The Multipolar Content of the Human Electrocardiogram ~ LEO G . HORAN, 2 R . CHRIS HAND, NANCY C. FLOWERS, AND J E N N I F E R C. JOHNSON

University of Louisville School of Medicine, Louisville, Kentucky/~0202 AND DANIEL A . BRODY

University of Tennessee Medical Units, Memphis, Tennessee 38163 Received M a r c h 16, 1976 The previously limited dipole or vector concept in electrocardiography m a y now be extended to the multipole concept, and the extraction of otherwise lost surface reflections of myocardial electrical activity may now be obtained. The geometric form and orientation for each of the 15 components of a three-stage multipole located at the heart's center have been characterized. This permitted determination of the patterns of potential distribution on the chest resulting from the activation of each of the respective components. The 15 leads have been employed to determine dipolat~quadripolar-octapolar moment of instantaneous body surface potentials, first calculated from a 20-dipole model of ventricular depolarization and, second, actually recorded from normal h u m a n subjects. The new information in the quadripolar and oetapolar leads appears related b o t h to the anatomic displacement of the mean heart vector and to the estimate of opposed simultaneous electrical forces in the myocardium which ordinarily average or "cancel out" in conventional electrocardiographic and veetorcardiographie leads and thus go unreported. Octapolar strength was found to be greatest in mid-QRS in normal subjects b u t less than quadripolar in early and late QRS. The quadripolar strength remained approximately one-half t h a t of the dipole or heart vector throughout the heart cycle.


In 1913, Einthoven et al. (1913) illustrated what they called "the manifest orientation of cardiac electrical activity" by an arrow. IIe related the orientation of the arrow to the sides of the equilateral Einthoven triangle and thus in turn the amplitudes of the inscriptions in leads I, II, and III of the early electrocardiogram. As later demonstrated by Burger et al. (1946) the manner Supported by Veterans Administration Hospital, Louisville, Kentucky; Grants from the American Heart Association No. 69 783 and U.S. Public Health Services No. HL-11667, HL-14032, HL-01362, and HL-09405. 2 Address for reprints : Leo G. Horan, M.D., D e p a r t m e n t of Medicine, University of Louisville, School of Medicine, Louisville, K e n t u c k y 40202. 280 Copyright ~ 1976 by Academic Press, Inc.

All rights of reproduction in any form reserved.






b b








' l'" z




:'-.1 '%*~




FIG. 1. Diagram of a theoretical cell in right sagittal view undergoing successive instants of depolarization from back to front. The cell is assumed to be immersed in a homogeneous spherical volume eonduetor ten times greater in diameter with ideal dipolar, quadripolar, and oetapolar leads attached. The potentiM recorded on the surface of the spherical conductor at each of 602 points is computed by dividing the internal cell also into 602 facets and computing the effect of each faeet considered as a dipolar generator. The cell is located on the X-axis slightly to the left of the eenter of the surrounding sphere. The top panel illustrates the effect on the multipolar sensitive leads. The top three leads are dipolar, the middle five are quadripolar, and the bottom seven ate oetapolar. Note that the back-to-front depolarization specifically affects the third lead (corresponding to Z on the VCG). The middle panel illustrates instant A of the top panel, and the bottom panel illustrates instant B of the top panel. In both A and B, the cell is shown in horizontal view and the dipole and quadripole reconstructions are similarly viewed. The dipole content for each instant is the same and is so shown in the dipole representation. But the quadripole reflects a difference: at A, the quadripole lies in the horizontal plane with one pair of poles (positive and negative) paralleling or imitating the actual locus of the wavefront and the equivalent dipole (shown at its determined locus) and the other pair acting as an equal-and-opposite image. When point B is reached the quadripole has shifted the "imitator pair" fcrward to mimie the altered dipole position and the image pair has moved backward (see text. for discussion). in w h i c h E i n t h o v e n r e l a t e d t h e o r i e n t a t i o n of t h e a r r o w t o t h e f i n d i n g s in t h e d i p o l a r e l e c t r o c a r d i o g r a p h i c l e a d s f o l l o w e d t h e b a s i c r u l e s of v e c t o r c a l c u l u s . T h e c o n c e p t e m b o d i e d in t h e a r r o w h a s p r o v e n e x t r a o r d i n a r i l y u s e f u l w h a t e v e r




TABLE 1 Generator-Coefficient Equations ~ 1. 2. 3. 4. 5. 6. 7. 8.

alo a,1 bH a2o a21 b21 a22 be2

= = = = = = = =

9. an0 = 10. an1 = 11. b31 = 12. a32 =

13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

b32 = aaa =

b3a = a40 = a41 = b41 = a,2 = b42 = a4a = b,a = a44 = b44 =

~llx My Mz 2 x M x - y M y -- z M z x M y -4- y M z xMz + zMx 89 -- z M z ) 89 ~- z M y ) 3 (x2 - 89 _ 89 2) M x - 3 x y M y - 3 x z M z 2 x y l i l x ~ ~ ( 4 x : - 3 y 2 -- z 2 ) M y - 8 9 2xzMx - 89 + 88 - y2 _ 3 z 2 ) M z [ ( y 2 _ z 2 ) M x .4_ x y M y - 8 9 89 + 89 + 89 [(y2 _ z 2 ) M y .Z [ y z M z [ y z M y A- ~(y2 _ z 2 ) M z 2x(2x ~ -- 3y ~ --3z2)Mx -- ~(4x 2 - ye _ z ~) ( y M y 44- z M z ) 3 y ( x 2 -- y~-/4 -- z 2 / 4 ) M x -- x ( x 2 -- 9 / 4 y 2 -- 8 8 -- ~ x y z M z 3z(x 2 -y2/4 - z 2 / 4 ) M x - ~ x y z M y A- x ( x 2 -- ~y2 _ 9 / 4 z : ) M z 89 ~ - z:),~lx A- y / 6 ( 3 x 2 -- y"-)My -- z / 6 ( 3 x e -- z 2 ) M z x y z M x 44- 89 2 - y 2 / 2 - z 2 / 6 ) M y ~- 89 ~ - y : / 6 - z : / 2 ) M z z / 2 4 ( y : - 3 z : ) M x A- x / 8 ( y ~ - z 2 ) M y -- 8 8 z / 2 4 ( 3 y : - z e ) M x A- 8 8 -b x / 8 ( y 2 - z e ) M z y / 4 8 ( y ~ - 3 z 2 ) M y - z / 4 8 ( 3 y 2 -- z e ) M z z / 4 8 ( 3 y 2 -- z 2 ) M y A- y / 4 8 ( y ~ - 3 z : ) M z

