Chaste: using agile programming techniques to develop computational biology software

Unit and regression tests of scientific software: A study on SWMM

Testing helps assure software quality by executing a program and uncovering bugs. Scientific software developers often find it challenging to carry out systematic and automated testing due to reasons like inherent model uncertainties and complex floating-point computations. Extending the recent work on analyzing the unit tests written by the developers of the Storm Water Management Model (SWMM) [32], we report in this paper the investigation of both unit and regression tests of SWMM. The results show that the 2953 unit tests of SWMM have a 39.7% statement-level code coverage and a 82.4% user manual coverage. Meanwhile, an examination of 58 regression tests of SWMM shows a 44.9% statement-level code coverage and a near 100% user manual coverage. We also observe a "getter-setter-getter" testing pattern from the SWMM unit tests, and suggest a diversified way of executing regression tests.

Electrophysiological and anatomical factors determine arrhythmic risk in acute myocardial ischaemia and its modulation by sodium current availability

Acute myocardial ischaemia caused by coronary artery disease is one of the main causes of sudden cardiac death. Even though sodium current blockers are used as anti-arrhythmic drugs, decreased sodium current availability, also caused by mutations, has been shown to increase arrhythmic risk in ischaemic patients. The mechanisms are still unclear. Our goal is to exploit perfect control and data transparency of over 300 high-performance computing simulations to investigate arrhythmia mechanisms in acute myocardial ischaemia with variable sodium current availability. The human anatomically based torso-biventricular electrophysiological model used includes representation of realistic ventricular anatomy and fibre architecture, as well as ionic to electrocardiographic properties. Simulations show that reduced sodium current availability increased arrhythmic risk in acute regional ischaemia due to both electrophysiological (increased dispersion of refractoriness across the ischaemic border zone) and anatomical factors (conduction block from the thin right ventricle to thick left ventricle). The asymmetric ventricular anatomy caused high arrhythmic risk specifically for ectopic stimuli originating from the right ventricle and ventricular base. Increased sodium current availability was ineffective in reducing arrhythmic risk for septo-basal ectopic excitation. Human-based multiscale modelling and simulations reveal key electrophysiological and anatomical factors determining arrhythmic risk in acute ischaemia with variable sodium current availability.

NetLogo agent-based models as tools for understanding the self-organization of cell fate, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium

Interactions between primordium cells and their environment determines the self-organization of the zebrafish posterior Lateral Line primordium as it migrates under the skin from the ear to the tip of the tail forming and depositing neuromasts to spearhead formation of the posterior Lateral Line sensory system. In this review we describe how the NetLogo agent-based programming environment has been used in our lab to visualize and explore how self-generated chemokine gradients determine collective migration, how the dynamics of Wnt signaling can be used to predict patterns of neuromast deposition, and how previously defined interactions between Wnt and Fgf signaling systems have the potential to determine the periodic formation of center-biased Fgf signaling centers in the wake of a shrinking Wnt system. We also describe how NetLogo was used as a database for storing and visualizing the results of in toto lineage analysis of all cells in the migrating primordium. Together, the models illustrate how this programming environment can be used in diverse ways to integrate what has been learnt from biological experiments about the nature of interactions between cells and their environment, and explore how these interactions could potentially determine emergent patterns of cell fate specification, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium.

A demonstration of modularity, reuse, reproducibility, portability and scalability for modeling and simulation of cardiac electrophysiology using Kepler Workflows

Multi-scale computational modeling is a major branch of computational biology as evidenced by the US federal interagency Multi-Scale Modeling Consortium and major international projects. It invariably involves specific and detailed sequences of data analysis and simulation, often with multiple tools and datasets, and the community recognizes improved modularity, reuse, reproducibility, portability and scalability as critical unmet needs in this area. Scientific workflows are a well-recognized strategy for addressing these needs in scientific computing. While there are good examples if the use of scientific workflows in bioinformatics, medical informatics, biomedical imaging and data analysis, there are fewer examples in multi-scale computational modeling in general and cardiac electrophysiology in particular. Cardiac electrophysiology simulation is a mature area of multi-scale computational biology that serves as an excellent use case for developing and testing new scientific workflows. In this article, we develop, describe and test a computational workflow that serves as a proof of concept of a platform for the robust integration and implementation of a reusable and reproducible multi-scale cardiac cell and tissue model that is expandable, modular and portable. The workflow described leverages Python and Kepler-Python actor for plotting and pre/post-processing. During all stages of the workflow design, we rely on freely available open-source tools, to make our workflow freely usable by scientists.

