OpenCMISS: a multi-physics & multi-scale computational infrastructure for the VPH/Physiome project

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.

A brief history of tissue models for cardiac electrophysiology

The last four decades have produced a number of significant advances in the developments of computer models to simulate and investigate the electrical activity of cardiac tissue. The tissue descriptions that underlie these simulations have been built from a combination of clever insight and careful comparison with measured data at multiple scales. Tissue models have not only led to greater insights into the mechanisms of life-threatening arrhythmias but have been used to engineer new therapies to treat the consequences of cardiac disease. This paper is a look back at the early years in the cardiac modeling and the challenges facing the field as models move toward the clinic.

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.

A multiscale chemo-electro-mechanical skeletal muscle model to analyze muscle contraction and force generation for different muscle fiber arrangements

The presented chemo-electro-mechanical skeletal muscle model relies on a continuum-mechanical formulation describing the muscle's deformation and force generation on the macroscopic muscle level. Unlike other three-dimensional models, the description of the activation-induced behavior of the mechanical model is entirely based on chemo-electro-mechanical principles on the microscopic sarcomere level. Yet, the multiscale model reproduces key characteristics of skeletal muscles such as experimental force-length and force-velocity data on the macroscopic whole muscle level. The paper presents the methodological approaches required to obtain such a multiscale model, and demonstrates the feasibility of using such a model to analyze differences in the mechanical behavior of parallel-fibered muscles, in which the muscle fibers either span the entire length of the fascicles or terminate intrafascicularly. The presented results reveal that muscles, in which the fibers span the entire length of the fascicles, show lower peak forces, more dispersed twitches and fusion of twitches at lower stimulation frequencies. In detail, the model predicted twitch rise times of 38.2 and 17.2 ms for a 12 cm long muscle, in which the fibers span the entire length of the fascicles and with twelve fiber compartments in series, respectively. Further, the twelve-compartment model predicted peak twitch forces that were 19% higher than in the single-compartment model. The analysis of sarcomere lengths during fixed-end single twitch contractions at optimal length predicts rather small sarcomere length changes. The observed lengths range from 75 to 111% of the optimal sarcomere length, which corresponds to a region with maximum filament overlap. This result suggests that stability issues resulting from activation-induced stretches of non-activated sarcomeres are unlikely in muscles with passive forces appearing at short muscle length.

Unraveling liver complexity from molecular to organ level: challenges and perspectives

Biological responses are determined by information processing at multiple and highly interconnected scales. Within a tissue the individual cells respond to extracellular stimuli by regulating intracellular signaling pathways that in turn determine cell fate decisions and influence the behavior of neighboring cells. As a consequence the cellular responses critically impact tissue composition and architecture. Understanding the regulation of these mechanisms at different scales is key to unravel the emergent properties of biological systems. In this perspective, a multidisciplinary approach combining experimental data with mathematical modeling is introduced. We report the approach applied within the Virtual Liver Network to analyze processes that regulate liver functions from single cell responses to the organ level using a number of examples. By facilitating interdisciplinary collaborations, the Virtual Liver Network studies liver regeneration and inflammatory processes as well as liver metabolic functions at multiple scales, and thus provides a suitable example to identify challenges and point out potential future application of multi-scale systems biology.

Emulating facial biomechanics using multivariate partial least squares surrogate models

A detailed biomechanical model of the human face driven by a network of muscles is a useful tool in relating the muscle activities to facial deformations. However, lengthy computational times often hinder its applications in practical settings. The objective of this study is to replace precise but computationally demanding biomechanical model by a much faster multivariate meta-model (surrogate model), such that a significant speedup (to real-time interactive speed) can be achieved. Using a multilevel fractional factorial design, the parameter space of the biomechanical system was probed from a set of sample points chosen to satisfy maximal rank optimality and volume filling. The input-output relationship at these sampled points was then statistically emulated using linear and nonlinear, cross-validated, partial least squares regression models. It was demonstrated that these surrogate models can mimic facial biomechanics efficiently and reliably in real-time.

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.

Constitutive Relations for Pressure-Driven Stiffening in Poroelastic Tissues

Vascularized biological tissue has been shown to increase in stiffness with increased perfusion pressure. The interaction between blood in the vasculature and other tissue components can be modeled with a poroelastic, biphasic approach. The ability of this model to reproduce the pressure-driven stiffening behavior exhibited by some tissues depends on the choice of the mechanical constitutive relation, defined by the Helmholtz free energy density of the skeleton. We analyzed the behavior of a number of isotropic poroelastic constitutive relations by applying a swelling pressure, followed by homogeneous uniaxial or simple-shear deformation. Our results demonstrate that a strain-stiffening constitutive relation is required for a material to show pressure-driven stiffening, and that the strain-stiffening terms must be volume-dependent.

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.

