Theoretical considerations on the electrocardiogram of ventricular hypertrophy

J. ELECTROCARDIOLOGY, 9 (2) 133-138

Theoretical Considerations on the Electrocardiogram of Ventricular Hypertrophy BY SABURO MASHIMA, M.D.

SUMMARY

however, myocardial alterations other than hypertrophy, as well as individual variations in the body build and surrounding tissues, obscure the genuine effect of hypertrophy. This is the major reason why a quantitative relationship b e t w e e n electrical and anatomical findings has not been clearly demonstrated. Yet, it is a common belief that the increased myocardial mass produces a larger QRS and consequently, the secondary changes of the recovery wave. Since ventricular hypertrophy is essentially a gradual process, a quantitative evaluation of the direct effect of hypertrophy is desirable for better understanding of the electrocardiographic findings and for the recognition of what is abnormal. This communication provides the concept of ideal hypertrophy for a quantitative approach to the problem. Expected results of the idealized model will be compared with measurements made in clinical cases with ventricular hypertrophy.

1) The electrical effect of v e n t r i e u l a r hyp e r t r o p h y is evaluated with an idealized model. P e r f e c t l y symmetrical hypertrophy is e x p e c t e d to enlarge the QRS c o m p l e x with a certain proportion of the amplitude and d u r a t i o n . I f the c o n d u c t i o n v e l o c i t y is u n a l t e r e d , t h e Q R S area will be increased proportionally to the m y o c a r d i a l mass. 2) B a s e d on the preservation of the ventricular gradient, the secondary T change is expressed as a function of the QRS and G vectors. A t h e o r e t i c a l l y i n t e r e s t i n g par a m e t e r , G / Q R S r a t i o , is d e f i n e d as a measure of the " v e n t r i c u l a r gradient density," which is i m p o r t a n t for the over-all r e c o v e r y pattern. This ratio is decreased in v e n t r i c u l a r hypertrophy and is closely related to the QRS-T angle. 3) F r o m the v i e w p o i n t o f the t h e o r y , clinical cases with left ventricular hypert r o p h y are e x a m i n e d . The t h e o r y describes t h e c a s e s w i t h u n c o m p l i c a t e d h y p e r t e n s i o n f a i r l y well, a l t h o u g h variat i o n s f r o m c a s e to c a s e are n o t s m a l l . Underlying a s s u m p t i o n s and causes of deviations in actual cases are discussed.

I D E A L H Y P E R T R O P H Y MODEL Ideal hypertrophy refers to a condition where the ventricular muscle increases its volume without any alterations in the activation sequence. The size of the ventricle is enlarged in a perfect proportion. This is a conceptual device for the evaluation of the effect of hypertrophy. Figure 1 illustrates an arbitrary muscle strip (A) and a symmetrically hypertrophied one (B). Figure 1, a and b are the QRS complex caused by the excitation of the corresponding strip. In ideal hypertrophy, ~ times increase in size causes ~ times increase in volume. The activation wave front is the same in configuration and is ~2 times larger in area. Assuming that the strength of the double layer is unaltered, the QRS voltage will be increased as ~2. If the conduction velocity is also unaltered, the QRS duration will be increased times normal, since the activation wave has to travel ~ times longer than normally. Hence, the QRS area will be ~3 times normal and is proportional to the ventricular volume (Fig. 1, b). The direction of the QRS vector is pre-

A number of studies have been performed on the electrocardiogram (ECG) of ventricular hypertrophy. 1-7 The increase in the voltage and duration of the QRS complex and the ST-T changes are known as the main electrical manifestations of ventricular hypertrophy. Usually,

From The Second Department of Internal Medicine, University of Tokyo, Tokyo, Japan. Reprint requests to: Saburo Mashima, M.D., The Second Department of Internal Medicine, University of Tokyo, Tokyo, Japan. 133

1 34

MASHIMA

p

A i

!(

i

QRS, T and G vectors. If the G vector is constant, the increase in the magnitude of the QRS vector from QRS~ to QRS2 and to QRSz causes changes in both magnitude and duration of the T vector from T1 to T2 and to T3. The direction of the T vector is related to the relative value of the G and QRS magnitude, that is, the G to QRS ratio is important for the determination of over-all direction of recovery. The ratio g = G/QRS

)!

