An interactive 3D anisotropic cellular automata model of the heart

An Automata-Based Cardiac Electrophysiology Simulator to Assess Arrhythmia Inducibility

Personalized cardiac electrophysiology simulations have demonstrated great potential to study cardiac arrhythmias and help in therapy planning of radio-frequency ablation. Its application to analyze vulnerability to ventricular tachycardia and sudden cardiac death in infarcted patients has been recently explored. However, the detailed multi-scale biophysical simulations used in these studies are very demanding in terms of memory and computational resources, which prevents their clinical translation. In this work, we present a fast phenomenological system based on cellular automata (CA) to simulate personalized cardiac electrophysiology. The system is trained on biophysical simulations to reproduce cellular and tissue dynamics in healthy and pathological conditions, including action potential restitution, conduction velocity restitution and cell safety factor. We show that a full ventricular simulation can be performed in the order of seconds, emulate the results of a biophysical simulation and reproduce a patient’s ventricular tachycardia in a model that includes a heterogeneous scar region. The system could be used to study the risk of arrhythmia in infarcted patients for a large number of scenarios.

Actin droplet machine

The actin droplet machine is a computer model of a three-dimensional network of actin bundles developed in a droplet of a physiological solution, which implements mappings of sets of binary strings. The actin bundle network is conductive to travelling excitations, i.e. impulses. The machine is interfaced with an arbitrary selected set of k electrodes through which stimuli, binary strings of length k represented by impulses generated on the electrodes, are applied and responses are recorded. The responses are recorded in a form of impulses and then converted to binary strings. The machine's state is a binary string of length k: if there is an impulse recorded on the ith electrode, there is a '1' in the ith position of the string, and '0' otherwise. We present a design of the machine and analyse its state transition graphs. We envisage that actin droplet machines could form an elementary processor of future massive parallel computers made from biopolymers.

Towards fungal computer

We propose that fungi Basidiomycetes can be used as computing devices: information is represented by spikes of electrical activity, a computation is implemented in a mycelium network and an interface is realized via fruit bodies. In a series of scoping experiments, we demonstrate that electrical activity recorded on fruits might act as a reliable indicator of the fungi's response to thermal and chemical stimulation. A stimulation of a fruit is reflected in changes of electrical activity of other fruits of a cluster, i.e. there is distant information transfer between fungal fruit bodies. In an automaton model of a fungal computer, we show how to implement computation with fungi and demonstrate that a structure of logical functions computed is determined by mycelium geometry.

A general framework dedicated to computational morphogenesis Part I - Constitutive equations

In order to understand living organisms, considerable experimental efforts and resources have been devoted to correlate genes and their expressions with cell, tissue, organ and whole organisms' phenotypes. This data driven approach to knowledge discovery has led to many breakthrough in our understanding of healthy and diseased states, and is paving the way to improve the diagnosis and treatment of diseases. Complementary to this data-driven approach, computational models of biological systems based on first principles have been developed in order to deepen our understanding of the multi-scale dynamics that drives normal and pathological biological functions. In this paper we describe the biological, physical and mathematical concepts that led to the design of a Computational Morphogenesis (CM) platform baptized Generic Modeling and Simulating Platform (GMSP). Its role is to generate realistic 3D multi-scale biological tissues from virtual stem cells and the intended target applications include in virtuo studies of normal and abnormal tissue (re)generation as well as the development of complex diseases such as carcinogenesis. At all space-scales of interest, biological agents interact with each other via biochemical, bioelectrical, and mechanical fields that operate in concert during embryogenesis, growth and adult life. The spatio-temporal dependencies of these fields can be modeled by physics-based constitutive equations that we propose to examine in relation to the landmark biological events that occur during embryogenesis.

Image-Based Structural Modeling of the Cardiac Purkinje Network

The Purkinje network is a specialized conduction system within the heart that ensures the proper activation of the ventricles to produce effective contraction. Its role during ventricular arrhythmias is less clear, but some experimental studies have suggested that the Purkinje network may significantly affect the genesis and maintenance of ventricular arrhythmias. Despite its importance, few structural models of the Purkinje network have been developed, primarily because current physical limitations prevent examination of the intact Purkinje network. In previous modeling efforts Purkinje-like structures have been developed through either automated or hand-drawn procedures, but these networks have been created according to general principles rather than based on real networks. To allow for greater realism in Purkinje structural models, we present a method for creating three-dimensional Purkinje networks based directly on imaging data. Our approach uses Purkinje network structures extracted from photographs of dissected ventricles and projects these flat networks onto realistic endocardial surfaces. Using this method, we create models for the combined ventricle-Purkinje system that can fully activate the ventricles through a stimulus delivered to the Purkinje network and can produce simulated activation sequences that match experimental observations. The combined models have the potential to help elucidate Purkinje network contributions during ventricular arrhythmias.

