Effect of Extracellular Calcium Concentration on Controlling Cardiac Alternans

Abstract

IntroductionCardiac arrhythmia is a condition where heartbeats are abnormal. Every year, millions of people worldwide experience arrhythmias and many of them can return to their normal lives if the arrhythmias are treated at early stages and properly. However, many arrhythmias are dangerous and may lead to sudden cardiac death.Cardiac alternans [1,2], which can be induced by fast pacing, is the condition of having alternate-beat oscillation in the electrical activity (the action potential durations, APDs, oscillate in a long-short-long-short pattern) or alternating strong and weak beats in a heart under a constant pacing. It may lead to life-threatening cardiac arrhythmias [3,4], such as ventricular tachycardia and ventricular fibrillation, or sudden cardiac death [4,5] if it is left without any further medical treatment or intervention. Therefore, searching for an effective alternans control method is crucial.Besides the earlier proposed methods for alternans suppression: the proportional feedback control [6,7] and adaptive scheme [8][9][10], a new control scheme, the T+T-feedback control [11][12][13][14] was proposed recently. The basic pacing period T in this method is designed to change between two values, T +  and T - (where  is a predetermined control parameter and is much less than T), repeatedly until the alternans is suppressed. Experiments [11,13] and theoretical [11][12][13][14] studies have been carried out and the results showed that the T+T-control method can suppress alternans effectively. However, when the pacing rate continues to increase, the amplitude of the alternans also increases and becomes more difficult to be controlled. Thus, it is necessary to look into how the T+T-control method can be improved to suppress alternans induced by rapid pacing.During cardiac alternans, the intracellular calcium concentration ([Ca] [18,19] showing that lowering extracellular calcium concentration ([Ca]o) can suppress alternans, it is interesting to examine the combination of T+T-control method and low [Ca]o as a possible more effective alternans control method. In this study, we investigated the time needed to suppress cardiac alternans using the T+T-control method with lower [Ca]o during the control. The details of the control scheme and numerical calculation are given in the next section, followed by the results. In the last section, we discuss our significant findings and the clinical implications. MethodsThe Hund-Rudy dynamic (HRd) model of canine ventricular action potential [2,20], which is one of the typical mathematical models used to study cardiac alternans, was used in this study to simulate the alternans of a single cell. The HRd model includes the ionic-currents, pumps, exchangers, dynamic concentration change of ions, and calcium cycling. The rate of change of the membrane potential (V) is described by the following equation: