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

3D finite element electrical model of larval zebrafish ECG signals

Assessment of heart function in zebrafish larvae using electrocardiography (ECG) is a potentially useful tool in developing cardiac treatments and the assessment of drug therapies. In order to better understand how a measured ECG waveform is related to the structure of the heart, its position within the larva and the position of the electrodes, a 3D model of a 3 days post fertilisation (dpf) larval zebrafish was developed to simulate cardiac electrical activity and investigate the voltage distribution throughout the body. The geometry consisted of two main components; the zebrafish body was modelled as a homogeneous volume, while the heart was split into five distinct regions (sinoatrial region, atrial wall, atrioventricular band, ventricular wall and heart chambers). Similarly, the electrical model consisted of two parts with the body described by Laplace’s equation and the heart using a bidomain ionic model based upon the Fitzhugh-Nagumo equations. Each region of the heart was differentiated by action potential (AP) parameters and activation wave conduction velocities, which were fitted and scaled based on previously published experimental results. ECG measurements in vivo at different electrode recording positions were then compared to the model results. The model was able to simulate action potentials, wave propagation and all the major features (P wave, R wave, T wave) of the ECG, as well as polarity of the peaks observed at each position. This model was based upon our current understanding of the structure of the normal zebrafish larval heart. Further development would enable us to incorporate features associated with the diseased heart and hence assist in the interpretation of larval zebrafish ECGs in these conditions

Effects of amiodarone on short QT syndrome variant 3 in human ventricles: a simulation study.

Background Short QT syndrome (SQTS) is a newly identified clinical disorder associated with atrial and/or ventricular arrhythmias and increased risk of sudden cardiac death (SCD). The SQTS variant 3 is linked to D172N mutation to the KCNJ2 gene that causes a gain-of-function to the inward rectifier potassium channel current (I K1), which shortens the ventricular action potential duration (APD) and effective refractory period (ERP). Pro-arrhythmogenic effects of SQTS have been characterized, but less is known about the possible pharmacological treatment of SQTS. Therefore, in this study, we used computational modeling to assess the effects of amiodarone, class III anti-arrhythmic agent, on human ventricular electrophysiology in SQT3. Methods The ten Tusscher et al. model for the human ventricular action potentials (APs) was modified to incorporate I K1 formulations based on experimental data of Kir2.1 channels (including WT, WT-D172N and D172N conditions). The modified cell model was then implemented to construct one-dimensional (1D) and 2D tissue models. The blocking effects of amiodarone on ionic currents were modeled using IC50 and Hill coefficient values from literatures. Effects of amiodarone on APD, ERP and pseudo-ECG traces were computed. Effects of the drug on the temporal and spatial vulnerability of ventricular tissue to genesis and maintenance of re-entry were measured, as well as on the dynamic behavior of re-entry. Results Amiodarone prolonged the ventricular cell APD and decreased the maximal voltage heterogeneity (δV) among three difference cells types across transmural ventricular wall, leading to a decreased transmural heterogeneity of APD along a 1D model of ventricular transmural strand. Amiodarone increased cellular ERP, prolonged QT interval and decreased the T-wave amplitude. It reduced tissue’s temporal susceptibility to the initiation of re-entry and increased the minimum substrate size necessary to sustain re-entry in the 2D tissue. Conclusions At the therapeutic-relevant concentration of amiodarone, the APD and ERP at the single cell level were increased significantly. The QT interval in pseudo-ECG was prolonged and the re-entry in tissue was prevented. This study provides further evidence that amiodarone may be a potential pharmacological agent for preventing arrhythmogenesis for SQT3 patients

In silico assessment of the effects of quinidine, disopyramide and E-4031 on short QT syndrome variant 1 in the human ventricles.

