The Electrocardiogram

The rhythmical contraction of the heart can also be measured from outside the body (non-invasively) using electrocardiogram (ECG) electrodes. This technique provides valuable insight into the underlying dynamics of the heart. In particular, the ECG electrodes do not measure directly the mechanical motion of the heart, but rather the electrical excitation patterns. During the usual sinus rhythm, the electrocardiogram provides a characteristic signal (schematic representation in Fig. 2.8), where each part can be associated to different stages of the contraction.

The mechanical contraction starts with the depolarization of the atria, which can be asso-ciated with theP wave in the electrocardiogram, followed by thePR segment (propagation of the signal through the atrioventricular bundle) which lasts until the ECG drops, defin-ing the start of the QRS complex (for comparison to the electrical conduction system, see section 2.1.2 on page 17). After the signal has passed the atrioventricular bundle, the inter-ventricular septum depolarizes, inducing a drop of the ECG signal (Q wave), followed by the depolarization of the remaining ventricular muscle (R wave). Afterwards, the repolarization of the ventricles is reflected in the ST segment, the T wave and theU wave. Since the dif-ferent parts of the ECG (at least partially) refer to distinct regions of the heart, physicians can deduce (possibly pathological) anatomical variations of the heart from alterations of the normal shape of the ECG. In the conventional way, the ECG is mainly used for analyses of the sinus rhythm, and related heart diseases. In the study of section 3.3 on page 102 we extend this concept, by introducing a multiple electrode measurement during ventricular fibrillation, and derive statements about the spatio-temporal state of the heart during the chaotic dynamics.

2.1.5 Defibrillation of the Heart

Defibrillation describes a process that terminates cardiac arrhythmias (e.g. ventricular fibrillation), via the application of electrical high-energy far field shocks to the heart. This procedure, and in particular the significant side effects of current standard defibrillation technique provide the main motivation of this thesis. The purpose of a defibrillation attempt is, to terminate chaotic excitation patterns present in the heart, and to restore sinus rhythm.

In the following, the underlying mechanism of the application of high-energy far field shocks, and their effect on cardiac tissue is discussed.

Virtual Electrodes

The concept of virtual electrodes is fundamental for the understanding of the underlying mechanisms of defibrillation [28, 29]: The cardiac muscle is not a homogeneous substrate but heterogeneities of various size and structure are present in the tissue. Essential for the mechanism here are changes in the conductivities which emerge for example due to blood vessels, or discontinuities between bundles and sheets of fibers [30], but also the inner and outer boundary of the muscle (endocardium and epicardium, respectively) are crucial from this point of view. When an electrical field is applied for a certain amount of time (“far field shock”), the ions present in the tissue experience the Lorentz force. These charged particles are slightly shifted due to the force and accumulate at heterogeneities (or more precisely, at regions of a varying conductivity). Since the conductivities are different in the intra-and extracellular space, the membrane potential exceeds the excitation threshold at specific locations, which then triggers an action potential there. In this way, heterogeneities can be denoted as “virtual electrodes”, since excitation waves induced by an external electrical field are created here. The process of creating an excitation wave (using an external electrical field) at a certain heterogeneity is also termed “recruiting” the heterogeneity.

Quantitatively, the actual field strength plays an important role for the defibrillation pro-cess. Studies indicate, that a certain field strength of the external electrical field, can only

“recruit” heterogeneities down to a specific size or shape [28, 29, 31]. That means, with a lower field strength, excitation waves are created only at some heterogeneities. For exam-ple, P. Bittihn et al. showed [31], that the curvature of the heterogeneity is essential for the recruiting process (Fig. 2.9). Boundaries with a negative curvature (convex) can be excited with significantly lower field strengths, whereas heterogeneities with a flat or positive cur-vature (concave), are recruited only with high field strengths. That means, with an increase of the field strength, more and more heterogeneities can be recruited, and thus the regions of the heart where excitation waves are created grows monotonously.

2.1. Complexity of the Heart

Figure 2.9: Recruiting of excitation sites in cardiac tissue dependent on the field strength.

Results of numerical simulations using the Fenton-Karma model, based on a micro-CT (computed tomography) scan of the left ventricle of a rabbit heart. Excitation waves are depicted, which were created by the application of an electrical field for 5 ms with a varying field strength E. The plots show snapshots of the excitation patterns at different points in time (from left to right) and with different field strengths ((a) 0.2 V/cm, (b) 0.4 V/cm, and (c) 1.0 V/cm, respectively). Reprinted from [31] under the terms of the Creative Commons Attribution 3.0 License.

Figure 2.10: The dose response curve. In a defibrillation study [32] with 23 Langendorff-perfused rabbit hearts, the defibrillation success rate (dose response curve) was determined statistically in 273 shock episodes. The sigmoid-like behavior of the success rate reflects the underlying mechanism of the defibrillation, which is based on the (energy dependent) recruitment of virtual electrodes. Reprinted from [32], with permission from Wolters Kluwer Health, Inc. .

The Dose Response Curve

In this picture, the standard defibrillation procedure (one high-energy shock) uses such a huge field strength, that it excites basically the whole tissue at once. In this way, the excitation waves which perpetuate the current arrhythmia cannot further propagate, the whole tissue is excited and decays then globally in the refractory state. Afterwards, the conduction system can restart the sinus rhythm and the ordered contraction of the heart.

Using such a high energy/field strength ensures (in most cases) the termination of the cardiac arrhythmia, but comes along with significant side effects (discussed in section 1.2 on page 4), which are often related to the resulting electrical currents.

In comparison, using lower field strengths decreases the number of recruited heterogeneities.

That means, the electrical field does not excite the whole tissue, but only parts of it. How-ever, with a certain probability, the induced excitation waves can still terminate the present dynamics of the arrhythmia. Naturally, this probability is (in general) proportional to the field strength (and thus the number of excitation sites) [21]. Thedose response curve(DRC), which gives the statistically determined success rate of a defibrillation shock dependent on the electrical field strength, reflects this behavior (Fig. 2.10).

Apparently, using a lower field strength/energy for defibrillation significantly reduces the probability for the termination of the arrhythmia (which is not acceptable regarding a clinical application). That is, why low energy defibrillation protocols (e.g. [21]) need to adjust parameters like the number, frequency or timing of the shock(s) in order to guarantee a reasonably high success rate.