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Electrocardiograms that represent the potential variations of a single electrode
ELECTROCARDIOGRAMS VARIATIONS
THAT
REPRESENT
OF’ A SINGLE
THE
POTENTIAL
ELECTRODEat
FRANK N. WILSON, M.D., FRANKLIN D. JOHNSTOP~, M.D., MACLEOD, M.D., AND PAUL S. BARKER, M.D. ANN ARBOR, MICH.
A. GARRARD
INTRODUCTIOX
I
N STUDYING the electrical field produced by the heartbeat under various circumstances, we have frequently ma.de use of precordial leads, pad leads, and direct leads in animal experiments, and of precordial leads in clinical investigations.l$ 2 In taking these special leads one electrode (the indifferent electrode) is placed upon one of the extremities,$ and the other (the exploring electrode) upon the precordium, upon a large gauze pad soaked in saline and laid upon the exposed heart, or directly upon the exposed heart as the case might be. In direct leads taken in this way the potential of the exploring electrode fluctuates through so wide a range in comparison with that of the indifferent electrode t,hat no material error is made if the potential of the latt)er is rega.rded as constant throughout the cardiac cycle. In pad leads, and particularly in precordial leads, the potential variations of the indifferent electrode, although no greater in absolute magnitude than in direct leads, are much larger in comparison with those of the exploring electrode, and play a considerably greater rale in determining the form of the curve recorded. In standard leads the two electrodes are approximately equidistant from the heart; on the average their potential variations are of about the same magnitude and influence the form of the electrocardiogram in equal measure. In general the curves obtained by means of the special leads mentioned are more or less helpful in solving electrocardiographic problems in proportion to the amount of information that can be gained by comparing the deflections of one lead with those inscribed in another during the same phase of the cardiac cycle. The deflections of pad leads and precordial lea,ds are compared with each other and with the corresponding deflections of direct and standard leads. The analysis depends in the main upon the discovery of similarities, of deflections that are alike in form and correspond in time. Differences between the leads compared with respect to the relative magnitude of the potential variations of the *From the Department of Internal Medicine, University School. tA prekninary report based on the material incorporated published in Proc. Sot. Exper. Biol. & Med 29: 1011, 1932. Sit has usually been placed upon the left !eg in taking thp left hind leg in animal experunencs. 447
of
Michigan in
clinical
this curves
Medical article and
was uDon
two eleetrodcs ted to obscr~c these similaritiw iiJl(l of’ten nmkc tht: interpretation of the cur~8 dificult. hi ordw to ohh deflectioris of simila,r size the string galvarrometcr must bt: made al)proxirnately tcbn t.imes as sensitive when taking ])rt\cordial as whe11taking direct leads. Defections due to varia,tions in the poteutial OSthtt indifferent electrode are t.herefore ten times as large and ten times its conspicuous in the The differences between direct and standard former as in the latter. leads are even grcat,cr, and the principles followed in the interpret~ation of the curves obtained by n)cans of the one canl~lot be applied to thosth obtained by means of the other. In order to orercomc these difhculties we have devised leads that record the potential variations of a single electrode. It is the purpose of this article to explain the methods adopted to achieve this end and to show that when they are followed thr I)otential variat,ions of the indifferent electrode are negligible. METHOIX The method upon the right
of leading arm, left
referred arm, and
SN L, Bl’l’,\RAT
IX
to is illustratwl in Fig. left leg, in exactly the
1. Electrodes are placed same manner as in ta.king
Fig. I.-Diagram illustrating the method of leading used to record *he potential variations of a sfngle electrode. Electrodes on the right arm (R), left arm (L), and left leg (P) are connected through equal resistances of 5,000 ohms to a central terminal (T), The central terminal and an exploring electrode, or one of the extremity electrodes as indicated here. are connected to the input terminals of a vacuumtube amplifier with a balanced plate circuit in which the string galvanometer is inserted. They are connected, each through 3 separate noninducthe three standard jeads. tive resistance (r), to a central terminal. The three resistances used must be equal an.d should be large in compar~~un with the largest body resistance between any two of the three electrodes. In our earliest experiments Tve employed resmtanccs of 25,000 ohms, but this made onr apparatus so sensitive to stray alternating currents that resistances of 5,000 ohms lvere finally substituted. These greatly reduced the amount of stray current picked up, and proved to be reasonably satisfactory if The central terminal serves as the int,he skin resistance was kept sufficiently low. different electrode, and we shall show that its potential is not materially affected by the heart’s electrical field. The exploring electrode may be placed upon the precordium or upon any other part of the body Whose potential variations arc to 110
The central terminal :tml the exploring elwtrolle :IW wnnwtcvl to tlw input The string g:tlr:tnonwtrr terminals of a vacnurn tnlw xitll a balancwl plYtc c~in%it. n rariablc rcsistanee ant1 is joinctl to the plate circuit in such n wty 3s to incladc The v:Aw of the rcsistancc is :L lmrtlon of the plxtc battery lvtwcvn its tcrmin:As. iu’u63s it dltc to the #$tc vnrrfant when the so :uljustt4 tilat the drop in i,Ott’llti:ll inljut terminals of the tulle are shortc~ircwited i.3 rswtly l~alancell ly the volfag;, drop in the ineiuded portiou of the battery. Whru the plate current changes in reto that of the filament, spwx3e to a change in the potential of the grid with respect this bniunce is disturl)ctl and a small fraction of the plate rurrent flows through tll(, string galvanometer. One of the chief advantages of this arrangement is the very high resistance in the input circuit. The addition of twent,y-five, iifty, or ercn one hundred thousaml ohms to the resistance in this circuit does not appreciably alter the size of the string deflection producetl t7hen an electromotive forrc of one millivolt is throffn into it. sensitivity at the beginning The tension of the string is adjusted to give the proper of a set of observations and usually dots not nerd to be changed thereafter. SO overshooting, due to the condenser-like effect of the skin, occurs when the skin TRsistance is high. Tile flow of current in the input circuit is so small that elec%odcs of almost any type can be used mithout fear of polarization effects. Since prartically no current flows, the potential differences that it is desired to measure are not altered. The chief disndvantagc lies in the difficulty of avoiding interference by qtray alternating current. This is much greater than \chen the string galvanometer is used in the ordinary xay, and it increases rapidl:? v-ith an incrrnse in tllc p?;tcrxllt rcsistanPc of the inlxlt rirvnit. E’OTENTIAL
OF
THE
C’ESTHAL
‘l’I~RMIS\‘:?I,
At any instant t,he sum of the differences in potent,ial bctwctvl the central t,erminal and any three electrodes connected to it is zero. !l%C mean potential of these electrodes and the potential of the central terminal ase equal. To prove these statements, let VT represent the potential of the central termin& and 1’ the magnitude of the equal resistances through which it is joined to three clcctrodes in contact with If the potentials of the three electrodes arc: represented by the body. VA, VB, and T’c and the currents flowing from these electrodes toward the eentrd t.ermikval by f,z, fB, and Jr, rcspcetivci:-, these rlnantit,i>s must satisfy the following equations :
By adding thr>se I’ qnations
we obl ain
*The circuit we are using is essentially the same as that employed in Dr. W. J. V. Osterhout’s laboratory at the Rockefeller Institute for Medical Research. We wish to thank Dr. Osterhout and his associate, Dr. S. IC. Hill. for supplying us with a diagram of this circuit and with the data necessary for its construction. .?Rrsintance external to the varuum tnbc.