We present a computational workflow as a proof of concept for integration and implementation of a reusable and reproducible cardiac multi-scale electrophysiology model that is expandable, modular and portable. This framework enables scientists to create intuitive, user-friendly and flexible end-to-end automated scientific workflows using a graphical user interface. Kepler is an advanced open-source platform that supports multiple models of computation. The underlying workflow engine handles scalability, provenance, reproducibility aspects of the code, performs orchestration of data flow, and automates execution on heterogeneous computing resources. One of the main advantages of workflow utilization is the integration of code written in multiple languages Standardization occurs at the interfaces of the workflow elements and allows for general applications and easy comparison and integration of code from different research groups or even multiple programmers coding in different languages for various purposes from the same group. A workflow driven problem-solving approach enables domain scientists to focus on resolving the core science questions, and delegates the computational and process management burden to the underlying Workflow. The workflow driven approach allows scaling the computational experiment with distributed data-parallel execution on multiple computing platforms, such as, HPC resources, GPU clusters, Cloud etc. The workflow framework tracks software version information along with hardware information to allow users an opportunity to trace any variation in workflow outcome to the system configurations.

Three-Dimensional Spatiotemporal Modeling of Colon Cancer Organoids Reveals that Multimodal Control of Stem Cell Self-Renewal is a Critical Determinant of Size and Shape in Early Stages of Tumor Growth

We develop a three-dimensional multispecies mathematical model to simulate the growth of colon cancer organoids containing stem, progenitor and terminally differentiated cells, as a model of early (prevascular) tumor growth. Stem cells (SCs) secrete short-range self-renewal promoters (e.g., Wnt) and their long-range inhibitors (e.g., Dkk) and proliferate slowly. Committed progenitor (CP) cells proliferate more rapidly and differentiate to produce post-mitotic terminally differentiated cells that release differentiation promoters, forming negative feedback loops on SC and CP self-renewal. We demonstrate that SCs play a central role in normal and cancer colon organoids. Spatial patterning of the SC self-renewal promoter gives rise to SC clusters, which mimic stem cell niches, around the organoid surface, and drive the development of invasive fingers. We also study the effects of externally applied signaling factors. Applying bone morphogenic proteins, which inhibit SC and CP self-renewal, reduces invasiveness and organoid size. Applying hepatocyte growth factor, which enhances SC self-renewal, produces larger sizes and enhances finger development at low concentrations but suppresses fingers at high concentrations. These results are consistent with recent experiments on colon organoids. Because many cancers are hierarchically organized and are subject to feedback regulation similar to that in normal tissues, our results suggest that in cancer, control of cancer stem cell self-renewal should influence the size and shape in similar ways, thereby opening the door to novel therapies.

Progress in Mathematical Modeling of Gastrointestinal Slow Wave Abnormalities

Gastrointestinal (GI) motility is regulated in part by electrophysiological events called slow waves, which are generated by the interstitial cells of Cajal (ICC). Slow waves propagate by a process of "entrainment," which occurs over a decreasing gradient of intrinsic frequencies in the antegrade direction across much of the GI tract. Abnormal initiation and conduction of slow waves have been demonstrated in, and linked to, a number of GI motility disorders. A range of mathematical models have been developed to study abnormal slow waves and applied to propose novel methods for non-invasive detection and therapy. This review provides a general outline of GI slow wave abnormalities and their recent classification using multi-electrode (high-resolution) mapping methods, with a particular emphasis on the spatial patterns of these abnormal activities. The recently-developed mathematical models are introduced in order of their biophysical scale from cellular to whole-organ levels. The modeling techniques, main findings from the simulations, and potential future directions arising from notable studies are discussed.

