- Email: [email protected]
Re-evaluation of the electrocardiographic diagnostic criteria for left ventricular hypertrophy by means of linear discriminant functions
· ELECfROCARDlOLOGY, 1, (2), 191-198, 1968
Re-evaluation of the Electrocardiographic Diagnostic Criteria for Left Ventricular Hypertrophy by Means of Linear Discriminant Functions * ny mcm KNURA, M.D. Al"D lIIROKAZU HAYAKAWA, M.D.
SUMMARY Three discriminant equations derived from thirteen measurements in lead V5 were shown to be able to differentiate between each pair of patients with hypertension or aortic insufficiency and normal persons. The electrocardiographic findings most useful for the diagnosis of left ventricular hypertrophy were pointed out by comparing the degree of contribution of each finding to the discrimination by means of these equations. INTRODUCfION Electrocardiographic diagnostic criteria for left ventricular hypertrophy proposed by various authors~-6.B.IO.12-H usually consist of such findings as the amplitude of S wave in VIand R wave in Vs, delay in ventricular activation time, and left axis deviation. These findings, however, arc not considered to be equally important in the diagnosis of left ventricular hypertrophy. It would be more appropriate to establish criteria in which reasonable weight is given to each item. Left ventricular hypertrophy can be roughly classified in two groups: concentric hypertrophy as seen in hypertensive heart disease and eccentric hypertrophy as seen in aortic insufficiency, Although it has been pointed out that electrocardiographic findings arc different in these two kinds of hypertrophy to some extent," this difference has not been taken into account in the diagnostic CI iteria. In 1961, Rikli and his associates!' reported that left ventricular hypertrophy in aortic insufficiency and arterial hypertension can be differentiated by electrocardiographic findings by using discriminant functions. The purpose of this present study is to examine the contribution of individual find-
• From the Department of Internal Medicine, Nippon Medical School. 1-1-5 Sendagi, Bunkyo-ku, Tokvo. Janan.
ings of the waves to the diagnosis of left ventricular hypertrophy with the aid of discriminant functions. MATERIALS AND METHODS Forty-seven cases of hypertension, nineteen cases of aortic insufficiency, and thirty normal controls were used in this study. The cases with aortic insufficiency were diagnosed by phonocardiograph and other clinical signs. Some of them were confirmed at autopsy. As hypertensive subjects, cases with both systolic pressure over 160 mmHg and diastolic pressure over 95 mmHg were employed. These two disease groups contain cases which do not show a typical pattern of left ventricular hypertrophy in the electrocardiogram. Although it is desirable to usc all the measurements in the routine twelve leads to derive the discriminant equations, such equations would have more than 100 terms even if some of the time values common to the leads were omitted. Such a large number of terms is not appropriate for our present consideration. Therefore, lead Vs alone was used in this study, following Rikli's paper, because this lead is regarded as having the largest amount of information concerning left ventricular hypertrophy. There arc statistical methods to derive a discriminant equation which differentiates three or more diseases simultaneously. However, such methods arc rather inferior to those used by us in the accuracy of differentiation. From such a viewpoint, we employed in the present study the simplest form of discriminant equation, that is, the equation to differentiate between each pair of diseases. Thirteen measurements as indicated in Table 1 were used to derive each discriminant equation. They arc considered to be all values rncasureablc in a single electrocardiographic lead. The symbols used in the table follow those of Rikli et al., differing from the general usc. "a" means the
192
KI:\IURA AI'D IIAYAKAWA
" a m plitude" or "deviation," "d" the "duration" or " interval," and "s" the length of the "segment." "PRs" means the interval between the end of the P wave and the beginning of the QRS deflection, but not the "P-R interval" as is generally meant. Similarly, "QTs" is the interval between the end of the QRS deflection and the beginning of the T wave, and not the "Q-T interval" or the electric duration of ventricular systole. The beginning of the T wave wa s determined by the ma ximal curvature (i.e. the maximum and minimum of the differential coellicicnt of the second order), measuring with our eyes. Out such a point cannot be determined in cases in which the SoT segment shows an obliquely ascending or descending straight line, continuing to the positive or negative T wave. In these cases, the be-
Formula 1 (HT -
N)
=
Formula 3 (AI -
RESULTS 1. Differentiation of the diseases by discriminant equations. Using the thirteen measurements in lead V:" three equations were derived to differentiate between hypertension and the normal (Formula 1), aortic insufficiency and the normal (Formula 2), and hypertension and aortic insufliciency (Formula 3), respectively.
+ +
0.01210gPa - 0.905Qa - 4.965 10g(Ra 1) - 1.328Sa 1.167Ta 0.9721a 7.213STa - 4.146Pd 1.070 10g(QRSd - 0.(2) 13.464 QRd 2.465Td 1.987PRs - 3.705QTs 8.416
+
+
Formula 2 (AI - N)
ginning of the T wave in onc of the other leads, where this po int was easily measurable, was used instead of th at in lead V5. SoT deviation (STa) was measu red at the point 0.04 sec. after the SoT junction; the baseline was drawn by connecting the origins of two successive P waves.
