Experimental comparison of four inverse electrocardiographic constructs in the isolated rabbit heart

J. ELECTROCARDIOLOGY 11 (1), 1978, 57-65

Experimental Comparison of Four Inverse Electrocardiographic Constructs in the Isolated Rabbit Heart BY DAVID M. M!RVIS, M.D., FRANCIS W. KELLER, B.S.E.E. AND JOHN W. Cox, B.S.M.E.

and the DPQP models provided as good a fit of recorded potential as did the CMS during m u c h of depolarization. The potential ability of the TMD and D P Q P constructs to localize as well as to characterize the cardiac sources suggests an important role for these models in inverse electrocardiography. T h e first equi val ent cardiac generator was the fixed location dipole proposed by Einthoven 1 in 1913. Over the ensuing h a l f century, efforts to test this simple model and to develop more complex, but hopefully more adequate, m a t h e m a t i c a l representations of the heart's el ect ri cal a c t i v i t y h a v e been described. 2~ More recently, computational techniques to locate as well as to q u a n t i t a t e the equivalent cardiac generat or have been devised, s-ll E x p e r i m e n t a l e v a l u a t i o n s of the equivalency of the electrical field generated by these models and by the h e a r t itself have likewise been reported. 12-17 P r i o r reports from this laboratory have documented t he inadequacy of a centric dipole construct and the relative superiority of a single moving dipole and a t h r e e e l e m e n t c e n t r i c m u l t i p o l e series as equi val ent generators. 15'17 Other, y e t more complex systems, such as the two-moving dipole and moving dipole-quadripole functions, have been proposed and tested using a simulated canine h e a r t model is and experimentally induced epicardial dipolar sources. ~~ In t h e studies to be described here, we have t e s t e d and c o m p a r e d t h e a b i l i t y of f o u r g e n e r a t o r models - - t he centric multipole series, the single moving dipole, the two moving dipole and t h e m o v i n g dipole-moving quadripole - - to reproduce the electrical field generated by an isolated m a m m a l i a n heart d u r i n g normal vent ri cul ar activation.

SUMMARY Complex models of the heart's electrical activity have been proposed as being superior to the fixed-location-dipole equivalent cardiac generator. To test and to compare the adequacy of four such proposals, i.e., a four element centric multipole series (CMS), a single moving dipole (SMD), two moving dipoles (TMD), and a moving dipole-quadripole pair (DPQP), the electrical fields generated by thirty isolated, perfused rabbit hearts placed in a spherical volume conductor were studied. Waveforms recorded from 32 surface electrodes were sampled 2500 times per second per channel, and generator parameters were c o m p u t e d u s i n g previously reported methods. A CMS accounted for 99.5 -- 0.21% (mean _+ S.E.M.) of sum-squared surface potential recorded during ventricular depolarization. The dipole, quadripole, octapole, and hexadecapole terms fit 3.3 to 98.2%, 7.2 to 70.8%, 0.2 to 29.9% and 0.02 to 12.7% of observed potential, respectively. A SMD fit 90.9 + 0.25% of surface activity, whereas the TMD and D P Q P constructs accounted for 98.4 _+ 0.21% and 99.2 _+ 0.21% of surface potential, respectively. The CMS accounted for significantly more (p <0.01) surface potential than did a centric dipole or a SMD throughout the QRS. In contrast, the TMD From the Section of Medical Physics, Department of Medicine, University of Tennessee Center for the Health Sciences, Memphis, Tennessee. This work was supported by grants HL-01362 and HL-09495 from the National Heart, Lung and Blood Institute. Dr. Mirvis was supported in part by National Research Service Award HL-05323 from th e N a t i o n a l H e a r t , L ung and Blood Institute. The costs of publication of this article were defrayed i n part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. w1734 solely to indicate this fact. Reprint requests to: David M. Mirvis, M.D., University of Tennessee Center for the Health Sciences, 951 Court Ave., Room 339M, Memphis, TN 38163.