Aims Short QT syndrome (SQTS) is an inherited disorder associated with abnormally abbreviated QT intervals and an increased incidence of atrial and ventricular arrhythmias. SQT1 variant (linked to the rapid delayed rectifier potassium channel current, IKr) of SQTS, results from an inactivation-attenuated, gain-of-function mutation (N588K) in the KCNH2-encoded potassium channels. Pro-arrhythmogenic effects of SQT1 have been well characterized, but less is known about the possible pharmacological antiarrhythmic treatment of SQT1. Therefore, this study aimed to assess the potential effects of E-4031, disopyramide and quinidine on SQT1 using a mathematical model of human ventricular electrophysiology. Methods The ten Tusscher et al. biophysically detailed model of the human ventricular action potential (AP) was modified to incorporate IKr Markov chain (MC) formulations based on experimental data of the kinetics of the N588K mutation of the KCNH2-encoded subunit of the IKr channels. The modified ventricular cell model was then integrated into one-dimensional (1D) strand, 2D regular and realistic tissues with transmural heterogeneities. The channel-blocking effect of the drugs on ion currents in healthy and SQT1 cells was modeled using half-maximal inhibitory concentration (IC50) and Hill coefficient (nH) values from literatures. Effects of drugs on cell AP duration (APD), effective refractory period (ERP) and pseudo-ECG traces were calculated. Effects of drugs on the ventricular temporal and spatial vulnerability to re-entrant excitation waves were measured. Re-entry was simulated in both 2D regular and realistic ventricular tissue. Results At the single cell level, the drugs E-4031 and disopyramide had hardly noticeable effects on the ventricular cell APD at 90% repolarization (APD90), whereas quinidine caused a significant prolongation of APD90. Quinidine prolonged and decreased the maximal transmural AP heterogeneity (δV); this led to the decreased transmural heterogeneity of APD across the 1D strand. Quinidine caused QT prolongation and a decrease in the T-wave amplitude, and increased ERP and decreased temporal susceptibility of the tissue to the initiation of re-entry and increased the minimum substrate size necessary to prevent re-entry in the 2D regular model, and further terminated re-entrant waves in the 2D realistic model. Quinidine exhibited significantly better therapeutic effects on SQT1 than E-4031 and disopyramide. Conclusions The simulated pharmacological actions of quinidine exhibited antiarrhythmic effects on SQT1. This study substantiates a causal link between quinidine and QT interval prolongation in SQT1 and suggests that quinidine may be a potential pharmacological agent for treating SQT1 patients

Decoupled time−marching schemes in computational cardiac electrophysiology and ECG numerical simulation

International audienceThis work considers the approximation of the cardiac bidomain equations, either isolated or coupled with the torso, via first order semi-implicit time-marching schemes involving a fully decoupled computation of the unknown fields (ionic state, transmembrane potential, extracellular and torso potentials). For the isolated bidomain system, we show that the Gauss-Seidel and Jacobi like splittings do not compromise energy stability; they simply alter the energy norm. Within the framework of the numerical simulation of electrocardiograms (ECG), these bidomain splittings are combined with an explicit Robin-Robin treatment of the heart-torso coupling conditions. We show that the resulting schemes allow a fully decoupled (energy) stable computation of the heart and torso fields, under an additional hyperbolic-CFL like condition. The accuracy and convergence rate of the considered schemes are investigated numerically with a series of numerical experiments

Stochastic Finite Element Method for Torso Conductivity Uncertainties Quantification in Electrocardiography Inverse Problem

The purpose of this paper is to study the influence of errors and uncertainties of the input data, like the conductivity, on the electrocardiography imaging (ECGI) solution. In order to do that, we propose a new stochastic optimal control formulation, permitting to calculate the distribution of the electric potentiel on the heart from the measurement on the body surface. The discretization is done using stochastic Galerkin method allowing to separate random and deterministic variables. Then, the problem is discretized, in spatial part, using the finite element method and the polynomial chaos expansion in the stochastic part of the problem. The considered problem is solved using a conjugate gradient method where the gradient of the cost function is computed with an adjoint technique. The efficiency of this approach to solve the inverse problem and the usability to quantify the effect of conductivity uncertainties in the torso are demonstrated through a number of numerical simulations on a 2D analytical geometry and on a 2D cross section of a real torso