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Cardiovascular Research 2005 67(2):256-262; doi:10.1016/j.cardiores.2005.04.010
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Copyright © 2005, European Society of Cardiology

The U wave in the electrocardiogram: A solution for a 100-year-old riddle

Henk J. Ritsema van Eck*, Jan A. Kors and Gerard van Herpen

Department of Medical Informatics, Erasmus University Medical Center, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands

* Corresponding author. Tel.: +31 10 4088116; fax: +31 10 4089447. Email address: h.ritsemavaneck{at}erasmusmc.nl

Received 27 December 2004; revised 1 April 2005; accepted 7 April 2005


   Abstract
Top
 Abstract
1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Conclusion
 References
 
Objective: In the electrocardiogram (ECG) the U wave follows the T, which is considered to reflect the repolarization of the cardiac ventricles. Despite the U wave's well-known clinical relevance, a satisfactory explanation of its origin is still outstanding. We have undertaken to explain the formation of the U wave by means of a simple digital model of the left ventricle.

Methods: The model employs a multi-layered segment of the myocardium. To each layer an action potential (AP) is assigned with shape and duration according to published data. The potential differences between the APs produce time-varying electrical sources. Each source contributes to the potentials in an arbitrary point P of the body. The strength of this contribution is determined by a specific coefficient, the "lead vector", linking P to the source. The ECG recorded at P is calculated as the sum of all potential contributions.

Results: The repolarization waves constructed in this way reproduce the natural aspects of a T wave followed by a U wave. The creation of a U wave is conditional on small voltage differences between the tail ends of the APs. No fundamental demarcation exists between U wave and preceding T wave. The morphology of the T–U wave is dependent on the geometrical position of P with respect to the myocardium.

Conclusion: T and U form a continuum. Together they are the resultant of one and the same process of repolarization of the ventricular myocardium. This has implications for the measurement of QT duration and for safety testing of drug-induced QT prolongation.

KEYWORDS ECG; Computer modeling; Membrane potential; Repolarization

This article is referred to in the Editorial by Conrath and Opthof (pages 184–186) in this issue.


   1. Introduction
Top
 Abstract
 1. Introduction
2. Methods
 3. Results
 4. Discussion
 5. Conclusion
 References
 
In the electrocardiogram (ECG) the U wave is the deflection that follows the waves of depolarization (QRS) and repolarization (T) of the heart chambers. Its polarity is normally the same as that of the T wave. The first description and the name were given by Einthoven [1], shortly after his first string-galvanometer recording of the human ECG a century ago. A few years later Einthoven remarked that "the significance of it and the reason for its inconstancy are for the present not known with surety" [2].

Today a satisfactory explanation of its origin is still outstanding despite the U wave's well-known clinical relevance in conditions like cooling, electrolyte disturbances, and drug-induced or congenital long-QT syndromes. Three hypotheses are being entertained about the underlying mechanism. They are based on: (1) the tardy repolarization of the subendocardial Purkinje fibres [3]; (2) the prolonged repolarization reported to exist in the cells of the mid-myocardium ("M cells") [4]; and (3) after-potentials [5], possibly caused by mechanical forces in the ventricular wall [6]. However, none of these hypotheses has received general acceptance [7].

We present a simple digital model of the left ventricle that simulates the formation of the U wave on the basis of known electrophysiological processes responsible for the electrical sources in the myocardium, and of the physical laws, embodied in the lead vector concept, which link the potentials in or on the body to these sources. The model employs an anatomically stylized slice of the left ventricle. To explain the principles of the method recourse is had to a simplified "string" model, a single column of cells across the ventricular wall.


   2. Methods
Top
 Abstract
 1. Introduction
 2. Methods
3. Results
 4. Discussion
 5. Conclusion
 References
 
A slice of the left ventricular myocardium is mapped out in a hexagonal grid with an inter-knot distance of 1 mm. Each grid point can be thought of as the center of a small "volume" of myocardium or "cell". The boundaries of the myocardial slice are drawn in such a fashion that the wall contains 12 cell layers, 1 layer representing the endocardium, 10 layers the mid-myocardium, and 1 layer the epicardium. Each layer is an assembly of identical cells. The 12 layers thus fill a cross section of the ventricle with a wall thickness of approximately 1 cm (Fig. 1). The myocardial string consists of the same 12 cell layers but with only 1 cell per layer (Fig. 1, insert).


