IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 1, JANUARY 1979
21
In conclusion, it should be pointed out that this method, tracer methods." M. Sc. Thesis, Technion-Israel Institute of Technology, Haifa, Israel. as well as the one presented by Oleksy et al.4 avoids a numerKarlsson, H., G. J. Rossenhamer, and 0. Wigertz, (1971). "Oneical deconvolution.7 However, the "second" correction pre- 7. stage digital correction of distorted dye-dilution curves," Scand. J. sented here provides a means to bring the derived curve into Clin. Lab. Invest., 27: 287-291. much closer agreement with the measured curve than is possible with the method of Oleksy, et al.
REFERENCES 1. Bloomfield, D. A. (Ed.), (1974). Dye Curves: Theory and Practice, University Park Press, Baltimore. 2. Weinstein, H., and M. P. Dudukovic, (1975). "Tracer Methods in the Circulation," in Topics in Transport Phenomena, C. Gutfinger, Ed., Hemisphere Publishing Corp., Washington, D.C. 3. Schlossmacher, E. J., H. Weinstein, S. Lochaya, and A. Shaffer, (1967). "Perfect mixers in series model for fitting venoarterial indicator-dilute curves," J. Appl. Physiol., 22: 327-332. 4. Oleksy, S. J., H. Weinstein, and A. B. Shaffer, (1969). "Correction of dye-curve distortion with the use of perfect mixers in series model." J. Appl. Physiol., 26: 227-232. 5. Fu, B., (1970). "Tracer analysis of recirculating systems." Ph.D. Thesis, Illinois Institute of Technology, Chicago, Illinois. 6. Nassi, M., (1975). "Evaluation of congenital heart defects by
M. Nassi, cation.
photograph and biography not available at the time of publi-
J. Dayan, cation.
photograph and biography not available at the time of publi-
S. Braun (M'74), photograph and biography not available at the time of publication.
H. Weinstein, photograph and biography publication.
not available at the time of
Integral Characteristics of the Human Cardiac Electrical Generator from Electric Field Measurements by Means of an Automatic Cylindrical Coordinator P. KNEPPO AND L. I. TITOMIR Abstract-An automated electronic system based upon a cylindrical coordinator was constructed for measurement and preliminary computational processing of the heart electrical potentials on the surface of a human torso and of the coordinates of this surface. The potential distribution on the body surface at consecutive instants of time and the geometrical parameters of the body received as the output of the measuring system can be used for investigation of various types of mathematical descriptions, or models of the cardiac electrical generator. One such mathematical description, a set of integral characteristics of the cardiac electrical generator, is studied in this work. These characteristics are: three components of the heart dipole moment, three coordinates of the moving cardiac electrical center and the com-
Manuscript received June 27, 1977; revised May 4, 1978. P. Kneppo is with the Department of Bioelectrical Measurement, Institute of Measurement and Measuring Technique, Slovak Academy of Sciences, Bratislava, Czechoslovakia. L. I. Titomir is with the Computational Laboratory, Institute of Problems of Information Transmission, Academy of Sciences of U.S.S.R.,
Moscow, U.S.S.R.
plexity parameter of the cardiac generator. The results of experimental measurement of the cardiac electrical field and calculation of the inte-
gral characteristics of the cardiac generator are presented for a group of healthy
men.
Physical and electrophysiological significance of the
results is briefly discussed.
MsETHODS of quantitative investigation of cardiac electrical generators using computational equipment play an increasingly important role in modem electrocardiology [1]. These methods require formulation of a set of quantitative characteristics that accurately describe properties of the heart as an electrical generator, and should not depend on extracardiac factors such as anatomical configuration of the body, structure of the lead system and so on. If an idealized electrical generator with a known structure is ascribed to such a set of characteristics then it is called "equivalent electrical generator of the heart." The parameters of the mathematical
0018-9294/79/0100-0021 $00.75 © 1979 IEEE
22
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 1, JANUARY 1979
tween electrodes and the skin; measurement of coordinates of each lead point while providing stability of the coordinates during the measuring procedure; synchronous measurements of the potentials or synchronization of the signals using a special reference lead; preliminary processing of the lead signals, in particular amplification, special filtration, analog-to-digital conversion and insertion into the digital computer memory. All these operations were provided for by the automated measuring system described below. The main unit of the system is the cylindrical coordinator CK-2 (Fig. 1) constructed in the Institute of Measurement and Measuring Technique of the Slovak Academy of Sciences [14]. This device provides for determination of the coordinates of the chest surface points where the cardiac electrical field potentials, i.e., electrocardiograms are measured. The design principle of the coordinator is based on the fact that the shape of the human chest resembles a cylinder whose axis coincides with the vertical axis of the human body. Thus for the design of the coordinator a cylindrical coordinate system was chosen with the Y axis oriented vertically and passing through the middle point of the torso transverse section. It has the same direction as the Y axis of the standard vectorcardiographic 1. MEASURING SYSTEM coordinate system (Fig. 2). The patient to be measured is To determine the surface distribution of cardiac potentials placed in the coordinator in a sitting position (Fig. 3). The many authors [2-9] designed automatic methods of measure- sensing electrodes are fixed on an elliptical frame that surment with utilization of computers. Several works including rounds the chest of the subject and can be displaced along the sets of maps obtained by an automatic sequential record of vertical axis. In the horizontal plane the electrodes are situgroups of 5 to 15 electrocardiograms together with a time ated with an angular interval of 150 on the front and the left reference lead on a multichannel analog tape recorder, have sides of the chest, the regions that are the closest to the heart, been published since 1963. After digital conversion the data and with an angular interval of 300 on the back and the right are adapted by the computer and either printed by a printer sides; the full number of electrodes on the frame is 18. The terminal, or recorded by a plotter in the form of equipoten- distribution of the electrodes in space is shown in Fig. 4. The tial lines in the plane of developed chest surface for chosen electrodes are placed on the body surface automatically by time instants. The maps constructed by such methods con- extending them in a radial direction up to the required length sist of data recorded during different heart beats. It is known at the given instants of the measuring process. The displacethat the subsequent beats are in general not identical because of ment of the electrodes is provided by a pneumatic system the influence of breathing, the heart rhythm, and other phenom- which simultaneously ensures uniformly pressing the elecena influencing the electric field. For solution of the inverse trodes against the body surface. Special devices attached to problem it is necessary to know, in addition to the surface each electrode provide measurement of the radial coordinates potentials, the shape of the chest. Some authors [10-13] have of the lead point. The contact surface of the electrode is a constructed a special device, a coordinator, for this purpose. disk with a diameter of 18 mm. During the measurement The measurement of both the cardiac potential and the coordi- process the frame with the electrodes is automatically shifted nates of the chest surface is performed gradually and it takes a along the vertical axis at required instants. It is possible to rather long time. A special measuring method together with choose space intervals equal to 1, 2, or 3 cm between the horian automatic measuring system were designed to reduce the zontal planes in which the system of electrodes is fixed. Durinfluence of most of the mentioned imperfections. The auto- ing the measuring process this interval is set automatically by matic measuring system allows simultaneous measurements of special devices of the coordinator. For example, if a 2 cm discardiac potentials as well as geometric measurements of the tance between the horizontal planes is chosen then it is usually chest at chosen points. The system simplifies and automates possible to carry out measurements in 14 planes for a man the procedure of fixation of electrodes over the body surface with medium height, or at 252 points. The automatic function of the whole measuring system is and it also allows measurement, at the determined respiratory phase positions of the chest. The second standard lead is re- secured by the corresponding electronic devices [15]. The corded in order to check eventual gross changes of the cardiac scheme of the measuring system is shown in Fig. 5. The measured data, potentials El to E18 and radial coordinates RIB, electric field. The procedure of cardiac electrical field measurement raises are fed to the multiplexer of the analog-to-digital converter the following main problems: choice of the number and loca- of the computing system DEClab 11/10 E. The ECG signals, tion of sites for leads that provide the required accuracy of the with the potential of Wilson's terminal used as a reference, are electrical field characteristics investigated; fixation of the lead first amplified in a special 20-channel amplifying unit AU electrodes over the body surface with reliable contacts be- made by the firm CHIRANA. The amplified signals El to
description of the cardiac generator are found from measured potentials on the body surface and the geometrical characteristics of the body by solving an "inverse problem." For its solution additional a priori information about the cardiac generator is sometimes necessary. A diagnostic conclusion is drawn on the basis of anatomic and physiological interpretation of values of the parameters determined for the examined patient. Such a determination of the values of a mathematical description of the cardiac electrical generator parameters requires the measurement of electric potentials on the chest surface and identification of the chest characteristic, the first approximation being represented by the geometry of the chest. The aim of this article is, first of all, to describe a new automated measuring system for detailed measurements of electric potentials on the human chest surface and its geometrical characteristics, as well as preliminary processing of the received signals before main processing by a multipurpose computer, and secondly, to present an effective mathematical description of the cardiac electrical generator together with the results of determination of its parameters from experimental measurements on a group of healthy men.
