models and growing need for specialization. To help bridge the gap between experimental and theoretical worlds that stands as a barrier to transformational breakthroughs, we present LongQt, which has the following key features:

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Cross-platform, threaded application with accessible graphical user interface.

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Facilitates advanced computational cardiac electrophysiology and arrhythmia studies.

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Does not require advanced programming skills.

The Cardiac Electrophysiology Web Lab

Computational modeling of cardiac cellular electrophysiology has a long history, and many models are now available for different species, cell types, and experimental preparations. This success brings with it a challenge: how do we assess and compare the underlying hypotheses and emergent behaviors so that we can choose a model as a suitable basis for a new study or to characterize how a particular model behaves in different scenarios? We have created an online resource for the characterization and comparison of electrophysiological cell models in a wide range of experimental scenarios. The details of the mathematical model (quantitative assumptions and hypotheses formulated as ordinary differential equations) are separated from the experimental protocol being simulated. Each model and protocol is then encoded in computer-readable formats. A simulation tool runs virtual experiments on models encoded in CellML, and a website (https://chaste.cs.ox.ac.uk/WebLab) provides a friendly interface, allowing users to store and compare results. The system currently contains a sample of 36 models and 23 protocols, including current-voltage curve generation, action potential properties under steady pacing at different rates, restitution properties, block of particular channels, and hypo-/hyperkalemia. This resource is publicly available, open source, and free, and we invite the community to use it and become involved in future developments. Investigators interested in comparing competing hypotheses using models can make a more informed decision, and those developing new models can upload them for easy evaluation under the existing protocols, and even add their own protocols.

Sharing Structure and Function in Biological Design with SBOL 2.0

The Synthetic Biology Open Language (SBOL) is a standard that enables collaborative engineering of biological systems across different institutions and tools. SBOL is developed through careful consideration of recent synthetic biology trends, real use cases, and consensus among leading researchers in the field and members of commercial biotechnology enterprises. We demonstrate and discuss how a set of SBOL-enabled software tools can form an integrated, cross-organizational workflow to recapitulate the design of one of the largest published genetic circuits to date, a 4-input AND sensor. This design encompasses the structural components of the system, such as its DNA, RNA, small molecules, and proteins, as well as the interactions between these components that determine the system's behavior/function. The demonstrated workflow and resulting circuit design illustrate the utility of SBOL 2.0 in automating the exchange of structural and functional specifications for genetic parts, devices, and the biological systems in which they operate.

MioLab, a rat cardiac contractile force simulator: Applications to teaching cardiac cell physiology and biophysics

INTRODUCTION

Understanding the basic concepts of physiology and biophysics of cardiac cells can be improved by virtual experiments that illustrate the complex excitation-contraction coupling process in cardiac cells. The aim of this study is to propose a rat cardiac myocyte simulator, with which calcium dynamics in excitation-contraction coupling of an isolated cell can be observed. This model has been used in the course "Mathematical Modeling and Simulation of Biological Systems". In this paper we present the didactic utility of the simulator MioLab(®).

METHODS

The simulator enables virtual experiments that can help studying inhibitors and activators in the sarcoplasmic reticulum sodium-calcium exchanger, thus corroborating a better understanding of the effects of medications, which are used to treat arrhythmias, on these compartments. The graphical interfaces were developed not only to facilitate the use of the simulator, but also to promote a constructive learning on the subject, since there are animations and videos for each stage of the simulation. The effectiveness of the simulator was tested by a group of graduate students.

RESULTS

Some examples of simulations were presented in order to describe the overall structure of the simulator. Part of these virtual experiments became an activity for Biomedical Engineering graduate students, who evaluated the simulator based on its didactic quality. As a result, students answered a questionnaire on the usability and functionality of the simulator as a teaching tool. All students performed the proposed activities and classified the simulator as an optimal or good learning tool. In their written questions, students indicated as negative characteristics some problems with visualizing graphs; as positive characteristics, they indicated the simulator's didactic function, especially tutorials and videos on the topic of this study.

CONCLUSIONS

The results show that the simulator complements the study of the physiology and biophysics of the cardiac cell.

Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to generate code for physiological simulations and provides a tool for studying cardiac electrophysiology.

Human cardiac systems electrophysiology and arrhythmogenesis: iteration of experiment and computation

Human cardiac electrophysiology (EP) is a unique system for computational modelling at multiple scales. Due to the complexity of the cardiac excitation sequence, coordinated activity must occur from the single channel to the entire myocardial syncytium. Thus, sophisticated computational algorithms have been developed to investigate cardiac EP at the level of ion channels, cardiomyocytes, multicellular tissues, and the whole heart. Although understanding of each functional level will ultimately be important to thoroughly understand mechanisms of physiology and disease, cardiac arrhythmias are expressly the product of cardiac tissue-containing enough cardiomyocytes to sustain a reentrant loop of activation. In addition, several properties of cardiac cellular EP, that are critical for arrhythmogenesis, are significantly altered by cell-to-cell coupling. However, relevant human cardiac EP data, upon which to develop or validate models at all scales, has been lacking. Thus, over several years, we have developed a paradigm for multiscale human heart physiology investigation and have recovered and studied over 300 human hearts. We have generated a rich experimental dataset, from which we better understand mechanisms of arrhythmia in human and can improve models of human cardiac EP. In addition, in collaboration with computational physiologists, we are developing a database for the deposition of human heart experimental data, including thorough experimental documentation. We anticipate that accessibility to this human heart dataset will further human EP computational investigations, as well as encourage greater data transparency within the field of cardiac EP.

The role of markup for enabling interoperability in health informatics

Interoperability is the faculty of making information systems work together. In this paper we will distinguish a number of different forms that interoperability can take and show how they are realized on a variety of physiological and health care use cases. The last 15 years has seen the rise of very cheap digital storage both on and off site. With the advent of the Internet of Things people's expectations are for greater interconnectivity and seamless interoperability. The potential impact these technologies have on healthcare are dramatic: from improved diagnoses through immediate access to a patient's electronic health record, to in silico modeling of organs and early stage drug trials, to predictive medicine based on top-down modeling of disease progression and treatment. We will begin by looking at the underlying technology, classify the various kinds of interoperability that exist in the field, and discuss how they are realized. We conclude with a discussion on future possibilities that big data and further standardizations will enable.

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.

Cellular cardiac electrophysiology modeling with Chaste and CellML

Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model code is auto-generated at compile or run time; it never has to be manually edited. We use ontological annotation to identify model variables describing certain biological quantities (membrane voltage, capacitance, etc.) to allow us to import any relevant CellML models into the Chaste framework in consistent units and to interact with them via consistent interfaces. This approach provides a great deal of flexibility for analysing different models of the same system. Chaste provides a wide choice of numerical methods for solving the ordinary differential equations that describe the models. Fixed-timestep explicit and implicit solvers are provided, as discussed in previous work. Here we introduce the Rush–Larsen and Generalized Rush–Larsen integration techniques, made available via symbolic manipulation of the model equations, which are automatically rearranged into the forms required by these approaches. We have also integrated the CVODE solvers, a ‘gold standard’ for stiff systems, and we have developed support for symbolic computation of the Jacobian matrix, yielding further increases in the performance and accuracy of CVODE. We discuss some of the technical details of this work and compare the performance of the available numerical methods. Finally, we discuss how this is generalized in our functional curation framework, which uses a domain-specific language for defining complex experiments as a basis for comparison of model behavior.