MATERIALS AND METHODS Thirty New Zealand white rabbits weighing 2.2 to 4.3 kg were studied. After systemic heparinization, the animal was stunned by a heavy occipital blow. A left thoracotomy was performed, and the heart was rapidly excised and placed in warmed Krebs-Henseleit solution. The cut end of the aortic root was affixed to an electrically insulated support 57

58

MIRVIS ET AL

Fig. 1. Schematic representation of the experimental chamber and isolated heart perfusion apparatus. The heart is tied to the support cannula and is perfused through the aortic root with oxygenated, warmed electrolyte solution. Posit i o n of t h e h e a r t w i t h i n t h e chamber is controlled by the orientation of the perfusion cannula, as determined by the azimuth dial. Electrical potentials are recorded from the electrodes located on the inner surface of the sphere.

AS,

TO DATA ACQUISITION SYSTEM

~

': ~1~

},, CENTRIC SERIES

ELECTR'DA4 . -

CENTER FIT

I l-~"~ SINGLE I I MOVING _I D,POLE I - ~'L_ET__I

i ITERATION I ON

MOLT,POLE t'4

COEFFICIENTS/| "I

Fig. 2. Flow chart of the computational procedures described in the text. Dotted lines indicate methods used to initialize iterative routines for computing model parameters.

and perfusion cannula (Fig. 1), which passed t h r o u g h the upper hemisphere of a precisely machined spherical chamber 6.35 cm in diameter. TM P e r f u s i o n was i m m e d i a t e l y i n s t i t u t e d w i t h warmed (37~ oxygenated electrolyte solution. The lower portion of the test chamber was bolted into place, enclosing the heart within an accur a t e l y defined volume c o n d u c t o r filled with perfusate. Electrocardiographic signals were recorded from each of 32 silver-silver chloride electrodes distributed on the inner surface of the test tank, and amplified by a bank of custom designed, differential amplifiers. Electrodes were paired to form 32 bipolar leads forming a closed Kirchoffs loop. The calibration, gain and offset of each amplifier were individually determined under computer control so that the output signal filled the input range of the analog-to-digital convertor. Analog-to-digital conversion was performed at a sampling rate of 2500

TWO

MOVING

t

DIPOLE I

~'FL___E/___I

ICONSTANTS~--I MOVING I ~

I

DIPOLE I ~IQUADRIPOLE ~"-I FIT

samples per channel per second. Digital data were passed directly to magnetic disc and later transferred to tape for offline processing. Eighteen seconds of data were acquired for each preparation. A series of beats, typically 16 in number, was selected as being morphologically similar by an automated autocorrelation routine 15 and averaged. The averaged bipolar waveforms were then reduced to unipolar form by referencing each bipolar complex to the mean potential recorded from 20 surface electrodes. All model fitting was performed on these unipolar, averaged waveforms. The computational schemes used to determine generator fit are depicted in Fig. 2. All models were fit to each data point during the QRS complex, i.e., at 400 t~sec intervals from the onset of QRS complex to its termination as manually determined. F o u r e q u i v a l e n t g e n e r a t o r c o n s t r u c t s were examined: 1. Centric Multipole Series. The parameters of a

J. ELECTROCARDIOLOGY, VOL. 11, NO. 1, 1978

ELECTROCARDIOGRAPHIC

four element centric multipole series 5'~ were computed by solution of 32 equations of the form: 1

Ve = ~

4 n~l

r-

2n+1

nRn+l

/

(cos 0) +

anoPn

L m=~l (anmCOSm~'+ bnmsin m~ Pnm(cos 0) J where

V = unipolar potential at electrode site e_on the chamber surface with_e= 1, 2, 3 ... 32, o = specific conductivity of the perfusate, R = inner radius of test chamber, O, ~= spherical coordinates of electrode with the origin of the reference system located at the tank's center, b = coefficients of the equivalent generator comanm, nm ponents, and p m = associated Legendre polynomial of nth degree n and ruth order.