B :l', Fig. 1: Ideal hypertrophy with perfect symmetry. If a normal muscle (A) produces the QRS complex of unit amplitude and duration (a), hypertrophied muscle (B) of ~ times normal size is associated with 2 timeslarger amplitude of the QRS. The QRS duration will be increased by a factor of ~ (b).

served because hypertrophy is symmetrical and the activation sequence is normal. There is a possibility that the thickening of fibers may increase the conduction velocity. The latter has been shown to be proportional to the square root of the fiber diameter, if other conditions remain the same. s However, the velocity of the activation front is not necessarily the same as that of the fiber conduction. 9 In actual cases, the fiber size is more or less inhomogeneous 1~ and the QRS duration is often prolonged because of the conduction abnormalities. For these reasons, the conduction velocity is simply assumed to be preserved in model hypertrophy. If the sequence of repolarization were the same as normal in hypertrophy, the T wave would be equally enlarged as the QRS complex. The resulting electrocardiogram (ECG) would be apparently normal in configuration. However, one of the common electrocardiographic findings is that the increased QRS area is accompanied by opposed T changes. Although the preservation of the ventricular gradient 11 (G) has not been rigorously proved, it is supported at least qualitatively by many clinical experiences. Hence, the constancy of the G vector is assumed here as an additional requirement for ideal hypertrophy. Then, the increase in the QRS magnitude causes the following secondary changes in the T vector. Figure 2 shows the vectorial relation of the

(1)

has the following meaning. The preservation of the G vector implies that the density of the ventricular g r a d i e n t is "diluted" in hypertrophied muscle. Since the QRS magnitude is proportional to the ventricular muscle mass in ideal hypertrophy, the ratio g serves as a measure of the G density or the ventricular gradient per unit volume of ventricular muscle. Defining the angle a between the QRS and G vectors, the magnitude of the T vector is obtained from Fig. 2 as t 2 = g2 _ 2gcos a + 1

(2)

where t = T/QRS. Ratios g and t are, so to speak, "standardized" values of the G and T magnitude with respect to the QRS magnitude. The direction of the T vector is indicated by the QRS-T angle O. cosO=

g cos a - 1 ~/g2_2g cos~+ 1

(3)

Equations (2) and (3) express the T vector as a function of the QRS and G vectors. The relation (3) of the QRS-T angle and g is illustrated in Fig. 3 for several values of angle ~ . In normal persons, the ratio g is usually over 1.5 and the QRS-T angle is largely determined by a, as indicated in the right half of Fig. 3, where curves are nearly horizontal. The enlargement of the QRS due to ventricular hypertrophy causes the reduction of the ratio g. and a leftward shift along one of the curves in Fig. 3. When g is less than 1.0, the principal determinant of the QRS-T angle is g instead of ~ , as indicated in the left half of Fig. 3.

QRS,

T~

T~

T,

QRS ~

QRS,

G

Fig. 2: Vectorial relation of the secondary T change due to the increase in the QRS magnitude with a constant G vector. J. ELECTROCARDIOLOGY, VOL. 9, NO. 2, 1976

VENTRICULAR HYPERTROPHY

135

QRS'T angle 180~

CLINICAL OBSERVATIONS Strictly, no clinical case has ideal hypertrophy. In particular, right ventricular hypertrophy is often associated with a drastic change in the QRS pattern, and the theory based on the normal activation is not applicable to this condition. But it may be of value for the assessment of a group of patients with a similar QRS pattern. In left ventricular hypertrophy, the proportion of the ventricular wall and the norreal activation pattern are relatively preserved except in special cases with asymmetrical hypertrophy, although minor abnormalities in the QRS pattern are often observed. In the literature, not many reports are available with measurements of both voltage and duration of the QRS on the same material. In this section, calculations will be made on the materials of our previous reports, 7,~2 where values of the maximal and mean QRS vectors as well as of the G vector are given. The study group consists of 60 normal persons, 84 hypertensive cases and 14 cases with aortic insufficiency (AI). Hypertensive cases are divided into two groups according to the absence (62 cases, HT~ group) or the presence (22 cases, HT2 group) of congestive heart failure or a history of failure. Cases with evidence of bundle branch block or ischemia of the local myocardium are excluded. Orthogonal ECGs and vectorcardiograms (VCGs) are recorded with Frank lead and the QRS and T area vectors are determined spatially. Table I shows the results of measurements in each group. Slight left axis deviation is observed in groups with left ventricular hypertrophy, especially in HT2 group. However, average figures show that the directional change in the QRS vector is not marked, although individual variations are considerable. One of the ways to compare the measurements with the idealized model is to examine the proportion of the amplitude and duration of the QRS complex. The latter is, however, not convenient for the accurate measurement. Instead, the mean QRS can be utilized for the comparison with the QRS amplitude. The hypertrophy index ~ mentioned in the previous section is calculated from the mean QRS vector and from the maximal QRS vector separately. The ratio of the mean QRS magnitude to the average of normal persons (30 ~ V sec) corresponds to ~ 3, according to the theory. The cubic root of this ratio is designated as ~mean of this case. Another ~ value (~max) is obtained by taking the square root of the ratio of the maximal QRS magnitude to the J. ELECTROCARDIOLOGY, VOL. 9, NO. 2, 1976

