Mathematical Modeling the Electrical Activity of the Heart (original) (raw)
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Mathematical Modelling of Human Heart as a Hydroelectromechanical System
Different electrical models of human heart, partial or complete, with linear or nonlinear models have been developed. In the literature, there are some applications of mathematical and physical analog models of total artificial heart (TAH), a baroreceptor model, a state-space model, an electromechanical biventricular model of the heart, and a mathematical model for the artificial generation of electrocardiogram (ECG) signals. Physical models are suitable to simulate real physiological data based on proper experimental set up present. This paper introduces a new mathematical modelling of human heart as a hydroelectromechanical system (HEMS). This paper simulates the human heart based on three main functions: hydraulic, electrical and mechanical parameters. Hydro-mechanical model developed then has been transformed into electrical domain and simulation has been carried out according to the mathematical model or formulations obtained using Laplace transform. This electrical model / circuit is then tested by MATLAB based simulations and results found are comparable with the normal ECG waveforms so that these simulated results may be useful in clinical experiments. In this model basic electrical components have been used to simulate the physiological functions of the human heart. The result is a simple electrical circuit consisting of main electrical parameters that are transformed from hydraulic models and medical physiological values. Developed MATLAB based mathematical model will primarely help to understand the proper functioning of an artificial heart and its simulated ECG signals. A comprehensive model for generating a wide variety of such signals has been targeted for future in this paper. This research especially focuses on modelling human heart as a hydro-electro-mechanical system with three case studies.
Mathematical and numerical models for the cardiac electromechanical function
Rendiconti Lincei - Matematica e Applicazioni, 2021
This paper deals with the mathematical model that describes the function of the human heart. More specifically, it addresses the equations that express the electromechanical process, that is the mechanical deformation (contraction and relaxation) of the heart muscle that is induced by the electrical field that, at every heartbeat, is generated in the sino-atrial node and then propagates all across the cardiac cells. After deriving the equations of the mathematical model from basic physical principles, we proceed to their numerical approximations and discuss issues such as stability, accuracy and computational complexity. We close the paper by illustrating a few numerical results on test problems of potential interest for clinical applications.
Models of cardiac tissue electrophysiology: Progress, challenges and open questions
Progress in Biophysics and Molecular Biology, 2011
Models of cardiac tissue electrophysiology are an important component of the Cardiac Physiome Project, which is an international effort to build biophysically based multi-scale mathematical models of the heart. Models of tissue electrophysiology can provide a bridge between electrophysiological cell models at smaller scales, and tissue mechanics, metabolism and blood flow at larger scales. This paper is a critical review of cardiac tissue electrophysiology models, focussing on the micro-structure of cardiac tissue, generic behaviours of action potential propagation, different models of cardiac tissue electrophysiology, the choice of parameter values and tissue geometry, emergent properties in tissue models, numerical techniques and computational issues. We propose a tentative list of information that could be included in published descriptions of tissue electrophysiology models, and used to support interpretation and evaluation of simulation results. We conclude with a discussion of challenges and open questions.
Modeling the cardiac electromechanical function: A mathematical journey
Bulletin of the American Mathematical Society
In this paper we introduce the electromechanical mathematical model of the human heart. After deriving it from physical first principles, we discuss its mathematical properties and the way numerical methods can be set up to obtain numerical approximations of the (otherwise unachievable) mathematical solutions. The major challenges that we need to face—e.g., possible lack of initial and boundary data, the trade off between increasing the accuracy of the numerical model and its computational complexity—are addressed. Numerical tests here presented have a twofold aim: to show that numerical solutions match the expected theoretical rate of convergence, and that our model can provide a preliminary valuable tool to face problems of clinical relevance.
A finite Element Model for the Electrical Activity in Human Cardiac Tissues
Biosimulation models of the heart action potential have become a very useful tool. It provides better understanding for the complex biophysical phenomena related to electrical activity in the heart such as cardiac arrhythmias. At cellular level, the electrical activity of cardiac tissues may be simulated by solving a system of ordinary deferential equations (ODEs) describing the electrical behavior of the cell membrane. Because the biophysical processes underlying this phenomenon are non-linear and change very rapidly, the ODE system is a challenge to be solved numerically. Furthermore, the implementation of these models is a hard task for commercial finite element software. In this paper a finite element formulation, model and code generation of monodomain equation has been conducted. The developed code is coupled with the modified FitzHugh-Nagumo (FHN) cell electrophysiological model in order to have isotropic excitation propagation starting from cell level to complete heart level. MTALAB programming language was used to build the proposed standalone finite element code. A two dimensional specimen of heart tissues is simulated to show the behavior of the excitation propagation and the repolarization phase for isotropic electrical activity. Simulation results of the cardiac action potential have shown good agreements with the experimental measurements obtained from published literature.