a These relationships are derived from the equations of Gabor and Nelson (1954), have been expressed in slightly different form b y Geselowitz (1960), and here conform to the development by Brody (1968) through the hexadecapole (Brody et al., 1973). They have at least three applications : (1) As "dipole-shift equations" : Dipole location is expressed in Cartesian coordinates with reference to the origin as x, y, and z. Dipole m o m e n t is represented as M x, M y , M z . If b o t h are known, the apparent effect of creating higher-order moments by "shifting" or dislocating the dipole from the origin can be calculated by substitution in the equations above number 3. (2) As estimators of generator m o m e n t from surface potential: The entire boundary of the surrounding medium of a homogeneous volume conductor must be characterized by a sufficient n u m b e r of surface facets of known area and orientation. These m a y be each specified as the m o m e n t of the outward normal vector to the facet N x , N y , and N z located at point i, j, k from the origin. Equation (1) becomes as0 = M x = ~ v N x , where v is the local potential at each facet and N x is the x-axially oriented component of the facet normal. Similarly, Eq. (4) m a y become a~0 = ~ v ( 2 i N x - j N y - k N z ) , whereby a value for the generator coefficient can be obtained. T h e n by using Eqs. (4) through (8) in their original form we m a y discover the location of the equivalent dipole. This approach is a numerical approximation of the Gabor-Nelson integration. (3) As estimators of generator m o m e n t from dipolar elements of a more complex internal generator : The internal generator m a y be an electromotive double layer divided into small facets each one of which is represented b y dipole normal to and located at the centroid of the facet. Each dipole m o m e n t is proportional to the area of its facet and is indicated as M x , M y , and M z at location x, y, z. Thus Eq. (1) becomes al0 = ~ M x and a2o = ~ ( 2 x M x - y M y -- 3 M z ) . In similar fashion, if the internal generator were a known quadripole or octapole centered a t the origin the resulting generator moments m a y be determined by summing the results from the constituent dipolar elements. the label: heart axis, heart vector, or equivalent cardiac dipole. Its widespread a d o p t i o n h a s b r o u g h t w i t h i t b o t h g o o d a n d b a d a s p e c t s . T h e g o o d a s p e c t is t h e g r e a t p o w e r of t h e v e c t o r o r d i p o l e t o p r o v i d e a n i n t u i t i v e g r a s p of t h e m e a n e l e c t r i c a l a c t i v i t y of t h e h e a r t a t a n y i n s t a n t a n d t o p e r m i t i n t u i t i v e







IO lY i






! i ......!,


li iV


,Y t






:7' /,



,jtJ.i < li


FIG. 2. The first 15 basic configurations of the equivalent cardiac multipolar generator. Arrays in columns A, B, and C illustrate the generator as composed of vectors (dipoles). Column A illustrates the three orientations of the dipole: A dipole of any orientation can be specified in terms of relative amounts of these three orthogonal coml~onents. Only the pertinent axis is shown with orientation. Column B illustrates the five moment components of the quadripole, and again, only the pertinent axes are shown. Thus, the first quadripolar component lies totally along X, the second array is in the X Y plane, the third is in the X Z plane, and the fourth and fifth both lie in the YZ plane: Column C contains the seven moment components of the octapole. They strongly parallel corresponding predecessors: The first lies along X, the second in X Y , and the third in XZ.~The fourth and fifth describe cubical arrays, but the sixth and seventh are each found completely in the Y Z planes.




c o r r e l a t i o n w i t h t h e s t a t e of t h e h e a r t as j u d g e d b y o t h e r m e t h o d s . T h e b a d a s p e c t is t h a t t h e v e c t o r c o n c e p t h a s so c o n c e n t r a t e d on t h e m e a n as to t h e o b s c u r e w h e t h e r t h a t a v e r a g e is r e p r e s e n t a t i v e of m o s t of t h e u n d e r l y i n g elect r i c a l a c t i v i t y or is m e r e l y t h e l e f t o v e r w h e n m o s t of t h e a c t i v i t y is o p p o s e d a n d canceling. W h a t s o r t of i n f o r m a t i o n is m i s s i n g in t h e s t a n d a r d v e c t o r a p p r o a c h t o e l e c t r o c a r d i o g r a p h y ; m o r e specifically, w h a t s o r t of i n f o r m a t i o n c a n b e h o p e d to be g a i n e d f r o m m u l t i p o l a r - s e n s i t i v e l e a d s ? F i g u r e 1 i l l u s t r a t e s a t h e o r e t i c a l cell (in r i g h t s a g i t t a l view) u n d e r g o i n g successive i n s t a n t s of d e p o l a r i z a t i o n f r o m b a c k to f r o n t . T h e cell is s i t u a t e d s l i g h t l y t o t h e left of t h e c e n t e r of t h e s u r r o u n d i n g s p h e r i c a l v o l u m e c o n d u c t o r . B o t h t h e p o t e n t i a l d i s t r i b u t i o n on t h e s u r f a c e of t h e s p h e r i c a l c o n d u c t o r ( n o t s h o w n ) a n d t h e c o n s e q u e n t effect on l e a d s s p e c i f i c a l l y s e n s i t i v e to e a c h c o m p o n e n t of t h e first t h r e e o r d e r s of e q u i v a l e n t g e n e r a t o r l o c a t e d a t t h e c e n t e r of s p h e r e c a n b e c o m p u t e d ( W i l s o n et al., 1950; B r o d y , 1968; B r o d y et al., 1973a, b). I n t h e u p p e r p a n e l , t h e t o p r o w of i n s c r i p t i o n s are t h e c a l c u l a t e d effect on d i p o l e - s e n s i t i v e l e a d s a p p l i e d t o a l a r g e s p h e r e c o n t a i n i n g t h e cell n e a r its center. T h e s e d i p o l a r l e a d s a r e TABLE 2 Orientation of Elements in the Manufacture of Orthogonal Multipolar Components Orientations~ D