The righthand side of this equation is clearly zero by Kirchkoff’s first law, which sta.tes that the algebraic sum of all the currends meeting at any point of a network is zero. Consequently. (VA - VT)
t
(VB ‘- TIT) i (V, - l’,Ti = 0
(5 )
01’ V2’ = +i (I’.1 -’ 17‘q i l’,.)
(6)
The same method ma.y be used t.o show that if the central terminal is joined through like resistances to any number of electrodes in contact with the body, the sum of the differences in potential between it and these electrodes must be zero, and the potential of the terminal must be equa,l to the mean potential of the electrodes. The difference in pot,ential between the central terminal and any one of three electrodes connected to it, may be expressed in terms of the differences in potential between that elect,rode and the other two. If tho electrodes a.re placed upon the right arm, left arm, and left leg, the difference in potential bet,ween the central terminal and the leg electrode, for example, is at a.11times one-third the sum of the differences in potential between this electrode and the electrodes on the two arms. We may write ( 1-c - Ir2’) ~’ ( 1-T -- V.() = V(! - v.., (7, ( T’c - I’rl - (l’r - V*) = I’(. - l’,, (81 Hy equation (5) ‘cTc- VT = ( 1-r - IT.,) 1 (I-, - I’,) (9) If we subst,itutc pb for 1-c - l’:i and or for IFr - I-n the addition tions (7) and (8) gives I’(,, - ITT =
y
In the same way it may be shown
of equa(10)
that if P,‘ is substituted
ra4 - TT = - 5q”
for Vs - T’.i (11)
and yR _ .1-T _ ??t?L? (12) 3 In deriving the foregoing equations (1 to 12 inclusive) we have made no assumptions of any kind. It should be not,ed, however, that the symbols T“i, I’B and VC appearing in these equa.tions represent the potentials of the three electrodes in contact with the body after these electrodes have been connected to t,he central terminal. We desire to study the electrical field produced by the heart under natural conditions, and we must take care that our method of measurement does not modify to a material extent the quantities that we wish to measure. The heart 'S electrical field must be altered by any procedure that changes the resistance between points that are at different potentials. Changes in re-
WI1 1 HOK
ET
AI..
~l,Ec’TKOCAHl)1(~OKAYS
:
451
sistance between points at the same potential have, of course, no effect upon the flow of current. The effects produced by attaching electrodes to the body surface must vary directly with the size and conductivit,y of the electrodes, and inversely with their dist,ances from the heart; the effect of connecting these electrodes to a cent,ral terminal must vary inversely with the magnitude of the resistances used for this purpose. The extremities may be regarded as linear conductors att,ached to the t.runk; between points on the same extremity there are no differences in potential of cardiac origin that can be detect,ed by measurements made with the string galva.nometer at the usual sensitivity. The potentials of the extremities are not, therefore, appreciably altered by placing even large electrodes upon them. The effect of connecting these elect.rodes to a central terminal may be neglected, if this procedure does not significantly change the potential difference between any two of them during any phase of the cardiac cycle. It. will bc seen that if we pla.ce our three electrodes upon the right arm, left, arm, and left leg, and make the resistance 7’ so la,rge that connecting them to the central t,erminal does not materially alter the size of the deflections in t,he three standard leads, we shall make no serious error if we t,rcat V,.t, I;, and VC as if they were the potentials of these extremities before the attachment of the electrodes, and regard e,, eh, and e, as the deflections in the three standard leads. It is clear that to accomplish our purpose we must make Y large in comparison with the largest body resistance bet,ween any two of the three extremities. A large part of the resistance between one extremity and another is due to the resistance of the skin beneath the electrodes, and if this is kept low 9. may be made smaller than would otherwise be the case. It will be observed that the resistance of the skin beneath a given electrode is a part of the resistance between the subcutaneous tissues and the central terminal. When the clectrodcs are placed on the right arm, left arm and left leg, the resistances between this terminal and the a.pices of Einthoven’s triangle, which arc represented by the junctions of these extremities with the trunk, canuot be regarded as even approximately equal unless 1’ is large in comparison with the skin resistance or unless the skin resistance is the same benea.th all three electrodes. In practice, however, we shall know that I’ is large enough for our purpose if t.he curves taken by meaals of the three standard leads before and those taken in the same wa.y after connecting the extremity electrodes to the central terminal arc uot significantly different. DEDUCTIONS
BASED
ON
EIKTHOVEN
‘S TRIANGIJX
In a, previous publication” it has been shown that if the assumptions upon which Einthoven’s triangle is based are valid, t.he potential of the
J,?
L
=
(1 -
(‘::
(14)
3
Nld vp
=
C?
c::
(15)
3
in which the deflections instant are represented that at every instant
in standard Leads I, 11, and 111 at the chosen by P,, p,, aald (lx, respectively. It will be seen v,
1 I;,
1. 1-p =
0.
