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The ventricular gradient vector and related vectors
The Ventricular Willium
Gradient
D. Angle,
M.D.,
Vector Omaha,
and Related
Vectors
Neb.
The main purpose of this article is to define the cardiac complex area vector and to discuss its significance as it relates to the ventricular gradient area vector. Studies of the variation of the ventricular gradient area vectors in several cases of intermittent conduction disturbance are presented.
The arithmetic mean or average value of n scalars is their algebraic sum divided by the number n. The scalar voltage recorded bl. an electrocardiograph is a function of time. An approximate mean value of the voltage with respect to time may be obtained for any particular interval of time by dividing this interval into n equal subintervals of time, constructing an ordinate from the base line to the curve at the midpoint of each subinterval and then averaging the n ordinates as shown in Fig. l,C. The error of this approximation obviousl\r tends to decrease as the number of time subintervals and corresponding ordinates are increased. time
The mean is defined
value of the voltage by the following,
with
respect
to time
for a given
interval
of
‘h /Mean value of v with respect to time from t = t, to t = tl] where the numerator on the right by the curve of recorded voltage, t = t,.
Vdt
=
.i ” ~~~L - to
is the definite integral v, the base line and
(1)
giving the area bounded the ordinates t = t, and
The mean or average vector of n vectors is their vector sum divided by the number n. In general, the direction of the mean vector of n vectors is not the mean of the directions of the n vectors, and the magnitude of the mean vector is not the mean of the magnitudes of the n vectors. The heart vector H may be considered an explicit function of time. An approximate mean vector with respect
Prom Clarkson Hospital and the 1;niversity of Nebraska Supported by grants from the Nebraska Heart .Associatiom. Received for publication Oct. 5. 19.59.
~‘ollege
of Rlrdicirw,
Omaha,
KC+.
750
Am. Heart J. May, 1960
ANGLE
to time for a particular portion of a vectorcardiogram may be graphically obtained by dividing this portion of the loop into II equal subintervals of time, constructing a vector from the origin to the loop at the midpoint of time of each subinterval, adding the n constructed vectors vectorially and dividing the magnitude of this vector sum by n, as shown in Fig. 1,D. The mean heart vector with respect to time for the time interval from t, to tl is defined by the following, ‘6 IMean H with respect to time from t = t, to t = t,]
=
Hdt :I ?L..-- ~._
(2)
t, - t,, where the numerator on the right is the area heart vector for the time interval from t, to tl. An area heart vector for any particular interval of time is equal to the mean heart vector with respect to time for this particular time interval multiplied by this time interval. The determination of an area vector from measurement of electrocardiographic complexes is depicted in Fig. 2. Hechtl has stated that it is obvious that the area which is enclosed by a vectorcardiogram is identical with the area vector for the corresponding electrocardiographic defEction. On the contrary, it is obvious that this is not true. The area enclosed by a vectorcardiogram is related to the area vector determined from the vectorcardiogram or the corresponding electrocardiogram onl>in a complex fashion of no practical significance. If it is considered that the ventricular gradient process and the repolarization process both extend throughout the QU interval, Wilson’s h>rpothesis may be stated as follows, tQ*sM~as + tgLlMX! = tuvlV. (3) where tans and tQU are the QRS and QU intervals, respectively, and MQRB, NIT”, and RI, are the mean vectors with respect to time for QRS, TU, and the ventricular gradient, respectively. If an isolated PT, complex is available, the areas of the P and ‘I‘, waves can be accurately approximated. Since the initial portion of atria1 repolarization occurs during atria1 depolarization, it may be considered that the P wave rests upon the initial portion of the T, wave, as shown in Fig. 3. This initial portion of the T, wave may be approximated by drawing a straight line between the points of onset and offset of the P wave. The net area of the P wave may then be approximated by measuring with respect to this constructed straight line. The T, wave may be considered to be based upon the true base line which may be approximated by drawing a straight line between the points of onset and offset of the ‘I‘, wave. The area of the T, wave is obtained, therefore, by measuring with respect to this constructed straight base line. The P and T, waves overlap in the area enclosed by the straight line drawn to approximate the initial portion of the T, wave, the straight base line constructed between the points of onset and offset of the T, wave, and the portion
\~r,lu1nc Surnlw
.i9 5
VENTIZICI~LAR
GRADIENT
VECTOR
AND
RELATED
WXTOKS
of the curve of the I’ wave between these two straight lines. opposite sign in the I’ and T3. areas, it will cancel when the added to obtain the net area of the I’T, complex. Consequently, to define the initial portion of the T, wave, the base of the P net PT, area. The net PT, area may be obtained simply by
751
Since this area is of P and TX areas are it is unnecessar> wave, to obtain the measuring the area
A.
Y
c.
Fig. 1.-;1, The first 0.06 sec. of a QRS loop and the corresponding portions of two QRS complexes recorded by two leads. X and U. Any two electrocardiographic leads when fed to the orthogonal paired deflection plates of an oscilloscope will yield a vectorcardiogram having the characteristic that the electrocardiograms recorded by these leads may he precisely derived from the vectorcardiogram by using an orthogonal lead diagram, and conversely. the vectorcardiogram may be precisely derived from the two simultaneously recorded electrocardiographic leads. B, Vectors are constructed from the origin to the time midpoint’s of the six equal subintervals of time along the QRS loop, and the corresponding ordinates are constructed from the base line to the curve at the midpoints of the corresponding tjime subintervals for the tw-o partial QRS complexes. C, The constructed ordinates are added algobraically by placing them end to end. as shown by the vertical dashed lines, and the means of these algebraic sums are found by dividing by 6. the number of ordinates added. D. The mean values of voltage with respect to time for the two partial QRS complexes determined in C are used to find the corresponding mean vector with respect to time. The vectors constructed in I3 are added vectorially by t.he origin-to-terminus method to yield their vector sum. indicated by the dashed line. Dividing the magnitude of this vector by the number 6 yields a mean vector with respect to time equal to that determined from the electrocardiographic complexes. This approximated mean vector with respect to time differed insignificantly from the correct mean vector calculated analytically using equations (1) and (2). which calculations were possible since the functions v = f (t) and H = F (t) were known in this particular example.