23
KNEPPO AND TITOMIR: HUMAN CARDIAC ELECTRICAL GENERATOR
Fig. 3. Subject with applied electrodes in the cylindrical coordinator.
/_300
12
13
9 \-8
14
x
I
i5
16
Fig. 1. Cylindrical coordinator CK-2.
wI
23
4
5
i 5;
z
Fig. 4. Distribution of lead electrodes.
Fig. 2. Choice of rectangular
together
E18
rectly
and
cylindrical coordinate systems.
with the second standard lead
to the DEClab
RIB signals corresponding
The
the measurement tentiometer
points
equalization
are
to the radial coordinates of
led to the
signal filtering and
unit FPEU where the
RI 8, corresponding to radial to B1 8 corresponding to the
signals
time-variation are
of the radial
separated.
of the measured person and the
A/D
at the selected time-instants is
to the chest
conversion of the ECG
provided by
the
timing
unit TU. The second standard ECG lead and the START
the computer, which is used to start the
according the
to the
timing
sequences
unit.
co-
For the
signal of the second stantiming of the measuring system,
The
i.e., the sequential application of the electrodes
f'rom
to
of the system the
dard ECG lead is used.
signals
po-
RI1
coordinates, and the signals Bl
ordinates due to respiratory motions,
synchronization
conveyed di-
are
analog input.
signal The
from the
timning
calibrating pulses
referred to the AU
terminal,
are
unit generates in
CP
M
led
as
inputs
to
predetermined
amplitude
of I mV
determining
the time
with the
input, the signal
pulse
measuring cycle
of measurement, the A/D conversion start pulse, the sampling pulses SP, the signal P determining the interval between successive measurements, and the FP pulse for the frame position control. After the measurement and storage of all the signals in one horizontal plane, the FP pulse activates the frame position controller FPC. This controller initiates the withdrawal of electrodes from the body surface, moving the frame down by a given distance and the next application of the electrodes. The pneumatic system effecting the movement of the electrodes consists of the electric exhauster EE and electromagnetic valve EV switching over to pressure and underpressure positions. The check of the constancy of the position of the measured body is secured by position sensors mounted on the frame. The sensors' output signals SI and S2 serve, after processing in a patient position controller PPC, for activating the display D, which indicates the correct position, and determining the direction of the eventual corrections. The display indicates simultaneously the time of the measurement (signal M) and the interval between measurements (signal P). The described arrangement of the automatic system is determined by the use of units designed originally for the first modification of the system working in the off-line mode and providing recording on a tape recorder. Using this automated measuring system it is possible within 10 to 15 min to acquire all the necessary information about the patient's torso. After analog-to-digital conversion and supplying the data to a computer the preliminary processing of
24
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 1, JANUARY 1979
CK- 2
CRT'
DECLAB 11/lbE
Fig. 5. Block diagram of automatic measuring system.
the data is carried out, namely the signal scaling, the setting of the isopotential level and the time synchronization. If external interference or noise are present then a digital filtration is made. A check of the recorded signal of the standard lead II is also provided by the system during the process of measurement. The result of the preliminary processing of the measured signals is a set of synchronized instantaneous values of potentials at all the lead points on the torso surface for a sequence of chosen instants of the heart cycle, the typical time interval between the instants being 2 ms. Thus the typical data received as result of the measurement and preliminary processing include a table of cylindrical coordinates of the lead points on the patient's torso surface and a set of tables of instantaneous potential distributions on this surface. These values of potentials and coordinates are the initial data for the determination of the parameters of any mathematical description, or model for the cardiac electrical generator. 2. MATHEMATICAL DESCRIPTION OF THE CARDIAC ELECTRICAL GENERATOR In modern electrocardiology several types of models, or equivalent electrical heart generators were suggested for mathematical description of the actual cardiac current generators. The large majority of these models is based upon the multipole or multidipole representations of the cardiac electrical activity. The most interesting of such models are described, for example in [16-221. It was considered reasonable to base the choice of characteristics for quantitative description of the cardiac electrical generator upon the following main requirements: 1. The set of characteristics should include as a separate element the vector of the heart dipole moment which expresses the most important and experimentally studied information about the electrical state of the heart. 2. The set of characteristics must include parameters de-
scribing the most significant properties of the cardiac electrical generator that can not be reflected by the dipole moment; these additional characteristics must have rather explicit physical interpretation, and their number must not be too large. 3. It should be possible to determine all these characteristics easily enough at the present state of the art from the potential distribution on the torso surface and the external geometrical parameters of the body without any significant assumptions as to structure of the actual electrical process in the heart, or the real cardiac generator, and to body surface
configuration. Consideration of various known types of mathematical description of the cardiac electrical generator, including multipole, multidipole, continuous topographical, and other types, shows that they do not satisfy all the above mentioned requirements. However, the multipole description has such features that allow using it as a basis for the sought set of characteristics. In particular, the multipole description satisfies the first and the third requirements formulated above. It does not, however, fully satisfy the second requirement, by not allowing an easy interpretation of its higher components physically and electrophysiologically, i.e., relating them to the structure of the real generator. This disadvantage significantly reduces the diagnostic usefulness of the multipole description. Hence, at the present time only the simplest version of the multipole description, namely the dipole model, is widely used for diagnostic purposes. This model serves as a basis for orthogonal vectorcardiography. Hence, it seems reasonable to transform the multipole components into a set of characteristics that would be more explicitly related to the structure of the electrical process in the heart both for normal and pathological conditions, and thus satisfy all the requirements mentioned. The set of characteristics that will be considered can be called "integral" since these characteristics describe some
25
KNEPPO AND TITOMIR: HUMAN CARDIAC ELECTRICAL GENERATOR
properties of the electrical process in the heart that are quantitatively expressed as integrals of distributed current sources over the space occupied by the active heart muscle [23]. The integral characteristics are determined on the basis of the fundamental theory of the multipole equivalent generator of the heart [24-261. The set of integral characteristics includes, firstly, the vector of the cardiac generator dipole moment, that is the first member of the multipole equivalent generator of the heart, without any transformation. The dipole moment of the heart has a sufficiently clear physical and electrophysiological interpretation. In particular, it characterizes the overall intensity of the electrical process in the heart corresponding to the main direction of propagation of the excitation wave. It was shown by theoretical, experimental and clinical investigations that the dipole moment contains the most important diagnostic information as compared with the multipoles of higher order. An effective use of this information is assured by the large cylindrical experience already accumulated, for example, in application of the corrected orthogonal vectorcardiographic system. Secondly, the set of integral characteristics includes the position vector of "the center of electrical forces," or "moving electrical center" of the heart. Following a criterion formulated in [27, 28] we define the electrical center of the heart as the localization point of the multipole equivalent generator providing the minimum least square contribution of the quadrupole to the measured potential. The position of the electrical center indicates an average point near which the elementary electrical sources are localized. Thirdly, the set of integral characteristics includes the complexity parameter of the cardiac generator. Unlike the previous characteristics it is a scalar quantity. The complexity parameter is defined as the ratio of the contribution to the measured potential of the quadrupole relative to that of the dipole, each determined with respect to an origin at the electrical center. Hence, it describes the structural complexity of the. real cardiac generator as reflected in the "residual" quadrupolar potential. In particular the value of the parameter increases when the edge of the excitation surface propagating in the heart during depolarization becomes more curved. The integral characteristics describe the electrical state of the heart at any given time instant and are determined for each instant independently of the heart state at the previous or the following time periods. Note that the simplest theoretical model of the heart excitation wave, namely the uniform electrical double layer with a planar rim, the dipole moment vector is oriented perpendicularly to the rim plane and is oriented to the positive side of the double layer; the electrical center for such a model coincides with the "center of gravity" of the plane region bounded by the rim, and the complexity parameter equals zero [29].