(16)
It should be pointed out that the derivation of these equations involves the assumption that an electromotive force generated by the heart and ha.ving a direction perpendicular to the plane of the three standard leads will not affect the potent.ial of the right arm, left arm, or left leg, This is equivalent to the assumption that the heart lies in the plane of Einthoven’s triangle. If electrodes on the right arm, left al-m, and left leg arc connected to a central terminal through like and sufficicntlp large resistances, we may substitute VX, VL, and VF, for V.I, Vs, and Vc, respect.ively, in any of the equations in which the latter occur. It is therefore evident from equations (6) and (16) that under the circumst,ances specified we may, without serious error, rega.rd the central terminal as at zero pot.ential throughout the cardiac cycle. By connecting one of t,he input terminals of the apparatus, described on a preceding page, to the central terminal and the other to the right-arm, left-arm, and left-leg electrodes in succession we obtain three ~rvcs, each of which rcprcsents the potential WC may designat,e these curves, which variations of a single extremity. arc so taken that relative negativity of the extremity electrode produces an upward deflection in the finishtd record, by 1’11. I-L, and VVJ”, respectively, and we shall refer to them collectively as extremity potentials. At any instant the sum u-f the M&ions in the right-arm, leftarm, and left-leg leads must, be zero. The position of the electrical asis map be determined bp means of the formula -L/T- J’p yz--L7~- (17) R I; in which U. is the angle ma& by the ctcctrical axis with that side of Einthoven’s triangle which corresponds to standard Lead T. The curves obtained by leading from the central terminal to itI1 cbxpioring electrode in contact wit,h the exposed heart,, with a pad of gauze laid upon the exposed heart, or with the prerordium represent the potential variations of the exploring electrode, and may be referred to as direct, pad, ton a =
In order to ttbsb the conceptions at which WC have arrived under conditions resembling those postulated as closely as possible, we have carried out a few experiments on a model. An cyuilateral triangle with sides 12.7 cm. in length was marked out on the bottom of a large shallow galvanized pan measuring 4S.3 by 40.6 cm. Electrodes were placed at the apices of the triangle, and two electrodes were placed close together near its center. These cclltral electrodes were 10 mm. apart and were so arranged that the center of the triangle was midway be-
,
-‘t----t1 E---+ys/~
--
kiiiGis= .gELzEziE
Fig. Z.-Records obtained in an experiment on a model (experiment 2, Table I). A deflection of 0.5 cm. equals one millivolt. V 1 shows the potential difference between the central terminal and a poi:lt equidistant from the wntul elcrtrodes (see text) :~nd 24 cm. from the center of the tri;lngh~.
twecn t,hem. After the pan had been filled to a. depth of 38 mm. with a weak solution (about 1 per cent) of copper chloride, they were connected to a 45 volt battery through a rotating circuit breaker, which closed the circuit momentarily with each revolution. The apical electrodes were joined to a central terminal through resistances of 5,000 ohms, and the potential variations of these electrodes (Vat VI,. a.nd VP) were recorded by connecting the central terminal and each of them in successionto the input terminals of the vacuum tube amplifier previously described (Fig. 2). The three leads corresponding to the three standard electrocardiographic leads were taken with the same instrument, in some instances both before and after connecting the apical elecbrodes to the central terminal, The potential of the central terminal was also
compared with t,hat of points dist.aut from t.hc at*ntel* of the triangle and equidistant from the two central electrodes; points which, theoretically, should be at zero potential. The difference in potential between surh points and the central terminal was always very small.
Note .-The measurements given above are *In this experiment Leads I. II, and III connecting the apical electrodes to the iThe angle between the line joining the triangle corresponding to standard Lead I. (lb)
Pig.
3.--Standard
electrocardiogram
in tenths of a millivolt. were taken before (la) central terminal. central electrodes and
of a normal
subject.
QRR
interval,
and that
again
after
side
of thee
0.063
second.
The results of two experimenk are shown in Table I. In the first t,he electrical axis was parallel to that, side of the triangle corresponding to standard Lead II, and in the second it’ was perpendicular to the side corresponding to standard Lea.d I (Fig. 2). The last column of the table gives the difference in potential between the central terminal and a point near the edge of the pan and on the perpendicular bisector of the line joining the two central electrodes. In the first experiment this point was 20 cm. a.nd in the second 24 cm. from the cent,er of the t.riangle. It will be noted that .the potential differences in Leads I, II, and III were somewhat greater before (la) than a.fter (lb) the apical electrodes were connected to the central terminal. The results of both experiments a.rc in good agreement with the theoretical predictions based on the equations given on preceding pages. CLINICAL
CURVES
We hope in the near future to describe in considerable detail the curves obtained under various circumstances when the method of leading described in this article is employed. We shall therefore confine our
WII,SOR
ET
AI,. :
EI,E(‘TROCARDIOGRAMS
4x5
remarks here to a single illustrat,ion. The standard clcct.rocardiograms of a normal subject are shown in Fig. 3, and the extremity and precordial potentials of the same subject in Fig. 4. It should he remembered that in the latter curves a negative variation in potential is WI)resented by an upward, a positive variation in potential by a downward deflection of the string sha.dow. The curves obtained from the right side of the precordium (V,, V,, and V,) show a small downward
Fig. 4.-Extremity and precordial potentials of the subject whose standard electrocardiogram fs shown in Fig. 3. In each instance the upper curve is standard fipad I. The lower curves represent the potential variations of the following points: a, right arm; YL, left arm. VP, left leg; VI, fourth rib at right sternal edge; V*, fourth rib at left sternal ‘edge: VJ. flfth rib halfway between left sternal edge and left nipple line: V,. flfth interspace just inside nipple line (apex) ; VS, sixth rib anterior axillary line: VE, ensiform cartilage. In the first three records 1 cm. equals 1 millivolt: in the last six 0.5 cm. equals 1 millivolt. The figures written on the records give the position of the chief upstroke of QRS with reference to the beginning of the QRS interval.
