Theoretical Study On The Effects Of Inhomogeneity On Spiral Waves In Cardiac Tissue

Spiral waves exist widely in various biological,physical and chemical systems.Clinical studies have shown that all kinds of fatal heart diseases are related to spiral waves in cardiac tissue,such as tachycardia and ventricular fibrillation.Both theoretical and experimental studies have shown that the inhomogeneity regions of cardiactissue play a crucial role in the formation,control and attraction of spiral waves.In addition,previous theoretical studies have found that under different conditions,inhomogeneity regions can attract and repel the wave tip,but there is a lack of a clear description on the dynamic process of the interaction between the wave tip and the inhomogeneity.This paper will focus on the dynamic process of the effect of the inhomogeneity region on the spiral wave when the wave tip is close to the inhomogeneity region in the cardiac tissue,which can provide some theoretical supports for the control of spiral waves and the treatment of heart diseases.Based on the Morris-Lecar(ML)model,a two-dimensional electrical conduction system in cardiac tissue is modeled.The spiral wave is excited by the "wave cutting" method,and a circular heterostructure area is placed near the spiral wave to simulate the obstruction of potassium channel in the cardiac tissue.In this paper,we calculate the spiral wave pattern evolution and the wave tip trajectory to demonstrate the dynamic process of the interaction between the inhomogeneity and wave tip.The study found that:(1)With the change of the external stimulation current parameters,the trajectory of the spiral wave tip will have complex changes,and the trajectory types include single-cycle rotation,multi-cycle rotation and quasi-periodic rotation.(2)When the spiral wave tip is in different areas outside the inhomogeneity region,the effect of inhomogeneity on spiral waves varies.When the wave tip is very close to the inhomogeneity region,it will be attracted and anchored to the inhomogeneity.When the tip is a bit further away from the inhomogeneity,the wave tip will be pushed to the distance.The existence of the inhomogeneity does not affect the motion of the wave tip while at a large distance.The paper also presents detailed phase diagrams of regional scope by above three different effects..(3)Study shows that degree(the blocking degree of the potassium ion channel)and size of inhomogeneity region can affect the width of the attraction region.The attractive area has larger width in smaller-size or higher-blocking inhomogeneityregions.While the inhomogeneity degree falls to a certain extent,the change of the attraction area width is not significant,despite varied sizes of inhomogeneity region.