Human In Silico Drug Trials Demonstrate Higher Accuracy than Animal Models in Predicting Clinical Pro-Arrhythmic Cardiotoxicity

Early prediction of cardiotoxicity is critical for drug development. Current animal models raise ethical and translational questions, and have limited accuracy in clinical risk prediction. Human-based computer models constitute a fast, cheap and potentially effective alternative to experimental assays, also facilitating translation to human. Key challenges include consideration of inter-cellular variability in drug responses and integration of computational and experimental methods in safety pharmacology. Our aim is to evaluate the ability of in silico drug trials in populations of human action potential (AP) models to predict clinical risk of drug-induced arrhythmias based on ion channel information, and to compare simulation results against experimental assays commonly used for drug testing. A control population of 1,213 human ventricular AP models in agreement with experimental recordings was constructed. In silico drug trials were performed for 62 reference compounds at multiple concentrations, using pore-block drug models (IC₅₀/Hill coefficient). Drug-induced changes in AP biomarkers were quantified, together with occurrence of repolarization/depolarization abnormalities. Simulation results were used to predict clinical risk based on reports of Torsade de Pointes arrhythmias, and further evaluated in a subset of compounds through comparison with electrocardiograms from rabbit wedge preparations and Ca²⁺-transient recordings in human induced pluripotent stem cell-derived cardiomyocytes (hiPS-CMs). Drug-induced changes in silico vary in magnitude depending on the specific ionic profile of each model in the population, thus allowing to identify cell sub-populations at higher risk of developing abnormal AP phenotypes. Models with low repolarization reserve (increased Ca²⁺/late Na⁺ currents and Na⁺/Ca²⁺-exchanger, reduced Na⁺/K⁺-pump) are highly vulnerable to drug-induced repolarization abnormalities, while those with reduced inward current density (fast/late Na⁺ and Ca²⁺ currents) exhibit high susceptibility to depolarization abnormalities. Repolarization abnormalities in silico predict clinical risk for all compounds with 89% accuracy. Drug-induced changes in biomarkers are in overall agreement across different assays: in silico AP duration changes reflect the ones observed in rabbit QT interval and hiPS-CMs Ca²⁺-transient, and simulated upstroke velocity captures variations in rabbit QRS complex. Our results demonstrate that human in silico drug trials constitute a powerful methodology for prediction of clinical pro-arrhythmic cardiotoxicity, ready for integration in the existing drug safety assessment pipelines.

Quantitative Comparison of Effects of Dofetilide, Sotalol, Quinidine, and Verapamil between Human Ex vivo Trabeculae and In silico Ventricular Models Incorporating Inter-Individual Action Potential Variability

Background:In silico modeling could soon become a mainstream method of pro-arrhythmic risk assessment in drug development. However, a lack of human-specific data and appropriate modeling techniques has previously prevented quantitative comparison of drug effects between in silico models and recordings from human cardiac preparations. Here, we directly compare changes in repolarization biomarkers caused by dofetilide, dl-sotalol, quinidine, and verapamil, between in silico populations of human ventricular cell models and ex vivo human ventricular trabeculae. Methods and Results:Ex vivo recordings from human ventricular trabeculae in control conditions were used to develop populations of in silico human ventricular cell models that integrated intra- and inter-individual variability in action potential (AP) biomarker values. Models were based on the O'Hara-Rudy ventricular cardiomyocyte model, but integrated experimental AP variability through variation in underlying ionic conductances. Changes to AP duration, triangulation and early after-depolarization occurrence from application of the four drugs at multiple concentrations and pacing frequencies were compared between simulations and experiments. To assess the impact of variability in IC50 measurements, and the effects of including state-dependent drug binding dynamics, each drug simulation was repeated with two different IC50 datasets, and with both the original O'Hara-Rudy hERG model and a recently published state-dependent model of hERG and hERG block. For the selective hERG blockers dofetilide and sotalol, simulation predictions of AP prolongation and repolarization abnormality occurrence showed overall good agreement with experiments. However, for multichannel blockers quinidine and verapamil, simulations were not in agreement with experiments across all IC50 datasets and IKr block models tested. Quinidine simulations resulted in overprolonged APs and high incidence of repolarization abnormalities, which were not observed in experiments. Verapamil simulations showed substantial AP prolongation while experiments showed mild AP shortening. Conclusions: Results for dofetilide and sotalol show good agreement between experiments and simulations for selective compounds, however lack of agreement from simulations of quinidine and verapamil suggest further work is needed to understand the more complex electrophysiological effects of these multichannel blocking drugs.

Biomaterials and Tissue Biomechanics: A Match Made in Heaven?

Biomaterials and tissue biomechanics have been traditionally separate areas of research with relatively little overlap in terms of methodological approaches. Recent advances in both fields on the one hand and developments in fabrication techniques and design approaches on the other have prepared the ground for joint research efforts by both communities. Additive manufacturing and rational design are examples of the revolutionary fabrication techniques and design methodologies that could facilitate more intimate collaboration between biomaterial scientists and biomechanists. This editorial article highlights the various ways in which the research on tissue biomechanics and biomaterials are related to each other and could benefit from each other’s results and methodologies.