752
.\m.
.4NGLR
under points
the complex with respect to the straight base liiie of onset and offset of the T, wave. Similar remarks apply to the measurement of the areas of an isolated ventricular complex. It is simpler QRSTU directly than to obtain this area by adding the and TIT.
constructed
Ilrart J. &lay, 1’760
between
the
QRS, TIJ, and QRSTU to measure the area of measured areas of QRS
A.
D. /-~~--jT
. \ \--\ \
-X
20
Hv.
1
Fig. 2.-A. The approximate area of the first 0.06 sec. of 1 wo partial QRY complexes found by constructing rectangles with one pair of sides equal to the corresponding ordinates of Fig. 1,H. and the other pair equal to the time subinterval. The areas of t,hase constructed rectangles are algebraically added to yield the sums shown by the larger rertangles. R, The approximate area vector determined from the values found in A. The same approximate area vector is obtained when t,he mean vector with respect t,o time from Fig. 1,D is multiplied by 0.06 sec. C. The variation of the magnitude and direction of the heart vector with respect to time for the partial QRS loop shown in Fig. 1. The mean magnitude and the mean direction with respect, to time for these functions are indicated. D. The partial QRS loop is indicated by a dashed curve. The vect’or with magnitude and direction equal to the means indicated in C is shown, as is the mean vector with respect to time previously determined in Fig. 1.D. It is apparent. as is generally true, that the direction of the mean vector with respect to time is not thr mean of the directions of the QRS vectors. and that the magnitude of the mean vector with respect to time is not the mean of the magnitudes of thr QRS vectors.
In the usual cardiac complex the ventricular complex is superimposed upon the T, wave, so that measurement of the T or TIT area is further complicated by the necessity of defining the terminal portion of the ‘I‘, wave. The area of PT,TU, however, may be simply measured with respect to a straight base line constructed between the point of onset of P and the point of offset of IJ, as shown in Fig. 3. The area of PT,QRSTU is likewise measured with respect to this constructed straight base line.
In this study, the IT wave is considered to be part of ventricular repolarization in regard to the ventricular gradient. If this assumption is correct and ii there is no atria1 gradient, the area vector found from measurement of 1’7;QRSTtT areas is the ventricular gradient :trea vector. I;or the studies presented in the subsequent portiou of this article it is immaterial whether or not there is ;LII atria1 gradient, inasmuch as the studies arc concerned with intraindividu~~l comparisons of the P’I~QRSTIT area vector over brief periods of time duriug which it may be assumed that the atria1 gradient is constant.
Fig. 3.--A, Arbitrary I’, T,. QRS, T, and L: waves shown for simplicity as isosceles triangles. N. When the PT:, complex is formed, the shape of the P wave is altered but its area remains t,hr same. The initial portion of t,he T,, wave. shown hy a dashed line, now forms the base of the P wave, and each ordinate from this base line to the curve has the same length as the corresponding ordinate from the horizontal base line to the curve of the isolated P wave in d. Since the sign of the terminal portion of the T, wave and the initial port)ion of the T wave is the same, either may be considered to originate along the horizontal base line. whereas the other is superposed. C’. The cardiac complex is completed by adding the QRS and U waves. The heavy outlines of QR8. T. and PT:,TI’ indicate the course along which a planimpter should travel in measuring these areas. For measurement of the PT,,QRSTU complex the planimeter should travel along the curve of the cardiac complex and then back to the point of onset along a constructed base line extending between the points of onset and offset of the complex. D. A different cardiac complex is obtained by changing the sign of the T w-ave so that the T area is now positive. The determination of the areas of QRS, T, and PT:,TI’ is again shown.
754
VENTKICUI,AR
GKADlENT
VECTOR
AND
RELATED
VECTORS
75.5
Fig. 4.-The electrocardiogram for a case of intermittent left bundle branch block. The areas of the cardiac complexes, in microvolt-sec.. are written by each complex and were determined with respect to a straight line constructed between the points of onset of successive P waves. A straight line beneath each lead was constructed parallel with the original horizontal paper markings. A, A tracing of Lead Va showing the upper and lower margins of the inscribed electrocardiogram. As was true for the other leads, t,he areas of the cardiac complexes for the upper curve are consistently greater than those for the lower curve. 1%. A midpoint tracing of I,ead Vq constructed along the midpoints of the vertical distances betwvrn the upprv and lower margin curves. Such midpoint curves arc illustrated for all of the other leads.
Fig. A.-.-l, I3, and C, Four complexes from Load aVF from a case of intermittent left bundle branch block. The cardiac complex areas are measured with respect to a straight line constructed between the peaks of successive P waves, between the points of onset of successive P waves, and between the points of onset of successive QRS complexes. In each case the difference between the measured areas of the normal and abnormal complexes is approximately the same. D, The cardiac complex areas are measured with respect to a horizontal straight line passing through the point of onset of the P wave. Such results are the best that can be obtained with electronic integrators currently in use. Obviously. the averaging of a large number of complexes would be necessary to obtain measurements of notable acGUI-WY.
Am. Iieart J May. 196C
.\NGIJi
756
Pig.
6.-J,imb lead complexes
plane from
vcctorcardiograms a case of intermittent
derived fr r the normally Wolff-Parkinson-While
atld ar~on~alously syndrome.