Three-dimensional cardiac computational modelling: methods, features and applications

The combination of computational models and biophysical simulations can help to interpret an array of experimental data and contribute to the understanding, diagnosis and treatment of complex diseases such as cardiac arrhythmias. For this reason, three-dimensional (3D) cardiac computational modelling is currently a rising field of research. The advance of medical imaging technology over the last decades has allowed the evolution from generic to patient-specific 3D cardiac models that faithfully represent the anatomy and different cardiac features of a given alive subject. Here we analyse sixty representative 3D cardiac computational models developed and published during the last fifty years, describing their information sources, features, development methods and online availability. This paper also reviews the necessary components to build a 3D computational model of the heart aimed at biophysical simulation, paying especial attention to cardiac electrophysiology (EP), and the existing approaches to incorporate those components. We assess the challenges associated to the different steps of the building process, from the processing of raw clinical or biological data to the final application, including image segmentation, inclusion of substructures and meshing among others. We briefly outline the personalisation approaches that are currently available in 3D cardiac computational modelling. Finally, we present examples of several specific applications, mainly related to cardiac EP simulation and model-based image analysis, showing the potential usefulness of 3D cardiac computational modelling into clinical environments as a tool to aid in the prevention, diagnosis and treatment of cardiac diseases.

A meshfree method for simulating myocardial electrical activity

An element-free Galerkin method (EFGM) is proposed to simulate the propagation of myocardial electrical activation without explicit mesh constraints using a monodomain model. In our framework the geometry of myocardium is first defined by a meshfree particle representation that is, a sufficient number of sample nodes without explicit connectivities are placed in and inside the surface of myocardium. Fiber orientations and other material properties of myocardium are then attached to sample nodes according to their geometrical locations, and over the meshfree particle representation spatial variation of these properties is approximated using the shape function of EFGM. After the monodomain equations are converted to their Galerkin weak form and solved using EFGM, the propagation of myocardial activation can be simulated over the meshfree particle representation. The derivation of this solution technique is presented along a series of numerical experiments and a solution of monodomain model using a FitzHugh-Nagumo (FHN) membrane model in a canine ventricular model and a human-heart model which is constructed from digitized virtual Chinese dataset.

Modelling of the ventricular conduction system

The His-Purkinje conduction system initiates the normal excitation of the ventricles and is a major component of the specialized conduction system of the heart. Abnormalities and propagation blocks in the Purkinje system result in abnormal excitation of the heart. Experimental findings suggest that the Purkinje network plays an important role in ventricular tachycardia and fibrillation, which is the major cause of sudden cardiac death. Nowadays an important area in the study of cardiac arrhythmias is anatomically accurate modelling. The majority of current anatomical models have not included a description of the Purkinje network. As a consequence, these models cannot be used to study the important role of the Purkinje system in arrhythmia initiation and maintenance. In this article we provide an overview of previous work on modelling of the Purkinje system and report on the development of a His-Purkinje system for our human ventricular model. We use the model to simulate the normal activation pattern as well as abnormal activation patterns resulting from bundle branch block and bundle branch reentry.

Cellular Automata With Object-Oriented Features for Parallel Molecular Network Modeling

Cellular automata are an important modeling paradigm for studying the dynamics of large, parallel systems composed of multiple, interacting components. However, to model biological systems, cellular automata need to be extended beyond the large-scale parallelism and intensive communication in order to capture two fundamental properties characteristic of complex biological systems: hierarchy and heterogeneity. This paper proposes extensions to a cellular automata language, Cellang, to meet this purpose. The extended language, with object-oriented features, can be used to describe the structure and activity of parallel molecular networks within cells. Capabilities of this new programming language include object structure to define molecular programs within a cell, floating-point data type and mathematical functions to perform quantitative computation, message passing capability to describe molecular interactions, as well as new operators, statements, and built-in functions. We discuss relevant programming issues of these features, including the object-oriented description of molecular interactions with molecule encapsulation, message passing, and the description of heterogeneity and anisotropy at the cell and molecule levels. By enabling the integration of modeling at the molecular level with system behavior at cell, tissue, organ, or even organism levels, the program will help improve our understanding of how complex and dynamic biological activities are generated and controlled by parallel functioning of molecular networks. Index Terms-Cellular automata, modeling, molecular network, object-oriented.