~/2 _~/21 - ~'/2


- ~12



s 9

-~/s ~-/4

~/2 ~-/2

~/6 -~/2 -~12

3~/8 -~/2 ~/2









-~/2 ~/2

3/S --~/4

~/2 ~/2

a Brackets enclose components of respective generators. For example, the three components of the dipole are concerned with the dipole orientation alone, but the five components of the quadripole consider orientation Q also, even though it remains aligned with the X axis for components 1 through 3. Orientation D = altitude (a) and azimuth (fl) of a dipole element measured from a standard X orientation. Element 1 (X component ) lies unmoved from, and therefore parallel to, the X axis; elenmnt 2 (Y component) has an altitude of ~r/2 (90 ~ and lies parallel to the Y axis; element 3 (Z component) has an azimuth of - r / 2 ( - 9 0 ~ and thus lies parallel to the Z axis. Orientation Q = altitude and azimuth of the axis of separation between basic dipole pairs, thus the orientation which characterizes a quadripole. Orientation 0 = altitude and azimuth of the axis of separation between basic quadripolar sets ("plates"), thus the orientation which characterizes an octapole. Orientation H = altitude and azimuth of the axis of separation between basic octapolar groups, thus the orientation which characterizes a hexadecapole.




/ \



o ~o o






FIG. 3. Diagrammatic illustration of relative position of mean dipole locus during QRS for each of 28 normal subjects and 75 patients with heart disease. The common reference axis was the intersection of the anteroposterior (defined by midaxillary lines), and the common reference point was the tip of xyphoid process. The cardiac and diaphragmmatic silhouette for one subject is superimposed. There was considerable variation in the position of these cardiac countours with regard to the arbitrary origin ; similar vertical variation in the mean location of the electrical center of ventricular depolarization is shown here. 9 marks the mean locus for the entire normal group, 9 for the abnormal group, and G for the arbitrary heart center used in these studies. idealized vectorcardiographie leads. Depolarization from back to front predictably affects the third lead corresponding to Z on the vectorcardiogram (here reversed from usual clinical polarity). The next two rows (still in the upper panel) report events in the simultaneous qu~dripolar and octa,polar leads. Particular attention should be given to instants A and B. At these two points in time, the size of the wave of activation is the same for each event and the amplitude of the Z-dipolar lead is also the same while the effect on the quadripolar leads is quite different, as seen in isolated detail in horizontal plane view in the middle and lower panels of Fig. 1. In the middle panel the dipole lead information for instant A has been converted into a centrie dipole representation; the quadripole lead information has been converted both into a centric quadripole and into an estimate of dipole location of best fit. Note t h a t instants A and B remain the same as far as the dipole content and representation is concerned. B u t there are two very obvious and significant differences between A and B : (1) the location of the dipole or heart vector and (2) the presence or absence of a large band of opposed forces (and therefore commonly presumed to be canceling) in the zone between the two lines A and B. Fortunately, the quadripole reflects this difference, for when the cell is only one-fifth depolarized, the quadripole lies in the horizontal plane suggesting location of the dipole with one pair of points parallel to the Z axis and like the equivalent dipole posterior to the center. As the wave and dipole move










forward to the point when the cell is four-fifths depolarized, the quadripole still lies in the horizontal plane b u t the "dipole-imitation" pair of points have m o v e d forward and the image pair have moved backward. Such theoretical considerations imply t h a t the quadripole provides valuable clues about the two difference states of the cell which the dipole reports as the same. B y analogy, the quadripole and perhaps the octapole m a y be expected to provide even more d a t a concerning such complex arrays as groups of cells or whole hearts. For example, the clinician frequently desires to be able to distinguish between the prominent R in V1 of right ventricular enlargem e n t from t h a t of posterior myocardial infarction. The possibility t h a t we might be able to obtain surface leads from the h u m a n b o d y to report the higherorder cousins of the dipole provided a strong motivation for this s t u d y (Brody et al., 1961). This s t u d y utilizes the concepts that the electrocardiographic surface m a p data provide a standard limit to information expected from the electrocardiogram and t h a t a fixed-location multipolar generator at the heart center m a y be used to condense and estimate the m a p information. This manuscript describes: (1) the development of a reproducible model 3 of the heart's instantaneous electrical activity as a dipole-plus-quadripole-plus-octapole at the common heart center; (2) the determination of sites of sensitivity and arrangem e n t of polarity on the h u m a n thorax to detect the o u t p u t of such an equivalent heart generator; (3) the appearance of the waveforms in such leads during the inscription of the QRS complex for the early Selvester model of ventricular activation (Selvester et al., 1967); and (4) the appearance of the corresponding waveforms from actual h u m a n subjects. We have omitted the description of m a n y dead-end excursions and have concentrated on those findings which led to the final result. M ETHODS

Preparation of a Forward Jllultipolar Generator Each higher-order generator m a y be constructed from an appropriate pair of the immediately previous lower-order generators: thus, a quadripole m a y be 3The term "nmdel" frequently is ambiguous in failing to distinguish the conceptual, the computational, the physical, or the biological. In this report the term is used exclusively in the computational (or occasionally conceptual) sense to specify two kinds of forward equivalent cardiac generator: the "heart model," a 20-element ventricular generator (of fixed-location, fixed- moment dipoles) of Selvester, and the "multitmle model," a 3-order fixed-location multipolar generator. In each instance the generator model will relate to a surrounding homogeneous torso "model" of the human thorax of specified description. FIG. 4. (A) Equipotential contour maps of the thoracic distribution of effect to unit current sources acting in each of three orthogonal components (X, Y, and Z) of the fixed cardiac dipole. For brevity and comparison, only the anterior views of the chest are shown. The shaded areas are those of negativity; the unshaded, positivity. The equipotential lines are separated by arbitrary but equal intervals based on peak value for each map. The rms value for each distribution is set at 271 uV. (B) Contour maps of the anterior thoracic distribution of effect of unit current sources acting along each of the five components of moment of a cardiac quadripole fixed at the arbitrary "heart center." (C) Similar contour maps for the effect of the seven components of a fixed cardiac octapole. Note that these surface distributions correspond by number to the component multipole configurations shown in Fig. 2.






