Chapter 15. Cardiac Simulation for Education: The Electrocardiogram According to Ecgsim

Most diagnostic methods used in clinical electrocardiography (ECG) are statistically based forms of pattern recognition. Over the years, the selection of the signal features used in these methods, such as timing, amplitude, and duration of wavelets, has been guided by knowledge gathered through linking clinical observations with ECG waveforms, along with insight gained from invasive electrophysiology. These methods have reached a diagnostic accuracy of up to 90% in some categories of cardiac disease. However, in other categories, the performance is much lower. Moreover, the manifestation in the ECG of some types of abnormality remains poorly understood. Examples of these problematic domains are the diagnosis of left ventricular hypertrophy, the interpretation of ST changes during acute ischemia, the electric manifestation of the Brugada syndrome, and the long QT syndrome. What these examples have in common is that the major features that play a role in the related ECG analysis are their waveforms, which are the result of the electric depolarization and repolarization processes of the membranes of cardiac myocytes, rather than rhythm abnormalities. Since Einthoven's day (late nineteenth century/early twentieth century),1,2 the development of diagnostic ECG criteria has been accompanied by the development of biophysical models aimed at linking the electrophysiology of cardiac function with the waveforms of the ECG signals observed on the body surface. In such an approach, two aspects of the bioelectric generator need to be specified—a source model of the cardiac electric activity, and a volume conductor model, which is a model for describing the passive effects on the observed data of the body tissues that surround the active electric sources.

This chapter focuses on these model-based explanations of ECG morphology, in particular on the ECG components that reflect the electric activity of the ventricles. It does not include an analysis of cardiac rhythm. The emphasis of the approach lies on the ventricular activity. However, it applies in a similar manner to the electric activity of the atria.

The topic is illustrated by simulations from a computer program ECGSIM,3 which allows the user to interactively change the major source parameters: the timing of depolarization and repolarization on the ventricular surface and the local source strength. The program is available, free of charge, from the Web site http://www.ecgsim.org. The program was designed specifically to serve both as a tool in teaching the basic link between electrophysiology and ECG morphology and as an instrument in research applications.

In ECGSIM, the expression of the cardiac sources in terms of electric potential fields and signals (the handling of the so-called forward problem) is worked out in a realistic volume conductor model that accounts for the spreading out of the electric currents in a three-dimensional (3D) representation of the tissues surrounding the heart. Images are presented of the distribution of these parameter values over the ventricular surface as well as those of the accompanying potentials on the ventricular surface and on the body surface.

The theory behind the forward computation is outlined only briefly, focusing on the most essential part of it—a description of the nature of the source and of the source parameters that can be changed interactively. The remaining part of the chapter discusses a selection of the applications of this tool, summarized as "the ECG according to ECGSIM."

The Equivalent Double Layer

The cardiac electric source in ECGSIM is the equivalent double layers (EDL) model. It expresses the entire electrical activity within the ventricular walls by means of a double layer source situated on the closed surface Sh bounding the mass of all ventricular myocytes: endocardium, epicardium, and their connection at the base. Referring to the surface as closed expresses the fact that any ant moving about inside such a surface would be able to reach all interior points but not be able to make its way out.

The EDL can be viewed as a generalization of the classic uniform double layer (UDL) source model, the model based on the analysis of Wilson et al4 in 1933. This source model has been shown to be very effective in describing the sources at the depolarization wave fronts.5 The link between the UDL and the EDL models, explained in detail in van Oosterom,6 is summarized here to facilitate the introduction of the EDL concept.

To this end, in Fig. 15–1, a schematic diagram is presented of the activation of the ventricular wall initiated at a single site on the endocardium, shown in a transmural cross-section. The heavy solid lines mark the wave fronts (ie, the boundaries between activated tissue [in grey] and the regions that are still at rest). The wave front propagates along the local normals, marked by UDL. The gradients of the intracellular potential of the myocytes across the wave fronts (≈100 mV/mm) act as the dominant electric forces for the potential field generated in the medium outside the myocardium. In the UDL source model, the sources are taken to be an electric double layer of uniform strength. The double layer can be viewed as an infinite number of current dipoles of uniform (infinitesimally small) strength that are evenly distributed over the activation boundary, each oriented normal to its local surface and pointing toward the tissue still at rest, the direction of the arrows marked UDL in Fig. 15–1. In an infinite medium, the potential at any point that is exterior to the myocardium generated by the UDL source is proportional to the solid angle subtended by the wave front at the observation point. The sign of the potential, with reference to the potential at infinity defined as zero, is positive if the observation point faces the approaching side of the wave front; elsewhere, it is negative.4,7-9

In Fig. 15–1A, the intersection between the wave front and the ventricular wall is marked by a heavy dashed line segment. This borders the depolarized zone of the (closed) ventricular surface. At an exterior observation point, the solid angle subtended by this zone is identical to the one subtended by the wave front, because their rim is identical.10 As a consequence, instead of the source distribution at the wave front, the potential field in the exterior medium may be described by a virtual double layer, acting as an equivalence surface source distribution all over Sh. In order to apply this to the situation shown in panel A, the strength of the EDL over the depolarized part of Sh is taken to be nonzero, equal to the UDL strength at the wave front. Over the remaining part of Sh, the strength is zero. Note that for an exterior observation point close to the depolarized zone, the sign of the potential is negative, in agreement with measured electrophysiologic data (electrograms).

The situation depicted in Fig. 15–1B represents a later stage of the depolarization process, following epicardial breakthrough. Here, the EDL can be introduced in the same manner: For any exterior observation point, the potential generated by the UDL source(s) at the complete wave front(s) is the sum of the potentials generated by each of the subsections of the wave front. As before, the strength of the EDL is taken to be equal to the UDL strength (at the wave front) over any depolarized part of Sh, and to be zero elsewhere. The addition of the contributions of subsections is justified by the nature of the EDL. Just like that of the UDL, the nature of the EDL is that of a current source, specified by a current dipole surface distribution (see next section), for which the superposition (addition) principle holds true.

Generalization of the EDL

The EDL, just like the UDL, has the nature of an electric double layer. It differs from the UDL in that its strength is nonuniform over Sh. In the preceding introduction, the strength of the EDL is taken to be uniform over the depolarized parts of Sh and zero over the remaining parts. In this manner, the EDL may serve to explain the potential field during the depolarization phase only. At the end of this phase, the entire Sh borders depolarized tissue, and the EDL covers this closed surface. As a consequence, at this time, the contribution to the exterior potential field is zero because the solid angle subtended by any closed surface at any exterior observation point is zero.

In its generalization, the true electric source—the second-order spatial derivative of the transmembrane potential field throughout ventricular mass—is replaced by an equivalent source—an equivalent dipole surface density at the surface Sh bounding the myocardium. The time course of the local EDL strength is taken to be proportional to the local transmembrane potentials (TMP), Vm(t), of the myocytes near Sh, with a proportionality constant set by the local values of the electric conductivity of the tissue. Its background can be found in the literature.11 Its complete validity rests on an assumed spatial uniformity throughout the myocardium of the anisotropy ratio of intracellular and extracellular electric conductivities.12 Although this assumption represents a so-called first-order approximation only, the EDL is currently the only model available with a direct link to cardiac electrophysiology that is able to describe the most prominent aspects of the genesis of the ECG. This applies in particular to the cardiac sources during the repolarization phase (ie, for describing the genesis of the T wave of the surface ECG).13

Prior to depolarization, all ventricular myocytes are polarized, with a resting potential Vm(t) ≈ −80 mV. This creates a uniform EDL strength over Sh and, hence, a zero contribution to the external potential field and zero potential differences in all ECG leads. This is analogous to the situation of a single cell in its fully polarized state. By the time all myocytes have been activated, normally say 80 ms later, all values of the TMPs Vm(t), which set the EDL strength at Sh, are close to a state having reversed polarity, Vm(t) ≈ +10 mV, a state generally referred to as the depolarized state. If all Vm(t) values were uniform over Sh, the external potential field would, once again, be zero. In fact, close to the parts of Sh where depolarization started, the Vm(t) values will already have progressed more toward their resting value than at the parts activated last. This causes a nonuniform distribution of Vm(t) values over Sh and, hence, produces a nonzero external field, causing nonzero values at the end of the QRS interval, with higher magnitudes the nonuniformity is greater. In the same manner, the nonuniformity in the Vm(t) values over Sh values throughout the repolarization phase acts as the (EDL) source of the T wave voltages of the ECG. Significantly, if the time course during repolarization of Vm(t) of all myocytes was the same, the T wave amplitudes in all ECG lead signals would be zero. Finally, if the myocardium is fully repolarized, and if all resting state values of Vm(t) values are uniform, the external field is once more zero, accompanied by a return to zero baseline values of all ECG lead signals.