The 24 a~m and bnm terms thus computed included the three dipolar, the five quadripolar, the s e v e n o c t a p o l a r and the nine h e x a d e c a p o l a r parameters. 2. Single Moving Dipole. The three location and the three moment parameters defining the single dipole best accounting for the observed surface were constructed of the form:

MODEL COMPARISON

59

fit or when a maximum of 40 iterations had been performed. 3. Two Moving Dipoles. The twelve independent parameters of the two independently locatable dipole model, i.e., three location and three moment terms for each dipole, were computed by solution of 32 equations describing the potential at a given point generated by two independent dipoles. Each equation is a superposition of potential functions of the form of Eq. (2). A nonlinear minimization technique was used as above. The routine was initialized with the 12 location and m o m e n t p a r a m e t e r s computed by ~iteration on tbe multipole terms" determined previously. 6'7 Accordingly, 24 equations were constructed relating each multipole coefficient to the 12 model parameters, and solved using an iterative least squares method. Initialization of the Marquardt algorithm with a computed initial guess led to more rapid convergence of the iteration on potential algorithm than when a randomly selected constant was used. 4. Moving Dipole-Moving Quadripole. The 14 parameters defining this model, i.e., the three dipole moment terms, the five quadripole moment terms, and the three location terms for each component, were likewise computed from solution of 32 simultaneous nonlinear equations. 7 Each equation was formed from the superposition of Eq. (2) and Eq. (3), giving the potential at a point on the sphere due to a contained eccentric quadripole:

V = (4Vxx +2Vzz) a22 + Vzza20 + 4Vxyb22 + 2Vyzb21 + 2Vxza21

Xe-X 2(Xe-X) + - - - r ~ + r3

where

Xe -R-

R r+R 2_(Xe X+Yeu

l+

z)J

Similar term in Y / + J

MzI Similar term in Z I

I

where unipolar potential from electrode_e, r =

distance from dipole to electrode,

R= chamber radius, O=

specific conductivity of medium,

Xe, Ye, Ze = coordinates of electrode e

Ve = unipolar potential recorded from electrode_e, a20, a21, a22, b21, b22 = quadripolar moment terms; and V./s q = functions relating quadripole and electrode locations.

The nonlinear minimization routine was initialized by an arbitrarily selected constant. All generator parameters were normalized to reflect the summed square (SSQ) potential projected to the surface of the sphere by a given component. Generator fits were expressed as the fraction of total recorded SSQ potential attributable to a given generator model or component. As such, the arithmetic sum of the fraction of total potential accounted for and that not accounted for must equal unity.

X , Y , Z = coordinates of the dipole, and Mx, My & Mz = X, Y and Z moment components of the dipole.

Solution of these equations relied upon an iteratire, nonlinear minimization routine described by Marquardt. 19 The technique was initialized with the location coordinates computed by the quadripole shift equation or %lectrical center" method of Geselowitz. 2~ The iterative routine was halted when successive iterations failed to yield a better

J. ELECTROCARDIOLOGY, VOL. 11, NO. 1, 1978

RESULTS All 30 a n i m a l s w e r e s t u d i e d d u r i n g n o r m a l sinus r h y t h m . QRS d u r a t i o n w a s 34.9 -- 8.6 m s e c ( m e a n _+ s t a n d a r d deviation). Recorded ST segments were isoelectric without evidence of h e a r t i n j u r y d u r i n g p r e p a r a t o r y phases. Centric Multipole Series. A centric m u l t i p o l e s e r i e s t h r o u g h t h e h e x a d e c a p o l e t e r m accounted for 99.5 -+ 0.21% ( m e a n _+ I S.E.M.) of

60

MIRVIS ET AL

DIPOLE

B

QUADRIPOLE

C

OCTAPOLE

D

HEXADECAPOLE

IOO 8O o E

40

20

20

I0

~_~o B ~ 2o

I0

0

0

I

Fig. 3. Relative strengths of each of the four elements of the centric multipole equivalent cardiac generator. The percent of the summed-square chamber surface potential that can be accounted for by a centric dipole (A), quadripole (B), octapole (C), or hexadecapole (D) is plotted vertically. Normalized time durations of QRS are plotted horizontally. Plots from each of the 30 preparations are superposed.

surface unipolar potentials recorded throughout the QRS complex. The m a x i m u m percentage not attributable to this series, i.e., the residual potential, in any animal was 5.2%, while the m i n i m u m percentage was 0.001%. Strengths of the individual terms of the series are depicted in Fig. 3 and 4. QRS complexes of all 30 preparations were normalized to a common time interval and plots of the percentage of total surface SSQ unipolar potential attributable to a given series element throughout the QRS were superposed (Fig. 3). Mean behavior of the group, with regard to each series element, and the plus-minus 35% range are plotted in Fig. 4. Because negative values of SSQ potential would be physically untenable, logarithmic transformation of SSQ values was performed prior to calculation of means and standard deviations. 1~ Apparent from Fig. 3 is the wide range of percentages of potential attributable to each element of the series. A centric dipole accounted for 3.3% to 98.2% of observed poten-

A.