45 Msec






45 Msec

FIG. 5. Maps of body surface potential distribution for a given instant of activation (35 msec after onset) for b o t h the theoretical 20-dipole heart model and for a normal h u m a n subject. The shaded areas are those of negativity; the unshaded, positivity; and the two are separated by the bold zero or null line. Other equipotential lines are separated by intervals of one-fifth the peak value. Panel A shows the observed potentials, displayed in equipotential contour m a p grid form. The upper maps are displays of the original data, while the lower maps are reconstructions utilizing dipolar, quadripolar, and octapolar components specified by the instantaneous values found in the 15 scalar leads (Fig. 8). Panel B illustrates the same data displayed in isometric projection form. Each grid intersection is a recording site. The map extreines are the paravertebral lines. The top



produced b y two opposed and parallel dipoles, and an octapote m a y be produced from two parallel and opposingly oriented quadripoles (Stratton, 1941). I t folh)ws t h a t sufficient appropriate dipoles can be used to construct not only quadripoles but octapoles, hexadecapoles, dotriakontapoles, and so on. Th(~ potential distribution on the surface of the surrounding medium for a 4-point source can be very closely approximated by adding the effects of two appropriately placed and oriented dipoles. If the separation between centers remains small relative to the distance to the b o u n d a r y the discrepancy between the thus-calculated or experimentally determined result and a mathematically ideal generator (with infinitely small separation between points) is negligible. Arrays which satisfy the dipole-shift equations or generator-coefficient equations (Table 1) are shown in Fig. 2 and were constructed b y the ordered series of orientations shown in Table 2.

Adaptation of the Fixed Generators to the Computational Model of the Torso T h e dimensions of a h u m a n torso of average shape were obtained b y averaging the spatial coordinates of 142 electrode positions for 28 normal subjects in whom serial body surface potential maps had been obtained (Horan et al., 1972). To enhance later numerical approximation of surface integration, we interpolated between these points to produce a 602-element thoracic surface. Next, we sought a reasonable electrical heart center at which to place the origin of the coordinate system for computation. For each of the 28 normal subjects, the instantaneous potential values throughout the QRS complex were summed msec-by-msec to obtain a mean potential distribution for each subject's QRS complex. Application of the first eight generator coefficient equations of Table 1 to each surface site and summation over the torso surface yielded b o t h m o m e n t and location for an equivalent dipole for each of these mean potential distributions. A mean site from these 28 locations was determined and a convenient point near it was arbitrarily designated the cardiac electrical eentroid and made the origin of the coordinate system for describing the torso and applying the equations (see the triangle in Fig. 3). A similar mean for 75 patients with myocardial infarction was so near this location t h a t the original arbitrary designation was not changed. Finally, the torso surface potential distribution for each generator component shown in Fig. 2 when individually placed at the electrical center of the torso was calculated. This was done dipole-element-by-dipole-element. The distribution of surface potential for each such element was obtained by extending the m e t h o d of assay previously described (Horan et al., 1972). (In effect, this m e t h o d is a rapidly convergent search for the thoracic surface disrow is at the sterno-clavicular level, the bottom row at the umbilicus. The plane above the grid is set at the 1 mV level. In the middle column, the original potential distribution is at the top, the reconstruction immediately below, and the residual (original minus reconstruction) at the bottom. In the right column, the contributions of each of the three orders of generator making up the reconstruction are shown separately: the dipolar portion at the top, quadripole in the middle, and the octapole at the bottom.



A IIIG~41 SkOl11J,L


t IIC'M1k L



.j 3 ~



4 5


FIGURE 6 tribution which reduces to the specified dipole or heart vector inside, as determined by the generator-coefficient equations.) The resulting patterns for unit X, Y, and Z dipoles shown in Fig. 4 may be interpreted as descriptions of the vector field for unit X, Y, and Z, respectively. Further, the resulting transfer value for X at each electrode site when multiplied by the X component of the equivalent dipole estimates the magnitude of the potential found for that site. The relationship between the X component of the equivalent dipole or heart vector and the right-left division of surface effect is easily appreciated intuitively upon inspecting Fig. 4. The respective relationships for Y in terms of upper-lower division or for Z as front-back effect also follow. More complex but still intuitively appreciable are the components of quadripolar and octapolar moment. By extending the method of dipole assay to each of the five elements of quadripole moment and the seven elements of octapole moment, similar surface distributions of sensitivity were found (Figs. 4B and 4C). The relationships between the surface patterns and the Cartesian coordinate system were less apparent than for the dipole. We no longer found half the chest negative ~nd the other half positive. Instead, the distributions