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Fig. 3: The relation (3) in the text of the QRS-T angle to the G/QRS ratio with several values of the QRS-G angle (~). average of normal persons (1.65 mV). Thus obtained two ~ values in each case are compared in Fig. 4. A proportional increase in the height and duration of the QRS should result in the plot on the 45 degree line. Numerical mean and ~ max values in each group of patients are listed in Table 1. Average figures indicate that in normal persons and in HT1 group, both ~ values are close together. In other groups, ~ mean exceeds ~ max, which means an unproportional increase in the QRS duration. Figure 4 also shows that the majority of cases in HT2 and AI groups are above the 45 degree line. The discrepancy is greatest in HT2 group, which is in accord with pathological observations that congestive heart failure is often associated with structural changes of the myocardium, lo The average magnitude of the G vector is smaller in the HT2 group but is not significantly different in other groups. The QRS-G angle is 35 ~ _+ 20 ~ in normal persons and again the difference between groups is not marked. The normal value of the G/QRS ratio is 2.87 _+'0.79. This ratio is decreased considerably in groups with left ventricular hypertrophy. As far as average figures are concerned, it appears that the major part of the T change in HT1 and AI groups is, as a whole, secondary to the QRS chang e . In Fig. 5, the QRS-T angle is plotted against the G/QRS ratio, which corresponds to the theoretical curves in Fig. 3. Curves in relation of the QRS-T angle and the ratio g is very close in cases with larger QRS-T angle. In other words, the relative decrease in the G magnitude in these cases is manifested as the widening of the QRS-T angle,

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MASHiMA

TABLE I Results of the Measurement of the Mean QRS, Maximal QRS and the G Vectors in Normal Persons and in Cases with Left Ventricular Hypertrophy

Normal 60

Number of Cases mean QRS magnitude (~V sec) mean QRS direction (deg) Frontal Horizontal maximal QRS magnitude (mV) mean

62

30

-+

47 -12 1.65 1.00

-+ • _+ •

9

59

6 24 0.35 0,12

80

G direction (deg) Frontal Horizontal

72

74

• 16 + 21 • 0.89 • 0.19

1.22 •

• 22

0.20

• 34

14 -15 2.61 1,33

G/QRS ratio

26 • 31 31 _+ 33 1.35 _+ 0.71

QRS-G angle (deg)

35

47

_+ 24

14

+_ 37 • _+ _+ _+

19 20 1.04 0.21

1.23 _+ 0.24 54

44 _+ 12 27 _+ 17 2.87 _+ 0.79 _+ 20

Aortic Insufficiency (AI)

22

• 30

28 -21 2,50 1,23

1.00 _+ 0.12

~' max G magnitude (FV sec)

Hypertension with heart failure (HT2)

Hypertension (HT1)

_+ 26

29 • 45 -10 • 56 0.83 • 0.34 32

• 27

91 28 -34 3.11 1.41

• 41 _+ _+ _+ •

18 15 1.13 0.23

1.35 _+ 0.22 82

• 31

43 +_ 35 24 _+ 47 1.11 • 0.62 48

_+ 20

mean and ~ max are the hypertrophy index calculated from the mean ORS and maximal ORS magnitude, respectively. See text.