followed by a large upward movc~mcnt. The chicfif upstroke occurs early in the QRS interval. The CUIW~S obt;lillcbd from the It42 side of the prccot&urn (7, mid IT-J hhow a much derpcr ~Iow~M.:II~ movement, ;111ci the chief upstroke is MC‘. In one of these (YI’VCS ( I-,) a slight, rise precedes the first descent . This summit, IS seldom if PW~ large in normal subjcctr;. Thcs polclltial varintiol(s of the right arm are similar t 0 th0sC rc~cor&d 011 the right sidtl of 1he prccordiunl, illld the potential variations of the left leg arc similar to 1hose recorded on the left side of the precordium. ,$s is usually the case in normal subjects, the potential variations of the left arm arc small. In left axis deviation the chief deflection of t,he left arm 1ea.d is downward; in right axis deviation it is upward. The dir&ion and size of t.his deflection may bc used prcas a rough index in estimating the kind and grade of ventricular ponderancc. Esamirmtion of equation (141 shows that it, is similar in significance to the indices used for t,his purpose by JIcwis4 and by White and Bock.5 COMMEPU’TS
It should be emphasized t,hat the potential variations of the central terminal cannot be shown to be negligible unless certain assumptions referred to are those upon which Einare made. The assumptions thoven’s method of determining the position of the electrical axis is based a,nd especially the assumption that electromotive forces arising in the heart and having a. direction perpendicular to the plane of the three standard leads have no effect upon the potential of the right arm, left arm, or left leg.* Some further discussion may serve to indicate the magnitude of the error t,hat may have been introduced into our calculations by this last assumption. Let us assume that the clectrieal field produced in the body at a, given instant by the heart may be satisfactorily represented by the electrical field produced by a doublet located at the cent,er of a homoAt any point on the surface of geneous sphere of conducting material. such a sphere the potential due to a cent,ral doublet is proportional to t,he cosine of the angle between the radius drawn to that point and the axis of the doublet (CaaAld,G Wilson. Macleod and BarkeY). Tf the axis of the doublet is parallel to the plane determined by three surfacr points lying at the apices of an qnilateral triangle, the mean potential of these points is zero. If the axis of the doublet, is not parallel to the plane ment.ioned, the mean potential of the three points, is not zero unless this plane passes through the ~ellter of the sphere. The doublet may be: regartlrd as the snm of two cr)mponPrlts : a doublet. whose axis is parallel and a doublet whose axis is pcrpendicu1a.r to the specific>ti *Einthoven’s assumption formed by the three leads that the heart and the three it was necessary to assume triangle,
that the heart is at the center amounts to the same thing, if leads are in the same plane. only that the hcarl, is equidistant
of an equilateral trian&’ it is understood to mean For his purpose, however, Prom the apices of this
1,lanc. Any difference in potential between the three points must be The potential due to the perattributed to the parallel component. 1)endicular component is the same at all of them and is directly proportional to tlic distance from their plane to the center of the spfl~~c~. This is easily understood, for t,his distance measures the cosine of thcl angle formed by the radius drawn to any one of the three IJoints and the axis of the perpendicular doublet. The mean potential of four surface points lying at the apices of an equilateral tetrahedron is zero, whatever the position of t.he axis of the central dotiblet may be. The potential of a central terminal connected to four such points through like resistances must also be zero, and leads from this terminal to each of these point,s would give the data ncccssary for the determination of the orientation of the axis of the doublet in t.hree-dimensional space. WC have therefore considered the ac'l~isd~ilit.~of connecting the central terminal ill our esperimcnts not only to the right arm, left arm, and left leg, but also to an electrode p!accd on the back directly behind the heart. In the cast of the theoretical model under consideration the error that would be made by considering t,he potential of the central terminal zero would be greater or less when it was connected to the apices of an equiIatcra1 triangle than when it was also connected to a fourth point at the more distant extremity of the diameter perpendicular to the -plane of the triangle according as t,he distance from the plane of the triangle to the center of the sphere was more or less than one-seventh of the radius.” If 1-hefour points lay at the apices of an equilateral tetrahedron, this distance would, of course: be exactly one-third of the radius. The plane of the three standard leads is not very well defined, but it would seem that it must be regarded as passing through the heart. If this is the cnqe, it is improbable that connecting the central terminal to an additional electrode on the back would reduce whatever error is made by considering the potential of this terminal zero. This procedure may, however, prove useful for the purpose of determining the projection of the electrical axis upon a sagittal as well as upon a frontal plane. Over other ways of doing this it has the advantage t,hnt when the distances from the heart t.o the electrodes are unequal the error made by assuming that the heart is at the center and the electrodes are at the apices of an equilateral tetrahedron (or triangle) may be partly or wholly eliminated by making the resistances between the central terminal and the electrodes unequal. *The Errol made by using the four points spxiAed could be corrected by making the resistance between the fourth point and the central terminal greater or less than the other three. If, for example, the distance from the plane of the triangle to the center of the sphere was exactly one-seventh of the radius it would be necessary in order to bring the potential of the central terminal to zero to make this resistance seven-thirds of the resistance between the central terminal and each apex of the triangle.
458
THE
AMERICAN
HEART
JOURNAI.
SUMMARY
In order to simplify the analysis of the curves obtained by leading from the precordium and for certain other purposes, we have devised leads that record the potential variations of a single electrode. Electrodes are placed on the right arm, left arm, and left leg in the usual way and connected through like resistances to a, central terminal. The resistances used for this purpose should be large in comparison with the resistance of the body in standard leads. Theoretical considerations and experiments on a model indicate t,hat under these circumstances the potential variations of the central terminal are negligible. The curves obtained by leading from an exploring electrode in contact with any part of the body to the central terminal represent the variations in potential produced by the heart.beat in t.he region in contact with the former. The potential variations of the right arm, left. arm, and left leg are recorded by leading from the electrodes placed on these extremities to the central terminal. They ma,y be compared with the potential variations that occur in various parts of the precordium. To increase the resistance in the input circuit of our recording apto the balanced paratus we have connected the string galvanometrr plate circuit of a one-stage vacuum-t,ube amplifier. REFERENCES 1. Wilson, 2. Wilson, i:3 Lewis:’ Wilson
Macleod, and Barker: AM. HEART J. 7: 305, 1932. Macleod, Barker, Johnston, and Klostermeyer: Heart 16: Heart Macleod, 5: and Barker: 1913-14. AM. HEART J. 7: 207, 1931. 367, 5. White and Bock: Am. J. M. SC. 156: 17, 1918. 6. Canfield: Heart 14: 102, 1927. 7. Wilson, Macleod, and Barker: J. Gen. Physiol. 16: 423, 1933.
