J. ELECTROCARDIOLOGY, 3 (2) 161-168, 1970

A Study of the Normal QRS-T Angle in the Frontal Plane*

BY RICHARD ZIEGLERt~ AND DANIEL K. BLOOMFIELD, M.D., F.A.C.C.~

SUMMARY

The noimal limits of A~ and A~ in the frontal plane and their relationship to each other have been defined. It has been shown that the QRS-T angle in the frontal plane is not only a function of magnitude but depends on the ab- solute A~ direction itself. As A~ shifts left, A~ lags behind so that when A~ is less than 0 ~ the normal A~ is always to the right of A~ A converse relationship has been demon- strated in vertical hearts. These findings should be of practical value to the interpretor of 12-1ead electrocardiograms in which the Einthoven tri- angle defines the frontal plane. However, we are aware of the limitation of our results which are obtained from a sample of hospitalized patients with a normal cardiovascular system.

INTRODUCTION

Deviation of the mean electrical QRS axis of the heart in the frontal plane (A~ from ap- parent normal values 1-5 has been considered

evidence of electrocardiographic abnormality. Similarly, the normal range of the mean electrical T axis in the frontal plane (A~ has been de- scribed ~,6. The difference between A~ and A~ the QRS-T angle, has also proven useful in defining electrocardiographic normality and ab-

normality. It has generally been accepted that a QRS-T angle in the frontal plane which exceeds 45 ~ 50 ~ or 60 ~176 is abnormal. We have

studied the value of the QRS-T angle in normal and abnormal electrocardiograms, and have noted the normal A~ ranges between --15 ~ and +85 ~ on the hexaxial reference system 4, s,12 and locates

centrally from normal QRS vectors that vary from -30 ~ to -[-95 ~ . It is the purpose of this

*From the Division of Medicine, Mt. Sinai Hos- pital, Cleveland, Ohio.

t Research Assistant. Associate in Medicine.

Reprint Requests: D. K. Bloomfield, M.D., School of Basic Med. Sci., Univ. of Illinois, Urbana, I11,

paper to describe the normal QRS-T angle rela- tionships in the frontal plane for adults over 35 years of age and to provide a practical approach, based upon the hexaxial reference system, for the interpreter of electrocardiograms to use these angles.

MATERIAL AND METHOD

Three hundred and one normal electrocardio- grams (143 male, 158 female) were selected at random from the records of hospitalized patients over 35 years of age. These records had been pre- viously read as normal by one of ten qualified physicians. The criteria for a normal record were that the interpreter, in his experience, had indi- cated that the record was normal and that there was no clinical evidence of heart disease. The age distribution of these records is noted in Table 1.

In determining the vectorial direction of A~ and A~ the transitional zone technique using the QRS and T wave amplitudes as dis- cussed by Graettinger, et al. 12 was used. In all cases, estimations of both A~ and A~ were made to the nearest five degrees on the hexaxial reference system. The absolute magnitude of A~ and A~ was not determined.

RESULTS

A~ of the 301 normal electrocardiograms varied between --30 ~ and + 95 ~ with a mean of +33.3 ~ -4- 28.1 ~ A~ for the sample fell be- tween --15 ~ and + 85 ~ with a mean of +40.1 ~ -4- 17.2 ~ . Both the range and standard deviations

indicate that the normal A~ varies less than the normal A~

Fig. 1 shows the distribution of A~ with respect to A~ for the sample. The line A~ = A~ drawn through the distribution shows that no simple value of the normal QRS-T angle (such as 60 ~ can accurately and fully de- scribe the normal limits of A~ with respect to A~ The A~ values are not distributed evenly on each side of the A~ = A~ line. Even the two bordering lines encompassing ap-

161

162 ZIEGLER AND BLOOMFIELD

301

A ~ T v s A ~ O R S

F R O N T A L P L A N E

N O R M A L E L E C T R O C A R D I O G R A M S

90 o .