A fast computational model for the electrophysiology of the whole human heart
Journal of Computational Physics, 2022
In this study we present a novel computational model for unprecedented simulations of the whole cardiac electrophysiology. According to the heterogeneous electrophysiologic properties of the heart, the whole cardiac geometry is decomposed into a set of coupled conductive media having different topology and electrical conductivities: (i) a network of slender bundles comprising a fast conduction atrial network, the AV-node and the ventricular bundles; (ii) the Purkinje network; and (iii) the atrial and ventricular myocardium. The propagation of the action potential in these conductive media is governed by the bidomain/monodomain equations, which are discretized in space using an inhouse finite volume method and coupled to three different cellular models, the Courtemanche model [1] for the atrial myocytes, the Stewart model [2] for the Purkinje Network and the ten Tusscher-Panfilov model [3] for the ventricular myocytes. The developed numerical model correctly reproduces the cardiac electrophysiology of the whole human heart in healthy and pathologic conditions and it can be tailored to study and optimize resynchronization therapies or invasive surgical procedures. Importantly, the whole solver is GPU-accelerated using CUDA Fortran providing an unprecedented speedup, thus opening the way for systematic parametric studies and uncertainty quantification analyses.
arXiv (Cornell University), 2020
We propose an integrated electromechanical model of the human heart, with focus on the left ventricle, wherein biophysically detailed models describe the different physical phenomena concurring to the cardiac function. We model the subcellular generation of active force by means of an Artificial Neural Network, which is trained by a suitable Machine Learning algorithm from a collection of pre-computed numerical simulations of a biophysically detailed, yet computational demanding, high-fidelity model. To provide physiologically meaningful results, we couple the 3D electromechanical model with a closed-loop 0D (lumped parameters) model describing the blood circulation in the whole cardiovascular network. We prove that the 3D-0D coupling of the two models is compliant with the principle of energy conservation, which is achieved in virtue of energy-consistent boundary conditions that account for the interaction among cardiac chambers within the computational domain, pericardium and surrounding tissue. We thus derive an overall balance of mechanical energy for the 3D-0D model. This provides a quantitative insight into the energy utilization, dissipation and transfer among the different compartments of the cardiovascular network and during different stages of the heartbeat. In virtue of this new model and the energy balance, we propose a new validation tool of heart energy usage against relationships used in the daily clinical practice. Finally, we provide a mathematical formulation of an inverse problem aimed at recovering the reference configuration of one or multiple cardiac chambers, starting from the stressed configuration acquired from medical imaging. This is fundamental to correctly initialize electromechanical simulations. Numerical methods and simulations of the 3D-0D model will be detailed in Part II.
The Electrical Activity of Cardiac Tissue via Finite Element Method
For the treatment of certain cardiac disorders sometimes electrical currents are used as therapy, as it happens when fibrillation. This phe-nomenon manifest itself with chaotic and accelerated heart rhythm, pre-venting the pumping of blood to the rest the organism. In considering this type of heart disease, introduce mathematical models to analyze the dynamics and behavior of these discharges, in particular, bidomain model is one of the most studied in order to understand the electrical process in cardiac tissue as a phenomenon that can be mathematically modeled .
Mathematical Modelling and Electrical Analog Equivalent of the Human Cardiovascular System
Cardiovascular Engineering, 2010
The objective of this study is to develop a model of the cardiovascular system capable of simulating the normal operation of the systemic and pulmonary circulation, starts from aorta, and follows by upper and lower extremities vessels, finally ends with pulmonary veins. The model consists of a closed loop lumped elements with 43 compartments representing the cardiovascular system. The model parameters have been extracted from the literature. Using MATLAB software, the mathematical model has been simulated for the cardiovascular system. Each compartment includes a Resistor-Inductor-Capacitor (RLC) segment. The normal cardiovascular operation is characterised by the pressure-volume curves in different parts of the system. Model verification is performed by comparing the simulation results with the clinical observation reported in the literature. The described model is a useful tool in studying the physiology of cardiovascular system, and the related diseases. Also, it could be a great tool to investigate the effects of the pathologies of the cardiovascular system.