\ Y




Fro. 6. Diagrammatic representation of the orientation of the fixed-location dipole (vector) and quadripole (parallelogram) at 30, 45, and 60 msec after onset of the QRS complex for a 20-element model of ventricular activation (A) and for a normal human subject (B). The QRS waveforms for each set are shown on the right. Also shown diagrammatically is the position of the wavefront in slices through the ventricular mass for the model (calculated) and for the live subject (surmised). These accompany both the right sagittal and frontal views of the vector and quadripole. Note the general correspondence between the orientation of the dipole and the conventional expectation from orientation of the wavefront at each instant. Note, however, that the rotation of the parallelogram does not follow that of the vector in any consistent fashion. Both the dipole and the quadripole are shown at unit size in each instant to illustrate orientation; the amplitude varied as indicated in Fig. 7. Of the 15 scalar lead waveforms shown in A and B, the first threee waveforms are dipolar, the next five are quadripolar, and the last seven are oetapolar. Note the similarity between the dipolar waveform and X, Y, and Z of the conventional vectoreardiogram. Note also the great amplitude seen in octapolar waveform number 14 (see text for discussion.) reflected t h e m o r e c o m p l e x p a t t e r n s of t h e c o m p o n e n t s of t h e m o r e c o m p l e x generators. F o r t u n a t e l y , i n t e r p r e t a t i o n m a y be continued in analogy: the patt e r n s m a y b e u s e d as t h e basis for m a n u f a c t u r i n g scalar leads or for r a p i d c o m p u t a t i o n of each e l e m e n t of h i g h e r - o r d e r m o m e n t .



"~ o : -~








0 5




8 ^


0 9









90 msec

I ] I 90


FIG. 7. The mean and two standard deviations of current strength for the components of dipole (top row), quadripole (middle row), and octapole (bottom row) for 28 normal healthy young men. At the far right is shown the absolute current strength for each order of generator (total magnitude values). In each panel the abscissa is time and the ordinate is in units of current strength; for the dipole, one unit of current strength produces 271 ~V rms over the 142-electrode body surface. Standardization for the quadripole and octapole was set so that one current strength unit in either also produced a surface potential distribution of 271 ~V rms. In the total magnitude displays on the right, the shaded area below the baseline represents an artificial expectation produced by the minus-two-standard-deviations value. These computations developed two sets of transfer coefficients. The original set, derived from generator-coetticient equations of Table 1, when multiplied b y electrode voltages yielded esthnates of generator m o m e n t ; we labeled these "inward." The set which, when multiplied b y components of generator m o m e n t yielded estimates of surface voltage, we labeled " o u t w a r d . " The outward matrix thus made it possible to dissect out the surface effect of various generators, as shown in Fig. 5B. A distinct and separate outward matrix was determined for the 20-element model of the ventricle determined b y dipole assay (Horan et al., 1972). This permitted estimation of surface potential t h r o u g h o u t a theoretical activation sequence (Selvester et al., 1967). The equivalent generator components at the



common fixed site were computed for this sequence of calculated surface potentials of the ventricular model from the generator-coefficient equations and expressed as waveforms (Fig. 6A). Similarly, the digitized 142-lead body surface map data for human subjects was reduced for each millisecond during the QRS complex to scalar lead waveform corresponding to components of the nmltipolar generator (Fig. 6B). RESULTS

Examination of the Methods with Data from a 20-Segment Model of Ventricular Activation A series of hypothetical surface potential distributions for a multiple-dipole cardiac generator was obtained. These surface potential distributions were computed by adding together the appropriate relative contributions from each of the surface effects of each of the 20 ventricular elements in Selvester's model; the relative contributions were varied for successive instants in time according to the sequence of activation postulated by Selvester and his group (Selvester et al., 1967). Then, the moments for each of the 15 components of the threeorder fixed multipolar generator were computed for each instant by applying the generator coefficient equations of Table 1 to the potential surface distributions. Hypothetical QRS complexes for each of the "multipolar leads" were obtained by displaying successive moment values for the postulated sequence of activation (Fig. 6A). As shown in Fig. 5, reconstruction of surface potential distribution from these leads proved highly satisfactory.

The Configuration of the 15-Moment Waveforms in Normal Subjects Figure 6B illustrates body surface potential data during the QRS interval expressed as 15 scalar leads for a normal 26-year-old man. The convention as to sign which we adopted for consistency in formulation and computer programming recognizes as positive aspects of the respective X, Y, and Z axes on the left side, the head, and the front of the chest. Considering this specified polarity note that the first three resemble X, Y, and Z leads of the vectorcardiogram, albeit idealized and purified of nondipolar elements (Flowers et al., 1974). The next five waveforms portray the time courses for the individual moment components of the quadripole; the last seven, the moment components of the octapole. These same findings can also be reduced to a geometric orientation. For convenience, only the dipolar and quadripolar orientation for selected instants in the QRS complex are also shown in the left-hand parts of Figs. 6A and B. The probable activation wave front is diagrammed on slices through the ventricular mass accompanying the right sagittal and frontal views of both the dipole (shown as a vector) and quadripole (shown as a parallelogram with two positive and two negative corners). For *the model (Fig. 6A) these were constructed from Selvester's data (Selvester et al., 1967) ; for the live data from the normal subject, the expectation as to wavefront was drawn freehand



(Fig. 6B). The significant findings here illustrated for the selected points in time of the QRS complex are that the orientation of the fixed-location dipole moves with conventional expectation for the orientation of the wavefront but that the fixed-location quadripole rotates and evolves in an independent fashion. The configuration of the fifteen scalar waveforms during ventricular activation were examined for 28 normal young men. As would be expected, from the body of experience in electrocardiography and vectorcardiography, there was similarity of waveforms throughout the group, with minor individual variations. All showed greater relative amplitude of the quadripolar and octapolar waveforms than predicted by the heart model. The relative prominence of amplitude in waveforms number 8 and 14 was consistent throughout as was relatively greater current strength of octapole as compared to quadripole in mid-QRS but not early and not late (see Fig. 7). DISCUSSION