Figure 1
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  		Fig. 1 A slice of the left ventricular myocardium. The insert shows the string of 12 hexagonal cells as used in the string model. The AP90 durations are rendered by shades of grey, with the shortest in white at the epi- and endocardial surfaces and the longest in the mid-myocardium in black (figures in ms).

 
An action potential (AP) is assigned to each cell assembly. The shape of these APs is based on the functions proposed by Wohlfart [8]. The parameters controlling AP duration and terminal slope (phase 3) in these functions were varied in order to modify the shape of the AP.

Fig. 2 shows the APs as they were assigned to the endocardium, myocardium, and epicardium. The terminal slope is steep for the endocardium, less precipitous for the epicardium, and gentler still for the mid-myocardial layers.


Figure 2
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  		Fig. 2 Action potentials as assigned to endocardium, mid-myocardium and epicardium. The vertical marker at 350 ms coincides with AP90 of the endocardial layer. The AP90 of the epicardium is 342 ms but occurs at 364 ms owing to 22 ms start delay.

 
The AP durations, given at 90% repolarization (AP90), are 350 ms at the endocardium, and 342 ms at the epicardium. The mid-myocardium is assumed to contain a certain proportion of M cells with prolonged repolarization. In the first approximation we gave all 10 mid-myocardial layers M-cell characteristics. Their AP90 values range from 372 ms (subendocardial) over a maximum of 378 ms to 352 ms (subepicardial). These various figures are comparable to the AP durations reported by Drouin et al. [9] for human myocardial APs. The AP90 is a cut-off point that excludes from consideration the tail end of the repolarization, precisely that part which is in temporal relation to the U wave. In the literature there is evidence that phase 3 of the AP does not end abruptly but gently tapers down to 0 in a more or less asymptotic fashion [10,11], providing the tailed APs postulated in our model.

The timing of the APs follows a simulated excitation sequence. The excitation starts at the endocardial layer of the mid-septum where the left bundle inserts, and spreads from knot point to knot point through the mid-myocardium and the epicardium in steps of 2 ms (Fig. 3a). Conduction between neighboring endocardial cells, however, occurs 6 times as fast, in steps of 0.33 ms, to account for their activation by the fast Purkinje network. The transmural excitation in this manner takes approximately 22 ms, which is in accordance with published normal activation times of the free left ventricular wall [12] and also corresponds with a myocardial conduction velocity of 40–60 cm/s. The endocardial excitation, spreading at a velocity of about 300 cm/s, reaches the outermost endocardial cells in 28 ms. Total activation time of the slice is 46 ms.


Figure 3
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  		Fig. 3 (a) Excitation sequence of the myocardial slice. Isochrones are 2 ms apart. Start is at the arrows. (b) Repolarization times, defined as the summation of activation time and AP90, of the cells in the myocardial slice. Isochrones are 10 ms apart.

 
Repolarization times, defined as activation time plus AP90, of the cells in the myocardial slice are shown in Fig. 3b. It can been seen that endocardial cells repolarize before epicardial cells, with a bulge in repolarization times in the mid-myocardium.

The model premises that a current dipole is generated between each pair of adjacent myocardial cells. The magnitude of this dipole is given by the instantaneous potential difference between their APs [13], as they are given in Fig. 2. Its direction is given by the axis connecting the centers of the 2 cells. For each cell the sources it generates, with respect to all its six neighboring cells, are vectorially summed and the resultant vector is assigned to the grid point representing the cell. In this way the dipole source vectors D1,...,DN are obtained (N = 1328, the total number of cells in the model).

A potential will be generated at a given point P in or on the body by each dipole source D. This potential is a function of the magnitude of the dipole vector D and the so-called lead vector. This lead vector L of P is determined by the geometrical position of P relative to the location of D and by the electrical properties of the interposed tissues [14–16]. The potential at point P is then given by:


Formula 1

where {alpha} is the angle between D and L. Each single dipole Di has its own lead vector Li and will, therefore, make a differently weighted contribution to VP. The closer P is to the source Di, the larger Li becomes; in addition, VP is maximal for {alpha} = 0, but zero for lead vectors perpendicular to the dipole axis.

Considering that the potential field generated by the different sources is linear, by superposition the potential VP at point P is obtained as the sum of the weighted contributions of all N source vectors. Since the dipole sources are time-varying and consequently also VP, we write:


Formula 2

with N the number of cells in the model. VP(t) is nothing else than the ECG recorded in a lead between the exploratory electrode at point P and an arbitrary zero.

