Chaste: Cancer, Heart and Soft Tissue Environment.

Chaste (Cancer, Heart And Soft Tissue Environment) is an open source simulation package for the numerical solution of mathematical models arising in physiology and biology. To date, Chaste development has been driven primarily by applications that include continuum modelling of cardiac electrophysiology ('Cardiac Chaste'), discrete cell-based modelling of soft tissues ('Cell-based Chaste'), and modelling of ventilation in lungs ('Lung Chaste'). Cardiac Chaste addresses the need for a high-performance, generic, and verified simulation framework for cardiac electrophysiology that is freely available to the scientific community. Cardiac chaste provides a software package capable of realistic heart simulations that is efficient, rigorously tested, and runs on HPC platforms. Cell-based Chaste addresses the need for efficient and verified implementations of cell-based modelling frameworks, providing a set of extensible tools for simulating biological tissues. Computational modelling, along with live imaging techniques, plays an important role in understanding the processes of tissue growth and repair. A wide range of cell-based modelling frameworks have been developed that have each been successfully applied in a range of biological applications. Cell-based Chaste includes implementations of the cellular automaton model, the cellular Potts model, cell-centre models with cell representations as overlapping spheres or Voronoi tessellations, and the vertex model. Lung Chaste addresses the need for a novel, generic and efficient lung modelling software package that is both tested and verified. It aims to couple biophysically-detailed models of airway mechanics with organ-scale ventilation models in a package that is freely available to the scientific community. Chaste is designed to be modular and extensible, providing libraries for common scientific computing infrastructure such as linear algebra operations, finite element meshes, and ordinary and partial differential equation solvers. This infrastructure is used by libraries for specific applications, such as continuum mechanics, cardiac models, and cell-based models. The software engineering techniques used to develop Chaste are intended to ensure code quality, re-usability and reliability. Primary applications of the software include cardiac and respiratory physiology, cancer and developmental biology.

Lung Computational Models and the Role of the Small Airways in Asthma.

Rationale: Asthma is characterized by disease within the small airways. Several studies have suggested that forced oscillation technique-derived resistance at 5 Hz (R5) - resistance at 20 Hz (R20) is a measure of small airway disease; however, there has been limited validation of this measurement to date.Objectives: To validate the use of forced oscillation R5 - R20 as a measure of small airway narrowing in asthma, and to investigate the role that small airway narrowing plays in asthma.Methods: Patient-based complete conducting airway models were generated from computed tomography scans to simulate the impact of different degrees of airway narrowing at different levels of the airway tree on forced oscillation R5 - R20 (n = 31). The computational models were coupled with regression models in an asthmatic cohort (n = 177) to simulate the impact of small airway narrowing on asthma control and quality of life. The computational models were used to predict the impact on small airway narrowing of type-2 targeting biologics using pooled data from two similarly design randomized, placebo-controlled biologic trials (n = 137).Measurements and Main Results: Simulations demonstrated that narrowing of the small airways had a greater impact on R5 - R20 than narrowing of the larger airways and was associated (above a threshold of approximately 40% narrowing) with marked deterioration in both asthma control and asthma quality of life, above the minimal clinical important difference. The observed treatment effect on R5 - R20 in the pooled trials equated to a predicted small airway narrowing reversal of approximately 40%.Conclusions: We have demonstrated, using computational modeling, that forced oscillation R5 - R20 is a direct measure of anatomical narrowing in the small airways and that small airway narrowing has a marked impact on both asthma control and quality of life and may be modified by biologics.

The prediction of viscous losses and pressure drop in models of the human airways.

This paper examines the viscous flow resistance in branching tubes as applied to simplified models of the lungs and compares the results of computational fluid dynamics simulations for a range of conditions with measurement data. The results are in good agreement with the available measurement data for both inspiration and expiration. A detailed sensitivity analysis of the dissipation and viscous resistance in a branch then examines the ratio of the viscous resistance to that for a fully developed Poiseuille flow, Z. As other researchers have noted, the calculated resistances give lower values than those from the standard correlation of Pedley et al. The results demonstrate that the resistance is sensitive to the velocity profile upstream of the bifurcations and explain from fluid dynamical considerations the apparent sensitivity of the resistance to the generation number of the branch. The paper also suggests a revised value for the calibration constant in the expression for Z. Finally, a limited set of results are presented for junction losses, and for expiration.