For determination of the integral characteristics it is necessary to know the dipole and quadrupole elements of the multipole equivalent generator in reference to an arbitrarily chosn origin of coordinates inside the surface of potential measurement. Hence the computational procedure must consist of two steps:
1. a calculation of the dipole and quadrupole components from the measured potentials and the coordinates of the torso surface; 2. a calculation of the integral characteristics from these components. The electrodynamic relations used for the calculation apply to an electrical field of stationary current generated by current sources in homogeneous volume conductor bounded by a closed surface of arbitrary shape. It is known that for such conditions the field potential is described by the following partial differential equations: I (1) 7 for the region of the conductor (body) where the current sources (heart) exist,
Awp = -
(2)
Ap = 0 for all other regions of the conductor, and
alp = 0 (3) an on the bounding surface of the conductor. In these equations p is the electrical potential, I is the density of the current sources, y is the conductivity of the volume conductor, and n is the normal to the boundary surface. As was shown in [25] for this case the components of the multipole equivalent generator can be accurately computed from the surface potentials and coordinates; the components of the first two multipoles are given by the following expressions: Dipole
Alo =Dz = 7y ps dSz
All =DX=7 fpsdSx B1l =Dy=7fsosdSy
(4)
Quadrupole
A20 =
sy
s (- x
dSX - y dSy + 2z dSz)
A21 = sYps(z dSx +xdSz) B21 = 7f(ps(zdSy+ydSz)
A22 = B22
f ps(x dSx -ydSy)
Ifps (Y dSx + x dSy)
(5)
26
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 1, JANUARY 1979
where x, y, z are the coordinates of the surface points, dSx,
system to the torso surface. Note that the last equation holds
the planes perpendicular to corresponding coordinate axes, and ePs is the measured potential. The integration is carried out over the whole bounding surface of the conductor or body. Note that potential ps depends both on the space coordinates and the time; hence the multipole components are functions of time. Obviously, the influence of the internal heterogeneity, i.e., difference between conductivities of various tissues and organs of the body, is not considered in these equations. It seems, however, reasonable to use them at the present stage of the investigation since it is now impossible to take into account the heterogeneity factor because of insufficient information about the body electrical structure and because of mathematical difficulties. In addition, our preliminary estimates showed that neglecting the influence of the body heterogeneity will cause mainly systematic errors of relatively small value that must not significantly affect the interpretation of the resulting characteristics. When the dipole and quadrupole characteristics are known, the coordinates of the electrical center can be calculated using the following expressions received by minimization of the quadrupole potential [23, 27].
homogeneous spherical conductor with radius R. In order to execute all the above mentioned calculations on a multipurpose digital computer special computational programs were developed in Algol and later in Fortran. In the major program the equations (4) and (5) defining the dipole and quadrupole components are evaluated by numerical integration using a technique of triangulation of the torso surface similar to that described in [30]. The surface is approximated by a set of planar triangular elements formed by straight line segments connecting the points of measurement. The upper and the lower parts of the surface are closed by horizontal planes which also are divided into triangular elements by radial lines. The cylindrical coordinates are transformed into rectangular ones, and the surface integrals are replaced by sums of corresponding quantities calculated for each elementary triangle. The resulting discrete equations can easily be solved in a computation program. A preliminary analysis of the methodical errors has shown that the space discretization of measurements provides sufficient accuracy of determination of the integral characteristics. The vertical component of the dipole moment vector and the electrical center localization vector are determined somewhat less accurately in comparison with the transverse components.
dSy, dSz are the projection areas of the surface elements on strictly for potential distribution on the surface of bounded
Xc = 4D +
[-A20Cx(I + C2) + 2A2,Cz(2- C2) - 2B2,CxCyCz
2A22 CX(4
-
CX +C) + 4B22 Cy(2
-
C2)]
Yc =4D [-A20 Cy(l + Cz2) - 2A 21 CxCyCz + 2B21 Cz(2 - C%Y) - 2A22 Cy(4 + C - C) + 2B22 CX(2- C)]
1=4 [2C( A20C(3 - C2) + 2A21 Cx(2 zc4D +
2B21Cy(2-C-
)-
2A22Cz(Cx2
-
-
C2) Cy)-
4B22CxCyCz] (6)
where D= /D2 +D2 +D2 is the magnitude of the dipole moment vector and Cx = Dx/D, Cy = Dy/D, Cz = Dz/D are the direction cosines of this vector. The quadrupole components in the new coordinate system with its origin at the electrical center are given by the following expressions [251:
AC20 =A20 +xcDx +ycDy - 2zcDz AC21 =A21 -zcDx xcDz BC21 = B21 -ZcDy ycDz AC22 =A22 - 2XCDX + I YcDy BC22 =B22 I YCDX - 2 XCDy -
(7)
Finally, the complexity parameter is expressed as
KQ =
I
(Ab2O +3AC21 +3Bb21 + 12A 22 + 12B 22)
where R is the mean distance from the origin of the coordinate
3. RESULTS OF THE EXPERIMENTAL STUDY AND DISCUSSION
Experimental measurements of the torso surface potentials and coordinates were made for a group of healthy middleaged men, by means of the automatized measuring system described in Section 1. The data were processed by a digital computer and the integral characteristics of the cardiac electrical generator were found by using equations presented in Section 2. The results for one subject, a man with medium torso size, are presented in Fig. 6, a, b, c. Here the time interval between marked points on the curves is equal to 4 ms for QRS region and 20 ms for T region of the heart cycle. Fig. 6, a shows the trajectory of the heart dipole vector D in projections on frontal (F), transverse (T), and left sagittal (S) planes of the body, that is as planar loops corresponding to projections of the ideal orthogonal vectorcardiogram. Fig. 6, b shows the trajectory of the heart electrical center, also in projections on the coordinate planes. Fig. 6, c shows change in time of the complexity parameter of the heart generator KQ (lower graph, solid curve). The least square ratio of quadrupolar to dipolar potentials in the initial coordinate system, with the origin at the center of the transverse section, is also shown here as a dotted curve. The last quantity is calculated using equation (8) but with the values of quadrupole components in the initial coordinate system. The results for several normal cases are shown for comparison in Figs. 7-9, the vectorcardiograms and electrical center trajectories being presented only in transverse projections. Here, the time interval between the marked points on the curves is equal to 8 ms for QRS region and 24 ms for T region of the heart cycle. It can be seen from the illustrations that the trajectories of
KNEPPO AND TITOMIR: HUMAN CARDIAC ELECTRICAL GENERATOR
VC G T
F
27
3
2
1
Dz,mA cm
S
E TC zcn
-2
X,fC
50 224 -54
k,
WT -QRS
? f
-f
d-zcm I
Fig. 7. VCG loops transverse projections for 6 normal men.
yan
T5C7-
c
KQ
.
CRS
P
0
80
328 t,ms
164
CR9 0
20
40
60
2X02?O
in2
K0
2O
260
260
30
1
-I
1 2 3 4 x,Cm -1 0
-2
.-f
t
-2
s-3
-7
OR
2 3
4
x,cm
-f 0
.-?
x,cm
1 2 3 4
-2
T
x,cm
.-1
--3
-2 -3 -4
-5
--5
t,ms
316
t, ms
T
90
~~~~~4
308
164
ti,ms
T
CRS
1
308
O,1 0
5
6
z,cm -1 0
172
ORS
--6
z,cm
164
T
so
l
.-4 -5
5
60
0,1
fQRS
-3
....
QRS
T
--2
--6
4
. .
O
0
-1 01 2 3 4
-.f
0,1
3
[z,cm
~}ORS
-3 -4
?
2
z,cm
2
Tr
20
t,ms Fig. 6. Integral characteristics of the heart: a) ideal orthogonal vectorcardiogram; b) projections of electric center trajectory of the heart; c) complexity parameter calculated for origin in ECT (solid line) and for initial origin (dashed line). z,cm
1
T
0,1f 2 3 4
x,cm
T
ORS
92
0
228
ORS
0
6
T
'fN%d\
_ 92
220
t, ms
372
_
_ 364
tims
Fig. 8. ECT transverse projection for 6 normal men.