+
+
+ - 2.59710gPa - 2.277Qa - 3.143 log(Ra + 1) - 0.762Sa + 3.081Ta - 6.344Ja + 5.919STa - 3.765Pd - 0.161 10g(QRSd - 0.02) + 20.624 QRd - 0.025Td + 1.981 PRs - 4.687QTs - 0.096 - 0.842 10gPa - 1.978Qa - 0.688 10g(Ra + 1) + 0.047 Sa + 1.814Ta - 9.450Ja + 6.302STa
=
HT) =
+
+
- 13.788I'd - 1.198 10g(QRSd - 0.02) - 67.642 QRd - 0.617Td 3.276PRs - 3.684QTs 4.480
+
TABLE 1 Thirteen measured values in lead Vs Symbols
Measurements p
Q R S
QRS QR J
S·T T I'·R Q·T
height width depth height depth width width . (intrinsicoid deflection) deviation deviation height width interval between the end of P wave and the beginning of QRS deflection interval between the end of QRS deflection and the beginning of T wave
Pa I'd Qa Ra Sa QRSd QRd Ja STa Ta Td pRs QTs
+
The discriminant scores were obtained by substituting the actual measured values into the terms of the equations. Cases showing a negative score were diagnosed as belonging to the group on the left side of each pair, i.e. HT or AI, in the parenthesis before the formula, while those with a positive score were diagnosed as belonging to the group on the right side, i.e. N or HT. HT indicates hypertension, Al aortic insufficiency, and N normal. The various transformations for the several ECG variables to the logarithmic funct ion were made in order to reduce the skewness of the distribution of the measurements as shown in the formulae. Fig. I shows the distribution of the scores obtained by these equations. By formula 1, 74.5 % of cases with hypertension and 86.7% of normal controls were discriminated correctly. Formula 2 produced a more favorable result. Correct
193
LEFT VENmlCULAR IlYPERTROI'IIY Discriminant scores
-20
-30
Formula 1 urr -N)
o
-1.0
PC' rc e ntag e of
correctly interpreted c·~.e.
30
20
10
.:: :•••• i::·)· :11···:· ••••:••
.: .:
F'c r-rnul a l
n-·: .
(~,)
Normal controls
zct s»
(86.7)
Hype r t e ne ion
35/47
(74.5)
Normal controls
29/30
(AI - N)
:
.:
.:.•• -,:•••:. :,_00 H._.... Formula
,.
Aortic insufficiency
(89.5)
Hypertension
(83.0)
3
(AI - fiT)
t-
Aortic
••..!
(79.0)
insufficiency
Borderline of dilcrimin~tion
Fig. 1. Distribution of (he discriminant scores.
diagnosis was obtained in 89.5 % of aortic insufficiency and 96.7% of normal controls. The high percentages, namely 83.0% of hypertension and 79.0% of aortic insufficiency obtained by formula 3 indicated an accurate differentiation between these two diseases. 2. Contribution of each electrocardiographic finding to the differential diagnosis. The thirteen measurements employed to derive the discriminant equations are not considered to be equally useful in the differentiation of the diseases. Some items might be highly contributory to the diagnosis, while others not. In this respect, the influence of each term of the equations on the discriminant scores was examined and compared. Although the terms showing the greater value would seem to have a higher contribution to the diagnosis, they would not have a large effect on the differentiation if the variation of their values was not fairly large. Therefore, the variance or standard deviation of the values of each term is preferable as an' index of the degree of contribution. The terms showing the greater variance are regarded as having u larger influence on the discriminant score. On the other hand, since the discriminant scores vary in relation to the variation of the values of the individual terms, the terms with greater variation of values are considered to have a greater effect on the scores. Therefore, the correlation between the individual terms and discriminant scores is also employable as an index
of the degree of contribution. In this case, absolute values of the correlation coefficients must be compared, because only their magnitude is the subject of consideration. Figs. 2, 3 and 4 show the results of the forementioned analysis, in which the ordinate indicates the standard deviation and the abscissa the correlation coefficient. The higher values in both parameters may indicate that the findings are significant in the differentiation of the diseases. As shown in Fig. 2, the electrocardiographic
0.8
06
c a
.~
Td
>
"'"" "0
... "'.". "
T.
04
ST• PR.
(/)
In.
02
QRJ QRSd Pd
ll.
J. 02
1'.
0.4
06
Correlation coefficient
Fig. 2. Contribution of individual waves to thc differential diagnosis between hypertension and nor-
mal.
KI~tUR'\ A~D
findings which contributed most strongly to the differentiation between hypertension and normal were found to be the amplitude of the R wave (Ra). The deviation of the SAT segment (STa), the amplitude of the T wave (Ta), the depth of the S wave (Sa) and the interval between the end of the P wave and the beginning of the QRS deflection (PRs) were also regarded as useful information for differentiation. On the contrary, the depth of the Q wave (Qa) or the width of the P wave (Pd) were regarded to have little significance. As to the differentiation betw ccn aortic insufficiency and the normal, the most useful information was found in the amplitude of the T wave (Ta), as shown in Fig. 3. QTs, Ra, Pa, PRs and STa were also significant, but to a lesser extent. I.
oJ
IIAY,\KAW,\ I'll.
OB
06 c:
o
Il.
.~
>
"
"tl
... "".c: Vi -e
04
r• 02 Td
s. 0.2
0.4
0.6
Correlation coefficient
Fig. 4. Contribution of individual waves to the differential diagnosis between hypertension and aortic
insufficiency. 06 1'.
c:
.2 ~ .;;
. ""...
04
Vi
0 .2
-e
""..e
Q.
J. S.
R.
ST.
IlT.
I'H •
Olll I',
02
04
06
Correlatiun coefficient
Fig. 3, Contribution of individual waves to the differential diagnosis between aortic insufficiency and normal. The amplitude of the T wave (Ta) was also shown to be most significant for discrimination between hypertension and aortic insufficiency, as indicated in fig. 4. Other significant findings in this differentiation were QRd (ventricular activation time), Ja and I'd, while the amplitude of the R wave and the deviation of the S'Tvscgrnent were regarded as scarcely contributory. 3. Significance of the height of R wave in lead V o in the diagnosis of left ventricular hypertrophy. In most of thc criteria proposed by various investigators, some critical values are usually employed to decide whether the finding is ab-
normal or not. For example, Sokolow and Lyon'" set the critical value of the height of R wave in lead V o for left ventricular hypertrophy at 26 rnrn. Needless to say, this is not .an ideal procedure, because there will be a high possibility that normal cases which show the R wave to be higher than 26 mrn will be diagnosed as having left ventricular hypertrophy. From this viewpoint the contribution of the height of the R wave in lead V~ to thc dilfcrcntiation between hypertension and normal controls was examined . As indicated in Fig. 5, nearly half of the hypertensive cases have an R wave less than 26 rnm. IlUI most of such cases were diagnosed as having left ventricular hypertrophy by using the discriminant equation. Furthermore, all of the five normal cases showing the R wave to be higher than 26 rnm were judged as normal. A similar analysis was made in the differentiation between aortic insufficiency and the normal. As shown in Fig. 6, all cases of aortic insufficiency except two were diagnosed as aortic insufficiency, irrespective of the height of the R wave, Normal cases were also correctly diagnosed with only one exception. DISCUSSION Oui' results of the electrocardiographic differentiation between hypertension, aortic insufficiency
LUi
195
VENTR IC UL AR II Y/, £RTRO PII Y
60 Height of R wa v e in V :; ( m m )
50
•
H yp erten si on
x
Nor m a l
.:
40 30
.... ,.'
