Finding type and location of the source of cardiac arrhythmias from the averaged flow velocity field using the determinant-trace method

Abstract

Life threatening cardiac arrhythmias result from abnormal propagation of nonlinear electrical excitation waves in the heart. Finding the locations of the sources of these waves remains a challenging problem. This is mainly due to the low spatial resolution of electrode recordings of these waves. Also, these recordings are subjected to noise. In this paper, we develop a different approach: the AFV-DT method based on an averaged flow velocity (AFV) technique adopted from the analysis of optical flows and the determinant-trace (DT) method used for vector field analysis of dynamical systems. This method can find the location and determine all important types of sources found in excitable media such as focal activity, spiral waves, and waves rotating around obstacles. We test this method on in silico data of various wave excitation patterns obtained using the Luo-Rudy model for cardiac tissue. We show that the method works well for data with low spatial resolutions (up to 8 × 8) and is stable against noise. Finally, we apply it to two clinical cases and show that it can correctly identify the arrhythmia type and location. We discuss further steps on the development and improvement of this approach.

Control of spiral waves in myocardial tissue by optogenetics and temperature

“…Experimentally we can only get the membrane potential of myocardial tissue. Thus, a number of methods have been proposed to recognize PS by membrane potentials such as topological chargedensity method, Jacobian-determinant method and average flow velocity determinant-trace method [51][52][53]. In this paper, we uses Jacobi determinants to identify the PS of spiral waves [36]:…”

Chirality and curvature determine the meandering of spirals in multilayer excitable media

“…Moreover, the focal activity or reentrant seeds of spiral waves are organized by sites known as singularities (PS). Considerable efforts have been undertaken to determine the position of PSs [30,31], given that the drift of spiral waves often originates from their motion [32].…”

Unpinning of pinning sprial waves with pulses of radial electrical field

“…Ma等利用分布式电流去控制心肌组织中的螺旋波 [12] 。2015年Xu和Ma等研究了非 均匀耦合下神经网络内有序波的诱发问题 [13] 。2018年Li和Tang等在Luo-Rudy模型 下研究了心肌细胞中的钠电流对螺旋波的控制作用 [14] 。 据1990-2017年间中国过早死亡原因调查报告显示， 心脏疾病在致人死亡的因 素中排名第二 [15] 。心脏中的螺旋波会导致心律失常，严重时危及生命 [16] 。要治疗 心律失常疾病就要成功消除心脏中的螺旋波信号。当心脏中存在缺陷(如血管和 [17,18] ( wave emission from heterogeneities，简记为 WEH) 。缺陷上有钉扎的螺旋波时，在激发波与钉扎波的 相互作用下，原始钉扎波可能会离开缺陷成功脱钉。传统抗心动起搏过速 (anti-tachycardia pacing，简记为 ATP)方法是目前临床中治疗心律失常的常用 方法 [19] 。但是 ATP 方法只能凭借医者本身的临床经验去选择植入电极的位置，这 也在一定程度上限制了它的治疗效果。如今，随着医疗水平的提高，对心脏的了 解程度进一步加深。目前，已有新的方法可以准确探测心脏中二维电信号 [19][20][21] ， 基于这个低分辨率的二维信号，Li 等人提出的数值方法可准确地计算出缺陷的位 置和尺寸 [22] 。本文利用数值模拟方式研究了径向电脉冲(pulses of radial electrical field, 简记为 PREF)对螺旋波脱钉的影响。 本文采用二维Barkley模型 [23] 来模拟二维可激发介质中螺旋波的脱钉研究， 利用均匀电场(uniform electric field, 简记为UEF) [24] 、旋转电场(rotate electric pulses, 简记为REP) [25] 和圆极化电场(circularly polarized electric field, 简 记为CPEF) [26] 方法脱钉时，成功的关键由激发波和钉扎螺旋波的相位共同决定 的，只有加入电场的时机合适才能迅速脱钉 [25][26][27] 。而我们的方法在理论上则不存 waves could be unpinned from an obstacle effectively in a weakly excitable medium, but it could not be unpinned in a strongly excitable medium. The unpinning parameter space of a SPREF is larger than that of a Uniform Electric Field or Anti-tachycardia Pacing.…”