Fig. 9. CP time variation during a heart cycle for 6 normal men.
the dipole moment vector in all studied cases have shape features typical for vectorcardiographic normal category. The vectorcardiograms and "the second order characteristics," i.e., electrical center trajectories and complexity parameters, exhibit some qualitative features of resemblance as well as individual discrepancies between different cases. The position of the electrical center shows a mean localization of electrical forces of the heart. The shape properties of the trajectories of the electrical center qualitatively correspond to electrophysiological data conceming space movement of the electrical sources for normal excitation of a heart. Note that the criterion for determination of the electrical center localization used in this work does not fully exclude the possibility for this point to be situated outside the heart space. Such situation may be encountered when the electrical excita-
tion wave in the heart has a complex geometrical structure, in particular if it consists of several parts with dipole moments of nearly the same magnitudes but mutually opposite orientations. However, in all the studied cases the electrical center during the investigated parts of the ventricular cycle never move out of the space occupied by the heart ventricles. During a QRS period the electrical center trajectory in the transverse plane has a looplike shape and a trend of clockwise rotation. During a T period it has a simpler shape and is less spread in space than during the QRS period. An explicit correlation between QRS and T parts of the electrical center trajectory is not observed. As could be expected the value of the complexity parameter is always significantly less than the relative quadrupolar potential contribution in the initial coordinate system. During
28
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 1, JANUARY 1979
a T period the complexity parameter usually has a much smaller value and varies more smoothly than during the QRS period. In a QRS period it usually has one or two maxima which supposedly correspond to the instants when the cardiac generator structure is most complex. It is hoped that second order integral characteristics will be useful for recognition of the heart states and the diseases which are not explicitly enough reflected by the orthogonal vectorcardiogram. In particular, they may help the solution of such electrocardiological tasks as the determination of the spatial position and structure of local myocardial injuries, observation of translational shifts of the excitation wave in the heart and indication of changes of these shifts during given time periods, determination of changes of anatomical heart position, location of the artificial pacemaker, etc. In order to check the possibilities of using these characteristics for diagnostic procedures investigations are now being carried out with patients exhibiting some pathological alterations of the heart. REFERENCES
[1] The Theoretical Basis of Electrocardiology, ed. by C. V. Nelson
and D. B. Geselowitz, Oxford University Press, 1976. [2] M. S. Spach, W. P. Silberger, J. P. Boineau, R. C. Barr, E. C. Long, T. M. Gallie, J. B. Gabor, A. G. Wallace, "Body surface isopotential maps in normal children, ages 4 to 14 years";American Heart Journal, vol. 72, pp. 640-652, November 1966. [3] C. Yoshimoto, K. Takaya, Y. Iwai, T. Matozaki, Y. Yamagishi, S. Shibata, A. Yakata and M. Takahashi, "Computer animation of ECG field distribution." In: Proceedings of the 8th International Conference on Medical Biological Engineering, session 16-3. Palmer House, Chicago, Ill., 1969. [4] P. Kneppo, V. Rosik, E. Kohutova, V. Szathmairy, S. Rippa, "Vyuzitie samocinneho po6itaca pri mapovani elektrickeho pol'a srdca." Zbornik predndaok Medzindrodneho sympozia lkaiskd elektroniky, Duzm techniky CVTS, Ostrava, pp. 183188, 1970 (in Slovak). [5] R. B. Pearson, L. T. Gillespie, and R. H. Selvester, "On-line digital collection and display of total body surface ECG data." In: Vectorcardiography 2, ed. I. Hoffman, pp. 146-53, NorthHolland, Amsterdam, 1971. [6] C. Cottini, D. Dotti, E. Gatti and B. Taccardi, "A 240-probe instrument for mapping cardiac potentials," In: Proceeding of the Satellite Symposium of the 25th International Congress of Physiological Sciences (The electrical field of the heart) and the 12th Colloquium Vector-cardiographicum, ed. P. Rijlant, pp. 99-102, Presses Academiques Europeennes, Brussels, 1972. [7] B. C. Olliff, L. G. Horan and N. C. Flowers, "Correlative analysis of vectorcardiograms and serial instantaneous surface potential maps in normal young men." In: Am. Heart. J. 83, pp. 780-89, 1972. [8] B. D. Young, and T. D. Lawrie, "Body surface mapping in myocardial infarction," In: Proceedings of the Satellite Symposium of the 25th International Congress of Physiological Sciences (The electrical field of the heart) and the 12th Colloquium Vectorcardiographicum, ed. P. Rijlant, pp. 633-40, Presses Academiques Europeennes, Brussels, 1972. [9] H. Tatematsu, M. Wada, M. Okajima, and K. Yamada, "On-line conversational mode processing system for body surface mapping as designed for clinical application-an example: WPW syndrome," In: Body Surface Mapping of Cardiac Fields, ed. S. Rush and E. Lepeschkin, Advances in Cardiology 10, pp. 20-25, S. Karder, Basel, 1974. [101 V. Laufberger, Spatiocardiography, Publishing House of the Czechosloval Academy of Sciences, Praque 1965. [11] Ch. 0. Eddlemon, V. J. Ruesta, L. G. Horan, and D. A. Brody, "Distribution of heart potentials on the body surface in five normal young men," In: Am. J. Cardiology 21, pp. 860-870, 1968.
12] P. Kneppo, V. Szathmary, I. Ruttkay-Nedecky, "Investigation of the cardiac electric field by means of spherical coordinator," In: Physiol. Bohemoslovaca 18, p. 344, 1969. [13] A. Damen, "Epicardial potentials derived from skin potential measurements," In: Summaries of the International Conference Measuring and Modelling of the Cardiac Electrical Field, Smolenice near Bratislava, p. 9, 1976. [14] P. Kneppo, "The cylindrical coordinator CK-2-an equipment for body surface mapping of cardiac electric field," In: Summaries of the II. International Congress on Electrocardiology, Varna, p. 40, 1975. [15] P. Kneppo, V. Rosik, "Automatizovana sustava na meranie elektrickeho pol'a srdca," In: Zbornik prednasok EMISCON '75, Dom techniky SVTS Bratislava, pp. 29-33, 1975 (in Slovak). [16] E. J. Fischmann, M. R. Barber, "Aimed electrocardiography. Model studies using a heart consisting of six electrically isolated areas,"Am. Heart J. 65, pp. 628-637, 1963. [171 R. H. Selvester, R. Kalaba, C. R. Collier, R. Bellman, H. Kagiwada, "A digital computer model of the vectorcardiogram with distance and boundary effects: Simulated myocardial infraction," A. Heart J. 75, pp. 792-808, 1967. [18] D. A. Brody, "The inverse determination of simple generator configurations from equivalent dipole and multipole information." IEEE Trans. Biomed. Eng. BME-15 pp. 106-110, 1968. [19] R. A. Helm, T. CH. Chou, "Computation of a variable location dipole representation from body surface leads." Am. Heart J. 77, pp. 363-366, 1969. [20] J. H. Holt, A. C. L. Barnard, M. S. Lynn, P. Svendsen, "A study of the human heart as a multipole dipole electrical source." Circulation 40, p. 687, 1969. [21] J. Jagielski, J. Mozrzymas, "On the selection rules for the multiple generators of cardiac electric field," Institute of Theoretical Physics University of Wroclaw, Preprint NO 230, 1971. [22] P. Rijlant, "A twenty pole generator equivalent to the heart's generator system," In: Proceeding of the Satellite Symposium of the 25th International Congress of Physiological Sciences (The electrical field of the heart) and the 12th Colloquium Vectorcardiographicum, ed. P. Rijlant, pp. 454-461, Presses Academiques Europeennes, Brussels, 1972. [23] L. I. Titomir, "Integralnyje harakteristiki elektricheskoj volny vozbuzhdenija serdca," In: Biofizika 20, pp. 693-698, 1975 (in Russian). [24] D. Gabor, C. V. Nelson, "Determination of the resultant dipole of the heart from measurements on the body surface," J. Appl. Physics 25, pp. 413-416, 1954. [25] D. B. Geselowitz, "Multipole representation for an equivalent cardiac generator," In: Proc. IRE 48, pp. 75-79, 1960. [26] R. Plonsey, Bioelectric Phenomena, New York, McGraw-Hill, 1969. [27] D. B. Geselowitz, "Two theorems concerning the quadrupole applicable to electrocardiography," In: IEEE Trans. Biomed. Eng. BME-12, pp. 164-168, 1965. [28] R. M. Arthur, D. B. Geselowitz, S. A. Briller, R. F. Trost, "The path of the electrical center of the human heart determined from surface electrocardiograms," In: J. Electrocardiol. 4, pp. 29-33, 1971. [29] D. A. Brody, J. C. Bradshaw, "The equivalent generator components of uniform double layers," In: Bull. Math. Biophys. 24, pp. 183-195, 1962. [30] R. M. Arthur, D. B. Geselowitz, S. A. Briller, R. F. Trost, "Quadrupole components of the human surface electrocardiogram," In: A. Heart J. 83, pp. 663-670, 1972.