Potentials Generated by the EDL

By using the EDL, the potential field in the external medium following the initiation of depolarization can be computed by splitting up Sh into numerous small patches. Individual source strengths proportional to the local value of Vm(t) are assigned to each patch, weighted by the signed, individual solid angle that it subtends at the field point. Adding up the contributions of all patches (superposition theorem) then results in the value of the potential at the field point.

Any small membrane patch of a single cell acts as an elementary EDL that contributes to the extracellular field.4,14 The most particular nature of this type of source is emphasized in the following example, illustrated in Fig. 15–2. Figure 15–2A shows the projection of a disk-shaped patch carrying a uniform strength situated at x = 0 along an x-axis in 3D space (line segment a). The surface normal of the patch (ie, the direction of the double layer) is directed along the x-axis. In Fig. 15–2B, the solid trace depicts the potential profile along the x-axis, which is proportional to the signed solid angle subtended by the disk at different positions of the observation point along the x-axis. Note the abrupt change in the sign of the potential and the accompanying jump (discontinuity) in the potential when crossing the double layer,4 similar to the voltage jump observed when penetrating an active cellular membrane. The jump is the most characteristic feature of the double layer source. It occurs, with identical magnitude, irrespective of the angle at which the patch is crossed and irrespective of the point of intersection. The magnitude of the generated voltage jump, VD, can be used to specify the local double layer strength. When skimming the edge of the disk, as along line b on the upper panel, the discontinuity is still visible (Fig. 15–2C), but the magnitude is halved; potential profiles along lines that do not intersect the disk do not exhibit such discontinuities.

Dipolar Approximations of the EDL

At sufficiently large distances from the patch (as a rule of thumb, greater than twice the size of the patch), the potential field generated by the EDL is closely approximated by the field generated by a current dipole that is directed along the normal of the patch, as can be seen in Fig. 15–2. However, close to the patch, the potentials generated by the single dipole deviate greatly from the ones generated by the double layer. Note that in close proximity to the dipole location (track a; x = 0), the magnitude of the potential generated by the dipole tends to become infinite, which is a completely unphysiologic value.

The current dipole is probably the best known model of the cardiac electrical generator; it is the basis of vectorcardiography. In Einthoven's papers, as well as in his correspondence with Lewis and Wilson,15 we see it appearing as an arrow drawn on a plane, representing the "electromotive force" of the heart. At the side of the head of the arrow (see Fig. 15–2), current is injected into the surrounding medium. The location is referred to as the source of the dipole; just below it (at the side of the tail of the arrow), exactly the same current is withdrawn from the medium; the location is referred to as the sink of the dipole. The nature of the current dipole can be likened to that of a circulation pump inside an aquarium.

The single current dipole as used in vectorcardiography can be viewed as the vector sum of the current dipoles, approximating the EDL of all patches of the heart surface Sh. It is a gross approximation of the full complexity of the cardiac electric activity (a so-called equivalent generator) that can be used during the entire QRST interval. In this application, a single dipole performs surprisingly well; it accounts for approximately 80% (representation power) of the potentials observed on the body surface. This holds true irrespective of whether a detailed volume conductor model is involved. However, the dipole cannot be interpreted directly in terms of the underlying electrophysiology. Some limited physiologic interpretability of the single dipole is present in situations where the electric activity is restricted to a small part of the myocardium. Examples are sources during the time interval directly following activation (eg, Wolff-Parkinson-White syndrome, ectopic beats) or during very late phases in depolarization.

In Einthoven's papers, at first sight, the implied volume conductor model appears to be a large planar sheet of conductive paper. Inspected more closely, it is seen to relate to an infinite medium of homogeneous conductivity, at whose center the electric sources are situated. Unrealistic as this volume conductor model may be, it proves to be highly valuable in the appreciation of the most significant characteristics of the potential fields generated by bioelectric sources.

For a spherical volume conductor with uniform internal electric conductivity and zero external conductivity (a somewhat more realistic volume conductor), a current dipole at its center produces potentials on the boundary of the sphere that are three-fold those in the infinite medium.

Since Einthoven's day, volume conductor models have grown increasingly more realistic. Initially, the relationship between source strength and the resulting potentials was derived from measurements taken from physical phantoms (torso tank models). Later, following the pioneering work by Gelernter and Swihart,16 Lynn and Timlake,17 Barnard et al,18 and Barr et al,19 the model-based analysis moved on to computations using digital computers. At present, after vast improvements in computing power and numerical algorithms, such computations can be performed easily. In the thorax model implemented in ECGSIM, the individual geometries of the relevant conductivity interfaces are used, measured by means of magnetic resonance methods. The model takes into account the relatively low conductivity of the lungs and the relatively high conductivity of blood in the cavities.20,21

The remaining main point of interest in the simulation of cardiac potentials is the selection of an appropriate source model for the particular application in hand.