For the infinitesimal case, Eq. (2) assumes the classical, general form


Formula 3

in which


Formula

is the transmembrane potential field and L the lead field pertaining to point P, integrated over the heart volume.


   3. Results
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
4. Discussion
 5. Conclusion
 References
 
3.1. The string model
In the string model each dipole is determined by only 2 neighboring cells (Fig. 1, insert). Then, all dipoles are directed along the axis of the cell string. Let us first assume that the lead vectors Li (i = 1,...,12) are of equal strength, say C, and that P lies in the axis of the cell column (i.e., cos {alpha} = 1). Eq. (2) then simplifies to


Formula 4

and VP follows the pattern of Fig. 4a, which electrocardiographically is a biphasic T wave.


Figure 4
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  		Fig. 4 Repolarization patterns as computed for the string model in observation point P, in a homogeneous infinite medium, with P in the axis of the cell column. (a) Equal lead strengths for all layers. (b–f) Differential lead strengths. The distance of P to the epicardium is varied from 8 cm (b) to 4 cm (f) in 1 cm steps. The vertical marker is at 350 ms, as in Fig. 2.

 
However, the lead vectors are not of equal strength, since they are dependent on the location of the sources in the myocardium which are at different distances from the exploratory point P. Indeed, in real life the thickness of the ventricular wall is not negligible in relation to the distance between the epicardium and the electrode locations on the body surface, in particular those of the chest leads. In a homogeneous infinite conducting medium the lead strength is inversely proportional to the square of the distance of the source to the measuring point. The effect of varying the distance of observation point P to the epicardium on the appearance of the U wave, applying Eq. (2), is illustrated in Fig. 4b to f. At 8 cm (Fig. 4b) the lead strengths increase exponentially from 1 to 1.26 from endocardium to epicardium. The terminal part of the repolarization turns out to be almost isoelectric. At smaller distances this terminal part is seen to rise. At 6 cm (lead strengths ranging from 1 to 1.35), there is an unmistakable U wave (Fig. 4d). At 4 cm (lead strengths from 1 to 1.53) the prominent U wave of Fig. 4f arises. It should be noted that moving P out of the axis will increase {alpha} and decrease its cosine and will lead to a reduction of the lead strength differences and concomitant shrinking of the U wave.

3.2. The slice model
The dipole source vector Di in a gridpoint is now determined by the 6 directed potential differences with the surrounding cells. In contrast to the string model the directions of the instantaneous source dipole vectors vary, as do the directions of the lead vectors linking P to the cell centers. Fig. 5 illustrates the effect of not only varying distance, as was done in the string model, but also orientation of the observation point P on the appearance of the T and U wave. P is moved around a mid-cavitary orientation point, which is in the long axis of the ventricular slice. Anatomically this is the axis of symmetry of the ventricle, physiologically it is not because of the asymmetric electrical excitation of the ventricular wall. The rotation is performed in steps of 30°, from 120° to –30°, in analogy to the standard precordial leads. For each step the distance of P to the epicardium is kept the same for all directions. The direction at 90° is perpendicular to the ventricular axis. As said before, the signals may be read as ECGs with an exploratory electrode P and the opposing electrode at zero potential, at infinity. It can be seen that classical U waves are created in the directions at 90° and 60°. More to the left at 30° and 0° the terminal hump in the signal ceases to be clearly demarcated from the T wave but merges into it. Finally at –30° T and U coalesce into a single wave that conventionally would be called T, the last part of which, however, coincides with the U waves in the other leads and also concurs with the terminal T negativity which is observed at 120°. This suggests that this terminal part of the T is the equivalent of a U wave (or, for that matter, a U wave is the equivalent of the terminal part of an extended T). The overall amplitudes of the signals decrease with increasing distance of P from the epicardium, as they should. The U is largest at 30°, about the direction that a precordial lead V3 might have. Also, the amplitude ratio between T and U is highest at short distance, where the lead strength differences are most pronounced, and diminishes the farther away P is. In the slice model each of the 1328 cells has its own lead vector for each of the possible positions of the exploratory point P, by which its contribution to the potential in P is weighted. This much greater complexity of the slice model, as compared to the string model, does not lead to different results: U waves are generated in much the same way. The T–U patterns vary with orientation and distance of P analogous to what is seen in reality in the precordial leads.


Figure 5
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  		Fig. 5 Repolarization patterns as computed for the slice model. The observation point is moved around a mid-cavitary point in steps of 30°. For each direction the distance of observation point P to the epicardium is varied from 4 to 8 cm. The time scales are given in ms after start of the excitation process. Scale of the amplitude is arbitrary but the same for all figures.