DISCUSSION

c) The s t r e n g t h of the double layer and the velocity of the activation wave are the same as normal. d) The G vector is p r e s e r v e d . One of the principal effects of this model hypert r o p h y is the increase in the QRS area propor-

A s s u m p t i o n s which c h a r a c t e r i z e the ideal h y p e r t r o p h y model are listed below: a) H y p e r t r o p h y is diffuse and symmetrical. b) The sequence of activation is unaltered. 1.8 ~ I ( m e a n Q R S )

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Fig. 4: Comparison of mean and maximal QRS magnitude in normal persons and in cases with left ventricular hypertrophy. HT 1 and HT 2 are hypertension without complications and hypertension with congestive heart failure, respectively. AI indicates aortic insufficiency. ~mean and~max are the hypertrophy index derived from the mean QRS and the maximal QRS. See text.

J. ELECTROCARDIOLOGY, VOL. 91 NO. 2, 1976

VENTRICULAR

HYPERTROPHY

1 37

QRS-T angle 180"

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tional to the myocardial mass. In agreement with this, myocardial mass has been known as relatively well correlated to the QRS measurements in clinical cases. 3,4 But observed relations are by no means perfect, which seems to be due to several reasons. Even in normal conditions, there are considerable variations in electrocardiographic measurements indicating personal differences in the pattern of ventricular activation and in the heart-lead relationship. A quantitative relaiton will be affected very much by such personal variations. The theory is most adequately applied to the sequential change in a particular person. But comparison of different cases can also be made statistically with average figures of many cases. In abnormal conditions, asymmetry of the hypertrophic process, structural changes of the myocardium and the positional change of the heart will be additional causes of deviations. Assumptions listed above also include the preservation of the strength of the double layer. The latter may be altered by myocardial edema and other pathological processes. In spite of all these complicating factors, realization of the simple result of ideal hypertrophy could be of value in understanding electrocardiographic evolution of ventricular hypertrophy. Discrepancies in actual cases indicate deviations from the ideal state. Recent attempts to exclude some of intervening factors has improved the correlation between the dipole activity and the ventricular weight in cases with left ventricular hypertrophy. 6 Ideal h y p e r t r o p h y causes enlargement of the QRS magnitude but does not change the QRS direction. Slight left axis deviation observed in our cases may be the result of relatively less contribution of the right ventricle to the QRS complex. Recently, severe left axis deviation has been attributed to the block of J. ELECTROCARDIOLOGY, VOL. 9, NO. 2, 1976

5.0

6.0

Fig. 5: The QRS-T angle plotted against the G/QRS ratio in normal persons and in cases with left ventricular hypertrophy. Compare with curves in Fig. 3.

anterior subdivision of the left bundle branch. 13 It seems probable that the axis shift of moderate or severe degree in cases with left ventricular hypertrophy is due to associated conduction abnormalities rather than a direct result of hypertrophy. Another result of ideal hypertrophy is the proportion between the amplitude and duration of the QRS. Cases in this report show that the QRS duration tends to be unproportionally increased. Thickening of fibers can increase the velocity of impulse conduction and reduce the QRS area, which seems to be overcompensated by abnormalities in the activation spread. It has been known that the endocardial muscle layer is penetrated by Purkinje fibers and its contribution to the QRS is less than that of the epicardial layer. 14,15 In other words, the strength of the double layer is smaller in the endocardial portion of the ventricle. Whether the proportion of the Purkinje fiber penetration is preserved in the hypertrophied ventricle is not known. The increase in the QRS duration may be explained if hypertrophy occurs mainly with the epicardial muscle layer. The recovery process is analysed on the basis of the constant G vector. The existence of the ventricular gradient is mainly due to the endoand epicardial difference in the excitation duration. Whatever the cause of this difference is, it is conceivable that the difference is not influenced by the ventricular volume. If the QRS area is proportional to the ventricular volume, the G to QRS ratio represents the gradient per unit volume of ventricular muscle. In ventricular hypertrophy, reduction of the ratio g is of importance for the recovery pattern, which is manifested clinically as the widening of the QRS-T angle. An additional advantage of taking the ratio g is the standardization of the G value with respect to the transmission