P. Kneppo, photograph and biography not available at the time of
publication.
L. I. Titomir, photograph and biography not available at the time of
publication.
21
In conclusion, it should be pointed out that this method, tracer methods." M. Sc. Thesis, Technion-Israel Institute of Technology, Haifa, Israel. as well as the one presented by Oleksy et al.4 avoids a numerKarlsson, H., G. J. Rossenhamer, and 0. Wigertz, (1971). "Oneical deconvolution.7 However, the "second" correction pre- 7. stage digital correction of distorted dye-dilution curves," Scand. J. sented here provides a means to bring the derived curve into Clin. Lab. Invest., 27: 287-291. much closer agreement with the measured curve than is possible with the method of Oleksy, et al.
REFERENCES 1. Bloomfield, D. A. (Ed.), (1974). Dye Curves: Theory and Practice, University Park Press, Baltimore. 2. Weinstein, H., and M. P. Dudukovic, (1975). "Tracer Methods in the Circulation," in Topics in Transport Phenomena, C. Gutfinger, Ed., Hemisphere Publishing Corp., Washington, D.C. 3. Schlossmacher, E. J., H. Weinstein, S. Lochaya, and A. Shaffer, (1967). "Perfect mixers in series model for fitting venoarterial indicator-dilute curves," J. Appl. Physiol., 22: 327-332. 4. Oleksy, S. J., H. Weinstein, and A. B. Shaffer, (1969). "Correction of dye-curve distortion with the use of perfect mixers in series model." J. Appl. Physiol., 26: 227-232. 5. Fu, B., (1970). "Tracer analysis of recirculating systems." Ph.D. Thesis, Illinois Institute of Technology, Chicago, Illinois. 6. Nassi, M., (1975). "Evaluation of congenital heart defects by
M. Nassi, cation.
photograph and biography not available at the time of publi-
J. Dayan, cation.
photograph and biography not available at the time of publi-
S. Braun (M'74), photograph and biography not available at the time of publication.
H. Weinstein, photograph and biography publication.
not available at the time of
Integral Characteristics of the Human Cardiac Electrical Generator from Electric Field Measurements by Means of an Automatic Cylindrical Coordinator P. KNEPPO AND L. I. TITOMIR Abstract-An automated electronic system based upon a cylindrical coordinator was constructed for measurement and preliminary computational processing of the heart electrical potentials on the surface of a human torso and of the coordinates of this surface. The potential distribution on the body surface at consecutive instants of time and the geometrical parameters of the body received as the output of the measuring system can be used for investigation of various types of mathematical descriptions, or models of the cardiac electrical generator. One such mathematical description, a set of integral characteristics of the cardiac electrical generator, is studied in this work. These characteristics are: three components of the heart dipole moment, three coordinates of the moving cardiac electrical center and the com-
Manuscript received June 27, 1977; revised May 4, 1978. P. Kneppo is with the Department of Bioelectrical Measurement, Institute of Measurement and Measuring Technique, Slovak Academy of Sciences, Bratislava, Czechoslovakia. L. I. Titomir is with the Computational Laboratory, Institute of Problems of Information Transmission, Academy of Sciences of U.S.S.R.,
Moscow, U.S.S.R.
plexity parameter of the cardiac generator. The results of experimental measurement of the cardiac electrical field and calculation of the inte-
gral characteristics of the cardiac generator are presented for a group of healthy
men.
Physical and electrophysiological significance of the
results is briefly discussed.
MsETHODS of quantitative investigation of cardiac electrical generators using computational equipment play an increasingly important role in modem electrocardiology [1]. These methods require formulation of a set of quantitative characteristics that accurately describe properties of the heart as an electrical generator, and should not depend on extracardiac factors such as anatomical configuration of the body, structure of the lead system and so on. If an idealized electrical generator with a known structure is ascribed to such a set of characteristics then it is called "equivalent electrical generator of the heart." The parameters of the mathematical
0018-9294/79/0100-0021 $00.75 © 1979 IEEE
22
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 1, JANUARY 1979
tween electrodes and the skin; measurement of coordinates of each lead point while providing stability of the coordinates during the measuring procedure; synchronous measurements of the potentials or synchronization of the signals using a special reference lead; preliminary processing of the lead signals, in particular amplification, special filtration, analog-to-digital conversion and insertion into the digital computer memory. All these operations were provided for by the automated measuring system described below. The main unit of the system is the cylindrical coordinator CK-2 (Fig. 1) constructed in the Institute of Measurement and Measuring Technique of the Slovak Academy of Sciences [14]. This device provides for determination of the coordinates of the chest surface points where the cardiac electrical field potentials, i.e., electrocardiograms are measured. The design principle of the coordinator is based on the fact that the shape of the human chest resembles a cylinder whose axis coincides with the vertical axis of the human body. Thus for the design of the coordinator a cylindrical coordinate system was chosen with the Y axis oriented vertically and passing through the middle point of the torso transverse section. It has the same direction as the Y axis of the standard vectorcardiographic 1. MEASURING SYSTEM coordinate system (Fig. 2). The patient to be measured is To determine the surface distribution of cardiac potentials placed in the coordinator in a sitting position (Fig. 3). The many authors [2-9] designed automatic methods of measure- sensing electrodes are fixed on an elliptical frame that surment with utilization of computers. Several works including rounds the chest of the subject and can be displaced along the sets of maps obtained by an automatic sequential record of vertical axis. In the horizontal plane the electrodes are situgroups of 5 to 15 electrocardiograms together with a time ated with an angular interval of 150 on the front and the left reference lead on a multichannel analog tape recorder, have sides of the chest, the regions that are the closest to the heart, been published since 1963. After digital conversion the data and with an angular interval of 300 on the back and the right are adapted by the computer and either printed by a printer sides; the full number of electrodes on the frame is 18. The terminal, or recorded by a plotter in the form of equipoten- distribution of the electrodes in space is shown in Fig. 4. The tial lines in the plane of developed chest surface for chosen electrodes are placed on the body surface automatically by time instants. The maps constructed by such methods con- extending them in a radial direction up to the required length sist of data recorded during different heart beats. It is known at the given instants of the measuring process. The displacethat the subsequent beats are in general not identical because of ment of the electrodes is provided by a pneumatic system the influence of breathing, the heart rhythm, and other phenom- which simultaneously ensures uniformly pressing the elecena influencing the electric field. For solution of the inverse trodes against the body surface. Special devices attached to problem it is necessary to know, in addition to the surface each electrode provide measurement of the radial coordinates potentials, the shape of the chest. Some authors [10-13] have of the lead point. The contact surface of the electrode is a constructed a special device, a coordinator, for this purpose. disk with a diameter of 18 mm. During the measurement The measurement of both the cardiac potential and the coordi- process the frame with the electrodes is automatically shifted nates of the chest surface is performed gradually and it takes a along the vertical axis at required instants. It is possible to rather long time. A special measuring method together with choose space intervals equal to 1, 2, or 3 cm between the horian automatic measuring system were designed to reduce the zontal planes in which the system of electrodes is fixed. Durinfluence of most of the mentioned imperfections. The auto- ing the measuring process this interval is set automatically by matic measuring system allows simultaneous measurements of special devices of the coordinator. For example, if a 2 cm discardiac potentials as well as geometric measurements of the tance between the horizontal planes is chosen then it is usually chest at chosen points. The system simplifies and automates possible to carry out measurements in 14 planes for a man the procedure of fixation of electrodes over the body surface with medium height, or at 252 points. The automatic function of the whole measuring system is and it also allows measurement, at the determined respiratory phase positions of the chest. The second standard lead is re- secured by the corresponding electronic devices [15]. The corded in order to check eventual gross changes of the cardiac scheme of the measuring system is shown in Fig. 5. The measured data, potentials El to E18 and radial coordinates RIB, electric field. The procedure of cardiac electrical field measurement raises are fed to the multiplexer of the analog-to-digital converter the following main problems: choice of the number and loca- of the computing system DEClab 11/10 E. The ECG signals, tion of sites for leads that provide the required accuracy of the with the potential of Wilson's terminal used as a reference, are electrical field characteristics investigated; fixation of the lead first amplified in a special 20-channel amplifying unit AU electrodes over the body surface with reliable contacts be- made by the firm CHIRANA. The amplified signals El to
description of the cardiac generator are found from measured potentials on the body surface and the geometrical characteristics of the body by solving an "inverse problem." For its solution additional a priori information about the cardiac generator is sometimes necessary. A diagnostic conclusion is drawn on the basis of anatomic and physiological interpretation of values of the parameters determined for the examined patient. Such a determination of the values of a mathematical description of the cardiac electrical generator parameters requires the measurement of electric potentials on the chest surface and identification of the chest characteristic, the first approximation being represented by the geometry of the chest. The aim of this article is, first of all, to describe a new automated measuring system for detailed measurements of electric potentials on the human chest surface and its geometrical characteristics, as well as preliminary processing of the received signals before main processing by a multipurpose computer, and secondly, to present an effective mathematical description of the cardiac electrical generator together with the results of determination of its parameters from experimental measurements on a group of healthy men.
