16. Vectorcardiographic Lead Systems
16Vectorcardiographic Lead Systems
16.1 INTRODUCTION
In the first article concerning the human electrocardiogram
published in 1887, Augustus D. Waller pointed out the dipolar nature of the
cardiac electric generator (Waller, 1887; see Figure 1.17). Because it is possible to describe the
electric generator of the heart reasonably accurately with an equivalent dipole,
called the electric heart vector (EHV), it is natural to display it in
vector form. The measurement and display of the electric heart vector is called
vectorcardiography (VCG), or vectorelectrocardiography (VECG) to
separate it from vectormagnetocardiography. Theoretically,
an obvious way to display the behavior of the dipole is with an oscilloscope
that follows the trajectory of the end point of the vector projected on to
principal planes. This display is called spatial vectorcardiography. This
is illustrated in Figure 16.1. The rectangular coordinate system is a natural
selection. These coordinate axes may be either the body axes or the
cardiac axes. One can display
the temporal information (the time scale) by modulating the intensity of the
oscilloscope beam so that the trace is periodically interrupted (possibly at 2
ms intervals). By modulation the oscilloscope intensity with a triangular
waveform, each 2 ms segment has a teardrop shape which indicates the direction
of the trajectory. The signal may
also be displayed by showing the three vector components as functions of time.
This display is called scalar vectorcardiography. This display is not
used very often in vectorcardiography, because it provides no information that
is not in the scalar display of the 12-lead ECG
Fig. 16.1. The basic principle of vectorcardiography
is illustrated based on ideal uniform lead fields which are mutually
orthogonal being set up by parallel electrodes on opposite sides of the torso
(bipolar configuration).
There are both
uncorrected and corrected VCG lead systems. The uncorrected VCG
systems do not consider the distortions caused by the boundary and internal
inhomogeneities of the body. The uncorrected lead systems assume that the
direction of the spatial line connecting an electrode pair yields the
orientation of the corresponding lead vector. Currently it is known that this
assumption is inaccurate, as is discussed later. In any event, these uncorrected
lead systems are no longer in clinical use. The goal of the
corrected lead system is to perform an orthonormal measurement of the
electric heart vector. In an orthonormal measurement both of the following
requirements are fulfilled:
The three measured components of the electric heart vector are
orthogonal and in the direction of the coordinate axes (i.e., the lead
vectors are parallel to the coordinate axes, which are usually the body axes).
Furthermore, each lead field is uniform throughout the heart.
Each of the three components of the electric heart vector are detected
with the same sensitivity; that is, the measurements are normalized.
In the corrected vectorcardiographic lead systems the accuracy of the
orthonormal measurement is limited by the applied theoretical method. The
theoretical methods for analyzing volume sources and volume conductors were
discussed earlier in Chapter 9. Each of them has allowed for a VCG system to be
orthonormal within the limits of the performed correction. These lead systems
are discussed in detail later in this chapter. What is the
clinical importance of vectorcardiography? The answer is that the information
content of the VCG is the same, roughly, as that of the leads V2,
V6 and aVF in the 12-lead system, though it is obtained in
corrected (orthonormal) form. It is true that the information content in the VCG
signal is not greater than in the scalar ECG. However, the display system
provides an opportunity to analyze the progress of the activation front in a
different way, especially its initial and terminal parts. It is also much easier
to observe the direction of the heart vector from the VCG loops. Additionally,
the area of the loops, which is not easy to observe from a scalar display, may
have clinical importance. In this chapter
we introduce representative examples of the large number of uncorrected and
corrected vectorcardiographic lead systems.