COndUr’twJ
\-t~~STIZI(‘I~I,.\H
ITor the measurement original electroc~~rdiogram opticall>~, ;111d the upper were tr;weCl oilto p;lIxx
GK.\DIISNT
\‘I<(‘TOK
:\ND
I
\~l<(‘TOl
7.57
oi I”I‘JJIK~~.’ areas untlertnketl ill this stud>, the or ~~uhlishecl figure was enlnrgerl eight diameters antI lower margins of the itlscribecl electrocardiogram for j)lanimetric determili:~tioii. 1 t xvas frequejitlk i\Wil
c. 16\
20 WPW-N
d+?
Pig. 7.-A and LI, The vectorcardiograms from Fig. 6. C. The differroce by sxbt,ract,ing the loop in A from the loop in H. D, Derivation of the area in C. The dashed line indicates the vector sum which is to be divided by were added and then multiplied by the total time interval. E’, The card ac normally and anomalousIy conducted complexes obtained from the measured graphic complexes. F. The wntr.rular gradient area difference vector obtained from the abnormal cardiac complex area vector. This vector is the same
vnctorrardiogram obtained vector for the difkrence loop the number of vectors which complex area vectors for the areas of the elect,rocardioby subtracting the norma! as that obtained in D.
758
ANGLE
Am. Heart J. May, 1960
found that the areas determined from the upper and lower margin curves differed. For over a hundred complexes from the case of intermittent left bundle branch block to be presented the areas were consistently algebraically greater for the upper curve. This is obviously due to the vagaries of t.he heated St\-lus, and indicates the error of the common practice of r:mdomly changing from the upper to the lower margin in area measurement. THE
EXPERIMENT
OF
WILSON
AND
ASSOCIATES
In their original articles on the ventricular gradient, Wilson and associates2J described a dog experiment performed to investigate the constant\of the ventricular gradient area vector during marked alteration of ventricular depolarization. It was decided to determine the cardiac complex area vectors for this experiment. The values for the PT,QRSTU areas were first determined Lvith respect to a straight base line drawn between the points of onset of successive 1’ waves. The measured values for Lead I decreased somewhat irregularly from approximately 15 microvolt-sec. for the first complex to zero for the fifteenth complex, with one notable exception, complex 11. The values for Lead III were close to 38 microvolt-sec., with six exceptions, complexes 1, 3, 5, 12, 13, 15. \‘isunl examination of these complexes indicates that the base line is not accurately. approximated by a straight line drawn between the points of onset of successive I’ lvaves. Several methods were used in an attempt to find the true location of the base line, but only one such method will be described, since it. reveals the general approach. The complex in question and the t\vo preceding ant1 two succeeding complexes were adjusted so as to bring the constructed straight base lines to a horizontal 1)osition. All five adjusted complexes were then traced onto a single piece of paper so that the points of onset of the P waves and the adjusted straight. base lines were superimposed. A gradual transition of waveform from complex to complex was then apparent for all compleaes SIVC tllxt with the erroneous base line. On the basis of such study, the seven erroneous base lines were rctlra\vn and new values for the areas of the cardiac complexes were determined. These new values were consistent with the values previously tletermined for the other complexes. The magnitude of the Lead III vector for a dog ma)- be three times that of the Lead I vector, and the angle between these lead vectors may be close to 00”. On such a lead vector diagram the cardiac complex area vectors will vary through a range of about SO”, as the cardiac complex area in I*ead I varies from about 1.5 to zero microvolt-sec. Thus the termini of the ventricular gradient area vectors move from left to right as the center of stimulation of the ventricles moves from right to left. Variation of the equivalent cardiac generator with variation in the lead fields would explain the changing ventricular gradient area vectors. An alternate explanation is that Wilson’s hypothesis does not hold. Apparently, the issue cannot be settled without further animal experimentation wherein the animal heart is suspended in an extensive medium with distant electrodes, thereby
x%-z “5”
VENTRICULAR
GRADIENT
VECTOR
AND
RELATED
VECTORS
7.59
ensuring relatively constant lead vectors. If the ventricular gradient area vector is constant despite alteration in depolarization in such an experiment, Wilson’s hypothesis will finally have been demonstrated to hold for the isolated animal heart. THE
CASE
OF SIMONSON,
SCHMITT,
DAHL,
FRY
AND
BAKKJZN
Simonson and associates4 published three electrocardiograms taken over a ‘i--day period from a patient with right bundle branch block who subsequently developed complete atrioventricular block with a changing ventricular pacemaker. They stated that this case constitutes the human counterpart of the dog experiment of Wilson and associates. The magnitudes of the three ventricular gradient area vectors calculated from their data were similar. However, visual inspection of the Lead I complex for April 24, reveals that it has a net negative area, whereas Simonson and associates have measured the area of this complex as a net positive quantity to four significant figures. The nature of their error appears to be the use of a base line constructed along the lower margin of the inscribed curve, whereas the T area is measured along the upper margin. It appears that the authors used the second complex in Lead III on April 17, to determine the QRS area but used the first complex to determine the T area. Such a division between two QRST complexes is an illegitimate error, since, ii the ventricular gradient is ullchanged, the larger, second QRS would surely be followed by a larger negative 7‘. The cardiac complex area vectors were determined for these electrocardiograms and showed considerable variation in magnitude and direction. It is evident that the conclusions of Simonson and associates with respect to the ventricular gradient for these electrocardiograms are, in general, invalid. INTEKMITTENT
RIGHT
BcrNDLE
BRANCH
BLOCK
The cardiac complex areas were determined for the case of intermittent right bundle branch block published by Wilson and associates5 and for the case published by White.6 In both cases the areas for the blocked complexes were roughly half the areas for the normal complexes in the right precordial leads. Since both types of complexes had positive areas in the right precordial leads, the ventricular gradient area difference vector obtained by subtracting the normal from the blocked cardiac complex area vector was directed posteriorly in both cases. INTERMITTENT
LEFT
BUNDLE
BRANC‘H
BLOCK
The cardiac complex area vectors were determined for a case of intermittent left bundle branch block published by Segers and Boyadjian,7 and the magnitude of the vector for the blocked complexes was about two thirds of the magnitude of that for the normal complexes. The ventricular gradient area difference vector obtained by subtracting the normal from the blocked cardiac complex area vector was directed rightward and slightly inferiorly.