Using CellML with OpenCMISS to Simulate Multi-Scale Physiology

OpenCMISS is an open-source modeling environment aimed, in particular, at the solution of bioengineering problems. OpenCMISS consists of two main parts: a computational library (OpenCMISS-Iron) and a field manipulation and visualization library (OpenCMISS-Zinc). OpenCMISS is designed for the solution of coupled multi-scale, multi-physics problems in a general-purpose parallel environment. CellML is an XML format designed to encode biophysically based systems of ordinary differential equations and both linear and non-linear algebraic equations. A primary design goal of CellML is to allow mathematical models to be encoded in a modular and reusable format to aid reproducibility and interoperability of modeling studies. In OpenCMISS, we make use of CellML models to enable users to configure various aspects of their multi-scale physiological models. This avoids the need for users to be familiar with the OpenCMISS internal code in order to perform customized computational experiments. Examples of this are: cellular electrophysiology models embedded in tissue electrical propagation models; material constitutive relationships for mechanical growth and deformation simulations; time-varying boundary conditions for various problem domains; and fluid constitutive relationships and lumped-parameter models. In this paper, we provide implementation details describing how CellML models are integrated into multi-scale physiological models in OpenCMISS. The external interface OpenCMISS presents to users is also described, including specific examples exemplifying the extensibility and usability these tools provide the physiological modeling and simulation community. We conclude with some thoughts on future extension of OpenCMISS to make use of other community developed information standards, such as FieldML, SED-ML, and BioSignalML. Plans for the integration of accelerator code (graphical processing unit and field programmable gate array) generated from CellML models is also discussed.

Interactive simulator for e-Learning environments: a teaching software for health care professionals

There is an established tradition of cardiovascular simulation tools, but the application of this kind of technology in the e-Learning arena is a novel approach. This paper presents an e-Learning environment aimed at teaching the interaction of cardiovascular and lung systems to health-care professionals. Heart-lung interaction must be analyzed while assisting patients with severe respiratory problems or with heart failure in intensive care unit. Such patients can be assisted by mechanical ventilatory assistance or by thoracic artificial lung.

“In silico” cardiovascular simulator was experimented during a training course given to graduate students of the School of Specialization in Cardiology at ‘Sapienza’ University in Rome.

The training course employed CARDIOSIM^©: a numerical simulator of the cardiovascular system. Such simulator is able to reproduce pathophysiological conditions of patients affected by cardiovascular and/or lung disease. In order to study the interactions among the cardiovascular system, the natural lung and the thoracic artificial lung (TAL), the numerical model of this device has been implemented. After having reproduced a patient’s pathological condition, TAL model was applied in parallel and hybrid model during the training course.

Results obtained during the training course show that TAL parallel assistance reduces right ventricular end systolic (diastolic) volume, but increases left ventricular end systolic (diastolic) volume. The percentage changes induced by hybrid TAL assistance on haemodynamic variables are lower than those produced by parallel assistance. Only in the case of the mean pulmonary arterial pressure, there is a percentage reduction which, in case of hybrid assistance, is greater (about 40%) than in case of parallel assistance (20-30%).

At the end of the course, a short questionnaire was submitted to students in order to assess the quality of the course. The feedback obtained was positive, showing good results with respect to the degree of students’ learning and the ease of use of the software simulator.

Modeling biology spanning different scales: an open challenge

It is coming nowadays more clear that in order to obtain a unified description of the different mechanisms governing the behavior and causality relations among the various parts of a living system, the development of comprehensive computational and mathematical models at different space and time scales is required. This is one of the most formidable challenges of modern biology characterized by the availability of huge amount of high throughput measurements. In this paper we draw attention to the importance of multiscale modeling in the framework of studies of biological systems in general and of the immune system in particular.

Verification of computational models of cardiac electro-physiology

For computational models of cardiac activity to be used in safety-critical clinical decision-making, thorough and rigorous testing of the accuracy of predictions is required. The field of 'verification, validation and uncertainty quantification' has been developed to evaluate the credibility of computational predictions. The first stage, verification, is the evaluation of how well computational software correctly solves the underlying mathematical equations. The aim of this paper is to introduce novel methods for verifying multi-cellular electro-physiological solvers, a crucial first stage for solvers to be used with confidence in clinical applications. We define 1D-3D model problems with exact solutions for each of the monodomain, bidomain, and bidomain-with-perfusing-bath formulations of cardiac electro-physiology, which allow for the first time the testing of cardiac solvers against exact errors on fully coupled problems in all dimensions. These problems are carefully constructed so that they can be easily run using a general solver and can be used to greatly increase confidence that an implementation is correct, which we illustrate by testing one major solver, 'Chaste', on the problems. We then perform case studies on calculation verification (also known as solution verification) for two specific applications. We conclude by making several recommendations regarding verification in cardiac modelling.