.
20
'li e
;.
-:
Z b rnrri
'1(. 'l(
1(
•
'll
'l(
..
10
o '----_-'--_--'-_--"--_----'-__'--_....1..-_--'-_ _ -40 -30 -20 -10 o 10 30 20 D isc r im in ant s c o res Fig. 5. The height of the R wave in lead V, and the discrimi nant scores obta ined by formul a I in the cases of hypertension and normal cont rol.
Height of
R wave in
Vs (mm)
•
90
•
•
Ao rtic insufficiency
)(
Normal
70
•
60
••
50
•
40 30
•
•
•
20
..
x
.. ~
• •
x x
• • •
26mm
x x .x
"x l(
•x
10
xX
"" )(
x
x
X
X
X
x xx x
x
x X
•
o -40 -30 -20
I
-10
10
20
30
Discriminant scores Fig. 6. The height of th e R wave in lead Vs a nd the discriminant scores obtained by Form ula 2 in the cases of aort ic insufficiency a nd normal controls.
196
KI~IUI{j\
Ar-;D IIAYAK,\W,\
and normal controls by discriminant equations as shown in Fig. 1 were fairly good, and comparable to those obtained by Rikli et al., even though we used electrocardiographic information of lead V" alone and cases without the typical electrocardiographic pattern of left ventricular hypertrophy were included. More accurate differentiation could have been expected if we had used the electrocardiographic information in all twelve leads and typical cases alone had been included in the material. This means that these diseases produce electrocardiographic findings which will serve to differentiate them even at an early stage, when clinical signs are still obscure. The number of cases used in our series, especially those with aortic insufficiency, may not be large enough from the standpoint of statistics. If we would. have derived the discriminant equations using a larger number of the cases, even more valuable results would have been obtained. The discriminant equations derived in this study include various measurements which are not used in the daily electrocardiographic differential diagnosis. Probably such measurements would contribute to the differentiation if they arc included. The extent of contribution of each electrocardiographic information to the differentiation of the diseases can be shown by the relationship of each term of the equation to the discriminant score. The terms which exert a greater effect on the score are considered to playa more important role in the differentiation. However, an indisputable method of determining the degree of contribution of each of the terms to the discriminant score has not been found in statistics. One of the conceivable ways to solve this problem is as follows: Suppose that we take n terms to discriminate. We then write n discriminant equations consisting of n-I terms in which the i-th term (i = I, 2, .... , n) is omitted. Comparing the results obtained by those n equations, we reveal the effectiveness of each item in the discrimination. However, this is a very inefficient method even when an electronic computer is used. Referring to the literature for similar problems, we find that Miyoshi? described the method of comparing the magnitude of b,dj, which is a component of l:bid i corresponding to Mahalanobis general distance. Other investigators reported the use of the F test 1 or the evaluation of
the values representing the normalized discriminant coefficients." The method employed in our study is to evaluate the variance of each term by substituting the actually measured values and also by using the correlation coefficients between the values of each term lind the discriminant scores. The terms showing both a larger variance and a higher correlation coefficient can be regarded as more significant in the dilTerential diagnosis. By this procedure, amplitude of the R wave (Ra), deviation of the ST-segment (STa), height of the T wave (Ta), depth of the S wave (Sa), and the interval between the end of the P wave and the beginning of the QRS deflection (PRs) in lead Vi> were found to contribute most to the discrimination between hypertension and normal. Although Rikli et al. did not examine the contribution of each finding to the discrimination of left ventricular hypertrophy, they stated that most of the findings used in their discriminant functions appeared to be effective in the discrimination after an examination of the significance of the dilTerence between the two diseases. The dilTerence between their opinion and ours is probably due to the difference in the manner of selecting the subjects as well as in the method of examining the significance of the dilTercnce. The method of comparing the values representing the normalized discriminant coefficients is analogous in its consequence to the method of using the standard deviation, which is a part of our procedure. But the results obtained by the former method alone may be easily influenced by the magnitude of correlation between each measurement, thus involving some risk in the evaluation of the degree of contribution. In this regard, our method of using both the correlation coefficients and the standard deviation can be said to express the degree of contribution better and to be more useful because it needs only simple calculation. The electrocardiographic findings which were found to contribute to the differentiation between hypertension and the normal are almost the same as those used in the current diagnostic criteria for left ventricular hypertrophy, such as those proposed by Sokolow and Lyon," Myers!" or Mori. 8 Only the terms Sa and PRs have not been employed previously. These results indicate that the criteria generally used at present are in general valid. Very recently Dower et aP have
197
UIT VENTlUCUlAR HYPERTROPHY