156,
19%
THAT
REPRESENT
OF’ A SINGLE
THE
POTENTIAL
ELECTRODEat
FRANK N. WILSON, M.D., FRANKLIN D. JOHNSTOP~, M.D., MACLEOD, M.D., AND PAUL S. BARKER, M.D. ANN ARBOR, MICH.
A. GARRARD
INTRODUCTIOX
I
N STUDYING the electrical field produced by the heartbeat under various circumstances, we have frequently ma.de use of precordial leads, pad leads, and direct leads in animal experiments, and of precordial leads in clinical investigations.l$ 2 In taking these special leads one electrode (the indifferent electrode) is placed upon one of the extremities,$ and the other (the exploring electrode) upon the precordium, upon a large gauze pad soaked in saline and laid upon the exposed heart, or directly upon the exposed heart as the case might be. In direct leads taken in this way the potential of the exploring electrode fluctuates through so wide a range in comparison with that of the indifferent electrode t,hat no material error is made if the potential of the latt)er is rega.rded as constant throughout the cardiac cycle. In pad leads, and particularly in precordial leads, the potential variations of the indifferent electrode, although no greater in absolute magnitude than in direct leads, are much larger in comparison with those of the exploring electrode, and play a considerably greater rale in determining the form of the curve recorded. In standard leads the two electrodes are approximately equidistant from the heart; on the average their potential variations are of about the same magnitude and influence the form of the electrocardiogram in equal measure. In general the curves obtained by means of the special leads mentioned are more or less helpful in solving electrocardiographic problems in proportion to the amount of information that can be gained by comparing the deflections of one lead with those inscribed in another during the same phase of the cardiac cycle. The deflections of pad leads and precordial lea,ds are compared with each other and with the corresponding deflections of direct and standard leads. The analysis depends in the main upon the discovery of similarities, of deflections that are alike in form and correspond in time. Differences between the leads compared with respect to the relative magnitude of the potential variations of the *From the Department of Internal Medicine, University School. tA prekninary report based on the material incorporated published in Proc. Sot. Exper. Biol. & Med 29: 1011, 1932. Sit has usually been placed upon the left !eg in taking thp left hind leg in animal experunencs. 447
of
Michigan in
clinical
this curves
Medical article and
was uDon
two eleetrodcs ted to obscr~c these similaritiw iiJl(l of’ten nmkc tht: interpretation of the cur~8 dificult. hi ordw to ohh deflectioris of simila,r size the string galvarrometcr must bt: made al)proxirnately tcbn t.imes as sensitive when taking ])rt\cordial as whe11taking direct leads. Defections due to varia,tions in the poteutial OSthtt indifferent electrode are t.herefore ten times as large and ten times its conspicuous in the The differences between direct and standard former as in the latter. leads are even grcat,cr, and the principles followed in the interpret~ation of the curves obtained by n)cans of the one canl~lot be applied to thosth obtained by means of the other. In order to orercomc these difhculties we have devised leads that record the potential variations of a single electrode. It is the purpose of this article to explain the methods adopted to achieve this end and to show that when they are followed thr I)otential variat,ions of the indifferent electrode are negligible. METHOIX The method upon the right
of leading arm, left
referred arm, and
SN L, Bl’l’,\RAT
IX
to is illustratwl in Fig. left leg, in exactly the
1. Electrodes are placed same manner as in ta.king
Fig. I.-Diagram illustrating the method of leading used to record *he potential variations of a sfngle electrode. Electrodes on the right arm (R), left arm (L), and left leg (P) are connected through equal resistances of 5,000 ohms to a central terminal (T), The central terminal and an exploring electrode, or one of the extremity electrodes as indicated here. are connected to the input terminals of a vacuumtube amplifier with a balanced plate circuit in which the string galvanometer is inserted. They are connected, each through 3 separate noninducthe three standard jeads. tive resistance (r), to a central terminal. The three resistances used must be equal an.d should be large in compar~~un with the largest body resistance between any two of the three electrodes. In our earliest experiments Tve employed resmtanccs of 25,000 ohms, but this made onr apparatus so sensitive to stray alternating currents that resistances of 5,000 ohms lvere finally substituted. These greatly reduced the amount of stray current picked up, and proved to be reasonably satisfactory if The central terminal serves as the int,he skin resistance was kept sufficiently low. different electrode, and we shall show that its potential is not materially affected by the heart’s electrical field. The exploring electrode may be placed upon the precordium or upon any other part of the body Whose potential variations arc to 110
The central terminal :tml the exploring elwtrolle :IW wnnwtcvl to tlw input The string g:tlr:tnonwtrr terminals of a vacnurn tnlw xitll a balancwl plYtc c~in%it. n rariablc rcsistanee ant1 is joinctl to the plate circuit in such n wty 3s to incladc The v:Aw of the rcsistancc is :L lmrtlon of the plxtc battery lvtwcvn its tcrmin:As. iu’u63s it dltc to the #$tc vnrrfant when the so :uljustt4 tilat the drop in i,Ott’llti:ll inljut terminals of the tulle are shortc~ircwited i.3 rswtly l~alancell ly the volfag;, drop in the ineiuded portiou of the battery. Whru the plate current changes in reto that of the filament, spwx3e to a change in the potential of the grid with respect this bniunce is disturl)ctl and a small fraction of the plate rurrent flows through tll(, string galvanometer. One of the chief advantages of this arrangement is the very high resistance in the input circuit. The addition of twent,y-five, iifty, or ercn one hundred thousaml ohms to the resistance in this circuit does not appreciably alter the size of the string deflection producetl t7hen an electromotive forrc of one millivolt is throffn into it. sensitivity at the beginning The tension of the string is adjusted to give the proper of a set of observations and usually dots not nerd to be changed thereafter. SO overshooting, due to the condenser-like effect of the skin, occurs when the skin TRsistance is high. Tile flow of current in the input circuit is so small that elec%odcs of almost any type can be used mithout fear of polarization effects. Since prartically no current flows, the potential differences that it is desired to measure are not altered. The chief disndvantagc lies in the difficulty of avoiding interference by qtray alternating current. This is much greater than \chen the string galvanometer is used in the ordinary xay, and it increases rapidl:? v-ith an incrrnse in tllc p?;tcrxllt rcsistanPc of the inlxlt rirvnit. E’OTENTIAL
OF
THE
C’ESTHAL
‘l’I~RMIS\‘:?I,
At any instant t,he sum of the differences in potent,ial bctwctvl the central t,erminal and any three electrodes connected to it is zero. !l%C mean potential of these electrodes and the potential of the central terminal ase equal. To prove these statements, let VT represent the potential of the central termin& and 1’ the magnitude of the equal resistances through which it is joined to three clcctrodes in contact with If the potentials of the three electrodes arc: represented by the body. VA, VB, and T’c and the currents flowing from these electrodes toward the eentrd t.ermikval by f,z, fB, and Jr, rcspcetivci:-, these rlnantit,i>s must satisfy the following equations :
By adding thr>se I’ qnations
we obl ain
*The circuit we are using is essentially the same as that employed in Dr. W. J. V. Osterhout’s laboratory at the Rockefeller Institute for Medical Research. We wish to thank Dr. Osterhout and his associate, Dr. S. IC. Hill. for supplying us with a diagram of this circuit and with the data necessary for its construction. .?Rrsintance external to the varuum tnbc.