BeatBox-HPC simulation environment for biophysically and anatomically realistic cardiac electrophysiology

The BeatBox simulation environment combines flexible script language user interface with the robust computational tools, in order to setup cardiac electrophysiology in-silico experiments without re-coding at low-level, so that cell excitation, tissue/anatomy models, stimulation protocols may be included into a BeatBox script, and simulation run either sequentially or in parallel (MPI) without re-compilation. BeatBox is a free software written in C language to be run on a Unix-based platform. It provides the whole spectrum of multi scale tissue modelling from 0-dimensional individual cell simulation, 1-dimensional fibre, 2-dimensional sheet and 3-dimensional slab of tissue, up to anatomically realistic whole heart simulations, with run time measurements including cardiac re-entry tip/filament tracing, ECG, local/global samples of any variables, etc. BeatBox solvers, cell, and tissue/anatomy models repositories are extended via robust and flexible interfaces, thus providing an open framework for new developments in the field. In this paper we give an overview of the BeatBox current state, together with a description of the main computational methods and MPI parallelisation approaches.

Methods for enhancing the reproducibility of biomedical research findings using electronic health records

BACKGROUND

The ability of external investigators to reproduce published scientific findings is critical for the evaluation and validation of biomedical research by the wider community. However, a substantial proportion of health research using electronic health records (EHR), data collected and generated during clinical care, is potentially not reproducible mainly due to the fact that the implementation details of most data preprocessing, cleaning, phenotyping and analysis approaches are not systematically made available or shared. With the complexity, volume and variety of electronic health record data sources made available for research steadily increasing, it is critical to ensure that scientific findings from EHR data are reproducible and replicable by researchers. Reporting guidelines, such as RECORD and STROBE, have set a solid foundation by recommending a series of items for researchers to include in their research outputs. Researchers however often lack the technical tools and methodological approaches to actuate such recommendations in an efficient and sustainable manner.

RESULTS

In this paper, we review and propose a series of methods and tools utilized in adjunct scientific disciplines that can be used to enhance the reproducibility of research using electronic health records and enable researchers to report analytical approaches in a transparent manner. Specifically, we discuss the adoption of scientific software engineering principles and best-practices such as test-driven development, source code revision control systems, literate programming and the standardization and re-use of common data management and analytical approaches.

CONCLUSION

The adoption of such approaches will enable scientists to systematically document and share EHR analytical workflows and increase the reproducibility of biomedical research using such complex data sources.

A comparison of solver performance for complex gastric electrophysiology models

Computational techniques for solving systems of equations arising in gastric electrophysiology have not been studied for efficient solution process. We present a computationally challenging problem of simulating gastric electrophysiology in anatomically realistic stomach geometries with multiple intracellular and extracellular domains. The multiscale nature of the problem and mesh resolution required to capture geometric and functional features necessitates efficient solution methods if the problem is to be tractable. In this study, we investigated and compared several parallel preconditioners for the linear systems arising from tetrahedral discretisation of electrically isotropic and anisotropic problems, with and without stimuli. The results showed that the isotropic problem was computationally less challenging than the anisotropic problem and that the application of extracellular stimuli increased workload considerably. Preconditioning based on block Jacobi and algebraic multigrid solvers were found to have the best overall solution times and least iteration counts, respectively. The algebraic multigrid preconditioner would be expected to perform better on large problems.

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.

Testing Scientific Software: A Systematic Literature Review

CONTEXT

Scientific software plays an important role in critical decision making, for example making weather predictions based on climate models, and computation of evidence for research publications. Recently, scientists have had to retract publications due to errors caused by software faults. Systematic testing can identify such faults in code.

OBJECTIVE

This study aims to identify specific challenges, proposed solutions, and unsolved problems faced when testing scientific software.

METHOD

We conducted a systematic literature survey to identify and analyze relevant literature. We identified 62 studies that provided relevant information about testing scientific software.

RESULTS

We found that challenges faced when testing scientific software fall into two main categories: (1) testing challenges that occur due to characteristics of scientific software such as oracle problems and (2) testing challenges that occur due to cultural differences between scientists and the software engineering community such as viewing the code and the model that it implements as inseparable entities. In addition, we identified methods to potentially overcome these challenges and their limitations. Finally we describe unsolved challenges and how software engineering researchers and practitioners can help to overcome them.