described that voltage criteria arc most useful, although VAT and ST.T changes may be of value. Their opinion nearly coincides with ours, but VAT(QRd) was not found to be so important in our analysis as seen in Fig. 2. It is certain, however, that the use of some critical value in these criteria reduces the amount of information available in the electrocardiogram. For example, if this value is high, the false negativity increases, and if it is low, the false positivity increases. The diagnosis by the discriminant equations is superior to the current diagnostic criteria, because the actual measurements arc used without modification. Our results obtained by using the discriminant equations showed that the normal cases with an R wave in lead V;, higher than 26 rnrn were diagnosed as normal and most of hypertensive cases with an R wave lower than 26 mm were diagnosed to have hypertension, as shown in Fig. 5. These results further signify that findings other than the height of the R wave arc very important in the diagnosis of left ventricular hypertrophy in lead V;,. As shown in Fig. 2, the interval between the end of the I' wave and the beginning of the QRS deflection (PRs) was found to contribute to the differentiation between hypertension and normal controls. As far as we know, this fact has not been pointed out previously. Its morphological and hemodynamic substrates may be a subject of research in the future. The electrocardiographic information contributing to the differentiation between aortic insufficiency and the normal is somewhat different from that between hypertension and the normal. The most important information here was shown to be the height of the T wave, while the height of the R wave was less significant. This difference may be ascribed to the difference in the form of hypertrophy. Aortic insufficiency shows hypertrophy with dilatation, while in hypertension hypertrophy is not usually accompanied by dilatation unless the disease is in an advanced stage. Another interesting observation as seen in Fig. 3 is that the P wave plays a more significant role in the differentiation between aortic insufficiency and the normal than between hypertension .and the normal. This can be explained by the assumption that the auricular function is affected hemodynamically at an. earlier stage of aortic insufficiency or that hypertrophy with dilatation
deforms the auricles in some manner, changing the shape of the I' wave. One of the most noteworthy facts observed in our study is that hypertension and aortic insufficiency were fairly clearly differentiated by the discriminant equations. The most important sign was found to be the height of the T wave. The time of the intrinsic deflection (QRd), deviation of the SoT junction (Ja) and duration of the P wave (I'd) were also significant. The height of the R wave was not useful, as demonstrated by the fact that an increased height of R is common to both hypertension and aortic insufficiency. According to the concept generally accepted at the present time these diseases arc considered to be poorly differentiated by electrocardiographic findings alone. However, our result suggests that the differentiation between hypertension and aortic insufficiency is possible by electrocardiographic findings alone, and the difficulties experienced in the past might be ascribed to our insufficient knowledge and usc of the findings indicated above. Since hypertension and aortic insufficiency arc different in hemodynamic aspects, their difference must be reflected in the electrocardiographic pattern, which will contribute to differential diagnosis. CONCLUSIONS I. Three discriminant equations were derived to differentiate between each pair of hypertension, aortic insufficiency and normal controls, using thirteen measurements in lead Va alone. 2. Correct discrimination was obtained by each formula in 74.5 % of patients with hypertension and 86.7% of normal controls, 89.5% of aortic insufficiency and 96.7% of normal controls, and 83.0% of hypertension and 79.0% of aortic insufficiency. 3. The standard deviation of each term, substituted by the actual values, and the correlation coefficient between the individual terms and the discriminant scores were used to evaluate the contribution of each electrocardiographic finding to the discrimination. 4. For discrimination between hypertension and the normal controls by lead Vo, the amplitude of the R wave, the SoT deviation, the amplitude of the T wave, the depth of the S wave and the interval between the end of the P wave and the beginning of the QRS deflection were found useful.
198 5. The most significant information for differentiation between aortic insufficiency and the normal was shown to be the amplitude of the T wave. 6. The amplitude of the T wave was also most significant for differentiation between hypertension and aortic insufficiency. Ventricular activation time, deviation of the junction and duration of the P wave were also useful, while the amplitude ofR wave was scarcely contributory. 7. The false positivity and neg ativity caused by the usc of thc critical value of 26 mrn in V; lead for left ventricular hypertrophy can be largely prevented by use of discriminant equations. 8. These results indicate that the electrocardiogram contains findings which have not been generally used in the diagnosis of left ventricular hypertrophy. REFERENCES I. Caceres, A. c.: Integration of data in diagnosis. Circulation Res. 11: 563, 1962. 2. Cabrera, E., and Gaxiola, A.: Systolic and diastolic loading of the heart. Am. Heart J. 43: 669,1952. 3.' Dower, G . E. and Ziegler, W. G.: On electrocardiographic-autopsy correlations in left ventricular hypertrophy. A simple post-mortem ind ex of hypertrophy proposed. Am . Heart J. 701: 351,1967. 4. Goldberger, E.: Unipolar lead electrocardiography
5. 6. 7. 8.
9. 10.
II .
12. 13.
14.
and vectorcardiography, Ed. 3. Philadelphia, Lea & Fcbiger, 1953. Gubner, R., and Ungcrlcider, H. E.: Electrocardiographic criteria of left ventricular hypertrophy. Arch. Int. Med . 72: 196, 19·B. Katz, L. N.: Electrocardiography. Ed. 2. Philadelph ia, Lea & Feb iger, 19-16. Miyo shi, E.: Tok yo lgaku Zasshi 4: I, 1956 (in Japanese). Mori, H., Nakagawa, A., and Kawarnata, K.: New criteria for the electrocardiographic diagnosis of left ventricular hypertrophy (~ IVP). Jap. Circulation J. 201: 96-1, 196-1. Nagao, T ., and Harada , H.: Study of an analogue computer for mass survey of hypertension. Jap. Circulation J. 27: 729, 1963. Noth, 1'. H., Myers, G. B., and Klein, H. A.: Precordial electrocardiogram in left ventricular hypertrophy. J. Lab . Clin. Mcd, 32: 1517, 19-17. Rikli, A. E., Tolle s, W. E., Steinberg, C. A., Carbcry, W. J., Freiman, A. H., Abraham, S., and Caceres, C. A.: Computer analysis of electrocardiographic measurements. Circulation 201: 643, 1961. Schach, J . A., Rosenbaum, R. H., and Katz, L. N.: The aV limb leads in the diagno sis of ventricular strain. Am. Heart J. 40: 696 , 1950. Sokolow, M., and Lyon, T. P.: The ventricular complex in left ventr icular hypertrophy as obtained by unipolar precordial and limb leads. Am. Heart J. 37: 161, 19-19. Wilson, F. N., Rosenbaum, F. F., and Johnston, F. D.: Interpretation of the ventricular complex of the electrocardiogram. Advances in Internal Medicine. Vol. 2. Chicago, The Year Book Publishers, 1947.