DIPOLE

B.

tial (A); a centric quadripole accounted for 7.2% to 70.8% (B), the centric octapole for 0.2% to 29.9% and the hexadecapole for 0.02% to 12.7% of observed potential. Temporal clumping of peaks and troughs in accountability is also noted. Dipolarity peaked in individual plots (Fig. 3A) and in group mean data (Fig. 4A) early and, particularly, late during the QRS complex with an interposed nadir. Terminal portions of depolarization were also characterized by a fall in dipolar activity. Similarly, higher order terms assume greater importance (Fig. 3B-D, 4B-D) d u r i n g the nondipolar period. Mean residual potential remained under 1% of total SSQ potential through the QRS complex, but rose during the m i d d l e a n d t e r m i n a l s e g m e n t s (Fig. 5A and 6A). Single Moving Dipole. A single moving dipole accounted for 90.9 -+ 0.25% of SSQ surface potential observed at all points during depolarization in all 30 animals. The m a x i m u m percentage not attributable to this model was

OUADRIPOLE

C.

OC~POLE

D.

HEXADECAPOLE

100 50

25 I

8O

4O

2O

~" 60

50

15

I0

5

0

0

40 2O

o,o

Fig. 4. Means and plus-minus 35% ranges of the strengths of the centric multipole series model. The confidence levels were determined by logarithmic conversion of individual sum-squared values, calculation of standard deviations of these transformed values, and antilogarithmic reconversion. Value for the dipole (A), quadripole (B), octapole (C) and hexadecapole (D) terms are presented. Vertical and horizontal axes are as in Fig. 3. J. ELECTROCARDIOLOGY, VOL. 11, NO. 1, 1978

ELECTROCARDIOGRAPHIC MODEL COMPARISON A, CENTRIC MULTIPOLE SERIES

C.

SINGLE MOVING DIPOLE

61

D

TWO MOVING DIPOLE

DIPOLE-QUADRIPOLE

25'

50

50t

25

"6 2 0

40

40

20

~-isi

30

30

15

20

->O

10

5

Fig. 5. Superposed plots for each of the 30 preparations of the percentage of surface summed-square potential not attributable to a given equivalent cardiac generator (vertical axis) throughout the time-normalized QRS duration (horizontal axis). Models tested are the centric multipole series (A), a single moving dipole (B), two moving dipoles (C) and a moving dipole-quadripole pair (D).

61% while the m i n i m u m was 0.8%. Timedependent plots of percent residual of individual preparations are superposed in Fig. 5B and group mean and plus-minus 35% ranges are presented in Fig. 6B. Values in Fig. 6 were computed after logarithmic transformation, as in Fig. 4. The fraction of potential not attributable to a single moving dipole peaked again during the middle of the QRS, with lowest levels computed early and late during ventricular depolarization. Of 2623 QRS data points evaluated, the iterative solution located a ~r fit" within the allotted number of iterations in all but 1.9%. Two Moving Dipole Model. A two independently locatable dipole model fit 98.4 _+ 0.21% of SSQ surface potentials during the QRS complex. M a x i m u m and m i n i m u m percentages not a t t r i b u t a b l e to this model were 41.8% and 0.09% respectively. Superposed plots of residual potentials for the 30 preparations and group mean and plus-minus 35% ranges are presented in Fig. 5C and 6C. In A.