The righthand side of this equation is clearly zero by Kirchkoff’s first law, which sta.tes that the algebraic sum of all the currends meeting at any point of a network is zero. Consequently. (VA - VT)
t
(VB ‘- TIT) i (V, - l’,Ti = 0
(5 )
01’ V2’ = +i (I’.1 -’ 17‘q i l’,.)
(6)
The same method ma.y be used t.o show that if the central terminal is joined through like resistances to any number of electrodes in contact with the body, the sum of the differences in potential between it and these electrodes must be zero, and the potential of the terminal must be equa,l to the mean potential of the electrodes. The difference in pot,ential between the central terminal and any one of three electrodes connected to it, may be expressed in terms of the differences in potential between that elect,rode and the other two. If tho electrodes a.re placed upon the right arm, left arm, and left leg, the difference in potential bet,ween the central terminal and the leg electrode, for example, is at a.11times one-third the sum of the differences in potential between this electrode and the electrodes on the two arms. We may write ( 1-c - Ir2’) ~’ ( 1-T -- V.() = V(! - v.., (7, ( T’c - I’rl - (l’r - V*) = I’(. - l’,, (81 Hy equation (5) ‘cTc- VT = ( 1-r - IT.,) 1 (I-, - I’,) (9) If we subst,itutc pb for 1-c - l’:i and or for IFr - I-n the addition tions (7) and (8) gives I’(,, - ITT =
y
In the same way it may be shown
of equa(10)
that if P,‘ is substituted
ra4 - TT = - 5q”
for Vs - T’.i (11)
and yR _ .1-T _ ??t?L? (12) 3 In deriving the foregoing equations (1 to 12 inclusive) we have made no assumptions of any kind. It should be not,ed, however, that the symbols T“i, I’B and VC appearing in these equa.tions represent the potentials of the three electrodes in contact with the body after these electrodes have been connected to t,he central terminal. We desire to study the electrical field produced by the heart under natural conditions, and we must take care that our method of measurement does not modify to a material extent the quantities that we wish to measure. The heart 'S electrical field must be altered by any procedure that changes the resistance between points that are at different potentials. Changes in re-
WI1 1 HOK
ET
AI..
~l,Ec’TKOCAHl)1(~OKAYS
:
451
sistance between points at the same potential have, of course, no effect upon the flow of current. The effects produced by attaching electrodes to the body surface must vary directly with the size and conductivit,y of the electrodes, and inversely with their dist,ances from the heart; the effect of connecting these electrodes to a cent,ral terminal must vary inversely with the magnitude of the resistances used for this purpose. The extremities may be regarded as linear conductors att,ached to the t.runk; between points on the same extremity there are no differences in potential of cardiac origin that can be detect,ed by measurements made with the string galva.nometer at the usual sensitivity. The potentials of the extremities are not, therefore, appreciably altered by placing even large electrodes upon them. The effect of connecting these elect.rodes to a central terminal may be neglected, if this procedure does not significantly change the potential difference between any two of them during any phase of the cardiac cycle. It. will bc seen that if we pla.ce our three electrodes upon the right arm, left, arm, and left leg, and make the resistance 7’ so la,rge that connecting them to the central t,erminal does not materially alter the size of the deflections in t,he three standard leads, we shall make no serious error if we t,rcat V,.t, I;, and VC as if they were the potentials of these extremities before the attachment of the electrodes, and regard e,, eh, and e, as the deflections in the three standard leads. It is clear that to accomplish our purpose we must make Y large in comparison with the largest body resistance bet,ween any two of the three extremities. A large part of the resistance between one extremity and another is due to the resistance of the skin beneath the electrodes, and if this is kept low 9. may be made smaller than would otherwise be the case. It will be observed that the resistance of the skin beneath a given electrode is a part of the resistance between the subcutaneous tissues and the central terminal. When the clectrodcs are placed on the right arm, left arm and left leg, the resistances between this terminal and the a.pices of Einthoven’s triangle, which arc represented by the junctions of these extremities with the trunk, canuot be regarded as even approximately equal unless 1’ is large in comparison with the skin resistance or unless the skin resistance is the same benea.th all three electrodes. In practice, however, we shall know that I’ is large enough for our purpose if t.he curves taken by meaals of the three standard leads before and those taken in the same wa.y after connecting the extremity electrodes to the central terminal arc uot significantly different. DEDUCTIONS
BASED
ON
EIKTHOVEN
‘S TRIANGIJX
In a, previous publication” it has been shown that if the assumptions upon which Einthoven’s triangle is based are valid, t.he potential of the
J,?
L
=
(1 -
(‘::
(14)
3
Nld vp
=
C?
c::
(15)
3
in which the deflections instant are represented that at every instant
in standard Leads I, 11, and 111 at the chosen by P,, p,, aald (lx, respectively. It will be seen v,
1 I;,
1. 1-p =
0.
