Publication:

Numerical simulation of heart electrical activity

The goal of this thesis is the study of the electrical behaviour of the human heart by means of the numerical integration of a given model. Specifically, the idea is to get a mathematical view into the way the human heart, as well as most of the mammals’ hearts, generates electrical impulses in order to pump the blood through the whole body. The model that is used to determine these dynamics is the Luo-Rudy one, and its solution can be split into two main parts. The first one, known as Luo-Rudy phase I model, is the solution of the main 8 ordinary differential equations (ODEs) to known the values of the currents involved in the process as well as the value of the cell membrane voltage and the intracellular calcium concentration. To solve that ODE system we have used one of the ODE solvers included in Matlab. The voltage obtained is for a unit cell. The second part of this thesis consists of using that result to solve a parabolic partial differential equation (PDE) that describes the cell membrane potential in a two-dimensional cross section of the ventricle making use of the PDE Toolbox present in the Matlab software. These two main steps have been followed through the work of this thesis, an- alyzing the way the numerical methods are used to solve the different problems, and changing some parameters of the system of ODEs to known in a good way the electrical behaviour of the human heart regarding the action potential.