Why Multipolar Analysis? A rationale for multipolar analysis of the electrocardiogram may be developed in the following way. First, examine the vectorcardiographer's approach to the information in the electrocardiogram. While he knows the electrical source is a complex anatomic and physiologic arrangement of the heart muscle, he temporarily simplifies his view of the information source to asking what is the mean direction and volume of current flow at any instant. This is the same as asking for the moment of the instantaneous heart vector or equivalent dipole. The most efficient way to find this out is to ask for the projections on the three axes of dimensions, insisting that the axes be orthogonal to each other, i.e., no one of the three repeating information found on the others. Suppose we adopt and extend this viewpoint. A desirable electrical model of the heart would include not only information about mean direction of activation in the message we must decode, but also equally concise, nonredundant information about significant departures either from the mean direction in specific regions of electrically active nmscle mass or from the location as the time-course of the cardiac electrical cycle proceeds. Ideally, this additional message may be carried by a second signal based not on the dipole but on a four-point source, or quadripole, which would account for as much as possible of the information missing from the dipole-based signal. The second signal would have to be simultaneously sent on ~ second senderreceiver system with neither cross talk with the first signal nor internal redundancy among the five leads needed to characterize such a signal. Placing the receiver lead electrodes for X, Y, and Z can be intuitively appreciated (Fig. 4A) as placing the ends of the pickup leads on the opposed halves of the body which reflect the outwardly projected effect of each orthogonal component of the simple three-directional model generator of the VCG. In the same way, the receiver leads f~r the five scalar waveforms of the quadripole may be constructed by connecting the two negatively sensitive fourths of the body to one end and the two positively sensitive fourths to the other end for



each of the orthogonal surface distributions of the quadripole lead fields (Fig. 4B). The weighting factors for each electrode utilized should relate to the sensitivity of the electrode site to the component sought. If this were done by actual physical construction of leads rather than digital computation from the body surface map data, the weighting resistances would appropriately be chosen to produce those weighting coefficients which would correspond to the transfer coefficients of the "inward" matrix. The same considerations apply to the construction of the more complex octapolar leads. The ECG decoding process may now be reviewed in this way: The total surface electrocardiographic message contains several simultaneous submessages. The first, and the one we are most accustomed to, specifies the heart vector and its approximation on the VCG. Removing it still leaves a large residual. A second message describing the most significant local myocardial departures from the mean heart vector theme may be found in the residual and also removed, still leaving a sizable remainder. The strength (amplitude) of the second message was tentatively expected to be less than one-half the first, and the strength of a third such message was expected to be less than one-half the second. Inspection of results with the heart model indicated that this was not an unreasonable expectation when each order of generator (dipole, quadripole, or oetapole) was standarized so that unit generator strength produces 271 #V rms torso surface potential effect. However, for the normal human subject (Fig. 5), the root mean square of total surface signal in the instant illustrated was 552 uV; the dipolar expression accounted for 363 ~V; the quadripolar, 152 ttV; the oetapolar 250 uV; and the final residual was 212 ~V. The comparison of scalar results in Fig. 7 suggests further that not only does the more complexly distributed source of the living heart have a relatively lesser net dipole effect than does the 20-dipole heart model, the variance is also more three-dimensional than two-dimensional. Thus the greater oetapolar than quadripolar effect for the living generator is compatible with such differences in variance. However, not all of the apparent higher-order effects need come from the complexity of intrinsic geometric shape of the electrical wave front. Some effects may arise from the shifting in the mean center of electrical activity relative to the arbitrary origin. Further delineation of the nature of these differences will require comparison of the fixed generator representation and the moving dipole representation in which locator information is used and removed from the higher-order components. The residual after three messages seems relatively large, and when viewed cinematically appears to contain a valid sustained signal--perhaps hexadecapolar in nature. The work of Barr et al. (1971) would suggest that significant nonredundant information may be usable in as many as 24 leads. If so, it may become appropriate to add the nine hexadecapolar leads to the 15 of this study. However, we have concluded that the dipole-quadripole-oetapole combination seems a good place to pause in the multipolar series and permit time for examination of the new scalar leads for clinical and biological pertinence. It is, therefore, not yet appropriate to advocate the physical construction of such leads until more extensive examination of body surface map data has produced




insight into their utility and into the seriousness of the information loss in the residual.

Limitations Versus Advantages of the Method The present approach to characterizing the electrical information in the heart signal has evolved from simple beginnings. The forward relationship assumes that the current generator in the heart is known, that the transfer coefficients have been determined, and that what is sought is the body surface potential. The inverse relationship assumes that surface potential is known, that the out-to-in transfer coefficients have been determined, and that what is sought is the current source, or a reasonable equivalent (Plonsey, 1969). Combining the concept of the surface summation or integration to obtain components of internal generator moment (Gabor et al., 1954) in a volume conductor of any shape and the lead vector-lead field concept (Burger et al., 1947; 5/[cFee et al., 1954) to characterize the return effect of such components has permitted the development of both series of transfer coefficients for the fixed dipole, quadripole, octapole, and hexadecapole. An alternate presentation of equivalent generator is the moving dipole which depends on simultaneous solution of the quadripolar coefficient equations [-(4) through (8) in Table 1] or a least-squares fit to modified lead vector equations (Brody et al., 1975; Horan et al., 1971; Horan et al., 1972; Nelson et al., 1975; Arthur et al., 1971; Hehn et al., 1971). Thus at least a part of the information presented in a fixed-location quadripole and octapole format may be transmitted in the identification of dipole location for the moving dipole format. This study does not quantify the relative amount of dipole-locator information embedded in the higher-order components of the fixed-location equivalent multipole generator; nor does it examine the effect of removal of such information from the higher-order signals and the residual. The finding that the instantaneous dipole orientation is not coplanar with the simultaneous quadripole as shown in Fig. 6 is evidence that the quadripole content is not exclusively dipole-locator information. It should theoretically be possible to determine not only momen~ but also location for each successive instant in the heart cycle for both the quadripole and octapole, as well as the dipole from the higher series equations (Brody et al., 1973; Horan et al., 1972). This determination should give information capable of reproducing the surface potential pattern to a higher degree of accuracy than shown here. But such gain would be at the expense of loss of rapidity of computation, because at each instant completely new transfer coefficients for the dipole and then for the quadripole at the new location would have to be reiteratively determined. There is an expected loss of accuracy resulting from placing dipole, quadripole, and octapole at an arbitrary common site in an arbitrary average thoracic shape, but the gain in reduced computation time is great. Further, the theoretical possibility of converting to an on-line analog system comparable to an orthogonal vectorcardiographic system makes pursuit of the 15 essential leads for a fixed electrical heart center extremely