8 0 o J J 7 " "

70

6o �9 /~

50 ........................ ~>

40

~- 30

2O

10

0

-10

-20

-30

i I ] ] I -30 -2~0- l l 0 0 10 210 30 410 50 610 710 810 910 1~)0

A ~

Fig. 1. A~ vs. A~ in the frontal plane for 30l normal electrocardiograms in persons over age 35. The lines A~ --60 ~ = A~ and A~ +35 ~ = A~ encompass approximately 94 per cent of values.

proximately 94 per cent of the distribution do not accurately describe the A~ population. Rather it can be seen that from A~ --30 ~ to 0 ~ the normal A~ is always to the right of A~ (A~ always more than A~ This trend con- tinues from A~ 0 ~ to A~ + 3 0 ~ with a majority of the A~ values lying to the right of

A~ From A~ + 3 0 ~ to + 6 0 ~ A~ is

distributed evenly on each side of A~ From

A~ + 6 0 ~ to +100 ~ nearly all of the A~

values lie to the left of A~ (A~ less than A~

Fig. 2 is a plot of the mean and standard

deviations of A~ values for a given A~ A~ values have been grouped to make the number of A~ values ten or more for each A~ range. The curve of best fit through the mean A~ values of the sample indicates that two regression lines

with corresponding 95 7O confidence limits would describe the normal A~ related to a specific

A~ accurately. Since the slope of the curve of the mean A~ values becomes steeper past + 3 8 ~ regression lines for the A~ population on each side of + 38 ~ were calculated, along with

95 7o confidence intervals for these lines. From A~ --30 ~ to + 35 ~ , the equation for the regression line was found to be A~ = 0.059 A~ + 33.71 ~ with the expression 1.96

~/292.91 + .006 (A~ -- 11.15) 2 13 repre-

senting the 95 7o confidence limits of the normal A~ for any A~ from - 30 ~ to + 3 5 ~ From A~ + 4 0 ~ to +100 ~ the equation for the regression line was found to be A~ = 0.317 A~ + 38.18 ~ with the expression 1.96

~]309.71 + .0076 (A~ - 57.14~ 2 represent- ing the 95 70 confidence limits of the normal A~ for any A~ from + 4 0 ~ to +100 ~ . Fig. 3 shows each regression line with its respective 95 70 limits, and Table 2 gives the 9570 confidence limits of the normal A~ at any A~ from

FRONTAL PLANE NORMAL QRS-T ANGLE 163

Fig. 2.

A ~ T v s A ~ Q R S

M E A N a n d S T A N D A R D

D E V I A T I O N S f o r A ~ T

100 -

9 0 -

80

70

6 0

5 0 -

4 0 -

3 0 -

2 0 -

10-

0 -

- 1 0

- 2 0

- 3 (

,s j

18 14 1• 2 4 11 1~ ~ L f l ~ - ~ 1 4 - 4- I I

I I I I I I I I I I I I I I - 3 0 - 2 0 -10 0 10 20 30 40 50 60 70 80 90 100

A ~ Q R S

Normal A~ vs. A~ values plotted as mean and standard deviations of A~ values.

-30 ~ to 4.100 ~ Both Fig. 3 and Table 2 also compare our data with the earlier studies of

Helm la. The regression line for the total sample was also

calculated. The equation for this line is A~ = 0.227 A~ 4- 32.57 ~ with the expression

1.96 ~/255.84 4" .0012 (A~ -- 33.31) 2

representing the 95 % confidence limits of the normal A~ for any A~ value from --30 ~ to 4-100 ~ We believe that two separate regression lines describe the interrelationship of A~ and A~ better than one regression line. The fol- lowing reasons are offered for this view:

1. The confidence limits found using two sepa- rate regression lines describe our sample popula- tion much better than the confidence limits found by using one regression line (compare Figs. 1

and 3). 2. By use of the t-test for the confidence limits

of a regression coefficient, it was found that the

regression coefficient for the total sample popula- tion (b = 0.227) was significantly different (p ( .05) than the regression coefficients of the two separate regression lines (b = 0.059, b =