23
KNEPPO AND TITOMIR: HUMAN CARDIAC ELECTRICAL GENERATOR
Fig. 3. Subject with applied electrodes in the cylindrical coordinator.
/_300
12
13
9 \-8
14
x
I
i5
16
Fig. 1. Cylindrical coordinator CK-2.
wI
23
4
5
i 5;
z
Fig. 4. Distribution of lead electrodes.
Fig. 2. Choice of rectangular
together
E18
rectly
and
cylindrical coordinate systems.
with the second standard lead
to the DEClab
RIB signals corresponding
The
the measurement tentiometer
points
equalization
are
to the radial coordinates of
led to the
signal filtering and
unit FPEU where the
RI 8, corresponding to radial to B1 8 corresponding to the
signals
time-variation are
of the radial
separated.
of the measured person and the
A/D
at the selected time-instants is
to the chest
conversion of the ECG
provided by
the
timing
unit TU. The second standard ECG lead and the START
the computer, which is used to start the
according the
to the
timing
sequences
unit.
co-
For the
signal of the second stantiming of the measuring system,
The
i.e., the sequential application of the electrodes
f'rom
to
of the system the
dard ECG lead is used.
signals
po-
RI1
coordinates, and the signals Bl
ordinates due to respiratory motions,
synchronization
conveyed di-
are
analog input.
signal The
from the
timning
calibrating pulses
referred to the AU
terminal,
are
unit generates in
CP
M
led
as
inputs
to
predetermined
amplitude
of I mV
determining
the time
with the
input, the signal
pulse
measuring cycle
of measurement, the A/D conversion start pulse, the sampling pulses SP, the signal P determining the interval between successive measurements, and the FP pulse for the frame position control. After the measurement and storage of all the signals in one horizontal plane, the FP pulse activates the frame position controller FPC. This controller initiates the withdrawal of electrodes from the body surface, moving the frame down by a given distance and the next application of the electrodes. The pneumatic system effecting the movement of the electrodes consists of the electric exhauster EE and electromagnetic valve EV switching over to pressure and underpressure positions. The check of the constancy of the position of the measured body is secured by position sensors mounted on the frame. The sensors' output signals SI and S2 serve, after processing in a patient position controller PPC, for activating the display D, which indicates the correct position, and determining the direction of the eventual corrections. The display indicates simultaneously the time of the measurement (signal M) and the interval between measurements (signal P). The described arrangement of the automatic system is determined by the use of units designed originally for the first modification of the system working in the off-line mode and providing recording on a tape recorder. Using this automated measuring system it is possible within 10 to 15 min to acquire all the necessary information about the patient's torso. After analog-to-digital conversion and supplying the data to a computer the preliminary processing of
24
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 1, JANUARY 1979
CK- 2
CRT'
DECLAB 11/lbE
Fig. 5. Block diagram of automatic measuring system.
the data is carried out, namely the signal scaling, the setting of the isopotential level and the time synchronization. If external interference or noise are present then a digital filtration is made. A check of the recorded signal of the standard lead II is also provided by the system during the process of measurement. The result of the preliminary processing of the measured signals is a set of synchronized instantaneous values of potentials at all the lead points on the torso surface for a sequence of chosen instants of the heart cycle, the typical time interval between the instants being 2 ms. Thus the typical data received as result of the measurement and preliminary processing include a table of cylindrical coordinates of the lead points on the patient's torso surface and a set of tables of instantaneous potential distributions on this surface. These values of potentials and coordinates are the initial data for the determination of the parameters of any mathematical description, or model for the cardiac electrical generator. 2. MATHEMATICAL DESCRIPTION OF THE CARDIAC ELECTRICAL GENERATOR In modern electrocardiology several types of models, or equivalent electrical heart generators were suggested for mathematical description of the actual cardiac current generators. The large majority of these models is based upon the multipole or multidipole representations of the cardiac electrical activity. The most interesting of such models are described, for example in [16-221. It was considered reasonable to base the choice of characteristics for quantitative description of the cardiac electrical generator upon the following main requirements: 1. The set of characteristics should include as a separate element the vector of the heart dipole moment which expresses the most important and experimentally studied information about the electrical state of the heart. 2. The set of characteristics must include parameters de-
scribing the most significant properties of the cardiac electrical generator that can not be reflected by the dipole moment; these additional characteristics must have rather explicit physical interpretation, and their number must not be too large. 3. It should be possible to determine all these characteristics easily enough at the present state of the art from the potential distribution on the torso surface and the external geometrical parameters of the body without any significant assumptions as to structure of the actual electrical process in the heart, or the real cardiac generator, and to body surface
configuration. Consideration of various known types of mathematical description of the cardiac electrical generator, including multipole, multidipole, continuous topographical, and other types, shows that they do not satisfy all the above mentioned requirements. However, the multipole description has such features that allow using it as a basis for the sought set of characteristics. In particular, the multipole description satisfies the first and the third requirements formulated above. It does not, however, fully satisfy the second requirement, by not allowing an easy interpretation of its higher components physically and electrophysiologically, i.e., relating them to the structure of the real generator. This disadvantage significantly reduces the diagnostic usefulness of the multipole description. Hence, at the present time only the simplest version of the multipole description, namely the dipole model, is widely used for diagnostic purposes. This model serves as a basis for orthogonal vectorcardiography. Hence, it seems reasonable to transform the multipole components into a set of characteristics that would be more explicitly related to the structure of the electrical process in the heart both for normal and pathological conditions, and thus satisfy all the requirements mentioned. The set of characteristics that will be considered can be called "integral" since these characteristics describe some
25
KNEPPO AND TITOMIR: HUMAN CARDIAC ELECTRICAL GENERATOR
properties of the electrical process in the heart that are quantitatively expressed as integrals of distributed current sources over the space occupied by the active heart muscle [23]. The integral characteristics are determined on the basis of the fundamental theory of the multipole equivalent generator of the heart [24-261. The set of integral characteristics includes, firstly, the vector of the cardiac generator dipole moment, that is the first member of the multipole equivalent generator of the heart, without any transformation. The dipole moment of the heart has a sufficiently clear physical and electrophysiological interpretation. In particular, it characterizes the overall intensity of the electrical process in the heart corresponding to the main direction of propagation of the excitation wave. It was shown by theoretical, experimental and clinical investigations that the dipole moment contains the most important diagnostic information as compared with the multipoles of higher order. An effective use of this information is assured by the large cylindrical experience already accumulated, for example, in application of the corrected orthogonal vectorcardiographic system. Secondly, the set of integral characteristics includes the position vector of "the center of electrical forces," or "moving electrical center" of the heart. Following a criterion formulated in [27, 28] we define the electrical center of the heart as the localization point of the multipole equivalent generator providing the minimum least square contribution of the quadrupole to the measured potential. The position of the electrical center indicates an average point near which the elementary electrical sources are localized. Thirdly, the set of integral characteristics includes the complexity parameter of the cardiac generator. Unlike the previous characteristics it is a scalar quantity. The complexity parameter is defined as the ratio of the contribution to the measured potential of the quadrupole relative to that of the dipole, each determined with respect to an origin at the electrical center. Hence, it describes the structural complexity of the. real cardiac generator as reflected in the "residual" quadrupolar potential. In particular the value of the parameter increases when the edge of the excitation surface propagating in the heart during depolarization becomes more curved. The integral characteristics describe the electrical state of the heart at any given time instant and are determined for each instant independently of the heart state at the previous or the following time periods. Note that the simplest theoretical model of the heart excitation wave, namely the uniform electrical double layer with a planar rim, the dipole moment vector is oriented perpendicularly to the rim plane and is oriented to the positive side of the double layer; the electrical center for such a model coincides with the "center of gravity" of the plane region bounded by the rim, and the complexity parameter equals zero [29].