In ECGSIM, the simulation of the ECG is carried out by discretizing the EDL strength around N nodes of the numerical representation of the surface Sh at T subsequent time intervals of 1 ms. This is expressed by a matrix, S, having as its elements Sn,t, n = 1…N; t = 1…T. The temporal aspect of the source strength is described by a stylized version on a TMP wave form Vm(t). Two examples of these wave forms are shown in Fig. 15–3. These are generated as the product of a number of S-shaped curves, known as the logistic functions.22 Among the parameters involved in the specific variant of the wave forms, one is used for setting the local EDL strength at any node n, and two are used to specify the timing of local depolarization and repolarization, δn and ρn, respectively. The interval between these markers is the activation recovery interval (ARI), denoted here as αn = ρn – δn. This interval reflects the absolute refractory period of the tissue.23

The transfer between sources and resulting potentials is described by a single, precomputed matrix A, with elements Al,n, l = 1…L; n = 1…N, with L being the number of field points of interest. The potentials Φ at the field points are computed from the matrix multiplication Φ = AS.

Upon installing the ECGSIM software (from http://www.ecgsim.org), a window comes into view on which four sections are marked, which will be referred to as the "panes" of the window (Fig. 15–4). On the two panes on the left, the distribution over Sh of the EDL parameters may be displayed, such as the timing of local depolarization as shown on the Heart-pane and, on the TMP-pane, the TMP wave form assigned to the any of the nodes selected on the Heart-pane.

The two panes on the right display the results of the simulated surface potentials. The ECGs-pane in Fig. 15–4 displays a temporal image of the cardiac electric activity—that of the standard 12-lead ECG signals resulting from the default source parameter settings. On the Thorax-pane, an image of the corresponding body surface potential map (BSPM) is displayed, a snapshot taken at the time instant marked by the yellow bar drawn on the 12-lead signals shown on the ECGs-pane. This snapshot can be interpreted as a single frame of a movie animating the full spatiotemporal nature of the body surface potentials.

The ECGSIM software enables one to specify, or modify interactively, the timing of depolarization, dep(n) = δn, and repolarization, rep(n) = ρn of the TMPs at nodes n (n = 1..N), where N = 257 is the number of nodes at Sh. The difference dur(n) = αn = rep(n) – dep(n) is the ARI taken as a measure of the local action potential duration. In addition, a value str(n) (0 ≤ str(n) ≤ 100%), scaling the local magnitude of the TMP, can be set for each node. The effect of any such changes on the surface potentials (right panes) is shown instantaneously. An option is provided for viewing the animation (movie) of the sequence of BSPMs.

The potential field on Sh as generated by the EDL source may be displayed on the Heart-pane, the corresponding electrogram on the TMP-pane.

The interactive setting of any of the source parameters is mouse-controlled. The images desired to be displayed on the four panes may be selected from a toolbar, supported by pull-down menus. The two basic geometries shown on the upper panes may be rotated freely in space, thus providing different views of the total 3D aspects of the images. The boundaries of the panes may be shifted in order to increase the size of any pane of interest.

The ECGSIM package includes a full manual, specifying all of its options, as well as a brief introduction to its basic use. Specific options have been selected for creating the various images shown in the examples presented in the following sections.

In this section, we present several examples of how ECGSIM is able to provide a view on the link between electrophysiologic changes in the ventricles and the resulting changes in the body surface potentials. As an essential preliminary, we first describe the potentials resulting from the default parameter settings used to simulate the normal ECG. These potentials serve as a reference against which the effect of any implemented changes of the default parameters may be observed.

The Normal ECG

The current version of ECGSIM deals with the simulation of the potential field outside the heart generated by the electric activity inside the ventricular myocardium. The potentials shown on the ECGs-pane of Fig. 15–4 depict the 12-lead ECG of a healthy, male subject. The Heart-pane presents an anterior view of the heart in its natural orientation as observed by magnetic resonance imaging. The color-coded function displayed is the timing of depolarization, dep(n), on the surface Sh. The values of the factors scaling the TMP magnitude were given a (uniform) unit value. A slightly different view of the same data, exposing some parts of the septum and the endocardium, is shown in Fig. 15–5A. The timing of the local repolarization, rep(n), used in the simulation is shown in Fig. 15–5B.