0.317). 3. In comparing the mean A~ values of con-

secutive 30 ~ ranges (approximately) of A~ (Table 3), it can be seen that the mean A~ values for A~ -30 ~ to 0 ~ and for A~ 0 ~ to 4-35 ~ are not significantly different. However, for the next two A~ ranges (A~ -t-40 ~ to

4--60 ~ and A~ 4-60 ~ to 4,100 ~ the mean A~ values rise dramatically and, in each case,

are significantly different from the mean A~ values of the A~ range immediately preced-

ing. This table indicates the need to describe our

sample population with two regression lines; one

line for the A~ values for A~ --30 ~ to -1-35 ~ and another line for the A~ values for A~

4-40 ~ to 4-100 ~ .

164 ZIEGLER AND BLOOMFIELD

A ~ T vs A ~ ORS REGRESSION LINES AND 5% FIDUCIAL LIMITS ~','

110 . . ~

I00 v\~

90 O~ 0~>

80, 5% F IDUCIAL LIMITS /

70 - r ~ * ~ 1 7 6

5o- ..... , .~ . .~s,?~(oo"~._ ~02-a ~ ~,rr.. or'~ 1010 40- REGRESSION LINE ~ . . . Ipv ,'s ~.O

-30~ TO +35 ~ /.~ ,,,,.. ~A

< 3 0 - ,t.l', .~:.*~ ...... v,';. "~ . . . . . .

,,.,I.!.--- .0~~176176176 --

I0- ~ ." _.~o ~.2;." ..- % FIDUCIAL LIMITS

0- _ _ o . ~ , ~ .

- I 0 oO.**

- 2 0 ~~ ~

....,1%o"" -30" ..o s ..&~o

- 4 0 -

- 3 ' 0 - - 2 ' 0 - - 1 ~ ) (~ 1'0 2'0 3'0 4'0 5'0 6'0 7'0 8'0 9'0 1(30

A ORS Fig. 3. Regression lines and 5 per cent fiducial limits of A~ vs. A~ for the data in this paper con]pared

to Helm 14.

DISCUSSION

The purpose of this paper is to establish the

normal limits of the QRS-T angle in the frontal

plane using the hexaxial reference system and to

make this a useful tool for the individual who

interprets electrocardiograms. Several other

authors have commented in a general way on the

normal limits of the QRS-T frontal angle. Zao,

et al. s reported no normal QRS-T frontal angles

exceeding 45 ~ Arbeit, et al. n said that QRS-T

angles up to 60 ~ are within normal limits.

Graybiel et al. 9 said that the angle rarely exceeds

50 ~ Grant 7 indicated that for normal subjects,

the frontal QRS-T angle does not often exceed

45 ~ . However, Grant explained further that the

mean T vector varied less in direction in the frontal

plane than the QRS vector. He pointed out that

when the mean QRS vector deviated to a vertical

or horizontal direction, the normal T vector ac-

companied it but showed less deviation that the

QRS vector. Dimond 1~ came to similar conclu-

sions, stating that the "-F vector should lie to the

left of the QRS in electrically vertical hearts and

to the right of it in electrically horizontal hearts.

In the intermediate area, the T vector may lie on

either side of the QRS vector." Our work con-

firms and provides statistical support and limits

for the above observations.

Helm 14 considered the problem of the normal

limits of A~ in relation to A~ more specifi-

cally. Using 241 electrocardiograms of patients

over 20 years of age, he obtained a single regres-

sion line (A~ = 0.514 A~ -}- 20.9) for his

sample population and also calculated the 5 % and

1% fiducial confidence limits of A~ for a ran-

domly chosen A~ The 5 % limits are pre-

sented in Table 2 and Fig. 3. Based on these

FRONTAL PLANE NORMAL QRS-T ANGLE 165

limits He lm concluded " that any designated

upper limit o f normal (e.g. 50 ~ ) for the frontal

QRS-T angle may be too large when A ~ is

located on one side of A ~ and too small when

A ~ is located on the other side of A~ ' ' He

points out that this is particularly true when

A ~ is in a nearly horizontal or nearly vertical

position.