For determination of the integral characteristics it is necessary to know the dipole and quadrupole elements of the multipole equivalent generator in reference to an arbitrarily chosn origin of coordinates inside the surface of potential measurement. Hence the computational procedure must consist of two steps:
1. a calculation of the dipole and quadrupole components from the measured potentials and the coordinates of the torso surface; 2. a calculation of the integral characteristics from these components. The electrodynamic relations used for the calculation apply to an electrical field of stationary current generated by current sources in homogeneous volume conductor bounded by a closed surface of arbitrary shape. It is known that for such conditions the field potential is described by the following partial differential equations: I (1) 7 for the region of the conductor (body) where the current sources (heart) exist,
Awp = -
(2)
Ap = 0 for all other regions of the conductor, and
alp = 0 (3) an on the bounding surface of the conductor. In these equations p is the electrical potential, I is the density of the current sources, y is the conductivity of the volume conductor, and n is the normal to the boundary surface. As was shown in [25] for this case the components of the multipole equivalent generator can be accurately computed from the surface potentials and coordinates; the components of the first two multipoles are given by the following expressions: Dipole
Alo =Dz = 7y ps dSz
All =DX=7 fpsdSx B1l =Dy=7fsosdSy
(4)
Quadrupole
A20 =
sy
s (- x
dSX - y dSy + 2z dSz)
A21 = sYps(z dSx +xdSz) B21 = 7f(ps(zdSy+ydSz)
A22 = B22
f ps(x dSx -ydSy)
Ifps (Y dSx + x dSy)
(5)
26
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 1, JANUARY 1979
where x, y, z are the coordinates of the surface points, dSx,
system to the torso surface. Note that the last equation holds
the planes perpendicular to corresponding coordinate axes, and ePs is the measured potential. The integration is carried out over the whole bounding surface of the conductor or body. Note that potential ps depends both on the space coordinates and the time; hence the multipole components are functions of time. Obviously, the influence of the internal heterogeneity, i.e., difference between conductivities of various tissues and organs of the body, is not considered in these equations. It seems, however, reasonable to use them at the present stage of the investigation since it is now impossible to take into account the heterogeneity factor because of insufficient information about the body electrical structure and because of mathematical difficulties. In addition, our preliminary estimates showed that neglecting the influence of the body heterogeneity will cause mainly systematic errors of relatively small value that must not significantly affect the interpretation of the resulting characteristics. When the dipole and quadrupole characteristics are known, the coordinates of the electrical center can be calculated using the following expressions received by minimization of the quadrupole potential [23, 27].
homogeneous spherical conductor with radius R. In order to execute all the above mentioned calculations on a multipurpose digital computer special computational programs were developed in Algol and later in Fortran. In the major program the equations (4) and (5) defining the dipole and quadrupole components are evaluated by numerical integration using a technique of triangulation of the torso surface similar to that described in [30]. The surface is approximated by a set of planar triangular elements formed by straight line segments connecting the points of measurement. The upper and the lower parts of the surface are closed by horizontal planes which also are divided into triangular elements by radial lines. The cylindrical coordinates are transformed into rectangular ones, and the surface integrals are replaced by sums of corresponding quantities calculated for each elementary triangle. The resulting discrete equations can easily be solved in a computation program. A preliminary analysis of the methodical errors has shown that the space discretization of measurements provides sufficient accuracy of determination of the integral characteristics. The vertical component of the dipole moment vector and the electrical center localization vector are determined somewhat less accurately in comparison with the transverse components.
dSy, dSz are the projection areas of the surface elements on strictly for potential distribution on the surface of bounded
Xc = 4D +
[-A20Cx(I + C2) + 2A2,Cz(2- C2) - 2B2,CxCyCz
2A22 CX(4
-
CX +C) + 4B22 Cy(2
-
C2)]
Yc =4D [-A20 Cy(l + Cz2) - 2A 21 CxCyCz + 2B21 Cz(2 - C%Y) - 2A22 Cy(4 + C - C) + 2B22 CX(2- C)]
1=4 [2C( A20C(3 - C2) + 2A21 Cx(2 zc4D +
2B21Cy(2-C-
)-
2A22Cz(Cx2
-
-
C2) Cy)-
4B22CxCyCz] (6)
where D= /D2 +D2 +D2 is the magnitude of the dipole moment vector and Cx = Dx/D, Cy = Dy/D, Cz = Dz/D are the direction cosines of this vector. The quadrupole components in the new coordinate system with its origin at the electrical center are given by the following expressions [251:
AC20 =A20 +xcDx +ycDy - 2zcDz AC21 =A21 -zcDx xcDz BC21 = B21 -ZcDy ycDz AC22 =A22 - 2XCDX + I YcDy BC22 =B22 I YCDX - 2 XCDy -
(7)
Finally, the complexity parameter is expressed as
KQ =
I
(Ab2O +3AC21 +3Bb21 + 12A 22 + 12B 22)
where R is the mean distance from the origin of the coordinate
3. RESULTS OF THE EXPERIMENTAL STUDY AND DISCUSSION
Experimental measurements of the torso surface potentials and coordinates were made for a group of healthy middleaged men, by means of the automatized measuring system described in Section 1. The data were processed by a digital computer and the integral characteristics of the cardiac electrical generator were found by using equations presented in Section 2. The results for one subject, a man with medium torso size, are presented in Fig. 6, a, b, c. Here the time interval between marked points on the curves is equal to 4 ms for QRS region and 20 ms for T region of the heart cycle. Fig. 6, a shows the trajectory of the heart dipole vector D in projections on frontal (F), transverse (T), and left sagittal (S) planes of the body, that is as planar loops corresponding to projections of the ideal orthogonal vectorcardiogram. Fig. 6, b shows the trajectory of the heart electrical center, also in projections on the coordinate planes. Fig. 6, c shows change in time of the complexity parameter of the heart generator KQ (lower graph, solid curve). The least square ratio of quadrupolar to dipolar potentials in the initial coordinate system, with the origin at the center of the transverse section, is also shown here as a dotted curve. The last quantity is calculated using equation (8) but with the values of quadrupole components in the initial coordinate system. The results for several normal cases are shown for comparison in Figs. 7-9, the vectorcardiograms and electrical center trajectories being presented only in transverse projections. Here, the time interval between the marked points on the curves is equal to 8 ms for QRS region and 24 ms for T region of the heart cycle. It can be seen from the illustrations that the trajectories of
KNEPPO AND TITOMIR: HUMAN CARDIAC ELECTRICAL GENERATOR
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F
27
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E TC zcn
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Fig. 7. VCG loops transverse projections for 6 normal men.
yan
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.
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40
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t,ms Fig. 6. Integral characteristics of the heart: a) ideal orthogonal vectorcardiogram; b) projections of electric center trajectory of the heart; c) complexity parameter calculated for origin in ECT (solid line) and for initial origin (dashed line). z,cm
1
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0,1f 2 3 4
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Fig. 8. ECT transverse projection for 6 normal men.