Re-evaluation of the Electrocardiographic Diagnostic Criteria for Left Ventricular Hypertrophy by Means of Linear Discriminant Functions * ny mcm KNURA, M.D. Al"D lIIROKAZU HAYAKAWA, M.D.
SUMMARY Three discriminant equations derived from thirteen measurements in lead V5 were shown to be able to differentiate between each pair of patients with hypertension or aortic insufficiency and normal persons. The electrocardiographic findings most useful for the diagnosis of left ventricular hypertrophy were pointed out by comparing the degree of contribution of each finding to the discrimination by means of these equations. INTRODUCfION Electrocardiographic diagnostic criteria for left ventricular hypertrophy proposed by various authors~-6.B.IO.12-H usually consist of such findings as the amplitude of S wave in VIand R wave in Vs, delay in ventricular activation time, and left axis deviation. These findings, however, arc not considered to be equally important in the diagnosis of left ventricular hypertrophy. It would be more appropriate to establish criteria in which reasonable weight is given to each item. Left ventricular hypertrophy can be roughly classified in two groups: concentric hypertrophy as seen in hypertensive heart disease and eccentric hypertrophy as seen in aortic insufficiency, Although it has been pointed out that electrocardiographic findings arc different in these two kinds of hypertrophy to some extent," this difference has not been taken into account in the diagnostic CI iteria. In 1961, Rikli and his associates!' reported that left ventricular hypertrophy in aortic insufficiency and arterial hypertension can be differentiated by electrocardiographic findings by using discriminant functions. The purpose of this present study is to examine the contribution of individual find-
• From the Department of Internal Medicine, Nippon Medical School. 1-1-5 Sendagi, Bunkyo-ku, Tokvo. Janan.
ings of the waves to the diagnosis of left ventricular hypertrophy with the aid of discriminant functions. MATERIALS AND METHODS Forty-seven cases of hypertension, nineteen cases of aortic insufficiency, and thirty normal controls were used in this study. The cases with aortic insufficiency were diagnosed by phonocardiograph and other clinical signs. Some of them were confirmed at autopsy. As hypertensive subjects, cases with both systolic pressure over 160 mmHg and diastolic pressure over 95 mmHg were employed. These two disease groups contain cases which do not show a typical pattern of left ventricular hypertrophy in the electrocardiogram. Although it is desirable to usc all the measurements in the routine twelve leads to derive the discriminant equations, such equations would have more than 100 terms even if some of the time values common to the leads were omitted. Such a large number of terms is not appropriate for our present consideration. Therefore, lead Vs alone was used in this study, following Rikli's paper, because this lead is regarded as having the largest amount of information concerning left ventricular hypertrophy. There arc statistical methods to derive a discriminant equation which differentiates three or more diseases simultaneously. However, such methods arc rather inferior to those used by us in the accuracy of differentiation. From such a viewpoint, we employed in the present study the simplest form of discriminant equation, that is, the equation to differentiate between each pair of diseases. Thirteen measurements as indicated in Table 1 were used to derive each discriminant equation. They arc considered to be all values rncasureablc in a single electrocardiographic lead. The symbols used in the table follow those of Rikli et al., differing from the general usc. "a" means the
192
KI:\IURA AI'D IIAYAKAWA
" a m plitude" or "deviation," "d" the "duration" or " interval," and "s" the length of the "segment." "PRs" means the interval between the end of the P wave and the beginning of the QRS deflection, but not the "P-R interval" as is generally meant. Similarly, "QTs" is the interval between the end of the QRS deflection and the beginning of the T wave, and not the "Q-T interval" or the electric duration of ventricular systole. The beginning of the T wave wa s determined by the ma ximal curvature (i.e. the maximum and minimum of the differential coellicicnt of the second order), measuring with our eyes. Out such a point cannot be determined in cases in which the SoT segment shows an obliquely ascending or descending straight line, continuing to the positive or negative T wave. In these cases, the be-
Formula 1 (HT -
N)
=
Formula 3 (AI -
RESULTS 1. Differentiation of the diseases by discriminant equations. Using the thirteen measurements in lead V:" three equations were derived to differentiate between hypertension and the normal (Formula 1), aortic insufficiency and the normal (Formula 2), and hypertension and aortic insufliciency (Formula 3), respectively.
+ +
0.01210gPa - 0.905Qa - 4.965 10g(Ra 1) - 1.328Sa 1.167Ta 0.9721a 7.213STa - 4.146Pd 1.070 10g(QRSd - 0.(2) 13.464 QRd 2.465Td 1.987PRs - 3.705QTs 8.416
+
+
Formula 2 (AI - N)
ginning of the T wave in onc of the other leads, where this po int was easily measurable, was used instead of th at in lead V5. SoT deviation (STa) was measu red at the point 0.04 sec. after the SoT junction; the baseline was drawn by connecting the origins of two successive P waves.
+
+
+ - 2.59710gPa - 2.277Qa - 3.143 log(Ra + 1) - 0.762Sa + 3.081Ta - 6.344Ja + 5.919STa - 3.765Pd - 0.161 10g(QRSd - 0.02) + 20.624 QRd - 0.025Td + 1.981 PRs - 4.687QTs - 0.096 - 0.842 10gPa - 1.978Qa - 0.688 10g(Ra + 1) + 0.047 Sa + 1.814Ta - 9.450Ja + 6.302STa
=
HT) =
+
+
- 13.788I'd - 1.198 10g(QRSd - 0.02) - 67.642 QRd - 0.617Td 3.276PRs - 3.684QTs 4.480
+
TABLE 1 Thirteen measured values in lead Vs Symbols
Measurements p
Q R S
QRS QR J
S·T T I'·R Q·T
height width depth height depth width width . (intrinsicoid deflection) deviation deviation height width interval between the end of P wave and the beginning of QRS deflection interval between the end of QRS deflection and the beginning of T wave
Pa I'd Qa Ra Sa QRSd QRd Ja STa Ta Td pRs QTs
+
The discriminant scores were obtained by substituting the actual measured values into the terms of the equations. Cases showing a negative score were diagnosed as belonging to the group on the left side of each pair, i.e. HT or AI, in the parenthesis before the formula, while those with a positive score were diagnosed as belonging to the group on the right side, i.e. N or HT. HT indicates hypertension, Al aortic insufficiency, and N normal. The various transformations for the several ECG variables to the logarithmic funct ion were made in order to reduce the skewness of the distribution of the measurements as shown in the formulae. Fig. I shows the distribution of the scores obtained by these equations. By formula 1, 74.5 % of cases with hypertension and 86.7% of normal controls were discriminated correctly. Formula 2 produced a more favorable result. Correct
193
LEFT VENmlCULAR IlYPERTROI'IIY Discriminant scores
-20
-30
Formula 1 urr -N)
o
-1.0
PC' rc e ntag e of
correctly interpreted c·~.e.