The realism of the potentials as based on these parameter settings can be judged from Fig. 15–6. In Fig. 15–6A, the simulated 12-lead ECG traces are shown in red, as on the ECGs-pane of Fig. 15–4. In addition, traces in blue are included, which represent the ECGs measured on the healthy subject studied. In Fig. 15–6B, another image of the cardiac electric activity is presented: the vectorcardiogram. Both panels are copied from the ECGs-pane after selecting the desired type of display.

The close correspondence between the measured data and those based on the data simulated by means of the EDL model (see Fig. 15–6) is a necessary, but not sufficient, indication of the general validity of the EDL in this particular application. It depends more critically on the realism of the major default parameters used—those setting the timing of local depolarization and repolarization. Their values, shown in Fig. 15–5, were obtained by means of dedicated inverse procedures,13,24 the most recent upgraded version of which is described and evaluated in van Dam et al.25

The inversely computed depolarization sequence agrees qualitatively with the one observed in invasive procedures.26 For the repolarization sequence, no such data are available. However, subsequent use of the EDL, examples of which are shown in the sequel, has fully corroborated the effectiveness of the EDL in modeling for the signal components of the ECG during the ST-T interval.

As interesting as the close correspondence between the measured and the simulated data may be, the main significance of the interactive simulation tool lies in the opportunity that it provides for studying the effect of local changes in its default parameter settings as observed on the body surface potentials, as well as those on the surface Sh. All of the different parameter types can be varied interactively at a single node or in a region around the selected node, having a selectable size. The region affected may be restricted to the surface at which the node is situated (eg, the epicardium) or assigned to extend transmurally. In a basic variant, all parameters of a certain type [eg, the dep(n) values] may be globally (ie, uniformly) shifted in time or scaled relative to their mean value.

A unique feature of the simulation is that it enables the study of the mean value over the body surface of the potential field generated by the cardiac electric activity. As is demonstrated in a later example, this is highly relevant in the understanding of the nature of the ST-T changes in the ECG observed during ischemia.

Potential Field at Sh; Electrograms

As mentioned previously, next to simulating body surface potentials, ECGSIM provides images of the potential fields generated on Sh, as well as their temporal representation in the form of electrograms.

Although the magnitude of the EDL is driven by the local TMPs (expressed in the unit V), its true nature is that of an electric current dipole source density (unit: A/m), feeding electric current into the tissues exterior to the ventricles. The potential field generated in the exterior medium close to Sh is distinct from that of the field of the local TMPs. A demonstration of this is shown in Fig. 15–7. The magnitude of the voltages shown in Fig. 15–7A is in agreement with those observed in electrophysiologic measurements. The timing of the fast upstrokes of the local TMP coincides with the fastest part in the down stroke of the local electrogram, as is demonstrated in Fig. 15–8. For a node at a local minimum in the timing of depolarization (wave front expanding from the node), the local electrogram has a characteristic rS morphology (Fig. 15–8A); for nodes at a local maximum in the timing of depolarization (the wave front closing in around the node), the morphology is of the Rs type (Fig. 15–8B). For intermediate situations, the observed (|S|–R)/(|S|+R) ratio depends on the local curvature of the local wave front,27 in which R and |S| denote the extreme values of the R and S wavelets.

Basic Statistics of the Timing Parameters

One way of describing the genesis of the QRST wave forms is to attribute the sources to the dispersion of the timing of local depolarization and repolarization. Dispersion is a general term used for describing any inequality of the values of a set of parameters. Whatever the measure used for quantifying the dispersion, if the dispersion of the parameters specifying the wave forms of all TMPs were to be zero, a completely flat baseline in all ECG leads would be the result.

Crude, statistical measures for quantifying dispersion of any set of parameters are the standard deviation (SD) and their range (ie, the interval between their minimum and maximum values). Both measures are of interest when studying the way in which global changes in the TMPs affect the ECG wave forms. In Fig.15–9, a pop-up menu of ECGSIM is shown documenting these basic statistics for the default timing parameters (see Fig. 15–6). The sliders may be used to interactively change these global statistics and observe the effect on the body surface potentials (Thorax-pane and ECGs-pane). For the understanding of the origin of the morphology of the individual lead signals, the full distributions of the parameter values are required, such as the one shown in Fig. 15–5. Two examples of the effect of such global changes of the basic statistics are presented in the next paragraph.