Ensuring reliability of safety-critical clinical applications of computational cardiac models

Computational models of cardiac electrophysiology have been used for over half a century to investigate physiological mechanisms and generate hypotheses for experimental testing, and are now starting to play a role in clinical applications. There is currently a great deal of interest in using models as diagnostic or therapeutic aids, for example using patient-specific whole-heart simulations to optimize cardiac resynchronization therapy, ablation therapy, and defibrillation. However, if models are to be used in safety-critical clinical decision making, the reliability of their predictions needs to be thoroughly investigated. In engineering and the physical sciences, the field of “verification, validation and uncertainty quantification” (VVUQ) [also known as “verification and validation” (V&V)] has been developed for rigorously evaluating the credibility of computational model predictions. In this article we first discuss why it is vital that cardiac models be developed and evaluated within a VVUQ framework, and then consider cardiac models in the context of each of the stages in VVUQ. We identify some of the major difficulties which may need to be overcome for cardiac models to be used in safely-critical clinical applications.

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.

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.

Understanding the mechanisms amenable to CRT response: from pre-operative multimodal image data to patient-specific computational models

This manuscript describes our recent developments towards better understanding of the mechanisms amenable to cardiac resynchronization therapy response. We report the results from a full multimodal dataset corresponding to eight patients from the euHeart project. The datasets include echocardiography, MRI and electrophysiological studies. We investigate two aspects. The first one focuses on pre-operative multimodal image data. From 2D echocardiography and 3D tagged MRI images, we compute atlas based dyssynchrony indices. We complement these indices with presence and extent of scar tissue and correlate them with CRT response. The second one focuses on computational models. We use pre-operative imaging to generate a patient-specific computational model. We show results of a fully automatic personalized electromechanical simulation. By case-per-case discussion of the results, we highlight the potential and key issues of this multimodal pipeline for the understanding of the mechanisms of CRT response and a better patient selection.

Challenges and opportunities in cardiovascular health informatics

Cardiovascular health informatics is a rapidly evolving interdisciplinary field concerning the processing, integration/interpretation, storage, transmission, acquisition, and retrieval of information from cardiovascular systems for the early detection, early prediction, early prevention, early diagnosis, and early treatment of cardiovascular diseases (CVDs). Based on the first author's presentation at the first IEEE Life Sciences Grand Challenges Conference, held on October 4-5, 2012, at the National Academy of Sciences, Washington, DC, USA, this paper, focusing on coronary arteriosclerotic disease, will discuss three significant challenges of cardiovascular health informatics, including: 1) to invent unobtrusive and wearable multiparameter sensors with higher sensitivity for the real-time monitoring of physiological states; 2) to develop fast multimodal imaging technologies with higher resolution for the quantification and better understanding of structure, function, metabolism of cardiovascular systems at the different levels; and 3) to develop novel multiscale information fusion models and strategies with higher accuracy for the personalized predication of the CVDs. At the end of this paper, a summary is given to suggest open discussions on these three and more challenges that face the scientific community in this field in the future.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

Simulating a dual-array electrode configuration to investigate the influence of skeletal muscle fatigue following functional electrical stimulation

A novel, anatomically-accurate model of a tibialis anterior muscle is used to investigate the electro-physiological properties of denervated muscles following functional electrical stimulation. The model includes a state-of-the-art description of cell electro-physiology. The main objective of this work is to develop a computational framework capable of predicting the effects of different stimulation trains and electrode configurations on the excitability and fatigue of skeletal muscle tissue. Utilizing a reduced but computationally amenable model, the effects of different electrode sizes and inter-electrode distances on the number of activated muscle fibers are investigated and qualitatively compared to existing literature. To analyze muscle fatigue, the sodium current, specifically the K+ ion concentrations within the t-tubule and the calcium release from the sarcoplasmic reticulum, is used to quantify membrane and metabolic fatigue. The simulations demonstrate that lower stimulation frequencies and biphasic pulse waveforms cause less fatigue than higher stimulation frequencies and monophasic pulses. A comparison between single and dual electrode configurations (with the same overall stimulation surface) is presented to locally investigate the differences in muscle fatigue. The dual electrode configuration causes the muscle tissue to fatigue quicker.

Bridging experiments, models and simulations: an integrative approach to validation in computational cardiac electrophysiology

Computational models in physiology often integrate functional and structural information from a large range of spatiotemporal scales from the ionic to the whole organ level. Their sophistication raises both expectations and skepticism concerning how computational methods can improve our understanding of living organisms and also how they can reduce, replace, and refine animal experiments. A fundamental requirement to fulfill these expectations and achieve the full potential of computational physiology is a clear understanding of what models represent and how they can be validated. The present study aims at informing strategies for validation by elucidating the complex interrelations among experiments, models, and simulations in cardiac electrophysiology. We describe the processes, data, and knowledge involved in the construction of whole ventricular multiscale models of cardiac electrophysiology. Our analysis reveals that models, simulations, and experiments are intertwined, in an assemblage that is a system itself, namely the model-simulation-experiment (MSE) system. We argue that validation is part of the whole MSE system and is contingent upon 1) understanding and coping with sources of biovariability; 2) testing and developing robust techniques and tools as a prerequisite to conducting physiological investigations; 3) defining and adopting standards to facilitate the interoperability of experiments, models, and simulations; 4) and understanding physiological validation as an iterative process that contributes to defining the specific aspects of cardiac electrophysiology the MSE system targets, rather than being only an external test, and that this is driven by advances in experimental and computational methods and the combination of both.