D4

Moving Dipole-Moving Quadripole Model. The fitting of observed potentials with moving, independently locatable dipole and quadripole pair accounted for 99.2 _+ 0.21% of SSQ surface activity. Maximum and minimum residuals encountered were 15.8% and 0.04%, respectively. Superposed plots of residual perc e n t a g e s (Fig. 5D) and group m e a n d a t a (Fig. 6D) demonstrate lowest residuals early and late in the QRS. Only occasional percentages of nonfitted potential exceeded 5% with this model. In only 4.3% of 2,623 data points did the iterative techniqne not successfully converge within 40 iterations. Intermodel Comparisons. To compare the

8

CENTRICMULTJPOLE SERIES

~8

only occasional instances was the residual greater t h a n 10% of SSQ surface potential. Once again, poorest fit was observed during middle p o r t i o n s of the d e p o l a r i z a t i o n sequence. The iterative procedure performed less well for the two dipole t h a n for the one dipole model, with 34.5% of points not converging upon a '~best fit" within 40 iterations.

C. SINGLE MOVING DIPOLE

D. TWO MOVrNG DIPOLE

50

25

40

20

30

15

20

DIPOLE- QUADRIPOLE

6

4

5

Fig. 6. Means and plus-minus 35% confidence levels of the fractions of the summed-square potential not fit by the models under evaluation. Ranges were computed after logarithmic conversion as in Fig. 4. Percentages of potential fit are plotted vertically and times during the QRS are plotted horizontally. Constructs tested are the centric multipole series (A), single moving dipole model (B), two moving dipole model (C) and the moving dipole-quadripole pair (D). J. ELECTROCARDIOLOGY, VOL. 11, NO. 1, 1978

62

MIRVIS ET AL

A

B CENTRIC MULTIPOLEvs SINGLE MOVING DIPOLE

ii~I

C CENTRIC MULTIPOLEvs, TWO MOVING DIPOLE

.o

60

E

D CENTRIC MULTIPOLEvs DIPOLE- QUADRIPOLE

TWO MOVING DIPOLEvs. SINGLE MOVINGDIPOLE

DIPOLE- GUADRIPOLEv,~ TWO MOVING DIPOLE

6O

60

6C

60

o40

40

40

40

4O

~20

20

20

2O

~2

~

-IO 1

- - J ~ "

~

D

-I0

o

~10

-io -10

Fig. 7. Comparisons of the adequacy of the fit of surface potentials by each of two equivalent generator models. Plotted are the means and - 1 standard deviation (vertical axes) of the differences in percentages of surface potential fit by each of two models across the time normalized QRS period (horizontal axis). Segments of the QRS during which these differences are statistically significant (p < 0.01) are underscored (arrow, A-E). A: Percentage of potential fit by centric multipole series minus that fit by single moving dipole. B: Centric multipole series minus two moving dipoles. C: Centric multipole series minus moving dipole-quadripole pair. D: Two moving dipoles minus single moving dipole. E: Dipole-quadripole pair minus two moving dipoles.

adequacy of the fit obtained with one model to t h a t computed with a second, differences in p e r c e n t a g e s of SSQ surface p o t e n t i a l attributable to each of the two models were computed for all data points during the QRS complex. Means, standard deviations and the statistical significance (paired t-test, p < 0.01) of these differences are plotted in Fig. 7 and 8. A four term centric multipole series provided a better fit of observed data t h a n did a single moving dipole at all points during the QRS (Fig. 7A) with a peak difference in potential fit of 38%. Differences in percentages of potential fit by a centric multipole series and by a two-moving dipole (Fig. 7B) or by a moving dipole-quadripole pair (Fig. 7C) were smaller. Maximum difference in fit was 13% and 3% for these two comparisons, respec-

A, CENTRIC MULTIPOLE SERIESvs, CENTRIC DIPOLE

B CENTRID MULTIPOLE SERIESvs, CENTRID DIPOLE + QUADRIPOLE

tively; in large segments of the QRS complex, the differences were not s t a t i s t i c a l l y significant. The two-moving dipole model provided a better fit t h a n did a single moving dipole at all points d u r i n g t h e QRS (Fig. 7D); the m a x i m u m difference in percentage of SSQ potential fit with the two models was 11%. A moving dipole-quadripole pair, however, accounted for a significantly greater fraction of observed surface potential t h a n did a two dipole model for most of the QRS complex (Fig. 7E), although the maximal difference in potential fit was but 2%. Similar comparisons were made between a four element multipole series and a one and a two e l e m e n t series. The longer series accounted for greater percentages of potential t h a n did either a centric dipole (Fig. 8A) or a