In the first example (Fig. 15–10), the global dispersion of the apd values was reduced to zero, forcing their values over Sh to be uniform and, hence, the dispersion measures of dep and rep to be the same. The simulated T waves (red traces) in most of the 12-lead signals now show up with a polarity that is the reverse of the mean polarity of the simulated QRS complexes. These so-called nonconcomitant polarities are at odds with the ones observed on the measures data (blue traces), demonstrating that in reality the dispersion of apd values of the TMP is nonzero. The second example (Fig. 15–11) demonstrates the effect of increasing the dispersion of the timing of repolarization rep(n), while keeping its mean value and its pattern constant. Note the resulting increase of the magnitudes of the T waves. This effect is seen most clearly in the dominant T wave.28

The T Wave

As with the QRS complexes, the genesis of the T wave is related to the spatial distribution of the TMPs. In contrast to those during the depolarization phase, the sources are of a much smaller strength and located throughout the myocardium rather than restricted to narrow, clearly defined wave fronts and active over a much longer period (eg, 100 ms for depolarization and 350 ms during normal repolarization). In healthy subjects, throughout the ST-T segment, the spatial pattern of the potential field generated over the thorax is much more sober and much more stable over time. A snapshot of the potential field with reference to Wilson's central terminal (WCT), measured over the thorax at t = 293 ms after onset QRS is presented in Fig. 15–12. It demonstrates that in healthy subjects, most of the T waves in the standard 12-lead ECG are positive but, equally important, that vast areas are negative with respect to WCT. The pattern shown remains very stable over a period of more than 100 ms around the timing of apex T at t = 293 ms. This highly significant fact is illustrated in Fig. 15–13.

The dominant aspects of the normal BSPM pattern during the T wave are consistent with the distribution of the timing of repolarization found from the inverse procedure (see Fig. 15–5B). Following the complete depolarization of all myocytes, those that have depolarized early have progressed more toward their (negative) resting potential (repolarized) than those that depolarized later.27 As a consequence, there is a consistent intracellular gradient of the intracellular potential directed from the posterior basal part to the more anterior, apical part. The return current generated in the extracellular medium, demanded by the conservation of charge, sets up the pattern dominated by the local potential maximum commonly observed around the electrode sensing lead V3 and the minimum near the right shoulder.

Besides this dominant factor, intracellular transmural gradients in the intracellular TMP values continuously set up transmural current sources directed from regions that have repolarized first to those repolarizing later. The dominant geometry of the left ventricle, a thick wall ellipsoidal-like structure with opposing electric forces in anterior and posterior wall segments, tends to cancel such transmural effects.

During repolarization, active electric sources are continuously present throughout the myocardium, extending over distances that are easily more than 8 cm. In view of this, the origin of the T wave can only be studied in a full-scale model of the ventricles.

In our opinion, any cause of T wave abnormality can only be fully understood against the background of a model of the T wave genesis in healthy subjects. The EDL model used in ECGSIM is such a model. Both the temporal (see Fig. 15–6) and the spatial aspects (not shown in this chapter) are replicated in the simulated data.

Examples of the use of the EDL model in the appreciation of basic notions of the genesis of the T wave are those illustrated in Figs. 15–10 and 15–11. The example presented in Fig. 15–11 indicates that the timing of the extremes in the T waves (apex-T magnitudes) reflects the dispersion of the timing of repolarization. If the dispersion were zero, no T waves would be visible on the ECG. The timing of the extremes reflects the mean value of the inflection points in the down slopes of the TMPs of the myocytes. A biophysical explanation of this property is described in van Oosterom.28,29

The examples shown in Figs. 15–10 and 15–11 relate to global changes in the timing of repolarization. The effect of local TMP changes is demonstrated in a number of the following subsections.

Changing the TMP Parameters Locally

As mentioned before, all three major parameter types, dep(n), rep(n), and str(n), specifying the TMP(n) acting as the local strength of the EDL at node n can be varied interactively, either at any single node or in a region with a selectable size around it. In the example shown in Fig. 15–8A dep(n) = 31 ms, rep(n) = 265 ms, and str(n) = 100%. The region affected may be restricted to the surface on which the node is situated (eg, the epicardium) or be assigned to extend transmurally. In addition, an option is included in ECGSIM referred to as "focus" in the pull-down menu that pops up from the item "membrane" on the menu bar. By selecting this option, an activation sequence is computed throughout the myocardium according to propagation at a uniform speed (Huygens principle). The resulting activation sequence may be studied as such or merged with a previously existing one. The merging is carried out based on the "first come first served principle" (ie, the smaller of the two activation times determined at the nodes is used in the computation of the potentials). Two examples of the effect of local changes in the timing parameters are presented first. Next, the effect of varying the scaling factor of the TMPs, str(n), is shown in an application of the modeling of ECG changes during periods of acute ischemia.