CONCLUSIONS

Scientific software presents special challenges for testing. Specifically, cultural differences between scientist developers and software engineers, along with the characteristics of the scientific software make testing more difficult. Existing techniques such as code clone detection can help to improve the testing process. Software engineers should consider special challenges posed by scientific software such as oracle problems when developing testing techniques.

STI-GMaS: an open-source environment for simulation of sexually-transmitted infections

Background

Sexually-transmitted pathogens often have severe reproductive health implications if treatment is delayed or absent, especially in females. The complex processes of disease progression, namely replication and ascension of the infection through the genital tract, span both extracellular and intracellular physiological scales, and in females can vary over the distinct phases of the menstrual cycle. The complexity of these processes, coupled with the common impossibility of obtaining comprehensive and sequential clinical data from individual human patients, makes mathematical and computational modelling valuable tools in developing our understanding of the infection, with a view to identifying new interventions. While many within-host models of sexually-transmitted infections (STIs) are available in existing literature, these models are difficult to deploy in clinical/experimental settings since simulations often require complex computational approaches.

Results

We present STI-GMaS (Sexually-Transmitted Infections – Graphical Modelling and Simulation), an environment for simulation of STI models, with a view to stimulating the uptake of these models within the laboratory or clinic. The software currently focuses upon the representative case-study of Chlamydia trachomatis, the most common sexually-transmitted bacterial pathogen of humans. Here, we demonstrate the use of a hybrid PDE–cellular automata model for simulation of a hypothetical Chlamydia vaccination, demonstrating the effect of a vaccine-induced antibody in preventing the infection from ascending to above the cervix. This example illustrates the ease with which existing models can be adapted to describe new studies, and its careful parameterisation within STI-GMaS facilitates future tuning to experimental data as they arise.

Conclusions

STI-GMaS represents the first software designed explicitly for in-silico simulation of STI models by non-theoreticians, thus presenting a novel route to bridging the gap between computational and clinical/experimental disciplines. With the propensity for model reuse and extension, there is much scope within STI-GMaS to allow clinical and experimental studies to inform model inputs and drive future model development. Many of the modelling paradigms and software design principles deployed to date transfer readily to other STIs, both bacterial and viral; forthcoming releases of STI-GMaS will extend the software to incorporate a more diverse range of infections.

Best practices for scientific computing

We describe a set of best practices for scientific software development, based on research and experience, that will improve scientists' productivity and the reliability of their software.

On an infrastructure to support sharing and aggregating pre- and post-publication systems biology research data

The move towards in silico experimentation has resulted in the use of computational models, in addition to traditional experimental models, to generate the raw data that is analysed and published as research findings. This change requires new methods to be introduced to facilitate independent validation of the underlying models and the reported results. The promotion of co-operative research has the potential to help to both validate results and explore wider problem areas. In this paper we leverage and extend two existing software frameworks to develop an infrastructure that has the potential to both promote the sharing of data between researchers pre-publication and enable access to the data for interested parties post-publication. The pre-publication sharing of data would enable larger problem spaces to be explored by distributed research groups; enabling access to the data post-publication would allow reviewers and the wider community to independently verify the published results which would, in the longer term, help to increase confidence in published results. The framework is used to perform reproducible and numerically validated individual-based computational experiments into the onset of colorectal cancer. Existing results are verified and new insights into the top-down versus bottom-up hypothesis of colorectal crypt invasion are given.

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.

Toward the virtual stomach: progress in multiscale modeling of gastric electrophysiology and motility

Experimental progress in investigating normal and disordered gastric motility is increasingly being complimented by sophisticated multiscale modeling studies. Mathematical modeling has become a valuable tool in this effort, as there is an ever-increasing need to gain an integrative and quantitative understanding of how physiological mechanisms achieve coordinated functions across multiple biophysical scales. These interdisciplinary efforts have been particularly notable in the area of gastric electrophysiology, where they are beginning to yield a comprehensive and integrated in silico organ modeling framework, or 'virtual stomach'. At the cellular level, a number of biophysically based mathematical cell models have been developed, and these are now being applied in areas including investigations of gastric electrical pacemaker mechanisms, smooth muscle electrophysiology, and electromechanical coupling. At the tissue level, micro-structural models are being creatively developed and employed to investigate clinically significant questions, such as the functional effects of ICC degradation on gastrointestinal (GI) electrical activation. At the organ level, high-resolution electrical mapping and modeling studies are combined to provide improved insights into normal and dysrhythmic gastric electrical activation. These efforts are also enabling detailed forward and inverse modeling studies at the 'whole body' level, with implications for diagnostic techniques for gastric dysrhythmias. These recent advances, together with several others highlighted in this review, collectively demonstrate a powerful trend toward applying mathematical models to effectively investigate structure-function relationships and overcome multiscale challenges in basic and clinical GI research.