A vision and strategy for the virtual physiological human: 2012 update

European funding under Framework 7 (FP7) for the virtual physiological human (VPH) project has been in place now for 5 years. The VPH Network of Excellence (NoE) has been set up to help develop common standards, open source software, freely accessible data and model repositories, and various training and dissemination activities for the project. It is also working to coordinate the many clinically targeted projects that have been funded under the FP7 calls. An initial vision for the VPH was defined by the FP6 STEP project in 2006. In 2010, we wrote an assessment of the accomplishments of the first two years of the VPH in which we considered the biomedical science, healthcare and information and communications technology challenges facing the project (Hunter et al. 2010 Phil. Trans. R. Soc. A 368, 2595-2614 (doi:10.1098/rsta.2010.0048)). We proposed that a not-for-profit professional umbrella organization, the VPH Institute, should be established as a means of sustaining the VPH vision beyond the time-frame of the NoE. Here, we update and extend this assessment and in particular address the following issues raised in response to Hunter et al.: (i) a vision for the VPH updated in the light of progress made so far, (ii) biomedical science and healthcare challenges that the VPH initiative can address while also providing innovation opportunities for the European industry, and (iii) external changes needed in regulatory policy and business models to realize the full potential that the VPH has to offer to industry, clinics and society generally.

Modeling the chemoelectromechanical behavior of skeletal muscle using the parallel open-source software library OpenCMISS

An extensible, flexible, multiscale, and multiphysics model for nonisometric skeletal muscle behavior is presented. The skeletal muscle chemoelectromechanical model is based on a bottom-up approach modeling the entire excitation-contraction pathway by strongly coupling a detailed biophysical model of a half-sarcomere to the propagation of action potentials along skeletal muscle fibers and linking cellular parameters to a transversely isotropic continuum-mechanical constitutive equation describing the overall mechanical behavior of skeletal muscle tissue. Since the multiscale model exhibits separable time scales, a special emphasis is placed on employing computationally efficient staggered solution schemes. Further, the implementation builds on the open-source software library OpenCMISS and uses state-of-the-art parallelization techniques taking advantage of the unique anatomical fiber architecture of skeletal muscles. OpenCMISS utilizes standardized data structures for geometrical aspects (FieldML) and cellular models (CellML). Both standards are designed to allow for a maximum flexibility, reproducibility, and extensibility. The results demonstrate the model's capability of simulating different aspects of nonisometric muscle contraction and efficiently simulating the chemoelectromechanical behavior in complex skeletal muscles such as the tibialis anterior muscle.

FieldML, a proposed open standard for the Physiome project for mathematical model representation

The FieldML project has made significant progress towards the goal of addressing the need to have open standards and open source software for representing finite element method (FEM) models and, more generally, multivariate field models, such as many of the models that are core to the euHeart project and the Physiome project. FieldML version 0.5 is the most recently released format from the FieldML project. It is an XML format that already has sufficient capability to represent the majority of euHeart’s explicit models such as the anatomical FEM models and simulation solution fields. The details of FieldML version 0.5 are presented, as well as its limitations and some discussion of the progress being made to address these limitations.

Evaluation of an in silico cardiac safety assay: using ion channel screening data to predict QT interval changes in the rabbit ventricular wedge

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, QT prolongation 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.

Chaste: an open source C++ library for computational physiology and biology

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.

Code generator for distributed parameter biological model simulation with PDE numerical schemes

The physiological simulation at the tissue and organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and in cases like pharmacokinetics, distributed parameters add to the complexity of the PDE solution. These factors make most PDE solutions and their corresponding program codes tailored for specific problems. We propose a general approach for handling PDEs in computational models using a replacement scheme for discretization. This method allows for the handling of the different PDE types. The replacement scheme involves substituting all the partial differential terms with the numerical solution equations. Once the model equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to determine the simulation loop structure and generate the program code.

Simulating spiking neural networks on GPU

Modern graphics cards contain hundreds of cores that can be programmed for intensive calculations. They are beginning to be used for spiking neural network simulations. The goal is to make parallel simulation of spiking neural networks available to a large audience, without the requirements of a cluster. We review the ongoing efforts towards this goal, and we outline the main difficulties.

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.