The electrocardiogram from a previousI\. uttpublished case of intermittent left bundle branch block is showtt in I;ig. 4. It might be wondered whether the differences between the area measurements of the ttormal and blocked complexes are due to incorrect placement of the constructed base iitte with respect to which the measurements were made. In Fig. 5 these differences are shown to be independent of uniform vertical displacements of the constructed base litte such as would occur if each P wave were raised or io\vered ;I constant distance front the true base line by the preceding U wave. It might next be wondered whether there is an alternating vertical displacement of the constructed base line resulting from superposition of alternate P waves on varying II waves. Assume, for example, that the I’ wave of the normal complex initiates on the true base line while the I’ wave of the blocked complex is raised above the true base line by the preceding t7 wave. In this case the constructed straight base line for both the normal and the blocked complexes will rest on the true base line at one end of the complex and will be elevated above it a certain constant distance at the other end. Therefore, the error in area tneasurements of alternating block resulting frotn this type oi misplacement of the base line would be equal in amount for both t\yes of complexes, and, consequently, the difference between the tneasured areas would still be the correct difference. Some increase in the accuracy of the area measurements could have been obtained by adjustments of the straight constructed base lines in a manner similar to that described for some complexes from the dog experitnettt of \Viisott and associates. However, a sufficient number of complexes have been studied to permit averages for each type of complex from eitch leatl to be obtained, thus The magnitude of the cardiac complex making such adjustments unnecessary. area vector for the blocked complexes is slighti). less than half that for the normal complexes. The ventricular gradient area difference vector is directed right\vard, anteriorly and slighti?. inferiorly. For the normal tracing the cardiac complex area vector can be considered to consist of three component vectors, the atria1 gradient area vector and the right and left ventricular gradient area vectors. Thus,
-AP + AT:, + <s,tv + A1.lT,iv + AQHS,,,. + AT1 ,,~ = (it + (A\ + Gt.\ where tricular
LAII, AuItpI1,., .Aoll+,,V are the area depolarization,
vectors
for atria1
;ud right
AT:,, A%r1,(,., AA~~~.tVare the art‘;\ vectors
(3)
and left ven-
for atria1
and right
area vectors and left ventricular repoiarization, a1~1CL, (;ltI, G,., are the gradietlt for the atria and the right and left ventricles, respectively. Following the onset of left bundle branch block the normal left ventricular QRS and TlT area vectors become blocked left ventricular QRS and TIT area vectors, whereas the left ventricular gradient area vector will be unchanged if Wilson’s h>rpothesis holds. Thus,
where CLrr HRIlis the left ventricular bundle
branch
block.
gradient
area vector
in the presence
of left
\~“lUnw Numhrr
59 5
VENTRICL-L.4R
Subtracting
GRADIEXT
VECTOK
AND
KELATED
VEC’TORS
761
(3) from (4) yields
where either side of the equation is equal to the left ventricular gradient area differerrce vector obtained by- subtracting the cardiac complex area vector for the normal complexes from that for the blocked complexes. It may be that Wilson’s h>.pothesis does not hold and that the left ventricular gradient is changed b,- alteration of left ventricular depolarization. On the other hand, Wilson’s h).pothesis may be valid, in which case the finite difference vector is presumably due to alterations of the lead fields secondaq~ to altered ventricular depolarization.
\.ectorcardiograms for the plaue of the limb leads are derived in Fig. 6. Subtraction of these loops yields the difference vectorcardiogram shown in Fig. 7,C, from which the ventricular gradient area difference vector is derived in D. This difference area vector is obtained more directly in E and I; from the measured areas of the electrocardiographic cardiac compleses.
The concept of a mean vector with respect to time for a certain time interval is discussed. A simple method for determining the area vector for electrocardiographic cardiac complexes is presented, and the theoretical and practical advantages of its use are discussed. The ventricular gradient area difference vector is defined and is determined for the dog experiment of Wilson and associates, for two cases of right and two cases of left intermittent bundle branch block and for one case of intermittent anomalous atrioventricular e.ucitation. 1t is pointed out that in each case this difference vector ma). be due to alteration of the lead fields or ma); be an indication of invalidity of Wilson’s hypothesis. KI:FEKES(‘I?S
1. 2. 3. 1. 5. 6. 7.
Hecht,
H. H.: Basic Principles of Clinical Electrocardiograph!, Springfield, Ill., 1950, Charles C Thomas. Pnhlisher. \$!i!son, F. N.: MacLeod; A. G., and Baker, I’. S.: ‘l‘he ‘I‘ Deflection of the Electrocardiogram, 1 r. A. Am. Physicians 46:29, 1931, \Vilson, F. N., MacLeod, A. G., Barker, P. S., and Johnston, F. I).: The Determination and the Significance of the Areas of the Ventricular T>eflections of the Electrocardiogram, AM.~EART j. 10:46, 1931. Simonson, E., Schmitt, 0. H., Dahl, J.. Fry, I)., and Bakken, E. E.: The Theoretical and Experimental Bases of the Frontal Plane \‘entricular Gradient and Its Spatial Counterpart, AM. HEART J. 47:1X, 195-1. Wilson. F. N., Rosenbaum, F. F.. and Johnston, F. D.: Interpretation of the Ventricular Complex of the Electrocardiogram, IN =\d\.ances in Internal Medicine, New York, 1947, Interscience Publisher, Inc. IVhite, P. I?.: Heart Disease, Ney York, 1951, The Macmillan Co. Segers, M., and Boyadjian, N.: Etude critique du concept du gradient \-entriculaire, Arch. mal. coeur 42522, 1949.
