Simulation of transmembrane potential propagation in three dimensional ventricular tissue using Aliev Panfilov model

Seyedebrahimi, MirMehdi
Heart is a muscular tissue that circulates blood through the circulatory system, and has a role in providing oxygen and nutrition to body organs and removal of wastes from them. Any disorder in the function of this organ can lead to severe diseases, and even death. Thus, characterization of these diseases and their mechanisms is important, and helps the clinicians diagnose, treat, and predict these diseases. The contraction of heart muscle is dependent on its electrical activity, and determination of this activity could provide information about the functional state of the heart. Majority of these diseases can be diagnosed using clinical methods ranging from 12-lead electrocardiography (ECG) to open surgery. However, most of these methods either are considered to be invasive, or provides information at limited spatio-temporal resolution. Moreover, ethical permission problems, and fast electro-physiological changes constrain their application for investigation purposes. The main objective of this study is to mathematically model the heart's electrical activity for understanding the details of its function, and developing methods for prediction, diagnosis and treatment of various heart diseases. High spatio-temporal resolution maps, simple application could supply researchers and physicians necessary information that could not be acquired with other methods. In this work, we modelled the electrical activity of the heart in the three dimensional (3D) ventricular geometry based on transmembrane potential (TMP) distributions using anatomical information of the heart such as; property of myocardium, ber orientation. etc. We also use Aliev-Pan lov model to describe electrical activity of the heart at tissue level, which focuses on the potential wavefront propagation. In this model, it is also possible to include the anisotropy of the heart muscle. We rst focused on anisotropic tissue assumption, comparing it to isotropic assumption of cardiac tissue. Second, e ects of ber orientation variance representing geometrical errors was investigated. Third, we suggested a new method for simple, and reliable modelling of electrical activity of the heart by transferring cardiac information from a known heart to an unknown one. Then, using similar method of simulation, 3 dimensional mapping of TMP distribution and propagation of di erent functional states of the heart was simulated. First, propagation in the normal heart tissue based on normal and ectopic heart beats were modelled. Second, based on action potential morphology changes in a tissue with ischemia, we derived ischemic weight values and equation parameters for our model. Then by introducing ischemic regions on the ventricular geometry and using ischemic tissue properties and weight values, we simulated TMP distribution and propagation in ventricular geometry with partial ischemia. Finally, by introducing an abnormal conduction pathway, a heart with a pre-excitation disorder called Wolf-Parkinson-White syndrome was simulated. Our results of simulation were similar to previous clinical and simulation models. It was also shown that isotropic assumption of cardiac tissue can affect TMP simulation results signi cantly. This alteration was shown chie y in TMP wavefront propagation velocity, TMP potential value of each points and more importantly action potential duration. In contrast, it was shown that DTI based images in spite of additional micro-structural errors are the most reliable method for simulating the electrical activity of the heart.