16.2 UNCORRECTED VECTORCARDIOGRAPHIC LEAD
SYSTEMS
PRECONDITIONS:SOURCE: Dipole in a fixed
locationCONDUCTOR: Infinite, homogeneous volume conductor or
homogeneous sphere with the dipole in its center (the trivial solution)
16.2.1 Monocardiogram by Mann
Though Waller was the first to record a set of three nearly
orthogonal leads, namely mouth-to-left arm, mouth-to-left leg and back-to-front,
he did not display them in vector form. It was Hubert Mann who in 1920 first
suggested the concept of vectorcardiography by publishing a
monocardiogram, which he constructed manually from the limb leads of
Einthoven, as shown in Figure 1.18 (Mann, 1920). The monocardiogram of
Mann is the projection of the vector loop in the frontal plane, assuming the
validity of the Einthoven triangle lead vectors which it uses to interpret the
limb lead voltages. Therefore, it is only two-dimensional, and it excludes the
back-to-front information from the sagittal and transverse planes. (Note that
Mann placed the signals of the leads I, II, and III to the lead vectors in
opposite polarity. Therefore, the vector loop is oriented upward and right,
though it actually should be oriented downward and left.) Mann also
constructed a special mirror galvanometer that allowed the display of the
monocardiogram directly from ECG signals; see Figure 16.2 (Mann, 1938a). This
mirror galvanometer included three coils arranged in one plane and located
symmetrically in 120° intervals around a mirror. They were situated in a
constant magnetic field produced by a large coil. When the three coils were
driven by amplified ECG signals from leads I, II, and III, the net torque of
this coil assembly produced a deflection of the mirror, and a ray of light it
reflected, proportional to the electric heart vector. Thus Mann's mirror
galvanometer was actually an analog computer calculating the monocardiogram from
the three limb leads. The work of Mann was largely ignored for more than 15
years. It had to await the invention of the cathode ray tube in the 1930s when
it was possible to apply electronic devices to display the projections of the
vector loop (Mann, 1931, 1938b). An interesting
invention in the vectorcardiography instrumentation was the cathode ray tube of
W. Hollman and H. F. Hollman (1939). They used three pairs of deflection plates
arranged at 60° angles with respect to one another corresponding to the
directions of the three edges of the Einthoven triangle (see Figure 16.3). When
these deflection plates were driven with amplified leads I, II, and III, the
tube produced on the screen a monocardiogram similar to Mann's mirror
galvanometer on a film.
Fig. 16.2 The mirror vectorcardiograph constructed by
Hubert Mann was the first instrument to produce a vectorcardiogram. It has
three coils symmetrically placed at 120° intervals around a mirror. Thus it
produces a vectorcardiogram in the frontal plane from the three limb leads of
Einthoven. (Mann, 1938a).
Fig. 16.3 The cathode ray tube of W. Hollman and H. F. Hollman has
three pairs of deflection plates oriented in the directions of the edges of
the Einthoven triangle. Thus it produces the vectorcardiogram in the frontal
plane from the Einthoven limb leads. (Hollman and Hollman, 1937)
16.2.2 Lead Systems Based on Rectangular Body Axes
Most of the uncorrected and corrected vectorcardiographic lead
systems are based on the rectangular body axes. From the large number of such
uncorrected VCG lead systems, we briefly mention the following ones in this
section. After inventing the central terminal in 1932, Frank Norman Wilson
logically progressed to the development of a lead system for vectorcardiography.
Wilson and his co-workers published a lead system that added to the Einthoven
limb leads an electrode located on the back (about 2.5 cm to the left from the
seventh dorsal vertebra) (Wilson and Johnston, 1938, Wilson, Johnston, and
Kossmann 1947). The four electrodes formed the corners of a tetrahedron, as
shown in Figure 16.4, and consequently permitted the back-to-front component of
the heart vector to be recognized. The three components of the electric heart
vector were measured as follows (expressed in the consistent coordinate system
described in the Appendix): The x-component was measured between the
electrode on the back and the Wilson central terminal. The y-component
was lead I, and the z-component was lead -VF. This lead
system, called the Wilson tetrahedron, was the first to display the three
components of the electric heart vector. The lead system
of F. Schellong, S. Heller, and G. Schwingel (1937) is two-dimensional,
presenting the vector loop only in the frontal plane. The other lead systems -
those of Noboru Kimura (1939), Pierre Duchosal and R. Sulzer (1949), A. Grishman
and L. Scherlis (1952), and William Milnor, S. Talbot, and E. Newman (1953) -
also include the third dimension. These lead systems are illustrated in Figure
16.5. Because of their geometry, the lead system of Grishman and Scherlis was
called the "Grishman cube" and the lead system of Duchosal and Schultzer the
"double cube.".