30
20
10
.:: :•••• i::·)· :11···:· ••••:••
.: .:
F'c r-rnul a l
n-·: .
(~,)
Normal controls
zct s»
(86.7)
Hype r t e ne ion
35/47
(74.5)
Normal controls
29/30
(AI - N)
:
.:
.:.•• -,:•••:. :,_00 H._.... Formula
,.
Aortic insufficiency
(89.5)
Hypertension
(83.0)
3
(AI - fiT)
t-
Aortic
••..!
(79.0)
insufficiency
Borderline of dilcrimin~tion
Fig. 1. Distribution of (he discriminant scores.
diagnosis was obtained in 89.5 % of aortic insufficiency and 96.7% of normal controls. The high percentages, namely 83.0% of hypertension and 79.0% of aortic insufficiency obtained by formula 3 indicated an accurate differentiation between these two diseases. 2. Contribution of each electrocardiographic finding to the differential diagnosis. The thirteen measurements employed to derive the discriminant equations are not considered to be equally useful in the differentiation of the diseases. Some items might be highly contributory to the diagnosis, while others not. In this respect, the influence of each term of the equations on the discriminant scores was examined and compared. Although the terms showing the greater value would seem to have a higher contribution to the diagnosis, they would not have a large effect on the differentiation if the variation of their values was not fairly large. Therefore, the variance or standard deviation of the values of each term is preferable as an' index of the degree of contribution. The terms showing the greater variance are regarded as having u larger influence on the discriminant score. On the other hand, since the discriminant scores vary in relation to the variation of the values of the individual terms, the terms with greater variation of values are considered to have a greater effect on the scores. Therefore, the correlation between the individual terms and discriminant scores is also employable as an index
of the degree of contribution. In this case, absolute values of the correlation coefficients must be compared, because only their magnitude is the subject of consideration. Figs. 2, 3 and 4 show the results of the forementioned analysis, in which the ordinate indicates the standard deviation and the abscissa the correlation coefficient. The higher values in both parameters may indicate that the findings are significant in the differentiation of the diseases. As shown in Fig. 2, the electrocardiographic
0.8
06
c a
.~
Td
>
"'"" "0
... "'.". "
T.
04
ST• PR.
(/)
In.
02
QRJ QRSd Pd
ll.
J. 02
1'.
0.4
06
Correlation coefficient
Fig. 2. Contribution of individual waves to thc differential diagnosis between hypertension and nor-
mal.
KI~tUR'\ A~D
findings which contributed most strongly to the differentiation between hypertension and normal were found to be the amplitude of the R wave (Ra). The deviation of the SAT segment (STa), the amplitude of the T wave (Ta), the depth of the S wave (Sa) and the interval between the end of the P wave and the beginning of the QRS deflection (PRs) were also regarded as useful information for differentiation. On the contrary, the depth of the Q wave (Qa) or the width of the P wave (Pd) were regarded to have little significance. As to the differentiation betw ccn aortic insufficiency and the normal, the most useful information was found in the amplitude of the T wave (Ta), as shown in Fig. 3. QTs, Ra, Pa, PRs and STa were also significant, but to a lesser extent. I.
oJ
IIAY,\KAW,\ I'll.
OB
06 c:
o
Il.
.~
>
"
"tl
... "".c: Vi -e
04
r• 02 Td
s. 0.2
0.4
0.6
Correlation coefficient
Fig. 4. Contribution of individual waves to the differential diagnosis between hypertension and aortic
insufficiency. 06 1'.
c:
.2 ~ .;;
. ""...
04
Vi
0 .2
-e
""..e
Q.
J. S.
R.
ST.
IlT.
I'H •
Olll I',
02
04
06
Correlatiun coefficient
Fig. 3, Contribution of individual waves to the differential diagnosis between aortic insufficiency and normal. The amplitude of the T wave (Ta) was also shown to be most significant for discrimination between hypertension and aortic insufficiency, as indicated in fig. 4. Other significant findings in this differentiation were QRd (ventricular activation time), Ja and I'd, while the amplitude of the R wave and the deviation of the S'Tvscgrnent were regarded as scarcely contributory. 3. Significance of the height of R wave in lead V o in the diagnosis of left ventricular hypertrophy. In most of thc criteria proposed by various investigators, some critical values are usually employed to decide whether the finding is ab-
normal or not. For example, Sokolow and Lyon'" set the critical value of the height of R wave in lead V o for left ventricular hypertrophy at 26 rnrn. Needless to say, this is not .an ideal procedure, because there will be a high possibility that normal cases which show the R wave to be higher than 26 mrn will be diagnosed as having left ventricular hypertrophy. From this viewpoint the contribution of the height of the R wave in lead V~ to thc dilfcrcntiation between hypertension and normal controls was examined . As indicated in Fig. 5, nearly half of the hypertensive cases have an R wave less than 26 rnm. IlUI most of such cases were diagnosed as having left ventricular hypertrophy by using the discriminant equation. Furthermore, all of the five normal cases showing the R wave to be higher than 26 rnm were judged as normal. A similar analysis was made in the differentiation between aortic insufficiency and the normal. As shown in Fig. 6, all cases of aortic insufficiency except two were diagnosed as aortic insufficiency, irrespective of the height of the R wave, Normal cases were also correctly diagnosed with only one exception. DISCUSSION Oui' results of the electrocardiographic differentiation between hypertension, aortic insufficiency
LUi
195
VENTR IC UL AR II Y/, £RTRO PII Y
60 Height of R wa v e in V :; ( m m )
50
•
H yp erten si on
x
Nor m a l
.:
40 30
.... ,.'