(16)
It should be pointed out that the derivation of these equations involves the assumption that an electromotive force generated by the heart and ha.ving a direction perpendicular to the plane of the three standard leads will not affect the potent.ial of the right arm, left arm, or left leg, This is equivalent to the assumption that the heart lies in the plane of Einthoven’s triangle. If electrodes on the right arm, left al-m, and left leg arc connected to a central terminal through like and sufficicntlp large resistances, we may substitute VX, VL, and VF, for V.I, Vs, and Vc, respect.ively, in any of the equations in which the latter occur. It is therefore evident from equations (6) and (16) that under the circumst,ances specified we may, without serious error, rega.rd the central terminal as at zero pot.ential throughout the cardiac cycle. By connecting one of t,he input terminals of the apparatus, described on a preceding page, to the central terminal and the other to the right-arm, left-arm, and left-leg electrodes in succession we obtain three ~rvcs, each of which rcprcsents the potential WC may designat,e these curves, which variations of a single extremity. arc so taken that relative negativity of the extremity electrode produces an upward deflection in the finishtd record, by 1’11. I-L, and VVJ”, respectively, and we shall refer to them collectively as extremity potentials. At any instant the sum u-f the M&ions in the right-arm, leftarm, and left-leg leads must, be zero. The position of the electrical asis map be determined bp means of the formula -L/T- J’p yz--L7~- (17) R I; in which U. is the angle ma& by the ctcctrical axis with that side of Einthoven’s triangle which corresponds to standard Lead T. The curves obtained by leading from the central terminal to itI1 cbxpioring electrode in contact wit,h the exposed heart,, with a pad of gauze laid upon the exposed heart, or with the prerordium represent the potential variations of the exploring electrode, and may be referred to as direct, pad, ton a =
In order to ttbsb the conceptions at which WC have arrived under conditions resembling those postulated as closely as possible, we have carried out a few experiments on a model. An cyuilateral triangle with sides 12.7 cm. in length was marked out on the bottom of a large shallow galvanized pan measuring 4S.3 by 40.6 cm. Electrodes were placed at the apices of the triangle, and two electrodes were placed close together near its center. These cclltral electrodes were 10 mm. apart and were so arranged that the center of the triangle was midway be-
,
-‘t----t1 E---+ys/~
--
kiiiGis= .gELzEziE
Fig. Z.-Records obtained in an experiment on a model (experiment 2, Table I). A deflection of 0.5 cm. equals one millivolt. V 1 shows the potential difference between the central terminal and a poi:lt equidistant from the wntul elcrtrodes (see text) :~nd 24 cm. from the center of the tri;lngh~.
twecn t,hem. After the pan had been filled to a. depth of 38 mm. with a weak solution (about 1 per cent) of copper chloride, they were connected to a 45 volt battery through a rotating circuit breaker, which closed the circuit momentarily with each revolution. The apical electrodes were joined to a central terminal through resistances of 5,000 ohms, and the potential variations of these electrodes (Vat VI,. a.nd VP) were recorded by connecting the central terminal and each of them in successionto the input terminals of the vacuum tube amplifier previously described (Fig. 2). The three leads corresponding to the three standard electrocardiographic leads were taken with the same instrument, in some instances both before and after connecting the apical elecbrodes to the central terminal, The potential of the central terminal was also
compared with t,hat of points dist.aut from t.hc at*ntel* of the triangle and equidistant from the two central electrodes; points which, theoretically, should be at zero potential. The difference in potential between surh points and the central terminal was always very small.
Note .-The measurements given above are *In this experiment Leads I. II, and III connecting the apical electrodes to the iThe angle between the line joining the triangle corresponding to standard Lead I. (lb)
Pig.
3.--Standard
electrocardiogram
in tenths of a millivolt. were taken before (la) central terminal. central electrodes and
of a normal
subject.
QRR
interval,
and that
again
after
side
of thee
0.063
second.
The results of two experimenk are shown in Table I. In the first t,he electrical axis was parallel to that, side of the triangle corresponding to standard Lead II, and in the second it’ was perpendicular to the side corresponding to standard Lea.d I (Fig. 2). The last column of the table gives the difference in potential between the central terminal and a point near the edge of the pan and on the perpendicular bisector of the line joining the two central electrodes. In the first experiment this point was 20 cm. a.nd in the second 24 cm. from the cent,er of the t.riangle. It will be noted that .the potential differences in Leads I, II, and III were somewhat greater before (la) than a.fter (lb) the apical electrodes were connected to the central terminal. The results of both experiments a.rc in good agreement with the theoretical predictions based on the equations given on preceding pages. CLINICAL
CURVES
We hope in the near future to describe in considerable detail the curves obtained under various circumstances when the method of leading described in this article is employed. We shall therefore confine our
WII,SOR
ET
AI,. :
EI,E(‘TROCARDIOGRAMS
4x5
remarks here to a single illustrat,ion. The standard clcct.rocardiograms of a normal subject are shown in Fig. 3, and the extremity and precordial potentials of the same subject in Fig. 4. It should he remembered that in the latter curves a negative variation in potential is WI)resented by an upward, a positive variation in potential by a downward deflection of the string sha.dow. The curves obtained from the right side of the precordium (V,, V,, and V,) show a small downward
Fig. 4.-Extremity and precordial potentials of the subject whose standard electrocardiogram fs shown in Fig. 3. In each instance the upper curve is standard fipad I. The lower curves represent the potential variations of the following points: a, right arm; YL, left arm. VP, left leg; VI, fourth rib at right sternal edge; V*, fourth rib at left sternal ‘edge: VJ. flfth rib halfway between left sternal edge and left nipple line: V,. flfth interspace just inside nipple line (apex) ; VS, sixth rib anterior axillary line: VE, ensiform cartilage. In the first three records 1 cm. equals 1 millivolt: in the last six 0.5 cm. equals 1 millivolt. The figures written on the records give the position of the chief upstroke of QRS with reference to the beginning of the QRS interval.