Gradient
D. Angle,
M.D.,
Vector Omaha,
and Related
Vectors
Neb.
The main purpose of this article is to define the cardiac complex area vector and to discuss its significance as it relates to the ventricular gradient area vector. Studies of the variation of the ventricular gradient area vectors in several cases of intermittent conduction disturbance are presented.
The arithmetic mean or average value of n scalars is their algebraic sum divided by the number n. The scalar voltage recorded bl. an electrocardiograph is a function of time. An approximate mean value of the voltage with respect to time may be obtained for any particular interval of time by dividing this interval into n equal subintervals of time, constructing an ordinate from the base line to the curve at the midpoint of each subinterval and then averaging the n ordinates as shown in Fig. l,C. The error of this approximation obviousl\r tends to decrease as the number of time subintervals and corresponding ordinates are increased. time
The mean is defined
value of the voltage by the following,
with
respect
to time
for a given
interval
of
‘h /Mean value of v with respect to time from t = t, to t = tl] where the numerator on the right by the curve of recorded voltage, t = t,.
Vdt
=
.i ” ~~~L - to
is the definite integral v, the base line and
(1)
giving the area bounded the ordinates t = t, and
The mean or average vector of n vectors is their vector sum divided by the number n. In general, the direction of the mean vector of n vectors is not the mean of the directions of the n vectors, and the magnitude of the mean vector is not the mean of the magnitudes of the n vectors. The heart vector H may be considered an explicit function of time. An approximate mean vector with respect
Prom Clarkson Hospital and the 1;niversity of Nebraska Supported by grants from the Nebraska Heart .Associatiom. Received for publication Oct. 5. 19.59.
~‘ollege
of Rlrdicirw,
Omaha,
KC+.
750
Am. Heart J. May, 1960
ANGLE
to time for a particular portion of a vectorcardiogram may be graphically obtained by dividing this portion of the loop into II equal subintervals of time, constructing a vector from the origin to the loop at the midpoint of time of each subinterval, adding the n constructed vectors vectorially and dividing the magnitude of this vector sum by n, as shown in Fig. 1,D. The mean heart vector with respect to time for the time interval from t, to tl is defined by the following, ‘6 IMean H with respect to time from t = t, to t = t,]
=
Hdt :I ?L..-- ~._
(2)
t, - t,, where the numerator on the right is the area heart vector for the time interval from t, to tl. An area heart vector for any particular interval of time is equal to the mean heart vector with respect to time for this particular time interval multiplied by this time interval. The determination of an area vector from measurement of electrocardiographic complexes is depicted in Fig. 2. Hechtl has stated that it is obvious that the area which is enclosed by a vectorcardiogram is identical with the area vector for the corresponding electrocardiographic defEction. On the contrary, it is obvious that this is not true. The area enclosed by a vectorcardiogram is related to the area vector determined from the vectorcardiogram or the corresponding electrocardiogram onl>in a complex fashion of no practical significance. If it is considered that the ventricular gradient process and the repolarization process both extend throughout the QU interval, Wilson’s h>rpothesis may be stated as follows, tQ*sM~as + tgLlMX! = tuvlV. (3) where tans and tQU are the QRS and QU intervals, respectively, and MQRB, NIT”, and RI, are the mean vectors with respect to time for QRS, TU, and the ventricular gradient, respectively. If an isolated PT, complex is available, the areas of the P and ‘I‘, waves can be accurately approximated. Since the initial portion of atria1 repolarization occurs during atria1 depolarization, it may be considered that the P wave rests upon the initial portion of the T, wave, as shown in Fig. 3. This initial portion of the T, wave may be approximated by drawing a straight line between the points of onset and offset of the P wave. The net area of the P wave may then be approximated by measuring with respect to this constructed straight line. The T, wave may be considered to be based upon the true base line which may be approximated by drawing a straight line between the points of onset and offset of the ‘I‘, wave. The area of the T, wave is obtained, therefore, by measuring with respect to this constructed straight base line. The P and T, waves overlap in the area enclosed by the straight line drawn to approximate the initial portion of the T, wave, the straight base line constructed between the points of onset and offset of the T, wave, and the portion
\~r,lu1nc Surnlw
.i9 5
VENTIZICI~LAR
GRADIENT
VECTOR
AND
RELATED
WXTOKS
of the curve of the I’ wave between these two straight lines. opposite sign in the I’ and T3. areas, it will cancel when the added to obtain the net area of the I’T, complex. Consequently, to define the initial portion of the T, wave, the base of the P net PT, area. The net PT, area may be obtained simply by
751
Since this area is of P and TX areas are it is unnecessar> wave, to obtain the measuring the area
A.
Y
c.
Fig. 1.-;1, The first 0.06 sec. of a QRS loop and the corresponding portions of two QRS complexes recorded by two leads. X and U. Any two electrocardiographic leads when fed to the orthogonal paired deflection plates of an oscilloscope will yield a vectorcardiogram having the characteristic that the electrocardiograms recorded by these leads may he precisely derived from the vectorcardiogram by using an orthogonal lead diagram, and conversely. the vectorcardiogram may be precisely derived from the two simultaneously recorded electrocardiographic leads. B, Vectors are constructed from the origin to the time midpoint’s of the six equal subintervals of time along the QRS loop, and the corresponding ordinates are constructed from the base line to the curve at the midpoints of the corresponding tjime subintervals for the tw-o partial QRS complexes. C, The constructed ordinates are added algobraically by placing them end to end. as shown by the vertical dashed lines, and the means of these algebraic sums are found by dividing by 6. the number of ordinates added. D. The mean values of voltage with respect to time for the two partial QRS complexes determined in C are used to find the corresponding mean vector with respect to time. The vectors constructed in I3 are added vectorially by t.he origin-to-terminus method to yield their vector sum. indicated by the dashed line. Dividing the magnitude of this vector by the number 6 yields a mean vector with respect to time equal to that determined from the electrocardiographic complexes. This approximated mean vector with respect to time differed insignificantly from the correct mean vector calculated analytically using equations (1) and (2). which calculations were possible since the functions v = f (t) and H = F (t) were known in this particular example.