Fig. 16.4 The electrodes of the Wilson tetrahedron lead system.
Fig. 16.5 Uncorrected VCG lead systems based on rectangular body
axes.
16.2.3 Akulinichev VCG Lead Systems
Ivan T. Akulinichev developed two uncorrected VCG-lead systems,
one applying five display planes (Akulinichev, 1956) and another one applying
three planes (Akulinichev, 1960). In the five-plane system, which he proposed in
1951, the electrodes are located in the corners of a pyramid so that four
electrodes are on the anterior side of the thorax and the fifth is on the back,
left from the spine on the level of the inferior angle of the scapula. In the
five-plane Akulinichev system projection I is the frontal plane. The other four
projections have different posterior views (Figure 16.6A). Projection II
examines the left ventricle in a left-superior-posterior view. Projections III
and IV are right-inferior-posterior and left-inferior-posterior views,
respectively. Projection V examines the atria in a right-superior-posterior
view. Note that in the frontal plane the measurement between the electrodes 1
and 3 is oriented approximately along the main axis of the heart. The five
projections of the electric heart vector recorded with the Akulinichev system
are shown in Figure 16.6B. Because two projections are necessary and sufficient
for displaying a spatial vector loop, the five-plane Akulinichev system includes
more redundant information than systems with three projections. From the
five-plane VCG system, Akulinichev developed later the three-plane VCG system
(Akulinichev, 1960; Pawlov, 1966; Wenger, 1969). A characteristic of this lead
system is that the main coordinate axes of the system are oriented along the
main axes of the heart. The exact locations of the electrodes are (see Figure
16.7) as follows: 1 = right arm, 2 = left arm, 4 = V2, 5 =
V5, 6 = on the right side of xiphoid, 7 = V9 (on the
posterior surface of the thorax, at the left side of the spine on the level of
V4 and V5). The three projections are formed as follows:
projection I = electrodes 1, 2, 5, and 6 (i.e., the frontal plane); projection
II = electrodes 1, 7, 5, and 4 (i.e., parallel to the longitudinal axis of the
heart); projection III = electrodes 6, 7, 2, and 4 (i.e., the cross-sectional
plane of the heart). The Akulinichev
lead systems have been applied in the (former) Soviet Union and Bulgaria since
the 1960s and they are virtually the only clinical vectorcardiographic systems
used there to date.
Fig. 16.6 Five-plane Akulinichev VCG system. (A) Location
of the electrodes on the thorax and their five connections to the
oscilloscope. (B) The five projections of the electric heart vector.
Fig. 16.7 Three-plane Akulinichev VCG system.
16.3 CORRECTED VECTORCARDIOGRAPHIC LEAD
SYSTEMS
16.3.1 Frank Lead System
PRECONDITIONS:SOURCE: Dipole in a fixed
locationCONDUCTOR: Finite, homogeneous
In 1956 Ernest Frank (Frank, 1956) published a
vectorcardiographic lead system that was based on his previously published data
of image surface (Frank, 1954). Because the image surface was measured for a
finite, homogeneous thorax model, the volume conductor model for the Frank
VCG-lead system was also the same. In the following, we first discuss the design
principles of the Frank lead system. Then we discuss the construction of each
orthogonal component of the measurement system. Though we refer here to the
original publication of Frank, we use the consistent coordinate system described
in the Appendix.
Electrode Location Requirements
To measure the three dipole components, at least four
electrodes (one being a reference) are needed. Frank decided to increase the
number of electrodes to seven, in order to decrease the error due to
interindividual variation in the heart location and body shape. It is important
that the electrode location can be easily found to increase the reproducibility
of the measurement. The reproducibility of the limb electrodes is very good.