Fig. 9. CP time variation during a heart cycle for 6 normal men.
the dipole moment vector in all studied cases have shape features typical for vectorcardiographic normal category. The vectorcardiograms and "the second order characteristics," i.e., electrical center trajectories and complexity parameters, exhibit some qualitative features of resemblance as well as individual discrepancies between different cases. The position of the electrical center shows a mean localization of electrical forces of the heart. The shape properties of the trajectories of the electrical center qualitatively correspond to electrophysiological data conceming space movement of the electrical sources for normal excitation of a heart. Note that the criterion for determination of the electrical center localization used in this work does not fully exclude the possibility for this point to be situated outside the heart space. Such situation may be encountered when the electrical excita-
tion wave in the heart has a complex geometrical structure, in particular if it consists of several parts with dipole moments of nearly the same magnitudes but mutually opposite orientations. However, in all the studied cases the electrical center during the investigated parts of the ventricular cycle never move out of the space occupied by the heart ventricles. During a QRS period the electrical center trajectory in the transverse plane has a looplike shape and a trend of clockwise rotation. During a T period it has a simpler shape and is less spread in space than during the QRS period. An explicit correlation between QRS and T parts of the electrical center trajectory is not observed. As could be expected the value of the complexity parameter is always significantly less than the relative quadrupolar potential contribution in the initial coordinate system. During
28
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 1, JANUARY 1979
a T period the complexity parameter usually has a much smaller value and varies more smoothly than during the QRS period. In a QRS period it usually has one or two maxima which supposedly correspond to the instants when the cardiac generator structure is most complex. It is hoped that second order integral characteristics will be useful for recognition of the heart states and the diseases which are not explicitly enough reflected by the orthogonal vectorcardiogram. In particular, they may help the solution of such electrocardiological tasks as the determination of the spatial position and structure of local myocardial injuries, observation of translational shifts of the excitation wave in the heart and indication of changes of these shifts during given time periods, determination of changes of anatomical heart position, location of the artificial pacemaker, etc. In order to check the possibilities of using these characteristics for diagnostic procedures investigations are now being carried out with patients exhibiting some pathological alterations of the heart. REFERENCES
[1] The Theoretical Basis of Electrocardiology, ed. by C. V. Nelson
and D. B. Geselowitz, Oxford University Press, 1976. [2] M. S. Spach, W. P. Silberger, J. P. Boineau, R. C. Barr, E. C. Long, T. M. Gallie, J. B. Gabor, A. G. Wallace, "Body surface isopotential maps in normal children, ages 4 to 14 years";American Heart Journal, vol. 72, pp. 640-652, November 1966. [3] C. Yoshimoto, K. Takaya, Y. Iwai, T. Matozaki, Y. Yamagishi, S. Shibata, A. Yakata and M. Takahashi, "Computer animation of ECG field distribution." In: Proceedings of the 8th International Conference on Medical Biological Engineering, session 16-3. Palmer House, Chicago, Ill., 1969. [4] P. Kneppo, V. Rosik, E. Kohutova, V. Szathmairy, S. Rippa, "Vyuzitie samocinneho po6itaca pri mapovani elektrickeho pol'a srdca." Zbornik predndaok Medzindrodneho sympozia lkaiskd elektroniky, Duzm techniky CVTS, Ostrava, pp. 183188, 1970 (in Slovak). [5] R. B. Pearson, L. T. Gillespie, and R. H. Selvester, "On-line digital collection and display of total body surface ECG data." In: Vectorcardiography 2, ed. I. Hoffman, pp. 146-53, NorthHolland, Amsterdam, 1971. [6] C. Cottini, D. Dotti, E. Gatti and B. Taccardi, "A 240-probe instrument for mapping cardiac potentials," In: Proceeding of the Satellite Symposium of the 25th International Congress of Physiological Sciences (The electrical field of the heart) and the 12th Colloquium Vector-cardiographicum, ed. P. Rijlant, pp. 99-102, Presses Academiques Europeennes, Brussels, 1972. [7] B. C. Olliff, L. G. Horan and N. C. Flowers, "Correlative analysis of vectorcardiograms and serial instantaneous surface potential maps in normal young men." In: Am. Heart. J. 83, pp. 780-89, 1972. [8] B. D. Young, and T. D. Lawrie, "Body surface mapping in myocardial infarction," In: Proceedings of the Satellite Symposium of the 25th International Congress of Physiological Sciences (The electrical field of the heart) and the 12th Colloquium Vectorcardiographicum, ed. P. Rijlant, pp. 633-40, Presses Academiques Europeennes, Brussels, 1972. [9] H. Tatematsu, M. Wada, M. Okajima, and K. Yamada, "On-line conversational mode processing system for body surface mapping as designed for clinical application-an example: WPW syndrome," In: Body Surface Mapping of Cardiac Fields, ed. S. Rush and E. Lepeschkin, Advances in Cardiology 10, pp. 20-25, S. Karder, Basel, 1974. [101 V. Laufberger, Spatiocardiography, Publishing House of the Czechosloval Academy of Sciences, Praque 1965. [11] Ch. 0. Eddlemon, V. J. Ruesta, L. G. Horan, and D. A. Brody, "Distribution of heart potentials on the body surface in five normal young men," In: Am. J. Cardiology 21, pp. 860-870, 1968.
12] P. Kneppo, V. Szathmary, I. Ruttkay-Nedecky, "Investigation of the cardiac electric field by means of spherical coordinator," In: Physiol. Bohemoslovaca 18, p. 344, 1969. [13] A. Damen, "Epicardial potentials derived from skin potential measurements," In: Summaries of the International Conference Measuring and Modelling of the Cardiac Electrical Field, Smolenice near Bratislava, p. 9, 1976. [14] P. Kneppo, "The cylindrical coordinator CK-2-an equipment for body surface mapping of cardiac electric field," In: Summaries of the II. International Congress on Electrocardiology, Varna, p. 40, 1975. [15] P. Kneppo, V. Rosik, "Automatizovana sustava na meranie elektrickeho pol'a srdca," In: Zbornik prednasok EMISCON '75, Dom techniky SVTS Bratislava, pp. 29-33, 1975 (in Slovak). [16] E. J. Fischmann, M. R. Barber, "Aimed electrocardiography. Model studies using a heart consisting of six electrically isolated areas,"Am. Heart J. 65, pp. 628-637, 1963. [171 R. H. Selvester, R. Kalaba, C. R. Collier, R. Bellman, H. Kagiwada, "A digital computer model of the vectorcardiogram with distance and boundary effects: Simulated myocardial infraction," A. Heart J. 75, pp. 792-808, 1967. [18] D. A. Brody, "The inverse determination of simple generator configurations from equivalent dipole and multipole information." IEEE Trans. Biomed. Eng. BME-15 pp. 106-110, 1968. [19] R. A. Helm, T. CH. Chou, "Computation of a variable location dipole representation from body surface leads." Am. Heart J. 77, pp. 363-366, 1969. [20] J. H. Holt, A. C. L. Barnard, M. S. Lynn, P. Svendsen, "A study of the human heart as a multipole dipole electrical source." Circulation 40, p. 687, 1969. [21] J. Jagielski, J. Mozrzymas, "On the selection rules for the multiple generators of cardiac electric field," Institute of Theoretical Physics University of Wroclaw, Preprint NO 230, 1971. [22] P. Rijlant, "A twenty pole generator equivalent to the heart's generator system," In: Proceeding of the Satellite Symposium of the 25th International Congress of Physiological Sciences (The electrical field of the heart) and the 12th Colloquium Vectorcardiographicum, ed. P. Rijlant, pp. 454-461, Presses Academiques Europeennes, Brussels, 1972. [23] L. I. Titomir, "Integralnyje harakteristiki elektricheskoj volny vozbuzhdenija serdca," In: Biofizika 20, pp. 693-698, 1975 (in Russian). [24] D. Gabor, C. V. Nelson, "Determination of the resultant dipole of the heart from measurements on the body surface," J. Appl. Physics 25, pp. 413-416, 1954. [25] D. B. Geselowitz, "Multipole representation for an equivalent cardiac generator," In: Proc. IRE 48, pp. 75-79, 1960. [26] R. Plonsey, Bioelectric Phenomena, New York, McGraw-Hill, 1969. [27] D. B. Geselowitz, "Two theorems concerning the quadrupole applicable to electrocardiography," In: IEEE Trans. Biomed. Eng. BME-12, pp. 164-168, 1965. [28] R. M. Arthur, D. B. Geselowitz, S. A. Briller, R. F. Trost, "The path of the electrical center of the human heart determined from surface electrocardiograms," In: J. Electrocardiol. 4, pp. 29-33, 1971. [29] D. A. Brody, J. C. Bradshaw, "The equivalent generator components of uniform double layers," In: Bull. Math. Biophys. 24, pp. 183-195, 1962. [30] R. M. Arthur, D. B. Geselowitz, S. A. Briller, R. F. Trost, "Quadrupole components of the human surface electrocardiogram," In: A. Heart J. 83, pp. 663-670, 1972.
P. Kneppo, photograph and biography not available at the time of
publication.
L. I. Titomir, photograph and biography not available at the time of
publication.