attractive. Should such a system provide worthwhile, Table 2 and Fig. 6 suggest an avenue toward alternate forms of display: rotatory description of quadripole or octapole elements may well provide helpful visualization of the higher-order generators. At the moment, the orthogonal scalar waveforms alone provide a large field for study. Clinical Interpretation and Application The waveforms for this projected "IS-lead electrocardiogram," thus, are similar in gross appearance to any time-expanded QRS complexes of common clinical acquaintance, and contain directly the three orthogonal components of the vectorcardiogram in purified form. Laying aside questions of cost and ease of acquisition, the immediate disadvantage to the clinician is that there is no large empirical backlog of clinical and pathologic correlates for such new leads. The concept of aiming or utilizing leads which pick up selectively from specified cardiac sites (Geselowitz et al., 1971) may be applicable in interpreting the appropriate human observations and animM experimentation which will be needed to delineate the actual empirical relationships. What is now possible, however, is a method for subjecting surface electrocardiographic information to a systematic decoding process by which we may examine waveform information which has been either neglected or distorted by vectorcardiographic or vectorelectrocardiographic analysis (Flowers et al., 1974). Finally, there is the need for constructive compromise between too much and too little information. It appears to us desirable, simultaneously, to reduce the redundancy in information seen in multiple-electrode map studies of surface potential and to remedy the tremendous information loss of traditional recording methods (electrocardiogram and vectorcardiogram). Examining information content by factor analysis (Flowers et al., 1965) has been refined by Barr et al. (1971) to utilize previous experience codified by factor analysis as a basis for predicting surface map detail from a limited number of surface leads. Similarly, Kornreich (1973) has developed an approach for estimating map content from an empirically determined limited surface sample. The work we have described resembles such studies in respect to its utilizing a scheme for reducing body surface potential distributions composed of a large sampling of electrode sites to a nonredundant small number from which the original large set may be estimated. However, it differs in several important ways from other studies: (1) the formulation assumes, but does not depend upon, the torso of average size and shape and an expected electrical heart center, (2) the application requires no previous empirical determination of probabilities or waveforms, but is more analogous to Fourier analysis in its decomposition of data, (3) the nonredundant information may also be treated in terms of visualizable geometric generators of ordered complexity at the heart center. These, in turn, may be interpreted as an estimate of the mean instantaneous current strength in the electrically active myoeardium, and of the two- and three-dimensional variances from that mean. We believe that the mathematical and physical cleanness of the formulation as an orderly extension of the widely understood vector or dipolar approach recommends its consideration.



Purpose Arthur et al. (1972) has recommended the finding of the forward generator components by inversion of the generator-coefficient equations (Table 1). We sought an alternate approach because our results with a lesser number of facets in the torso surface (602 as compared with 1426) produced surface potential distributions which, because of isolated bizarre irregularities, did not appear physically realistic. We feared therefore, that we had obtained "pseudoinverses" which satisfied the generator-coefficient equations but which would not have resulted from true point sources. We therefore followed the suggestion of Stratton (1941), that the effect of higher-order generators may be found by systematic combination of those of lower order.

Definitions A distinction between the terms "generator" or "order" of equivalent generator and "component" of moment and "element" of component is appropriate. "Generator" refers to an equivalent cardiac generator as dipole, quadripole, octapole, hexadecapole, etc. "Component" of moment of a generator refers to one of the basic orthogonal descriptors characterizing each generator; for example, the first or X component of a dipole. Each generator requires a number of such components to describe it ; for example, three components (X, Y, and Z) or direction cosines specify the dipole, five components specify the quadripole, and seven components describe the oetapole. "Element" refers to one of the vector building blocks used to build a component. For the dipole, an element and a component are identical; but for the quadripole, each component (four-point prototype) is built up of two dipolar elements; and for each oetapole, each component (eight-point prototype) is built up of four dipolar elements~

Procedure The lack of an analytic approach to computing surface potential effect on the irregular boundary of the torso caused us to develop an iterative method for finding the effect for each component. Dipole components (=elements) were found as described earlier, but for higher-order components, each component was built up from vector elements as shown in Fig. 2. When the surface potential distributions of these elements were added together, the resulting potential distribution was reduced by the generator equations ("inward matrix") to mere approximations of the desired components. It was necessary to perform the discovery dipolar-element-bydipolar-element because of the geometric difference in fields created within the homogeneous torso as compared with the homogeneous sphere. It was possible to obtain in each instance a dipole in the sphere which would generate



a potential distribution which, when transferred to the torso, reduced to a pure dipole--but not so for the intact quadripole or octapole. Parallel elements in the sphere usually did not reduce to exactly parallel elements in the torso. Therefore, equations for generating quadripole potential distributions in the sphere (Brody et al., 1973b) were unsatisfactory for producing distributions successfully transferrable to the torso. However, once dipolar elements were created in the torso parallel to each other and appropriately located, it became possible to synthesize higher-order generators inside the irregular torso boundary. Attention in each instance was given to avoid the development of spurious elements in lower-order generators. No spurious lower-order components were found; however, within a given order, the effect was not unity for the desired component and zero for the remainder, but near values for each. Therefore, t h e following procedure was developed: 1. Specific vector arrays were made corresponding to those satisfactory for the homogeneous bounded sphere. For example, surface distributions were found which reduced to vector elements of unit size and axial orientation and location as illustrated in Figs. 2 and 4 for each component in the quadripolar series. 2. For each component, the surface distributions of the ingredient vector elements were added to produce the surface potential effect of the individual multipolar component. 3. The "location" and "moment" for each multipolar component was solved for. At this stage, the location values were usually not the same but near the origin (the electrical heart center). However, the moment values formed a square matrix of results for each order of generator (5 X 5 for the quadripole, 7 • 7 for the octapole). The off-diagonal elements expressed "contamination." 4. The square matrix was "purified" by subtracting from each basic potential distribution the amount of each of the other "contaminating" distributions indicated by the appropriate off-diagonal elements in the corresponding row of the square matrix. 5. The new location and moment for each of the purified potential distributions was now solved for. 6. The results of steps 5 and 3 were compared and the locations for appropriate vector elements in each array of step 1 were altered 25% of the way indicated by the difference in generator location in the two steps. The original orientation and separation of elements was, however, maintained. These results corresponded to a new solution to step 1. Iteration was continued until step 3 yielded a square matrix with off-diagonal units approaching zero (less than 0.01% of the diagonal element) and location error was less than 0.03 mm from the electrical heart center. REFERENCES Arthur, R. M., Geselowitz,D. B., Briller, S. A., and Trost, R. F. Path of the electrical center of the human heart determined from surface electrocardiograms. Journal of Electrocardiology 1971, 4, 29-33.