752
.\m.
.4NGLR
under points
the complex with respect to the straight base liiie of onset and offset of the T, wave. Similar remarks apply to the measurement of the areas of an isolated ventricular complex. It is simpler QRSTU directly than to obtain this area by adding the and TIT.
constructed
Ilrart J. &lay, 1’760
between
the
QRS, TIJ, and QRSTU to measure the area of measured areas of QRS
A.
D. /-~~--jT
. \ \--\ \
-X
20
Hv.
1
Fig. 2.-A. The approximate area of the first 0.06 sec. of 1 wo partial QRY complexes found by constructing rectangles with one pair of sides equal to the corresponding ordinates of Fig. 1,H. and the other pair equal to the time subinterval. The areas of t,hase constructed rectangles are algebraically added to yield the sums shown by the larger rertangles. R, The approximate area vector determined from the values found in A. The same approximate area vector is obtained when t,he mean vector with respect t,o time from Fig. 1,D is multiplied by 0.06 sec. C. The variation of the magnitude and direction of the heart vector with respect to time for the partial QRS loop shown in Fig. 1. The mean magnitude and the mean direction with respect, to time for these functions are indicated. D. The partial QRS loop is indicated by a dashed curve. The vect’or with magnitude and direction equal to the means indicated in C is shown, as is the mean vector with respect to time previously determined in Fig. 1.D. It is apparent. as is generally true, that the direction of the mean vector with respect to time is not thr mean of the directions of the QRS vectors. and that the magnitude of the mean vector with respect to time is not the mean of the magnitudes of thr QRS vectors.
In the usual cardiac complex the ventricular complex is superimposed upon the T, wave, so that measurement of the T or TIT area is further complicated by the necessity of defining the terminal portion of the ‘I‘, wave. The area of PT,TU, however, may be simply measured with respect to a straight base line constructed between the point of onset of P and the point of offset of IJ, as shown in Fig. 3. The area of PT,QRSTU is likewise measured with respect to this constructed straight base line.
In this study, the IT wave is considered to be part of ventricular repolarization in regard to the ventricular gradient. If this assumption is correct and ii there is no atria1 gradient, the area vector found from measurement of 1’7;QRSTtT areas is the ventricular gradient :trea vector. I;or the studies presented in the subsequent portiou of this article it is immaterial whether or not there is ;LII atria1 gradient, inasmuch as the studies arc concerned with intraindividu~~l comparisons of the P’I~QRSTIT area vector over brief periods of time duriug which it may be assumed that the atria1 gradient is constant.
Fig. 3.--A, Arbitrary I’, T,. QRS, T, and L: waves shown for simplicity as isosceles triangles. N. When the PT:, complex is formed, the shape of the P wave is altered but its area remains t,hr same. The initial portion of t,he T,, wave. shown hy a dashed line, now forms the base of the P wave, and each ordinate from this base line to the curve has the same length as the corresponding ordinate from the horizontal base line to the curve of the isolated P wave in d. Since the sign of the terminal portion of the T, wave and the initial port)ion of the T wave is the same, either may be considered to originate along the horizontal base line. whereas the other is superposed. C’. The cardiac complex is completed by adding the QRS and U waves. The heavy outlines of QR8. T. and PT:,TI’ indicate the course along which a planimpter should travel in measuring these areas. For measurement of the PT,,QRSTU complex the planimeter should travel along the curve of the cardiac complex and then back to the point of onset along a constructed base line extending between the points of onset and offset of the complex. D. A different cardiac complex is obtained by changing the sign of the T w-ave so that the T area is now positive. The determination of the areas of QRS, T, and PT:,TI’ is again shown.
754
VENTKICUI,AR
GKADlENT
VECTOR
AND
RELATED
VECTORS
75.5
Fig. 4.-The electrocardiogram for a case of intermittent left bundle branch block. The areas of the cardiac complexes, in microvolt-sec.. are written by each complex and were determined with respect to a straight line constructed between the points of onset of successive P waves. A straight line beneath each lead was constructed parallel with the original horizontal paper markings. A, A tracing of Lead Va showing the upper and lower margins of the inscribed electrocardiogram. As was true for the other leads, t,he areas of the cardiac complexes for the upper curve are consistently greater than those for the lower curve. 1%. A midpoint tracing of I,ead Vq constructed along the midpoints of the vertical distances betwvrn the upprv and lower margin curves. Such midpoint curves arc illustrated for all of the other leads.
Fig. A.-.-l, I3, and C, Four complexes from Load aVF from a case of intermittent left bundle branch block. The cardiac complex areas are measured with respect to a straight line constructed between the peaks of successive P waves, between the points of onset of successive P waves, and between the points of onset of successive QRS complexes. In each case the difference between the measured areas of the normal and abnormal complexes is approximately the same. D, The cardiac complex areas are measured with respect to a horizontal straight line passing through the point of onset of the P wave. Such results are the best that can be obtained with electronic integrators currently in use. Obviously. the averaging of a large number of complexes would be necessary to obtain measurements of notable acGUI-WY.
Am. Iieart J May. 196C
.\NGIJi
756
Pig.
6.-J,imb lead complexes
plane from
vcctorcardiograms a case of intermittent
derived fr r the normally Wolff-Parkinson-While
atld ar~on~alously syndrome.