Characterization and modeling of the peripheral cardiac conduction system

The development of biophysical models of the heart has the potential to get insights in the patho-physiology of the heart, which requires to accurately modeling anatomy and function. The electrical activation sequence of the ventricles depends strongly on the cardiac conduction system (CCS). Its morphology and function cannot be observed in vivo, and therefore data available come from histological studies. We present a review on data available of the peripheral CCS including new experiments. In order to build a realistic model of the CCS we designed a procedure to extract morphological characteristics of the CCS from stained calf tissue samples. A CCS model personalized with our measurements has been built using L-systems. The effect of key unknown parameters of the model in the electrical activation of the left ventricle has been analyzed. The CCS models generated share the main characteristics of observed stained Purkinje networks. The timing of the simulated electrical activation sequences were in the physiological range for CCS models that included enough density of PMJs. These results show that this approach is a potential methodology for collecting knowledge-domain data and build improved CCS models of the heart automatically.

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.

An Analysis of Process Characteristics for Developing Scientific Software

The development of scientific software is usually carried out by a scientist who has little professional training as a software developer. Concerns exist that such development produces low-quality products, leading to low-quality science. These concerns have led to recommendations and the imposition of software engineering development processes and standards on the scientists. This paper utilizes different frameworks to investigate and map characteristics of the scientific software development environment to the assumptions made in plan-driven software development methods and agile software development methods. This mapping exposes a mismatch between the needs and goals of scientific software development and the assumptions and goals of well-known software engineering development processes.

Orthogonal recursive bisection as data decomposition strategy for massively parallel cardiac simulations

We present the orthogonal recursive bisection algorithm that hierarchically segments the anatomical model structure into subvolumes that are distributed to cores. The anatomy is derived from the Visible Human Project, with electrophysiology based on the FitzHugh-Nagumo (FHN) and ten Tusscher (TT04) models with monodomain diffusion. Benchmark simulations with up to 16,384 and 32,768 cores on IBM Blue Gene/P and L supercomputers for both FHN and TT04 results show good load balancing with almost perfect speedup factors that are close to linear with the number of cores. Hence, strong scaling is demonstrated. With 32,768 cores, a 1000 ms simulation of full heart beat requires about 6.5 min of wall clock time for a simulation of the FHN model. For the largest machine partitions, the simulations execute at a rate of 0.548 s (BG/P) and 0.394 s (BG/L) of wall clock time per 1 ms of simulation time. To our knowledge, these simulations show strong scaling to substantially higher numbers of cores than reported previously for organ-level simulation of the heart, thus significantly reducing run times. The ability to reduce runtimes could play a critical role in enabling wider use of cardiac models in research and clinical applications.

Comparing a discrete and continuum model of the intestinal crypt

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.

Arrhythmic risk biomarkers for the assessment of drug cardiotoxicity: from experiments to computer simulations

In this paper, we illustrate how advanced computational modelling and simulation can be used to investigate drug-induced effects on cardiac electrophysiology and on specific biomarkers of pro-arrhythmic risk. To do so, we first perform a thorough literature review of proposed arrhythmic risk biomarkers from the ionic to the electrocardiogram levels. The review highlights the variety of proposed biomarkers, the complexity of the mechanisms of drug-induced pro-arrhythmia and the existence of significant animal species differences in drug-induced effects on cardiac electrophysiology. Predicting drug-induced pro-arrhythmic risk solely using experiments is challenging both preclinically and clinically, as attested by the rise in the cost of releasing new compounds to the market. Computational modelling and simulation has significantly contributed to the understanding of cardiac electrophysiology and arrhythmias over the last 40 years. In the second part of this paper, we illustrate how state-of-the-art open source computational modelling and simulation tools can be used to simulate multi-scale effects of drug-induced ion channel block in ventricular electrophysiology at the cellular, tissue and whole ventricular levels for different animal species. We believe that the use of computational modelling and simulation in combination with experimental techniques could be a powerful tool for the assessment of drug safety pharmacology.