Figs. 1, 2 and 3, and Table 2 show that our data

generally agrees with that of Helm. Table 2

shows that the lower limits of the normal A ~

in our sample vary f rom - -2 ~ to + 2 ~ and the

upper limits vary f rom + 66 ~ to + 70 ~ as A ~

goes f rom - - 3 0 ~ to + 3 5 ~ These limits indicate

that in nearly electrically horizontal hearts, the

normal A ~ always lies to the right of A ~

and that the QRS-T angle may be as large as 96 ~

F o r A ~ + 4 0 ~ to + 1 0 0 ~ the lower limits of

the normal A ~ range f rom + 1 2 ~ to + 3 0 ~ and

the upper limits range f rom + 6 9 ~ to + 8 9 ~ , These

limits show that for nearly vertical hearts, A ~

always lies to the left of A~ and the QRS-T

angle may be as large as 70 ~ .

Fig. 3 and Table 2 which compare the 95 ~o

confidence limits of our sample to those of He lm

show a general agreement between the two sam-

pies, especially between A ~ + 15 ~ and + 6 0 ~

However the two samples differ in several ways.

Helm's data is based on a smaller sample with an

age range of 20 to 71 years of age. Our data is

based strictly on persons over 35 years of age,

an age group in which nonspecific T wave changes

and variations in the QRS-T angle may have in-

creased significance. He lm used a single regression

line with the confidence limits of this line to

TABLE 1 Age Distribution of 301 Normal Electrocardiograms

in Persons Over Age 35

Age Group N

35-40 39 41--45 54 46-50 45 51-55 42 56-60 41 61-65 25 66-70 24 71-75 19 76-80 8 Greater than 80 4

Total: 301 Mean age of sample = 53.05

Median age of sample = 52.02

represent the range of the normal A ~ with

respect to A ~ for his sample. Our data indi-

cate that two regression lines, one with a nearly

zero slope and one with a decidedly steeper slope

along with the respective confidence intervals of

each, best represent our sample populat ion. The

regression coefficients for both of the regression

lines determined for our sample were significantly

different f rom the regression coefficient of the

regression line for Helm's sample (b = .514) at

the .05 level. Because of differences in the regres-

sion lines used, the limits of the normal A ~ of

the two samples show much disagreement at the

extremes of the normal A ~ range. Even for

A ~ values at the extreme leftward limit of the

normal A ~ range, our data suggest that any

A ~ value less than 0 ~ (T wave inverted in aVF)

is abnormal. Simonson 15 and Hiss et al. 5 came to

a similar conclusion with the former setting the

lower limit of T ampli tude in adults above 20

years of age at - -0 .2 ram. in aVF and the latter

giving no negative values for the T wave in aVF

for adults above 20 years of age. However , Helm's

TABLE 2 The Normal Relationship of A~ to A~ in

Persons Over Age 35

A~ (Degrees)

95 % Confidence Limits (in degrees) of A~

Ziegler and Bloomfield Helm (14)

--30 -- 2 t o + 6 6 --36 to +47 --25 -- 2 t o + 6 6 --32 to +48 - - 2 0 - - l t o + 6 6 - - 2 9 t o + 5 0

--15 -- 1 to +67 --25 to +51 --10 - - l t o + 6 7 --21 to +53 - - 5 0 to +67 --18 to +54

0 0 to +67 --14 to +56 5 0 to +68 --11 to +58

10 + l t o + 6 8 -- 8 t o + 6 0 15 + 1 to +68 -- 4 to +62 20 + l t o + 6 8 -- l t o + 6 4 25 + 2 t o +69 + 2 t o +66 30 + 2 t o + 6 9 + 5 t o + 6 8 35 + 2 to +70 + 7 to +70 40 +12 to +69 +10 to +73 45 +14 to +71 +12 to +76 50 +16 to +72 +15 to +78 55 +17 to +74 +17 to +81 60 +19 to +76 +19 to +84 65 +20 to +77 +22 to +87 70 +22 to +79 +24 to +90 75 +23 to +80 +25 to +93 80 +25 to +82 +27 to +97 85 +26 to +84 +29 to +100 90 +28 to +86 +31 to +104 95 +29 to +87