 

   4. Discussion
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
5. Conclusion
 References
 
4.1. Origin of the U wave
For an explanation of the U wave Einthoven did not go any further than "a potential difference developed even during the diastole" [2] and not much more was added during the following half century. The T wave was interpreted as the direct expression of the repolarization process. The U wave was regarded as an independent, though possibly related phenomenon that conveyed some diagnostic message when large, deformed, or encroaching upon the T wave.

Hoffman and Cranefield [3] conjectured that the Purkinje system is the origin of the U wave. Purkinje APs have a duration that is prolonged beyond that of the endocardial and epicardial cell layers [17]. Objections against this theory have been that the inconsiderable mass of the Purkinje network or its partial and patchy endocardial distribution would not produce detectable signals on the body surface [7]. Also, amphibia are not in the possession of Purkinje fibers but do show U waves [18].

Antzelevitch and Sicouri [4] reported that cells in the mid-myocardium (M cells) have APs that last well beyond the end of the T wave. It was, therefore, very attractive to credit this terminal activity with a function in the formation of the U wave. In 1992, Nesterenko and Antzelevitch [19] concluded on the basis of experiments with a linear cable model of cells (Luo–Rudy model) that the U wave may indeed be generated, at least in part, by the delayed repolarization of M cells. However, in later work from the same group the model did not produce the desired U waves [20].

Surawicz advanced a mechano-electrical hypothesis of U-wave genesis [6]. In this proposition the effect of mechanical stretch of the myocardial cells on the transmembrane potential is to produce an after-potential, which coincides, and might be causally connected, with the occurrence of the U wave. Earlier, Franz et al. [21] had recorded epicardial APs on in-situ beating canine hearts and had found that marked after-potentials developed under increasing volume load. Di Bernardo and Murray [5] also introduce after-potentials, of substantial size, which they assign to the endocardial and epicardial boundaries of their model to produce U waves. Such huge after-potentials as they bring into play, however, are unrealistic as they would be associated with the occurrence of serious ventricular arrhythmias, the incidence of which in the normal population is entirely negligible in comparison to the occurrence of U waves.

4.2. Lead vector differentials
Why is it that none of the other proposed models is capable of producing plausible U waves? For an explanation we return to the simplicity of the string model. With equal lead vectors (Eq. (4)) at any time instant the voltage at P results from the sum of all dipole magnitudes |D1|,...,|D12|, times a constant. These magnitudes are determined, with a certain common proportionality factor, by the potential differences between each cell and its neighbors. Thus, VP follows from (AP1–AP2)+...+(APi–1–APi+APi–APi+1)...+(AP11–AP12), which simply reduces to AP1–AP12. Consequently, without lead differentials a body surface potential will only show the differences between endocardial and epicardial potentials. This is what occurs in the models of Wohlfart [8], Nesterenko [19], and Di Bernardo [5]. However, the repolarization part of a normal action potential is a sigmoidally shaped curve. Two such functions will either not intersect or have only 1 intersection. Their difference values will thus be either positive or negative, or else biphasic (+/– or –/+), but cannot have 2 maxima with equal sign. Unless the endo- and epicardial repolarization curves are of very unusual appearance their differences, therefore, will not result in the double-humped deflection that ECG tradition labels as a separate T wave and U wave. If, on the other hand, lead vector differences are applied, the divergence in AP durations of the mid-myocardial layers is not nullified and a U wave appears. The U wave thanks its existence to potential differences occurring after AP90. Such potential differences are a necessary, not a sufficient condition: they will produce a positive or negative prolongation of the T wave, but without lead vector differentials no U wave will appear. The larger the lead vector differentials, the more conspicuous the U waves, such as in the central chest leads, where the wall thickness is far from negligible in proportion to the electrode distance. In certain leads of an ECG the U wave might not be observed as such in the repolarization part of the QRS-T complex. In such complexes the terminal part might be isoelectric due to perpendicular projection of the U vector on the lead axis, or the U wave is incorporated in the T wave, or it may be obscured by the following P wave.

The effect of lead vector differentials can further be illustrated by Fig. 3b, which shows a bulge in repolarization times centrally in the myocardial wall, with the endocardial cells repolarizing before the epicardial cells. This is contrary to the commonly held view that the course of repolarization should be inward, opposite to depolarization, in order to produce concordant T waves. However, when lead vectors are taken into account, concordant T waves can be produced very well even if the epicardial repolarization is later than the endocardial one. As long as the outwardly directed dipoles of the inward repolarization movement, assisted by their lead vectors, are stronger than their opponents, we will have concordant T waves.