.
20
'li e
;.
-:
Z b rnrri
'1(. 'l(
1(
•
'll
'l(
..
10
o '----_-'--_--'-_--"--_----'-__'--_....1..-_--'-_ _ -40 -30 -20 -10 o 10 30 20 D isc r im in ant s c o res Fig. 5. The height of the R wave in lead V, and the discrimi nant scores obta ined by formul a I in the cases of hypertension and normal cont rol.
Height of
R wave in
Vs (mm)
•
90
•
•
Ao rtic insufficiency
)(
Normal
70
•
60
••
50
•
40 30
•
•
•
20
..
x
.. ~
• •
x x
• • •
26mm
x x .x
"x l(
•x
10
xX
"" )(
x
x
X
X
X
x xx x
x
x X
•
o -40 -30 -20
I
-10
10
20
30
Discriminant scores Fig. 6. The height of th e R wave in lead Vs a nd the discriminant scores obtained by Form ula 2 in the cases of aort ic insufficiency a nd normal controls.
196
KI~IUI{j\
Ar-;D IIAYAK,\W,\
and normal controls by discriminant equations as shown in Fig. 1 were fairly good, and comparable to those obtained by Rikli et al., even though we used electrocardiographic information of lead V" alone and cases without the typical electrocardiographic pattern of left ventricular hypertrophy were included. More accurate differentiation could have been expected if we had used the electrocardiographic information in all twelve leads and typical cases alone had been included in the material. This means that these diseases produce electrocardiographic findings which will serve to differentiate them even at an early stage, when clinical signs are still obscure. The number of cases used in our series, especially those with aortic insufficiency, may not be large enough from the standpoint of statistics. If we would. have derived the discriminant equations using a larger number of the cases, even more valuable results would have been obtained. The discriminant equations derived in this study include various measurements which are not used in the daily electrocardiographic differential diagnosis. Probably such measurements would contribute to the differentiation if they arc included. The extent of contribution of each electrocardiographic information to the differentiation of the diseases can be shown by the relationship of each term of the equation to the discriminant score. The terms which exert a greater effect on the score are considered to playa more important role in the differentiation. However, an indisputable method of determining the degree of contribution of each of the terms to the discriminant score has not been found in statistics. One of the conceivable ways to solve this problem is as follows: Suppose that we take n terms to discriminate. We then write n discriminant equations consisting of n-I terms in which the i-th term (i = I, 2, .... , n) is omitted. Comparing the results obtained by those n equations, we reveal the effectiveness of each item in the discrimination. However, this is a very inefficient method even when an electronic computer is used. Referring to the literature for similar problems, we find that Miyoshi? described the method of comparing the magnitude of b,dj, which is a component of l:bid i corresponding to Mahalanobis general distance. Other investigators reported the use of the F test 1 or the evaluation of
the values representing the normalized discriminant coefficients." The method employed in our study is to evaluate the variance of each term by substituting the actually measured values and also by using the correlation coefficients between the values of each term lind the discriminant scores. The terms showing both a larger variance and a higher correlation coefficient can be regarded as more significant in the dilTerential diagnosis. By this procedure, amplitude of the R wave (Ra), deviation of the ST-segment (STa), height of the T wave (Ta), depth of the S wave (Sa), and the interval between the end of the P wave and the beginning of the QRS deflection (PRs) in lead Vi> were found to contribute most to the discrimination between hypertension and normal. Although Rikli et al. did not examine the contribution of each finding to the discrimination of left ventricular hypertrophy, they stated that most of the findings used in their discriminant functions appeared to be effective in the discrimination after an examination of the significance of the dilTerence between the two diseases. The dilTerence between their opinion and ours is probably due to the difference in the manner of selecting the subjects as well as in the method of examining the significance of the dilTercnce. The method of comparing the values representing the normalized discriminant coefficients is analogous in its consequence to the method of using the standard deviation, which is a part of our procedure. But the results obtained by the former method alone may be easily influenced by the magnitude of correlation between each measurement, thus involving some risk in the evaluation of the degree of contribution. In this regard, our method of using both the correlation coefficients and the standard deviation can be said to express the degree of contribution better and to be more useful because it needs only simple calculation. The electrocardiographic findings which were found to contribute to the differentiation between hypertension and the normal are almost the same as those used in the current diagnostic criteria for left ventricular hypertrophy, such as those proposed by Sokolow and Lyon," Myers!" or Mori. 8 Only the terms Sa and PRs have not been employed previously. These results indicate that the criteria generally used at present are in general valid. Very recently Dower et aP have
197
UIT VENTlUCUlAR HYPERTROPHY