Asynchronous adaptive time step in quantitative cellular automata modeling

BACKGROUND

The behaviors of cells in metazoans are context dependent, thus large-scale multi-cellular modeling is often necessary, for which cellular automata are natural candidates. Two related issues are involved in cellular automata based multi-cellular modeling: how to introduce differential equation based quantitative computing to precisely describe cellular activity, and upon it, how to solve the heavy time consumption issue in simulation.

RESULTS

Based on a modified, language based cellular automata system we extended that allows ordinary differential equations in models, we introduce a method implementing asynchronous adaptive time step in simulation that can considerably improve efficiency yet without a significant sacrifice of accuracy. An average speedup rate of 4-5 is achieved in the given example.

CONCLUSIONS

Strategies for reducing time consumption in simulation are indispensable for large-scale, quantitative multi-cellular models, because even a small 100 x 100 x 100 tissue slab contains one million cells. Distributed and adaptive time step is a practical solution in cellular automata environment.

The effect of volume currents due to myocardial anisotropy on body surface potentials

Changes in anterior and posterior body surface potential maps (BSPMs) due to myocardial anisotropy were examined using a highly heterogeneous finite element model of an adult male subject constructed from segmented magnetic resonance images. A total of 23 different tissue types were identified in the whole torso. The myocardial fibre orientations in the human heart wall were mapped from the fibre orientations of a canine heart which are available in the literature using deformable mapping techniques. The current and potential distributions in the whole torso were computed using dipolar sources in the septum, apical area, left ventricular wall or right ventricular wall. For each dipole x, y, z orientations were studied. An adaptive finite element solver was used to compute currents and potential distributions in the whole torso with an element size of 0.78 x 0.78 x 3 mm in the myocardium and larger elements in other parts of the torso. For each dipole position two cases were studied. In one case the myocardium was isotropic and in the other it was anisotropic. It was found that BSPMs showed a very notable difference between the isotropic and the anisotropic myocardium for all dipole positions with the largest difference for the apical dipoles. The correlation coefficients for the BSPMs between the isotropic and anisotropic cases ranged from 0.83 for an apical dipole to 0.99 for an RV wall dipole. These results suggest that myocardial fibre anisotropy plays an important role in determining the body surface potentials.

Issues in the design of medical ontologies used for knowledge sharing

Recent work in Medical Informatics is exploring the development and the use of formal ontologies as a way of specifying content-specific agreements for the sharing and reuse of knowledge among several computer systems. We describe the role of ontologies in supporting knowledge sharing activities in medicine Principles for the design of ontologies have been proposed, mainly in other domains: these principles include parsimony, clarity, representation of categories versus terms, and coherence. We analyze how and why these principles can or cannot be applied from case studies from medical systems. Regarding the fact that most of medical concepts are empirical, selected design decisions are discussed. An alternative representation choice consists in mapping principled general core ontologies and domain ontologies.

A flexible method for simulating cardiac conduction in three-dimensional complex geometries

In this article we present a method for creating a membrane-based computer model capable of representing a three-dimensional irregular domain. The spatial discretization of our model is based on the Finite Volume Method. In combination with a robust meshmaking tool, our method may be used to simulate conduction in an arbitrarily shaped, complex region. In this way, conduction in specific subregions of cardiac anatomy may be examined. The capabilities of this methodology are demonstrated through 3 examples. The first shows the influence of abrupt changes in tissue geometry on conduction parameters. The second highlights the ability of the model to incorporate interior boundaries and altered membrane properties. The final example shows the inclusion of a full description of the fiber architecture in a portion of the canine left ventricle. Future applications will make use of the model's capabilities to conduct investigations in complex regions including the atria.

Effect of myocardial anisotropy on the torso current flow patterns, potentials and magnetic fields

The effects of myocardial anisotropy on the torso current flow patterns, voltage and the magnetic field were examined using an anatomically realistic torso model of an adult male subject. A finite element model of the torso was built with 19 major tissue types identified. The myocardial fibre orientation in the heart wall was included with a voxel resolution of 0.078 x 0.078 x 0.3 cm. The fibre orientations from the canine heart which are available in the literature were mapped to our adult male subject's human heart using deformable mapping techniques. The current and potential distribution in the whole torso were computed using an idealized dipolar source of +/-1.0 V in the middle of the septum of the heart wall as a boundary condition. An adaptive finite element solver was used. Two cases were studied. In one case the myocardium was isotropic and in the other it was anisotropic. It was found that the current density distribution shows a very noticeable difference between the isotropic and anisotropic myocardium. The resultant magnetic field in front of the torso was computed using the Biot-Savart law. It was found that the magnetic field profile was slightly affected by the myocardial anisotropy. The potential on the torso surface also shows noticeable changes due to the myocardial anisotropy.