4.3. Limitations

(1) The APs used in the model were shaped according to literature data and varied only in a direction perpendicular to the myocardial wall. Regional variation was not taken into account. Notwithstanding all the painstaking work by various investigators the information about what is going on electrically in the human heart is fragmentary and bound to remain incomplete due to the self-evident restrictions of experiments in man. Drouin, to our knowledge, is the only one to provide data on APs in human heart muscle, but only in wedge preparations [9]. Taggart et al. [12,22] studied human hearts during by-pass surgery and measured transmurally activation recovery intervals. No systematic differences throughout the left ventricular wall are reported, although, based on their material, Conrath et al. [23] produce a graph where the actual repolarization times differ by approximately 20 ms on average. Other studies in intact hearts are on animals [24–26]. In all of them, APs are not measured directly but are estimated from the makeshift measurement of activation recovery intervals or effective refractory periods. The results, therefore, do not exclude differences in actual membrane potentials. Moreover, the terminal part of the repolarization process is systematically excluded, precisely the segment that is of interest for the U wave. At any rate, the creation of a U wave is conditional on the presence of small potential differences after the customary end of T. Whether these post-T potentials belong to what one wants to call the AP, or are regarded as after-potentials is not much more than a matter of semantics. The cardinal point is that they are an intrinsic part of the electrical processes that lead up to the next depolarization. In the experiments by Franz et al. [21] after-potentials were shown to depend on wall stress and wall stress, to a varying degree, is never absent in a normally functioning heart. It must be noted that the experiments by Taggart et al. were in patients on cardio-pulmonary by-pass, implying that their hearts were not mechanically loaded.
(2) In the model the septum is activated from the left bundle site, the right bundle contribution is neglected. More than that, the entire right ventricle is lacking in the model. It would not be difficult to implement one, but little is known about the shape of right-ventricular APs, let alone about how to assign them to the various cell assemblies.
(3) The ratio of the activation velocities of the Purkinje system to that between the myocardial cells is set at 6 and is kept constant throughout the slice. Variations of this ratio within reason were found not to produce essentially different results.
(4) We postulated the body as homogeneous and infinite. To take into account inhomogeneity and non-infinity would mean to pretentiously stretch the limits of a simple model. With greater computing effort the model can be expanded to an entire three-dimensional representation with more or less realistic estimates of tissue inhomogeneities and boundaries [27] and with P anywhere in space. A first simple three-dimensional model showed some variations in T- and U-wave configuration but not essentially different results.
(5) In the model the mid-myocardium consisted exclusively of M cells. When up to 7 of the 10 M-cell layers were replaced by layers with "conventional" APs, the results did not change essentially.


   5. Conclusion
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Conclusion
References
 
U waves are an integral component of ventricular repolarization and can be expected to occur in every ECG, perhaps modulated by wall stress. In our own material, through the use of a special measurement program [28], we found them present in every 12-lead ECG, in agreement with unpublished observations by Surawicz [6]. That they occur in most ECGs had already been noted by Lewis and Einthoven himself [2].

The measurement of QT duration has received increasing attention over the past decade. Recent requirements for drug safety testing [29,30] impose submission of data on possible drug-induced QT prolongation. Correct recognition of the end of the T wave, however, is often bedeviled by the presence of a U wave [5,20] (it even seemed to Surawicz that "the clinical significance of the U wave was limited to the occasional obfuscation of the end of T wave" [6]). And not only that: the differential lead vector model as presented here gives a different meaning to the definition of the end of the T wave. In our opinion T and U form a continuum without a sharp separation between the two. What is generally regarded as the end of T coincides more or less with the AP90 of endocardial repolarization. The repolarization of the myocardium in its totality is only completed at the end of the U wave. T and U together are the resultant of the same process, i.e., the total repolarization of the ventricular myocardium. This means that our ideas about QT duration and prolongation, whether drug-induced or congenital, must perhaps be viewed in a somewhat different perspective and that regulatory authorities should exert caution in imposing rules on drug testing based on measurement of QT duration.


   Notes
 
Time for primary review 14 days


   References
Top
 Abstract
 1. Introduction
 2. Methods
 3. Results
 4. Discussion
 5. Conclusion
 References
 

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C. E. Conrath and T. Opthof
The patient U wave
Cardiovasc Res, August 1, 2005; 67(2): 184 - 186.
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