described that voltage criteria arc most useful, although VAT and ST.T changes may be of value. Their opinion nearly coincides with ours, but VAT(QRd) was not found to be so important in our analysis as seen in Fig. 2. It is certain, however, that the use of some critical value in these criteria reduces the amount of information available in the electrocardiogram. For example, if this value is high, the false negativity increases, and if it is low, the false positivity increases. The diagnosis by the discriminant equations is superior to the current diagnostic criteria, because the actual measurements arc used without modification. Our results obtained by using the discriminant equations showed that the normal cases with an R wave in lead V;, higher than 26 rnrn were diagnosed as normal and most of hypertensive cases with an R wave lower than 26 mm were diagnosed to have hypertension, as shown in Fig. 5. These results further signify that findings other than the height of the R wave arc very important in the diagnosis of left ventricular hypertrophy in lead V;,. As shown in Fig. 2, the interval between the end of the I' wave and the beginning of the QRS deflection (PRs) was found to contribute to the differentiation between hypertension and normal controls. As far as we know, this fact has not been pointed out previously. Its morphological and hemodynamic substrates may be a subject of research in the future. The electrocardiographic information contributing to the differentiation between aortic insufficiency and the normal is somewhat different from that between hypertension and the normal. The most important information here was shown to be the height of the T wave, while the height of the R wave was less significant. This difference may be ascribed to the difference in the form of hypertrophy. Aortic insufficiency shows hypertrophy with dilatation, while in hypertension hypertrophy is not usually accompanied by dilatation unless the disease is in an advanced stage. Another interesting observation as seen in Fig. 3 is that the P wave plays a more significant role in the differentiation between aortic insufficiency and the normal than between hypertension .and the normal. This can be explained by the assumption that the auricular function is affected hemodynamically at an. earlier stage of aortic insufficiency or that hypertrophy with dilatation
deforms the auricles in some manner, changing the shape of the I' wave. One of the most noteworthy facts observed in our study is that hypertension and aortic insufficiency were fairly clearly differentiated by the discriminant equations. The most important sign was found to be the height of the T wave. The time of the intrinsic deflection (QRd), deviation of the SoT junction (Ja) and duration of the P wave (I'd) were also significant. The height of the R wave was not useful, as demonstrated by the fact that an increased height of R is common to both hypertension and aortic insufficiency. According to the concept generally accepted at the present time these diseases arc considered to be poorly differentiated by electrocardiographic findings alone. However, our result suggests that the differentiation between hypertension and aortic insufficiency is possible by electrocardiographic findings alone, and the difficulties experienced in the past might be ascribed to our insufficient knowledge and usc of the findings indicated above. Since hypertension and aortic insufficiency arc different in hemodynamic aspects, their difference must be reflected in the electrocardiographic pattern, which will contribute to differential diagnosis. CONCLUSIONS I. Three discriminant equations were derived to differentiate between each pair of hypertension, aortic insufficiency and normal controls, using thirteen measurements in lead Va alone. 2. Correct discrimination was obtained by each formula in 74.5 % of patients with hypertension and 86.7% of normal controls, 89.5% of aortic insufficiency and 96.7% of normal controls, and 83.0% of hypertension and 79.0% of aortic insufficiency. 3. The standard deviation of each term, substituted by the actual values, and the correlation coefficient between the individual terms and the discriminant scores were used to evaluate the contribution of each electrocardiographic finding to the discrimination. 4. For discrimination between hypertension and the normal controls by lead Vo, the amplitude of the R wave, the SoT deviation, the amplitude of the T wave, the depth of the S wave and the interval between the end of the P wave and the beginning of the QRS deflection were found useful.
198 5. The most significant information for differentiation between aortic insufficiency and the normal was shown to be the amplitude of the T wave. 6. The amplitude of the T wave was also most significant for differentiation between hypertension and aortic insufficiency. Ventricular activation time, deviation of the junction and duration of the P wave were also useful, while the amplitude ofR wave was scarcely contributory. 7. The false positivity and neg ativity caused by the usc of thc critical value of 26 mrn in V; lead for left ventricular hypertrophy can be largely prevented by use of discriminant equations. 8. These results indicate that the electrocardiogram contains findings which have not been generally used in the diagnosis of left ventricular hypertrophy. REFERENCES I. Caceres, A. c.: Integration of data in diagnosis. Circulation Res. 11: 563, 1962. 2. Cabrera, E., and Gaxiola, A.: Systolic and diastolic loading of the heart. Am. Heart J. 43: 669,1952. 3.' Dower, G . E. and Ziegler, W. G.: On electrocardiographic-autopsy correlations in left ventricular hypertrophy. A simple post-mortem ind ex of hypertrophy proposed. Am . Heart J. 701: 351,1967. 4. Goldberger, E.: Unipolar lead electrocardiography
5. 6. 7. 8.
9. 10.
II .
12. 13.
14.
and vectorcardiography, Ed. 3. Philadelphia, Lea & Fcbiger, 1953. Gubner, R., and Ungcrlcider, H. E.: Electrocardiographic criteria of left ventricular hypertrophy. Arch. Int. Med . 72: 196, 19·B. Katz, L. N.: Electrocardiography. Ed. 2. Philadelph ia, Lea & Feb iger, 19-16. Miyo shi, E.: Tok yo lgaku Zasshi 4: I, 1956 (in Japanese). Mori, H., Nakagawa, A., and Kawarnata, K.: New criteria for the electrocardiographic diagnosis of left ventricular hypertrophy (~ IVP). Jap. Circulation J. 201: 96-1, 196-1. Nagao, T ., and Harada , H.: Study of an analogue computer for mass survey of hypertension. Jap. Circulation J. 27: 729, 1963. Noth, 1'. H., Myers, G. B., and Klein, H. A.: Precordial electrocardiogram in left ventricular hypertrophy. J. Lab . Clin. Mcd, 32: 1517, 19-17. Rikli, A. E., Tolle s, W. E., Steinberg, C. A., Carbcry, W. J., Freiman, A. H., Abraham, S., and Caceres, C. A.: Computer analysis of electrocardiographic measurements. Circulation 201: 643, 1961. Schach, J . A., Rosenbaum, R. H., and Katz, L. N.: The aV limb leads in the diagno sis of ventricular strain. Am. Heart J. 40: 696 , 1950. Sokolow, M., and Lyon, T. P.: The ventricular complex in left ventr icular hypertrophy as obtained by unipolar precordial and limb leads. Am. Heart J. 37: 161, 19-19. Wilson, F. N., Rosenbaum, F. F., and Johnston, F. D.: Interpretation of the ventricular complex of the electrocardiogram. Advances in Internal Medicine. Vol. 2. Chicago, The Year Book Publishers, 1947.