COndUr’twJ
\-t~~STIZI(‘I~I,.\H
ITor the measurement original electroc~~rdiogram opticall>~, ;111d the upper were tr;weCl oilto p;lIxx
GK.\DIISNT
\‘I<(‘TOK
:\ND
I
\~l<(‘TOl
7.57
oi I”I‘JJIK~~.’ areas untlertnketl ill this stud>, the or ~~uhlishecl figure was enlnrgerl eight diameters antI lower margins of the itlscribecl electrocardiogram for j)lanimetric determili:~tioii. 1 t xvas frequejitlk i\Wil
c. 16\
20 WPW-N
d+?
Pig. 7.-A and LI, The vectorcardiograms from Fig. 6. C. The differroce by sxbt,ract,ing the loop in A from the loop in H. D, Derivation of the area in C. The dashed line indicates the vector sum which is to be divided by were added and then multiplied by the total time interval. E’, The card ac normally and anomalousIy conducted complexes obtained from the measured graphic complexes. F. The wntr.rular gradient area difference vector obtained from the abnormal cardiac complex area vector. This vector is the same
vnctorrardiogram obtained vector for the difkrence loop the number of vectors which complex area vectors for the areas of the elect,rocardioby subtracting the norma! as that obtained in D.
758
ANGLE
Am. Heart J. May, 1960
found that the areas determined from the upper and lower margin curves differed. For over a hundred complexes from the case of intermittent left bundle branch block to be presented the areas were consistently algebraically greater for the upper curve. This is obviously due to the vagaries of t.he heated St\-lus, and indicates the error of the common practice of r:mdomly changing from the upper to the lower margin in area measurement. THE
EXPERIMENT
OF
WILSON
AND
ASSOCIATES
In their original articles on the ventricular gradient, Wilson and associates2J described a dog experiment performed to investigate the constant\of the ventricular gradient area vector during marked alteration of ventricular depolarization. It was decided to determine the cardiac complex area vectors for this experiment. The values for the PT,QRSTU areas were first determined Lvith respect to a straight base line drawn between the points of onset of successive 1’ waves. The measured values for Lead I decreased somewhat irregularly from approximately 15 microvolt-sec. for the first complex to zero for the fifteenth complex, with one notable exception, complex 11. The values for Lead III were close to 38 microvolt-sec., with six exceptions, complexes 1, 3, 5, 12, 13, 15. \‘isunl examination of these complexes indicates that the base line is not accurately. approximated by a straight line drawn between the points of onset of successive I’ lvaves. Several methods were used in an attempt to find the true location of the base line, but only one such method will be described, since it. reveals the general approach. The complex in question and the t\vo preceding ant1 two succeeding complexes were adjusted so as to bring the constructed straight base lines to a horizontal 1)osition. All five adjusted complexes were then traced onto a single piece of paper so that the points of onset of the P waves and the adjusted straight. base lines were superimposed. A gradual transition of waveform from complex to complex was then apparent for all compleaes SIVC tllxt with the erroneous base line. On the basis of such study, the seven erroneous base lines were rctlra\vn and new values for the areas of the cardiac complexes were determined. These new values were consistent with the values previously tletermined for the other complexes. The magnitude of the Lead III vector for a dog ma)- be three times that of the Lead I vector, and the angle between these lead vectors may be close to 00”. On such a lead vector diagram the cardiac complex area vectors will vary through a range of about SO”, as the cardiac complex area in I*ead I varies from about 1.5 to zero microvolt-sec. Thus the termini of the ventricular gradient area vectors move from left to right as the center of stimulation of the ventricles moves from right to left. Variation of the equivalent cardiac generator with variation in the lead fields would explain the changing ventricular gradient area vectors. An alternate explanation is that Wilson’s hypothesis does not hold. Apparently, the issue cannot be settled without further animal experimentation wherein the animal heart is suspended in an extensive medium with distant electrodes, thereby
x%-z “5”
VENTRICULAR
GRADIENT
VECTOR
AND
RELATED
VECTORS
7.59
ensuring relatively constant lead vectors. If the ventricular gradient area vector is constant despite alteration in depolarization in such an experiment, Wilson’s hypothesis will finally have been demonstrated to hold for the isolated animal heart. THE
CASE
OF SIMONSON,
SCHMITT,
DAHL,
FRY
AND
BAKKJZN
Simonson and associates4 published three electrocardiograms taken over a ‘i--day period from a patient with right bundle branch block who subsequently developed complete atrioventricular block with a changing ventricular pacemaker. They stated that this case constitutes the human counterpart of the dog experiment of Wilson and associates. The magnitudes of the three ventricular gradient area vectors calculated from their data were similar. However, visual inspection of the Lead I complex for April 24, reveals that it has a net negative area, whereas Simonson and associates have measured the area of this complex as a net positive quantity to four significant figures. The nature of their error appears to be the use of a base line constructed along the lower margin of the inscribed curve, whereas the T area is measured along the upper margin. It appears that the authors used the second complex in Lead III on April 17, to determine the QRS area but used the first complex to determine the T area. Such a division between two QRST complexes is an illegitimate error, since, ii the ventricular gradient is ullchanged, the larger, second QRS would surely be followed by a larger negative 7‘. The cardiac complex area vectors were determined for these electrocardiograms and showed considerable variation in magnitude and direction. It is evident that the conclusions of Simonson and associates with respect to the ventricular gradient for these electrocardiograms are, in general, invalid. INTEKMITTENT
RIGHT
BcrNDLE
BRANCH
BLOCK
The cardiac complex areas were determined for the case of intermittent right bundle branch block published by Wilson and associates5 and for the case published by White.6 In both cases the areas for the blocked complexes were roughly half the areas for the normal complexes in the right precordial leads. Since both types of complexes had positive areas in the right precordial leads, the ventricular gradient area difference vector obtained by subtracting the normal from the blocked cardiac complex area vector was directed posteriorly in both cases. INTERMITTENT
LEFT
BUNDLE
BRANC‘H
BLOCK
The cardiac complex area vectors were determined for a case of intermittent left bundle branch block published by Segers and Boyadjian,7 and the magnitude of the vector for the blocked complexes was about two thirds of the magnitude of that for the normal complexes. The ventricular gradient area difference vector obtained by subtracting the normal from the blocked cardiac complex area vector was directed rightward and slightly inferiorly.