A numerical guide to the solution of the bi-domain equations of cardiac electrophysiology

Simulation of cardiac electrical activity using the bi-domain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bi-domain modelling. Each component of bi-domain simulations--discretization, ODE-solution, linear system solution, and parallelization--is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme.

An integrative computational model for intestinal tissue renewal

OBJECTIVES

The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation.

METHODS

At the subcellular level, deterministic models characterise molecular networks, such as cell-cycle control and Wnt signalling. The output of these models determines the behaviour of each epithelial cell in response to intra-, inter- and extracellular cues. The modular nature of the model enables us to easily modify individual assumptions and analyse their effects on the system as a whole.

RESULTS

We perform virtual microdissection and labelling-index experiments, evaluate the impact of various model extensions, obtain new insight into clonal expansion in the crypt, and compare our predictions with recent mitochondrial DNA mutation data.

CONCLUSIONS

We demonstrate that relaxing the assumption that stem-cell positions are fixed enables clonal expansion and niche succession to occur. We also predict that the presence of extracellular factors near the base of the crypt alone suffices to explain the observed spatial variation in nuclear beta-catenin levels along the crypt axis.

Simulation of cardiac electrophysiology on next-generation high-performance computers

Models of cardiac electrophysiology consist of a system of partial differential equations (PDEs) coupled with a system of ordinary differential equations representing cell membrane dynamics. Current software to solve such models does not provide the required computational speed for practical applications. One reason for this is that little use is made of recent developments in adaptive numerical algorithms for solving systems of PDEs. Studies have suggested that a speedup of up to two orders of magnitude is possible by using adaptive methods. The challenge lies in the efficient implementation of adaptive algorithms on massively parallel computers. The finite-element (FE) method is often used in heart simulators as it can encapsulate the complex geometry and small-scale details of the human heart. An alternative is the spectral element (SE) method, a high-order technique that provides the flexibility and accuracy of FE, but with a reduced number of degrees of freedom. The feasibility of implementing a parallel SE algorithm based on fully unstructured all-hexahedra meshes is discussed. A major computational task is solution of the large algebraic system resulting from FE or SE discretization. Choice of linear solver and preconditioner has a substantial effect on efficiency. A fully parallel implementation based on dynamic partitioning that accounts for load balance, communication and data movement costs is required. Each of these methods must be implemented on next-generation supercomputers in order to realize the necessary speedup. The problems that this may cause, and some of the techniques that are beginning to be developed to overcome these issues, are described.

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.

Numerical solution of the bidomain equations

Knowledge of cardiac electrophysiology is efficiently formulated in terms of mathematical models. However, most of these models are very complex and thus defeat direct mathematical reasoning founded on classical and analytical considerations. This is particularly so for the celebrated bidomain model that was developed almost 40 years ago for the concurrent analysis of extra- and intracellular electrical activity. Numerical simulations based on this model represent an indispensable tool for studying electrophysiology. However, complex mathematical models, steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scientific computing over the past 50 years has been to enable the solving of linear systems of algebraic equations that arise from discretizations of partial differential equations in an optimal manner, i.e. such that the central processing unit (CPU) effort increases linearly with the number of computational nodes. Over the past decade, such optimal methods have been introduced in the simulation of electrophysiology. This development, together with the development of affordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models, on geometries resembling a human heart. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for the solution of the bidomain model. This paper reviews the development of numerical methods for solving the bidomain model. However, the field is huge and we thus restrict our focus to developments that have been made since the year 2000.

Computational modeling of cardiac disease: potential for personalized medicine

Cardiovascular diseases are leading causes of death, reduce life quality and consume almost half a trillion dollars in healthcare expenses in the USA alone. Cardiac modeling and simulation technologies hold promise as important tools to improve cardiac care and are already in use to elucidate the fundamental mechanisms of cardiac physiology and pathophysiology. However, the emphasis has been on simulating average or exemplar cases. This report describes two classes of cardiac modeling efforts. First, electrophysiological models of channelopathies simulate the altered electrical activity that is thought to promote arrhythmias. Second, electromechanical models attempt to capture both the electrophysiological and mechanical aspects of heart function. One goal of the community is to develop models with sufficient patient customization to assist in personalized treatment planning. Some model aspects can be customized with existing data collection techniques to more closely represent individual patients while other model aspects will likely remain based on generic data. Despite important challenges, cardiac models hold promise to be important enablers of personalized medicine.