Arthur, R. M., Geselowitz, D. B., Briller, S. A., and Trost, R. F. Quadripole components of the human surface electrocardiogram. American Heart Journal 1972, 83, 663 677. Barr, I~. C., Spaeh, M. S., Herman-Giddens, G. S. Selection of the number and positionsofmeasuring locations for electrocardiography. I E E E Transactions on Biomedical Engineering 1971, 18, 125-138. Brody, D. A., Bradshaw, J. C., and Evans, J. W. The elements of an electrocardiographic lead tensor theory. Bulletin of Mathematical Biophysics 1961, 23, 31-42. Brody, D. A. The inverse determination of simple generator configurations from equivalent dipole and multil~ole information. I E E E Transactions on Biomedical Engineering 1968, 15, 106-110. Brody, D. A., Cox, J. W., and Horan, L. G. Hexadecapolar shift, equations applicable to equivalent cardiac generators of lower degree. Annals of Biomedical Engineering 1973a, 1,481-488. Brody, D. A., Terry, F. H., and Ideker, II. E. Eccentric dipole in a spherical medium: Generalized expression for surface potentiMs. I E E E Transactions on Biomedical Engineering 1973b, 20, 141-143. Brody, D. A., Cox, J. W., Jr., Keller, F. W., and Wennemark, J. l]. Dipole ranging in isolated rabbit hearts before and after right bundle branch block. Cardiovascular Research 1974, 8, 37-45. Burger, H. C., and van Milaan, J. B. Heart vector and leads, Part I. British Heart Journal 1946, 8, 157-161. Burger, H. C., and van Milaan, J. B. Heart vector and leads, Part II. British Heart Journal 1947, 9, 154-166. Einthoven, W., Fahr, G., and l)eWaart, A. On the direction and mainfest size of the variations of potentials in the human heart and on the influence of the position of the heart on the form of the electrocardiogram. Archiv fur die Gesamte Physiologic 1913, 150, 308. Translated by Hoff, H. E., and Sekelj, P. American Heart Journal 1950, 40, 163-211. Flowers, N. C., Hor~n, L. G., and Brody, D. A. Evaluation of multipolar effects in the highfidelity standard electrocardiogram by means of factor analysis. Circulation 1965, 32, 273-280. Flowers, N. C., Johnson, J. C., and Horan, L. G. The effect of u sensitivity to dipole content in detecting infarctional changes. Journal of Electrocardiology 1974, 7, 1-8. Gabor, D., and Nelson, C. V. Determinstion of the resultant dipole of the heart from measurements on the body surface. Journal of Applied Physics 1954, 25, 413-416. Geselowitz, D. B., and Arthur, R. M. Derivation of aimed electrocardiographic leads from the multipole expansion. Journal of Electrocardiology 1971, 4, 291-298. Geselowitz, D. B. Multipole representation for an equivalent cardiac generator. Proceediugs of the Institute of Radio Engineers 1960, 48, 75-79. Geselowitz, D. B. Determination of multipole components. In C. V. Nelson and D. B. Geselowitz (Eds.), The theoretical basis of electrocardiology. Oxford: Clarendon, 1976. Pp. 202-212. Hehn, R. A. and Chou, T. C. The use of a variably located dipole as an equivalent generator. In Ed. 2, I. Hoffman, R. Hamby, and E. Glassman (Eds.), Vectorcardiography. Amsterdam: North-Holland, 1971.2rid ed., pp. 98-106. Horan, L. G., and Flowers, N. C. Recovery of the moving dipole from surface potential recordings. American Heart Journal 1971, 82, 207-214. Hot'an, L. G., Flowers, N. C., and Miller, C. B. A rapid assay of dipolar and extradipolar content in the human electrocardiogram. Journal of Electrocardiology 1972, 5, 211-224. Kornreieh, F. The missing waveform information in the orthogonal electrocardiogram (Frank leads) : I. Where and how can this missing waveform information be retrieved? Circulation 1973, 48, 984. McFee, R., and Johnston, F. D. Electrocardiographic leads. III. Synthesis. Circulation 1954, 9, 868-880. Nelson, C. V., Hodgkin, B. C., and Voukydis, P. C. Determination of the locus of the heart vector from body surface measurements: model experiments. Journal of Electrocardiology 1975, 8, 135-146.



Plonsey, R. A simple example of the muir;pole theory applied to electrocardiography. American Heart Journal 1969, 77, 372-376. Selvester, R. H., Kalaba, R., Collier, C. C., Bellman, R., and Kaginada, H. A digital computer model of the vectorcsrdiogram with distance and boundary effects: simulated myocardial infarction. American Heart Journal 1967, 74, 792-808. Stratton, J. A. Electromagnetic theory. New York; McGraw-Hill, 1941. Pp. 176-183. Wilson, F. M., and Bayley, R. H. The electric field of an eccentric dipole in a homogeneous spherical conducting medium. Circulation 1950, 1, 84-92.

The multipolar content of the human electrocardiogram.

ANNALS OF BIOMEDICAL ENGINEERING 4, 280--301 (1976) The Multipolar Content of the Human Electrocardiogram ~ LEO G . HORAN, 2 R . CHRIS HAND, NANCY C...
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