A finite-element approach to the direct computation of relative cardiovascular pressure from time-resolved MR velocity data

The evaluation of cardiovascular velocities, their changes through the cardiac cycle and the consequent pressure gradients has the capacity to improve understanding of subject-specific blood flow in relation to adjacent soft tissue movements. Magnetic resonance time-resolved 3D phase contrast velocity acquisitions (4D flow) represent an emerging technology capable of measuring the cyclic changes of large scale, multi-directional, subject-specific blood flow. A subsequent evaluation of pressure differences in enclosed vascular compartments is a further step which is currently not directly available from such data. The focus of this work is to address this deficiency through the development of a novel simulation workflow for the direct computation of relative cardiovascular pressure fields. Input information is provided by enhanced 4D flow data and derived MR domain masking. The underlying methodology shows numerical advantages in terms of robustness, global domain composition, the isolation of local fluid compartments and a treatment of boundary conditions. This approach is demonstrated across a range of validation examples which are compared with analytic solutions. Four subject-specific test cases are subsequently run, showing good agreement with previously published calculations of intra-vascular pressure differences. The computational engine presented in this work contributes to non-invasive access to relative pressure fields, incorporates the effects of both blood flow acceleration and viscous dissipation, and enables enhanced evaluation of cardiovascular blood flow.

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.

Fast multiscale modeling of cardiac electrophysiology including Purkinje system

In this paper, we present a modeling methodology to couple the cardiac conduction system to cardiac myocytes through a model of Purkinje-ventricular junctions to yield fast and realistic electrical activation of the ventricles. A patient-specific biventricular geometry is obtained from processing computed tomography scan data. A one-manifold implementation of the fast marching method based on Eikonal-type equations is used for modeling heart electrophysiology, which facilitates the multiscale 1-D-3-D coupling at very low computational costs. The method is illustrated in in-silico experiments where we analyze and compare alternative pacing strategies on the same patient-specific anatomy. We also show very good agreement between the results from the proposed approach and more detailed and comprehensive biophysical models for modeling cardiac electrophysiology. The effect of atrioventricular delay on the distribution of activation time in myocardium is studied with two experiments. Given the reasonable computational times and realistic activation sequences provided by our method, it can have an important clinical impact on the selection of optimal implantation sites of pacing leads or placement of ablation catheter's tip in the context of cardiac rhythm management therapies.

Multi-scale modeling in biology: how to bridge the gaps between scales?

Human physiological functions are regulated across many orders of magnitude in space and time. Integrating the information and dynamics from one scale to another is critical for the understanding of human physiology and the treatment of diseases. Multi-scale modeling, as a computational approach, has been widely adopted by researchers in computational and systems biology. A key unsolved issue is how to represent appropriately the dynamical behaviors of a high-dimensional model of a lower scale by a low-dimensional model of a higher scale, so that it can be used to investigate complex dynamical behaviors at even higher scales of integration. In the article, we first review the widely-used different modeling methodologies and their applications at different scales. We then discuss the gaps between different modeling methodologies and between scales, and discuss potential methods for bridging the gaps between scales.

Considerations for the use of cellular electrophysiology models within cardiac tissue simulations

The use of mathematical models to study cardiac electrophysiology has a long history, and numerous cellular scale models are now available, covering a range of species and cell types. Their use to study emergent properties in tissue is also widespread, typically using the monodomain or bidomain equations coupled to one or more cell models. Despite the relative maturity of this field, little has been written looking in detail at the interface between the cellular and tissue-level models. Mathematically this is relatively straightforward and well-defined. There are however many details and potential inconsistencies that need to be addressed, in order to ensure correct operation of a cellular model within a tissue simulation. This paper will describe these issues and how to address them. Simply having models available in a common format such as CellML is still of limited utility, with significant manual effort being required to integrate these models within a tissue simulation. We will thus also discuss the facilities available for automating this in a consistent fashion within Chaste, our robust and high-performance cardiac electrophysiology simulator. It will be seen that a common theme arising is the need to go beyond a representation of the model mathematics in a standard language, to include additional semantic information required in determining the model's interface, and hence to enhance interoperability. Such information can be added as metadata, but agreement is needed on the terms to use, including development of appropriate ontologies, if reliable automated use of CellML models is to become common.