The electrocardiogram from a previousI\. uttpublished case of intermittent left bundle branch block is showtt in I;ig. 4. It might be wondered whether the differences between the area measurements of the ttormal and blocked complexes are due to incorrect placement of the constructed base iitte with respect to which the measurements were made. In Fig. 5 these differences are shown to be independent of uniform vertical displacements of the constructed base litte such as would occur if each P wave were raised or io\vered ;I constant distance front the true base line by the preceding U wave. It might next be wondered whether there is an alternating vertical displacement of the constructed base line resulting from superposition of alternate P waves on varying II waves. Assume, for example, that the I’ wave of the normal complex initiates on the true base line while the I’ wave of the blocked complex is raised above the true base line by the preceding t7 wave. In this case the constructed straight base line for both the normal and the blocked complexes will rest on the true base line at one end of the complex and will be elevated above it a certain constant distance at the other end. Therefore, the error in area tneasurements of alternating block resulting frotn this type oi misplacement of the base line would be equal in amount for both t\yes of complexes, and, consequently, the difference between the tneasured areas would still be the correct difference. Some increase in the accuracy of the area measurements could have been obtained by adjustments of the straight constructed base lines in a manner similar to that described for some complexes from the dog experitnettt of \Viisott and associates. However, a sufficient number of complexes have been studied to permit averages for each type of complex from eitch leatl to be obtained, thus The magnitude of the cardiac complex making such adjustments unnecessary. area vector for the blocked complexes is slighti). less than half that for the normal complexes. The ventricular gradient area difference vector is directed right\vard, anteriorly and slighti?. inferiorly. For the normal tracing the cardiac complex area vector can be considered to consist of three component vectors, the atria1 gradient area vector and the right and left ventricular gradient area vectors. Thus,
-AP + AT:, + <s,tv + A1.lT,iv + AQHS,,,. + AT1 ,,~ = (it + (A\ + Gt.\ where tricular
LAII, AuItpI1,., .Aoll+,,V are the area depolarization,
vectors
for atria1
;ud right
AT:,, A%r1,(,., AA~~~.tVare the art‘;\ vectors
(3)
and left ven-
for atria1
and right
area vectors and left ventricular repoiarization, a1~1CL, (;ltI, G,., are the gradietlt for the atria and the right and left ventricles, respectively. Following the onset of left bundle branch block the normal left ventricular QRS and TlT area vectors become blocked left ventricular QRS and TIT area vectors, whereas the left ventricular gradient area vector will be unchanged if Wilson’s h>rpothesis holds. Thus,
where CLrr HRIlis the left ventricular bundle
branch
block.
gradient
area vector
in the presence
of left
\~“lUnw Numhrr
59 5
VENTRICL-L.4R
Subtracting
GRADIEXT
VECTOK
AND
KELATED
VEC’TORS
761
(3) from (4) yields
where either side of the equation is equal to the left ventricular gradient area differerrce vector obtained by- subtracting the cardiac complex area vector for the normal complexes from that for the blocked complexes. It may be that Wilson’s h>.pothesis does not hold and that the left ventricular gradient is changed b,- alteration of left ventricular depolarization. On the other hand, Wilson’s h).pothesis may be valid, in which case the finite difference vector is presumably due to alterations of the lead fields secondaq~ to altered ventricular depolarization.
\.ectorcardiograms for the plaue of the limb leads are derived in Fig. 6. Subtraction of these loops yields the difference vectorcardiogram shown in Fig. 7,C, from which the ventricular gradient area difference vector is derived in D. This difference area vector is obtained more directly in E and I; from the measured areas of the electrocardiographic cardiac compleses.
The concept of a mean vector with respect to time for a certain time interval is discussed. A simple method for determining the area vector for electrocardiographic cardiac complexes is presented, and the theoretical and practical advantages of its use are discussed. The ventricular gradient area difference vector is defined and is determined for the dog experiment of Wilson and associates, for two cases of right and two cases of left intermittent bundle branch block and for one case of intermittent anomalous atrioventricular e.ucitation. 1t is pointed out that in each case this difference vector ma). be due to alteration of the lead fields or ma); be an indication of invalidity of Wilson’s hypothesis. KI:FEKES(‘I?S
1. 2. 3. 1. 5. 6. 7.
Hecht,
H. H.: Basic Principles of Clinical Electrocardiograph!, Springfield, Ill., 1950, Charles C Thomas. Pnhlisher. \$!i!son, F. N.: MacLeod; A. G., and Baker, I’. S.: ‘l‘he ‘I‘ Deflection of the Electrocardiogram, 1 r. A. Am. Physicians 46:29, 1931, \Vilson, F. N., MacLeod, A. G., Barker, P. S., and Johnston, F. I).: The Determination and the Significance of the Areas of the Ventricular T>eflections of the Electrocardiogram, AM.~EART j. 10:46, 1931. Simonson, E., Schmitt, 0. H., Dahl, J.. Fry, I)., and Bakken, E. E.: The Theoretical and Experimental Bases of the Frontal Plane \‘entricular Gradient and Its Spatial Counterpart, AM. HEART J. 47:1X, 195-1. Wilson. F. N., Rosenbaum, F. F.. and Johnston, F. D.: Interpretation of the Ventricular Complex of the Electrocardiogram, IN =\d\.ances in Internal Medicine, New York, 1947, Interscience Publisher, Inc. IVhite, P. I?.: Heart Disease, Ney York, 1951, The Macmillan Co. Segers, M., and Boyadjian, N.: Etude critique du concept du gradient \-entriculaire, Arch. mal. coeur 42522, 1949.