C

D. SINGLE MOVING DIPOLE vs, CENTRIC DIPOLE

MOVING DIPOLE QUADRIPOLE vs. CENTRIC DIPOLE+ QUADRIPOLE

80

=I EO

-~ 4D g g_ ~

20

~

0

Fig. 8. Comparisons between two electrocardiographic constructs computed and displayed as in Fig. 7. A: Centric multipole series minus centric dipole. B: Centric multipole series minus centric dipole plus centric quadripole. C: Single moving dipole minus centric dipole. D: Moving dipole-quadripole pair minus centric dipole plus centric quadripole. J. ELECTROCARDIOLOGY, VOL. 11, NO. 1, 1978

ELECTROCARDIOGRAPHIC MODEL COMPARISON

eentric dipole-quadripole pair (Fig. 8B). Peak differences in potential fits were 38% and 13% for these two comparisons. Finally, a single moving dipole and a moving dipole-quadripole pair were compared with their centric counterparts. A single moving dipole fit up to 29% more of the surface potential than did a centric dipole (Fig. 8C), while a moving dipole-quadripole pair fit up to 14% more potential than did a centric dipole and quadripole (Fig. 8D).

DISCUSSION The current study expands prior efforts of this laboratory to reduce the electrical field generated by the heart to a mathematically concise, although perhaps physically fictitious form. These studies have utilized an experimental preparation consisting of an isolated heart suspended in a volume conductor of known geometry filled with an electrolyte solution. The relatively small chamber size permitted quantitation of multipolar terms which are rapidly dissipated with distance, while the elimination of bodily tissue between the heart and the recording surface minimized the complex effects of electrical inhomogeneities. Thus, the sensed electrical field is perturbed by fewer noncardiac variables than in intact animal studies and may therefore more clearly represent the intrinsic properties of the cardiac electrical generator. Superposition of other factors, e.g., tissue inhomogeneity and irregular surface geometry, may be expected to increase the complexity of the surface pattern beyond that induced by the heart itself. Two specific methodologic differences between this and prior studies are significant. First, a m a m m a l i a n rather than reptilian heart modeP 5 has been employed. Results reported using an isolated turtle h e a r t are, however, similar to these data with regard to a centric multipole and single moving dipole models. In each, highly nondipolar zones of depolarization were identified; a centric multipole or a single moving dipole served as a more adequate equivalent cardiac generator. The evolutionary import of these findings remains speculative, although surface mapping techniques in dog 2~ and h u m a n ~6'22 studies have strongly suggested nondipolar activity. Additionally, expansion of the electrode system for 20 to 32 elements has permitted computation of hexadecapole coefficients of the multipole series and the parameters of the t w o d i p o l e a n d of t h e m o v i n g d i p o l e quadripole models. It thus became feasible to characterize further the previously reported nondipolar activity of the rabbit heart 17 (Fig. 3 and 4), as well as to test experimenJ. ELECTROCARDIOLOGY, VOL. 11, NO. 1, 1978