The first example (Fig. 15–14) demonstrates the use of the "focus" option in simulating the wave forms in cases of the Wolff-Parkinson-White syndrome. In such cases, the depolarization sequence results from the fusion of an early activation along an anomalous pathway linking the atrial and ventricular myocardium and the normal activation initiated somewhat later via the bundle branches. The simulation first uses the "statistics" option (see Fig. 15–9) for delaying the normal, default activation sequence by 50 ms (using the mean slider for the dep values). Next, the result is merged with an activation initiated at the location marked by the heavy dot shown on Fig. 15–14A. The propagation velocity starting from this "focus" at t = 0 was set at 0.8 m/s. Note the characteristic fast down slope of the QRS complexes.

The second example (Fig. 15–15) illustrates the effect of a local delay in the timing of repolarization. The default settings of rep(n) on Sh, resulting in the close correspondence between measured and simulated data (see Fig. 15–6), were reduced on a segment of the epicardium of the right ventricle around the heavy dot shown in Fig. 15–15A. The reduction was set at 20 ms at the center of the region, tapering off linearly to zero at the edge. The resulting simulated QRST wave forms of the standard 12-lead ECG are shown (in red) on the lower panel, and the measured reference signals are shown in blue. The locations of the six anterior electrodes of leads V1 to V6 are included in the display, visualized by using one of the options of the Heart-pane's menu bar. The electrode most proximal to the region of advanced timing of repolarization is the sensing electrode of lead V2 (WCT being the reference). Correspondingly, the effect of this advanced repolarization timing can be observed most clearly on lead V2: an increase of the apex-T value. Conversely, a local delay in the epicardial timing of this region gives rise to a reduced apex-T value (not shown here). By using ECGSIM, it can be easily demonstrated that a similarly advanced or delayed repolarization on the posteroinferior epicardium of the left ventricle having equal size gives rise to far smaller changes in the magnitudes of leads V1 to V6, with opposite polarity. The smaller magnitude reflects the larger distance between the affected region and the sensing electrodes.

The final example of the effect of changing the TMP parameters treats the topic of ECG changes during localized, acute ischemia. During such periods, the electric activity of the myocytes in the ischemic zone is abnormal; the magnitude of the TMP is smaller, the action potential duration (APD) is shorter, and the velocity of propagation in the ischemic zone is smaller than all of these factors compared with the nonischemic zone.30,31 The expression of these effects on the ECG depends on the location and extent of the ischemic region. In the current version of ECGSIM, the direct modeling of ischemia is restricted to the most prominent of these effects—the reduction of the magnitude of the TMPs in the ischemic zone. This is effected by reducing the local values of the scaling factors str(n) by means of the vertical slider in the TMP-pane (see Fig. 15–4). In this way, the resting potentials are set at smaller values (less negative values), as are the potentials following the upstroke (less positive values). The other two factors can be implemented by making the appropriate changes in the timing within the ischemic zone as well as in the surrounding nonischemic zone. This demands accurate information on how the timing might be affected, information that may not always be available. These two factors are indeed less prominently represented on the ECG.32

In the example shown in Fig. 15–16, an epicardial ischemic zone (shaded in Fig. 15–16A) has been modeled in this manner on the lateral free wall of the left ventricle. The value of str(n) at the center of the ischemic region was set at 80%; toward its edge, it increased linearly to the default normal setting of 100%. Figure 15–16A shows (in red) the simulated 12-lead ECG. The characteristic ST shifts observed during ischemia are brought out clearly through the comparison with normal (measured) reference data shown in blue. A BSPM at the middle of the ST-T segment (yellow time bar) is shown in Fig. 15–16B. Note that the ST-segment elevation is most pronounced in leads V5 and V6. The so-called reciprocal negativity (ST-segment depression above leads V1 and V2) can be seen to be poorly sampled by these leads, the local extreme in this case being located well above the electrodes sensing V1 and V2. The direction of the shifts (elevation/depression) is difficult to understand without taking into account the volume conduction effects in the passive medium surrounding the heart. Moreover, the presence of the required high-pass filtering and the subsequent baseline definition tends to confuse the issue. This topic is addressed in the next subsection.