followed by a large upward movc~mcnt. The chicfif upstroke occurs early in the QRS interval. The CUIW~S obt;lillcbd from the It42 side of the prccot&urn (7, mid IT-J hhow a much derpcr ~Iow~M.:II~ movement, ;111ci the chief upstroke is MC‘. In one of these (YI’VCS ( I-,) a slight, rise precedes the first descent . This summit, IS seldom if PW~ large in normal subjcctr;. Thcs polclltial varintiol(s of the right arm are similar t 0 th0sC rc~cor&d 011 the right sidtl of 1he prccordiunl, illld the potential variations of the left leg arc similar to 1hose recorded on the left side of the precordium. ,$s is usually the case in normal subjects, the potential variations of the left arm arc small. In left axis deviation the chief deflection of t,he left arm 1ea.d is downward; in right axis deviation it is upward. The dir&ion and size of t.his deflection may bc used prcas a rough index in estimating the kind and grade of ventricular ponderancc. Esamirmtion of equation (141 shows that it, is similar in significance to the indices used for t,his purpose by JIcwis4 and by White and Bock.5 COMMEPU’TS
It should be emphasized t,hat the potential variations of the central terminal cannot be shown to be negligible unless certain assumptions referred to are those upon which Einare made. The assumptions thoven’s method of determining the position of the electrical axis is based a,nd especially the assumption that electromotive forces arising in the heart and having a. direction perpendicular to the plane of the three standard leads have no effect upon the potential of the right arm, left arm, or left leg.* Some further discussion may serve to indicate the magnitude of the error t,hat may have been introduced into our calculations by this last assumption. Let us assume that the clectrieal field produced in the body at a, given instant by the heart may be satisfactorily represented by the electrical field produced by a doublet located at the cent,er of a homoAt any point on the surface of geneous sphere of conducting material. such a sphere the potential due to a cent,ral doublet is proportional to t,he cosine of the angle between the radius drawn to that point and the axis of the doublet (CaaAld,G Wilson. Macleod and BarkeY). Tf the axis of the doublet is parallel to the plane determined by three surfacr points lying at the apices of an qnilateral triangle, the mean potential of these points is zero. If the axis of the doublet, is not parallel to the plane ment.ioned, the mean potential of the three points, is not zero unless this plane passes through the ~ellter of the sphere. The doublet may be: regartlrd as the snm of two cr)mponPrlts : a doublet. whose axis is parallel and a doublet whose axis is pcrpendicu1a.r to the specific>ti *Einthoven’s assumption formed by the three leads that the heart and the three it was necessary to assume triangle,
that the heart is at the center amounts to the same thing, if leads are in the same plane. only that the hcarl, is equidistant
of an equilateral trian&’ it is understood to mean For his purpose, however, Prom the apices of this
1,lanc. Any difference in potential between the three points must be The potential due to the perattributed to the parallel component. 1)endicular component is the same at all of them and is directly proportional to tlic distance from their plane to the center of the spfl~~c~. This is easily understood, for t,his distance measures the cosine of thcl angle formed by the radius drawn to any one of the three IJoints and the axis of the perpendicular doublet. The mean potential of four surface points lying at the apices of an equilateral tetrahedron is zero, whatever the position of t.he axis of the central dotiblet may be. The potential of a central terminal connected to four such points through like resistances must also be zero, and leads from this terminal to each of these point,s would give the data ncccssary for the determination of the orientation of the axis of the doublet in t.hree-dimensional space. WC have therefore considered the ac'l~isd~ilit.~of connecting the central terminal ill our esperimcnts not only to the right arm, left arm, and left leg, but also to an electrode p!accd on the back directly behind the heart. In the cast of the theoretical model under consideration the error that would be made by considering t,he potential of the central terminal zero would be greater or less when it was connected to the apices of an equiIatcra1 triangle than when it was also connected to a fourth point at the more distant extremity of the diameter perpendicular to the -plane of the triangle according as t,he distance from the plane of the triangle to the center of the sphere was more or less than one-seventh of the radius.” If 1-hefour points lay at the apices of an equilateral tetrahedron, this distance would, of course: be exactly one-third of the radius. The plane of the three standard leads is not very well defined, but it would seem that it must be regarded as passing through the heart. If this is the cnqe, it is improbable that connecting the central terminal to an additional electrode on the back would reduce whatever error is made by considering the potential of this terminal zero. This procedure may, however, prove useful for the purpose of determining the projection of the electrical axis upon a sagittal as well as upon a frontal plane. Over other ways of doing this it has the advantage t,hnt when the distances from the heart t.o the electrodes are unequal the error made by assuming that the heart is at the center and the electrodes are at the apices of an equilateral tetrahedron (or triangle) may be partly or wholly eliminated by making the resistances between the central terminal and the electrodes unequal. *The Errol made by using the four points spxiAed could be corrected by making the resistance between the fourth point and the central terminal greater or less than the other three. If, for example, the distance from the plane of the triangle to the center of the sphere was exactly one-seventh of the radius it would be necessary in order to bring the potential of the central terminal to zero to make this resistance seven-thirds of the resistance between the central terminal and each apex of the triangle.
458
THE
AMERICAN
HEART
JOURNAI.
SUMMARY
In order to simplify the analysis of the curves obtained by leading from the precordium and for certain other purposes, we have devised leads that record the potential variations of a single electrode. Electrodes are placed on the right arm, left arm, and left leg in the usual way and connected through like resistances to a, central terminal. The resistances used for this purpose should be large in comparison with the resistance of the body in standard leads. Theoretical considerations and experiments on a model indicate t,hat under these circumstances the potential variations of the central terminal are negligible. The curves obtained by leading from an exploring electrode in contact with any part of the body to the central terminal represent the variations in potential produced by the heart.beat in t.he region in contact with the former. The potential variations of the right arm, left. arm, and left leg are recorded by leading from the electrodes placed on these extremities to the central terminal. They ma,y be compared with the potential variations that occur in various parts of the precordium. To increase the resistance in the input circuit of our recording apto the balanced paratus we have connected the string galvanometrr plate circuit of a one-stage vacuum-t,ube amplifier. REFERENCES 1. Wilson, 2. Wilson, i:3 Lewis:’ Wilson
Macleod, and Barker: AM. HEART J. 7: 305, 1932. Macleod, Barker, Johnston, and Klostermeyer: Heart 16: Heart Macleod, 5: and Barker: 1913-14. AM. HEART J. 7: 207, 1931. 367, 5. White and Bock: Am. J. M. SC. 156: 17, 1918. 6. Canfield: Heart 14: 102, 1927. 7. Wilson, Macleod, and Barker: J. Gen. Physiol. 16: 423, 1933.
156,
19%