At the heart of computational modelling

The link between experimental data and biophysically based mathematical models is key to computational simulation meeting its potential to provide physiological insight. However, despite the importance of this link, scrutiny and analysis of the processes by which models are parameterised from data are currently lacking. While this situation is common to many areas of physiological modelling, to provide a concrete context, we use examples drawn from detailed models of cardiac electro-mechanics. Using this biophysically detailed cohort of models we highlight the specific issues of model parameterization and propose this process can be separated into three stages: observation, fitting and validation. Finally, future research challenges and directions in this area are discussed.

Molecular bioelectricity in developmental biology: new tools and recent discoveries: control of cell behavior and pattern formation by transmembrane potential gradients

Significant progress in the molecular investigation of endogenous bioelectric signals during pattern formation in growing tissues has been enabled by recently developed techniques. Ion flows and voltage gradients produced by ion channels and pumps are key regulators of cell proliferation, migration, and differentiation. Now, instructive roles for bioelectrical gradients in embryogenesis, regeneration, and neoplasm are being revealed through the use of fluorescent voltage reporters and functional experiments using well-characterized channel mutants. Transmembrane voltage gradients (V(mem) ) determine anatomical polarity and function as master regulators during appendage regeneration and embryonic left-right patterning. A state-of-the-art recent study reveals that they can also serve as prepatterns for gene expression domains during craniofacial patterning. Continued development of novel tools and better ways to think about physical controls of cell-cell interactions will lead to mastery of the morphogenetic information stored in physiological networks. This will enable fundamental advances in basic understanding of growth and form, as well as transformative biomedical applications in regenerative medicine.

Modelling tissue electrophysiology with multiple cell types: applications of the extended bidomain framework

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.

In silico implementation of synthetic gene networks

Computational synthetic biology has borrowed methods, concepts, and techniques from systems biology and electrical engineering. Features of tools for the analysis of biochemical networks and the design of electric circuits have been combined to develop new software, where Standard Biological Parts (physically stored at the MIT Registry) have a mathematical description, based on mass action or Hill kinetics, and can be assembled into genetic networks in a visual, "drag & drop" fashion. Recent tools provide the user with databases, simulation environments, formal languages, and even algorithms for circuit automatic design to refine and speed up gene network construction. Moreover, advances in automation of DNA assembly indicate that synthetic biology software soon will drive the wet-lab implementation of DNA sequences.

Regulation of cell behavior and tissue patterning by bioelectrical signals: challenges and opportunities for biomedical engineering

Achieving control over cell behavior and pattern formation requires molecular-level understanding of regulatory mechanisms. Alongside transcriptional networks and biochemical gradients, there functions an important system of cellular communication and control: transmembrane voltage gradients (V(mem)). Bioelectrical signals encoded in spatiotemporal changes of V(mem) control cell proliferation, migration, and differentiation. Moreover, endogenous bioelectrical gradients serve as instructive cues mediating anatomical polarity and other organ-level aspects of morphogenesis. In the past decade, significant advances in molecular physiology have enabled the development of new genetic and biophysical tools for the investigation and functional manipulation of bioelectric cues. Recent data implicate V(mem) as a crucial epigenetic regulator of patterning events in embryogenesis, regeneration, and cancer. We review new conceptual and methodological developments in this fascinating field. Bioelectricity offers a novel way of quantitatively understanding regulation of growth and form in vivo, and it reveals tractable, powerful control points that will enable truly transformative applications in bioengineering, regenerative medicine, and synthetic biology.

Temporo-spatial model construction using the MML and software framework

Development of complex temporo-spatial biological computational models can be a time consuming and arduous task. These models may contain hundreds of differential equations as well as realistic geometries that may require considerable investment in time to ensure that all model components are correctly implemented and error free. To tackle this problem, the Modeling Markup Languages (MML) and software framework is a modular XML/HDF5-based specification and toolkits that aims to simplify this process. The main goal of this framework is to encourage reusability, sharing and storage. To achieve this, the MML framework utilizes the CellML specification and repository, which comprises an extensive range of curated models available for use. The MML framework is an open-source project available at http://mml.gsbme.unsw.edu.au.