63

tally two complex models requiring 32 sampling sites for accurate definition. TM It is not surprising that a single dipole, either centric or mobile, cannot generate an electrical field equivalent to that projected by t h e h e a r t . S t u d i e s of e p i c a r d i a l and i n t r a m u r a l e x c i t a t i o n p a t t e r n s 23-2~ have repeatedly documented multiple, simultaneously active wavefronts during much of ventricular depolarization, patterns not inversely reproducible by a single dipole. Indeed, even if a single front were detected, the eccentricity and the probable nonplanarity of its rim and the physical area which it encompassed would mandate the presence of nondipolar forces. 26 The greater dipolarity early and late during the QRS complex than during its midportion (Fig. 3 and 4) may find explanation in the e p i c a r d i a l and i n t r a m u r a l e x c i t a t i o n sequences reported by Spach and Barr. 25 The initial portions of depolarization are characterized by a single epicardial maximum over the right ventricle, which may be considered as a single electromotive surface with predominantly dipolar properties. 26 Introduction of multiple maxima later, however, correlates theoretically and temporally with the marked decrease in quantitated dipolarity. Late in excitation, much of the heart became enveloped by negative potentials with only small zones of positive, excitation potential persisting. Thus the heart could be reasonably modeled as a single electromotive shell with a theoretically expected and experimentally demonstrated highly dipolar behavior. 17,26 Terminal superposition of depolarization and repolarization effects would lead to increased terminal QRS nondipolarity. Although determined in a canine model, these sequences may be expected to be similar to those in other mammalian species. Three alternatives to a single dipole are described here. First, a four element centric multipole series performed significantly better as an equivalent cardiac generator than did either a single centric or moving dipole. This is to be expected again on theoretical grounds. It may be shown that the electrical behavior of any number of current dipoles in a linear, homogeneous and isotropic medium m a y be characterized by an infinite multipole series. 6 These dipoles m a y represent individual simple wavefronts or the unit dipoles of a complex electromotive surface. Addition of successive terms to the first, i.e., the centric dipole, would be anticipated to enhance the adequacy of the fit. Significant quadripole and octapolar content has been described for turtle and h u m a n models. 11-~5'27'2s The addition of a hexadecapolar term in this study resulted in the fitting of up to an additional 12.7% of surface effects. That the residual po-

64

MIRVIS ET AL

tentials not attributable to this four element series are small, i.e., less t h a n 6%of SSQ potentials in any animal, suggests t h a t expansion of the series to five or more terms would add little information. The addition of a second moving dipole or a moving quadripole to the single moving dipole model resulted in a markedly improved generator model (Fig. 5-7). Each element of these two component models m a y be interpreted as representing a separate wavefront or depolarization, e x t e n d i n g the i n t u i t i v e appeal and the physiologic relevance of the constructs. Additionally, the moving dipolequadripole form p e r m i t s conceptual compartmentalization of dipolar and nondipolar activity. Both have been tested on simulated but physiologically realistic data with admirable success; over 90% of SSQ potential generated by as many as 68 active dipoles was fit by a dipole-quadripole solution. Indeed, both models, but the dipole-quadripole pair in particular, performed as adequately as d i d the centric multipole series during much of depolarization in the isolated heart model. Computational difficulties, however, may limit the applicability of these models. Nonlinear components of the potential functions n e c e s s i t a t e t h e i n t r o d u c t i o n of i t e r a t i v e minimization routines. One difficulty is t h a t these procedures may fail to converge upon a global, optimal solution w i t h i n a practical number of iterations.7'ls This was particularly problematic with the two moving dipole solution; in over one-third of d a t a points, the "best" possible fit of data was not computed. Thus, a better accounting of observed potentials might be expected if m a n y more iterations were permitted. In the case of a single moving dipole, the inclusion of the results of another dipole ranging technique 2~ as the initial guess for the iterative solution obviated this difficulty. Application of other minimization routines may, however, improve the two moving dipole results. Motivation for overcoming these obstacles was derived from the aforementioned physiologic relevancies of these models. A centric multipole series, performing at least as well as an equivalent generator (Fig. 7), while being considerably easier to compute, cannot localize the active myocardial sites as can the models with one or more moving elements. For example, single and two moving dipole s o l u t i o n s can localize one or two epicardial burns to within 0.3 cm of the centroid of the lesion. 9''~ Additionally, the location of a single moving dipole throughout the QRS has been shown to relate to the epicardial excitation pattern. '~ Translocation of the multipole series to the electrical center of a uniform electromotive surface followed by appropriate generator rotation may, however,

provide for q u a n t i t a t i o n of the geometric parameters of its rim. G One implication of these data to clinical electrocardiography is t h a t the electrical field generated by the heart is more complex t h a n can be sensed by methods such as the vectorcardiogram, being based upon a single dipole heart model. As noted by Taccardi, ~ I f . . . the h y p o t h e s i s of t h e m u l t i p o l a r e q u i v a l e n t generator is valid, complete exploration of the body surface is necessary to get all the information about the electrical activity of the heart...,,21 Hence, the value of body surface isopotential mapping emerges. 21'22 W h e t h e r application of the q u a n t i t a t i v e methods tested in these experiments will be applicable to intact animal or h u m a n studies remains unclear. Effects of irregular surface boundaries and tissue inhomogeneities remain complex. However, the Gabor-Nelson equations 4 suggest t h a t single and two moving dipole solutions may be feasible from irr e g u l a r l y shaped surfaces. Indeed, several groups h a v e now described single dipole localization in man. 16'29 Most recently, Horan et a127 and Trost et al 2s have reported development of clinically applicable lead systems sensitive to m u l t i p o l a r information. These would not only permit a more concise, quantitative expression of the heart's electrical f i e l d t h a n do i s o p o t e n t i a l m a p p i n g techniques but may also allow computation of parameters of moving element models2 Thus, generators could be localized as well as quantitatively characterized.