100 +30 to +89

166 ZIEGLER AND BLOOMFIELD

data (Table 2, Fig. 3) indicate that the normal

A ~ can rotate as far left as - -36 ~ If this were so,

the normal T wave could be inverted in both II

and aVF. Al though one source ~6 lists a min imum

T wave in aVF of - -0 .6 ram. for adults over 20

years of age, none of the three sources 5,1~,~6 set

the lower limit of the T wave in II below 0 ram.

Furthermore, clinical expelience is strongly

against normal inverted T waves in aVF, even

though statistical treatment of the Helm data

may have led to this conclusion.

At the extreme rightward limit of the normal

A ~ range, our data suggests that the normal

A ~ never exceeds 89 ~ and thus that the normal

T wave is never inverted in I. Simonson ~5 placed

the lower limit of T wave amplitude for adults

over 20 years of age in lead I at 0.5 ram., and Hiss,

et al.:' show no negative T wave values for adults

over 20. However, Helm's data indicates that the

normal A~ can rotate as far tight at 104 ~ This,

too, is contrary to clinical experience.

By using one regression line fol his entire popu-

lation, Helm did not observe the change in the

A ~ populat ion as A ~ increases which we

have observed in our data. Since our data is based

on a larger sample and deals with an older popu-

lation, we believe the two separate regression lines

with corresponding confidence intervals more

accurately describe the relation of A~ to A ~

in persons over age 35.

We recognize that the method used for the

determinat ion of A ~ and A ~ is subject to

limitations. Zao, et al. s argued that the Einthoven

triangle upon which the hexaxial reference system

is based cannot give completely accurate results. The Burger triangle s,~7,1s is said by some to be

more accurate, but it is harder and less practical

TABLE 3 Comparison of A~ Populations for Different A~

Ranges in Persons Over Age 35

P Value Between

A~ Consecutive A~ Range N (mean 4- s.d.) Means

--30 ~ to 0 ~ 48 33.4 ~ 4- 19.8 ~ >0.1

+ 5 ~ to +35 ~ 108 34.7 ~ 4- 16.3 ~ <0.001

+ 4 0 ~ to +60 ~ 97 43.0 ~ 4- 14.2 ~ <0.001

+65 ~ to +100 ~ 48 54.3 ~ 4- 13.8 ~

to use. Both Hiss, et al. 5 and Zao, et al. s have

stated that 15 degrees is the limit of accuracy

obtainable f rom the hexaxial reference system.

Marr io t t 4 has given the system credit for greater

accuracy, perhaps even 5 degrees. Burch and

Winsor 19 and Ashman and Hull 2~ have pointed

out that true accuracy for A ~ and A ~ re-

quires measurement of the area encompassed by

the QRS and T waves. However , Simonson, et

al. 21 reported a high positive correlation between

the areas and the amplitudes of both the QRS

and T waves. We used the transitional zone tech-

nique t2 using only the wave amplitudes to de-

termine the angles because this method is the one

most useful to the day-to-day interpreter of

electrocardiograms who usually works with the

Einthoven triangle. Graettinger, et al. 12 point out

the fairly accurate results of this method.

The QRS-T frontal angle should be determined

both in magnitude (the absolute number of de-

grees of the angle) and in direction (the position

of A ~ to the right or left of the A~ Since

the hexaxial reference system is useful for every-

day electrocardiographic interpretation, the limits

of normali ty demonstrated in Fig. 3 and Table 2

for A ~ in relation to A ~ should be of im-

mediate practical value.

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FRONTAL PLANE NORMAL QRS-T ANGLE 167

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