The ST-T changes illustrated here are the consequence of a nontransmural, epicardial ischemic zone. For transmural situations, the magnitudes tend to be smaller.

Direct Current Recordings; ST-T Changes

The recording of the ECG signals involves the measurement of electric potential differences generated at different locations on the body surface. Such bioelectric potentials commonly observed by means of electrodes placed on the body surface are always contaminated by contact potentials at the electrode-tissue interface. The magnitudes of these potentials are much larger than those of the ECG, are unknown, and may change slowly over time—the so-called baseline wander or drift. This problem is treated by including a high-pass filter in the first stage of the recording system. The resulting signal is referred to as an alternating current (AC) recording or high-pass filtering. This produces an output signal, which, when computed over a long time, has a zero mean value; the direct current (DC) component of the signal of a single beat is reduced to zero. If rapid perturbations of the contact potential occur, the baseline of the signal (ie, the time markers at which observed signals should be assigned a zero value) must be specified on a beat-to-beat basis. Even if the dynamic range of the input stage encompasses the full range of the sensor potentials (allowing a DC recording despite the presence of the contact potentials, a common feature in the most recent ECG recorders), the subsequent shift to a zero level remains to be defined.

The treatment of the problem is generally referred to as baseline correction. However, this is a somewhat misleading term because it assumes that the signal level that should be specified as zero is self-evident, which is not the case.

The problem of baseline definition is most pressing for recordings taken during periods of acute ischemia. As discussed in the previous subsection, during ischemia, the TMPs of the myocytes within the ischemic region differ from those in the nonischemic region; the resting potential decreases (tends to zero), and the upstroke is reduced. The size of these changes varies during the various stages of ischemia.33 The intracellular coupling between myocytes in the ischemic region (I) and myocytes in the nonischemic region (NI) and the differences in the TMPs of the myocytes within these regions result in an electric current flow. During the time interval between the end of the T wave and the onset of the next QRS complex, the differences in the resting potentials in these regions result in a current flow in the intracellular myocardium directed from region I to region NI. In the extracellular domain, the direction of the current flow is in the opposite direction because charge is conserved. In the extracellular medium, this can be expressed by an equivalent current sink in the ischemic region, which lowers the nearby extracellular potentials.33 During the activation of the tissue surrounding the ischemic zone, the potential difference between the regions is smaller, as is the loading effect.

The basic signals simulated by ECGSIM are (obviously) free of any of the problems created at the electrode-tissue interface. This permits the simulation of the true potential differences on the body surface. An illustration of this is shown in Fig. 15–17. The measured reference ECG (nonischemic, shown in blue) demanded a definition of the zero baseline. This was defined at the onset of the QRS and the end of the T wave, in fact at the onset of the next beat. In this manner, any influence of ongoing atrial electric activity (repolarization of the atria) is minimized.34 The same procedure was applied to the (same) measured signals and the simulated ones shown in Fig. 15–16.

On the basis of the theory of the current flow between the ischemic and the nonischemic regions presented earlier, one would expect the potentials near leads V5 and V6 at the end of the T wave to be negative, whereas the potentials would be positive for the electrodes sensing V1 and V2. This is indeed observed in Fig. 15–17. The effect of the baseline correction applied to the ischemic signals shown in Fig. 15–16 is that the nonzero values at onset QRS and following the T wave show up in the baseline "corrected" signals as ST shifts having reversed polarity. This interpretation follows directly from the electrophysiologic studies by Janse et al.33

As demonstrated in this chapter, the imaging of the basic spatiotemporal aspects of the genesis of the cardiac electric signals provides a powerful addition to the type of explanations commonly found in standard readers on the theory of the ECG.

The examples of the use of ECGSIM included in this chapter are by no means exhaustive. Topics left out to economize on space include the imaging of the properties of the transfer matrix that links sources and resulting potentials35 and the animation of the spatiotemporal nature of the direction and magnitude of the dipole as used in vectorcardiography, linked to the geometry of ventricles and thorax.

In recent years, ECGSIM has attained world-wide application in different educational courses. Its major unique feature is the use of the EDL model, which is a source description that is far superior to that of the single current dipole. It has a direct link with the classic UDL model of cardiac activation and constitutes a source description of the electric sources during repolarization.

Next to its application in education, various papers have been published in which ECGSIM is applied as a research tool.36-40 The ones listed have been based on version 1.3, which was restricted to the electric activity of the ventricles. In November 2010 an upgraded version (2.0) was released in which the electric activity of the atria was included.