A stabilized finite element method for finite-strain three-field poroelasticity.

We construct a stabilized finite-element method to compute flow and finite-strain deformations in an incompressible poroelastic medium. We employ a three-field mixed formulation to calculate displacement, fluid flux and pressure directly and introduce a Lagrange multiplier to enforce flux boundary conditions. We use a low order approximation, namely, continuous piecewise-linear approximation for the displacements and fluid flux, and piecewise-constant approximation for the pressure. This results in a simple matrix structure with low bandwidth. The method is stable in both the limiting cases of small and large permeability. Moreover, the discontinuous pressure space enables efficient approximation of steep gradients such as those occurring due to rapidly changing material coefficients or boundary conditions, both of which are commonly seen in physical and biological applications.

Modelling responses of the inert-gas washout and MRI to bronchoconstriction.

Many lung diseases lead to an increase in ventilation heterogeneity (VH). Two clinical practices for the measurement of patient VH are in vivo imaging, and the inert gas multiple breath washout (MBW). In this study computational modelling was used to compare the responses of MBW indices LCI and scond and MRI measured global and local ventilation indices, σr and σlocal, to constriction of airways in the conducting zone of the lungs. The simulations show that scond, LCI and σr behave quite similarly to each other, all being sensitive to increases in the severity of constriction, while exhibiting little sensitivity to the depth at which constriction occurs. In contrast, the local MRI index σlocal shows strong sensitivity to depth of constriction, but lowered sensitivity to constriction severity. We finish with an analysis of the sensitivity of MRI indices to grid sizes, showing that results should be interpreted with reference to the image resolution. Overall we conclude that the application of both local and global VH measures may help to classify different types of bronchoconstriction.

A poroelastic model coupled to a fluid network with applications in lung modelling.

We develop a lung ventilation model based on a continuum poroelastic representation of lung parenchyma that is strongly coupled to a pipe network representation of the airway tree. The continuous system of equations is discretized using a low-order stabilised finite element method. The framework is applied to a realistic lung anatomical model derived from computed tomography data and an artificially generated airway tree to model the conducting airway region. Numerical simulations produce physiologically realistic solutions and demonstrate the effect of airway constriction and reduced tissue elasticity on ventilation, tissue stress and alveolar pressure distribution. The key advantage of the model is the ability to provide insight into the mutual dependence between ventilation and deformation. This is essential when studying lung diseases, such as chronic obstructive pulmonary disease and pulmonary fibrosis. Thus the model can be used to form a better understanding of integrated lung mechanics in both the healthy and diseased states. Copyright © 2015 John Wiley & Sons, Ltd.

Development and Analysis of Patient-Based Complete Conducting Airways Models.

The analysis of high-resolution computed tomography (CT) images of the lung is dependent on inter-subject differences in airway geometry. The application of computational models in understanding the significance of these differences has previously been shown to be a useful tool in biomedical research. Studies using image-based geometries alone are limited to the analysis of the central airways, down to generation 6-10, as other airways are not visible on high-resolution CT. However, airways distal to this, often termed the small airways, are known to play a crucial role in common airway diseases such as asthma and chronic obstructive pulmonary disease (COPD). Other studies have incorporated an algorithmic approach to extrapolate CT segmented airways in order to obtain a complete conducting airway tree down to the level of the acinus. These models have typically been used for mechanistic studies, but also have the potential to be used in a patient-specific setting. In the current study, an image analysis and modelling pipeline was developed and applied to a number of healthy (n = 11) and asthmatic (n = 24) CT patient scans to produce complete patient-based airway models to the acinar level (mean terminal generation 15.8 ± 0.47). The resulting models are analysed in terms of morphometric properties and seen to be consistent with previous work. A number of global clinical lung function measures are compared to resistance predictions in the models to assess their suitability for use in a patient-specific setting. We show a significant difference (p < 0.01) in airways resistance at all tested flow rates in complete airway trees built using CT data from severe asthmatics (GINA 3-5) versus healthy subjects. Further, model predictions of airways resistance at all flow rates are shown to correlate with patient forced expiratory volume in one second (FEV1) (Spearman ρ = -0.65, p < 0.001) and, at low flow rates (0.00017 L/s), FEV1 over forced vital capacity (FEV1/FVC) (ρ = -0.58, p < 0.001). We conclude that the pipeline and anatomical models can be used directly in mechanistic modelling studies and can form the basis for future patient-based modelling studies.