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REFERENCES EINTHOVEN, W, FAHR, G AND DEWAART, A: Uber die Richtung und die manifest Grosse der Potentialschwankungen im menschlichen Herzen and fiber den Einfluss der Herzlage auf die form des Electrokardiogram. Pfluger Arch Ges Physiol 150:275, 1913 GESELOWITZ,D B: The concept of an equivalent cardiac generator. In Biomedical Sciences Instrumentation. New York. Plenum 1:325-330, 1963 BRODY, D A AND SATO, T: Volume conductors and the electrocardiographic generator. In Proceedings XIth International Vectorcardiography Symposium, I. Hoffman, ed. North Holland Publ Co, Amsterdam, 1971, pp3-17 GABOR, C AND NELSON, C V: Determination of the resultant dipole of the heart from measurements on the body surface. J Appl Phys 25:413, 1954 GESELOWITZ,D B: Multipole representation for an equivalent cardiac generator. Proc IRE 48:75, 1960 BRODY, D A: The inverse determination of simple generator configurations from equivalent dipole and multipole information. IEEE Trans Biomed Eng 15:106, 1968 MARTIN,R O, COX,J W, KELLER,F W, TERRY,

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F H AND BRODY, D A: E q u i v a l e n t cardiac generators: Two moving dipoles and moving dipole and quadripole. Ann Biomed Eng 2:164, 1974 TERRY, F H, BRODY, D A, EDDLEMON, C O, COX, J W, KELLER, F W AND PHILLIPS, H A: Dipole, quadripole and octapole measurements in isolated beating heart preparations. IEEE Trans Biomed Eng 18:139, 1971 IDEKER,R E, BANDURA,J P, LARSEN,R A, Cox, J W, KELLER, F W ANDBRODY,D A: Localization of heart vector produced by epicardial burns and ectopic stimuli. Circ Res 36:105, 1975 MIRVIS, D M, KELLER,F W, IDEKER, R E, Cox, J W, DOWDIE, R F AND ZETTERGREN, D G: D e t e c t i o n and l o c a l i z a t i o n of a m u l t i p l e epicardial electrical generator by a two dipole ranging technique. Circ Res 41:551, 1977 IDEKER,R E, BANDURA,J P, Cox, J W, KELLER, F W, MIRV1S,D M ANDBRODY,D A: Path and significance of heart vector migration during QRS and ST-T complexes of ectopic beats in isolated perfused r a b b i t hearts. Circ Res 41:558, 1977 HLAVIN,J M AND PLONSEY,R: An experimental determination of a multipole representation of a turtle heart. IEEE Trans Biomed Eng 10:98, 1963 SCHUBERT,R W: An experimental study of the multipole series that represents the human electrocardiogram. IEEE Trans Biomed Eng 15:303, 1968 HEPPNER, D B: Dipole and quadripole measurements of an isolated turtle heart. IEEE Trans Biomed Eng 15:298, 1968 BRODY, D A, WARR, O S, WENNEMARK, J R, Cox, J W, KELLER, F W AND TERRY, F H: Studies of the equivalent cardiac generator behavior of isolated turtle hearts. Circ Res 29:512, 1971 HORAN, L G, FLOWERS, N C AND MILLER, C B: A rapid assay of dipolar and extradipolar content in the h u m a n electrocardiogram. J Electrocardiol 5:211, 1972 BRODY,D A, MIRVIS,D M, IDEKER,R E, Cox, J W, KELLER,F W, LARSEN,R A ANDBANDURA,J

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