138

MASHIMA

of the cardiac potential to the recording lead. Details of the recovery pattern in hypertrophied ventricle are difficult to estimate clinically as well as experimentally. A rough estimation of the recovery sequence based on observations of the vectorcardiographic T loop has been made in our previous report. ~ Equations in Section II are geometric theorems and are free from assumptions. With a constant QRS-G angle in addition, curves in Fig. 3 are obtained to show the sequential change in the T direction. It should be emphasized that the QRS and G are primary variables. The essential role of the G vector in several acute changes of the ECG has been noticed in our previous reports. '2,16 Changes in the heart rate or in the blood potassium concentration causes alterations in the G magnitude but not in its direction nor in the QRS vector. A chronic process such as hypertrophy of the ventricle will presumably occur with changes in the QRS but not in the G vector. As indicated in Fig. 3, a decrease in the G magnitude and the QRS enlargement have the same effect on the recovery pattern. The directional change of the G vector is of different meaning and must be distinguished from the change only in the G magnitude.

5.

6.

7.

8. 9. 10. 11.

12.

13. REFERENCES 1. SCOTT, RC: The correlation between the electrocardiographic pattern of ventricular hypertrophy and the anatomic findings. Circulation 21:256, 1960 2. DOWER, GE, HORN, HE AND ZIEGLER, WG: On electrocardiographic autopsy correlation in left ventricular hypertrophy. A simple postmortem index of hypertrophy proposed. Am Heart J 74:351, 1967 3. SELZER, A, NARUSE, D Y, YORK, E, KAHN, KA AND MATHEWS, H B: Electrocardiographic findings in concentric and eccentric left ventricular hypertrophy. Am Heart J 63:320, 1962 4. CARTER, WA AND ESTES, EH: Electrocardiographic manifestations of ventricular hypertrophy: a computer study of ECG-anatomic

14.

15.

16.

correlations in 319 cases. Am Heart J 68:173, 1964 BLUMENSCHEIN, D D, SPACH, MS, ROINEAU, J P, BARR, R C, GALLIE, T M, WALLACE, A G AND EBERT, PA: Genesis of body surface potentials in varying types of right ventricular hypertrophy. Circulation 38:917, 1968 ELLISON, RC, FISCHMANN, E J, MIETTINEN, D S AND HUGENHOLTZ, P G: Use of the dipole moment in the assessment of left ventricular hypertrophy. Circulation 40:719, 1969 MASHIMA, S, FU, L AND FUKUSHIMA, K: The ventricular gradient and the vectorcardiographic T loop in left ventricular hypertrophy. J Electrocardiol 2:55, 1969 HODGKIN, A L: A note on conduction velocity. J Physiol 125:221, 1954 PLONSEY, R: An evaluation of several cardiac activation models. J Electrocardiol 7:237, 1974 LINZBACH, A J: Heart failure from the point of view of quantitative anatomy. Am J Cardiol 5:370, 1960 WILSON, FN, MACLEOD, AG, BARKER, PS AND JOHNSTON, FD: The determination and significance of the area of ventricular deflections of electrocardiogram. Am Heart J 10:34, 1934 MASHIMA, S, Fu, L AND FUKUSHIMA, K: The normal ventricular gradient determined with Frank's lead system and its relation to the heart rate change induced by various procedures. Jap Heart J 5:334, 1964 ROSENBAUM,M B, ELIZARI, M V AND LAZZARI, J O: The Hemiblocks. Tampa Tracings, Oldsmar, FL, 1970 KENNAMER, R, BERNSTEIN, J L, MAXWELL, M H, PRINZMETAL, M AND SHAW, C M: Studies on the mechanism of ventricular activity V. Intramural depolarization potentials in the normal heart with a consideration of currents of injury in coronary artery disease. Am Heart J 46:379, 1953 SODI-FALLARES, D, MEDRANO, GA, DE MICHEL, A, TESTONI, MR AND BISTINI, A: Unipolar QS morphology and Purkinje potential of the free left ventricular wall. The concept of electrical endocardium. Circulation 23:836, 1961 MASHIMA, S, FU, L AND FUKUSHIMA, K: The effect of potassium chloride on the normal and abnormal electrocardiogram. Jap Heart J 6: 463, 1965

J. ELECTROCARDIOLOGY, VOL. 9, NO. 2, 1976