Dynamic flow characteristics in normal and asthmatic lungs.

Complex flow patterns exist within the asymmetric branching airway network in the lungs. These flow patterns are known to become increasingly heterogeneous during disease as a result of various mechanisms such as bronchoconstriction or alterations in lung tissue compliance. Here, we present a coupled model of tissue deformation and network airflow enabling predictions of dynamic flow properties, including temporal flow rate, pressure distribution, and the occurrence of reverse flows. We created two patient-specific airway geometries, one for a healthy subject and one for a severe asthmatic subject, derived using a combination of high-resolution CT data and a volume-filling branching algorithm. In addition, we created virtually constricted airway geometry by reducing the airway radii of the healthy subject model. The flow model was applied to these three different geometries to solve the pressure and flow distribution over a breathing cycle. The differences in wave phase of the flows in parallel airways induced by asymmetric airway geometry and bidirectional interaction between intra-acinar and airway network pressures were small in central airways but were more evident in peripheral airways. The asthmatic model showed elevated ventilation heterogeneity and significant flow disturbance. The reverse flows in the asthmatic model not only altered the local flow characteristics but also affected total lung resistance. The clinical significance of temporal flow disturbance on lung ventilation in normal airway model is obscure. However, increased flow disturbance and ventilation heterogeneity observed in the asthmatic model suggests that reverse flow may be an important factor for asthmatic lung function.

Quantitative study of the effect of tissue microstructure on contraction in a computational model of rat left ventricle.

Tissue microstructure, in particular the alignment of myocytes (fibre direction) and their lateral organisation into sheets, is fundamental to cardiac function. We studied the effect of microstructure on contraction in a computational model of rat left ventricular electromechanics. Different fibre models, globally rule-based or locally optimised to DT-MRI data, were compared, in order to understand whether a subject-specific fibre model would enhance the predictive power of our model with respect to the global ones. We also studied the impact of sheets on ventricular deformation by comparing: (a) a transversely isotropic versus an orthotropic material law and (b) a linear model with a bimodal model of sheet transmural variation. We estimated ejection fraction, wall thickening and base-to-apex shortening and compared them with measures from cine-MRI. We also evaluated Lagrangian strains as local metrics of cardiac deformation. Our results show that the subject-specific fibre model provides little improvement in the metric predictions with respect to global fibre models while material orthotropy allows closer agreement with measures than transverse isotropy. Nonetheless, the impact of sheets in our model is smaller than that of fibres. We conclude that further investigation of the modelling of sheet dynamics is necessary to fully understand the impact of tissue structure on cardiac deformation.

A comparison of fully automated methods of data analysis and computer assisted heuristic methods in an electrode kinetic study of the pathologically variable [Fe(CN)6](3-/4-) process by AC voltammetry.

Fully automated and computer assisted heuristic data analysis approaches have been applied to a series of AC voltammetric experiments undertaken on the [Fe(CN)6](3-/4-) process at a glassy carbon electrode in 3 M KCl aqueous electrolyte. The recovered parameters in all forms of data analysis encompass E(0) (reversible potential), k(0) (heterogeneous charge transfer rate constant at E(0)), α (charge transfer coefficient), Ru (uncompensated resistance), and Cdl (double layer capacitance). The automated method of analysis employed time domain optimization and Bayesian statistics. This and all other methods assumed the Butler-Volmer model applies for electron transfer kinetics, planar diffusion for mass transport, Ohm's Law for Ru, and a potential-independent Cdl model. Heuristic approaches utilize combinations of Fourier Transform filtering, sensitivity analysis, and simplex-based forms of optimization applied to resolved AC harmonics and rely on experimenter experience to assist in experiment-theory comparisons. Remarkable consistency of parameter evaluation was achieved, although the fully automated time domain method provided consistently higher α values than those based on frequency domain data analysis. The origin of this difference is that the implemented fully automated method requires a perfect model for the double layer capacitance. In contrast, the importance of imperfections in the double layer model is minimized when analysis is performed in the frequency domain. Substantial variation in k(0) values was found by analysis of the 10 data sets for this highly surface-sensitive pathologically variable [Fe(CN)6](3-/4-) process, but remarkably, all fit the quasi-reversible model satisfactorily.

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.

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.

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.

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.