However, the arm electrodes have the problem that the lead fields change
remarkably if the patient touches the sides with the arms, because the electric
current flows through the wet skin directly to the thorax. This problem has a
special importance to the left arm, since the heart is closer.
Determination of the Electrode Location
Based on the above requirements Frank devised a lead system,
now bearing his name, which yields corrected orthogonal leads. Electrode numbers
and positions were chosen very deliberately, and were based upon his image
surface model (Figure 11.14). He selected level 6 for electrode placement,
because the lead vectors are largest on this level. Specifically, he chose the
points designated A, E, I, and M on the left, front, right, and back,
respectively. He also chose point C between points A and E because it is close
to the heart. In addition, a point on the neck and one on the left foot were
included.
Right-to-Left Component (y-Component)
We begin with the right-to-left component (y-component)
because its construction is the simplest and easy to understand. The lead vector
in this direction is determined by applying previously mentioned methods to
Figure 16.8. This figure shows the anatomic view of level 6 as well as its image
surface as measured by Frank. The image space locations of electrodes A, C, and
I are also shown since these were chosen to sense the y-component of the
heart vector. The basic principle in the design of the y-component of the lead
system is to synthesize in image space, with the available electrode points, a
lead vector that is oriented in the y-direction. This is the only requirement
that must be fulfilled for the lead to record the y-component. Additionally,
it is advantageous to select from among all those lead vectors that are in the
y-direction the one that is the largest. This ensures a signal-to-noise ratio
that is as high as possible. If we designate
image space point I' as one end point of the selected lead vector parallel to
the y-axis, its other end point is found on line A'-C', and is labeled point a'.
Point a' divides A'-C' in the proportion 1:3.59. By connecting two resistors
having values in this ratio between the points A and C in real space, the point
a is realized at their intersection. From a
practical point of view it is important that the impedance the amplifier sees in
each lead be equal. A good balance ensures cancellation of common mode noise
signals. If we designate this impedance as R, we have to add such a resistor to
the lead in electrode I and to multiply the parallel resistors of electrodes A
and C by the factor 1.28. This yields resistor values 1.28R and 4.59R,
respectively. (Note that now the parallel resistance of these two resistors is
R.) From a measurement in image space we determine the length of the lead vector
y to be 174 relative units..
Fig. 16.8 Determination of the right-to-left component
(y-component) in the Frank lead system. The image space shown on the left
corresponds to the actual transverse plane on the right.
Foot-to-Head Component (z-Component)
From the image space in Figure 16.9, we can verify that if we
select for one end of the image vector the point H' on level 1 (i.e., on the
neck), there exists a point k' on line F'-M' such that K'-H' forms a lead vector
parallel to the z-axis. The point k' divides the axis in proportion 1:1.9. Again
the lead is balanced by placing a resistor R in series with electrode H and by
multiplying the resistors in electrodes F and M by a factor 1.53 which leads to
values of 1.53R and 2.90R, respectively. The length of the lead vector z is 136
units.
Back-to-Front Component (x-Component)
In the design of the x-component Frank wanted, in
addition to the previous requirements, to select such a weighing for the
electrodes that the lead vector variation throughout the heart would be as
uniform as possible. Consequently, Frank used all the five electrodes on level
6. The transverse plane projection of the image surface is shown again in Figure
16.10, and electrodes A, C, E, I, and M are described in both real and image
space. Frank drew the lines A'-M', E'-C' and g'-I' in the image space, from
which the point g' was located on the line E'-C'. Between the lines A'-M' and
g'-I' he drew a line segment f'-h' parallel to the x-axis. This is
the lead vector corresponding to the x-lead and fully meets the
requirements discussed above. The physical
realization of the lead that corresponds to the chosen lead vector is found as
follows: From the image space, it is possible to ascertain that the point f'
divides the segment of line A'-M' in the proportion 5.56:1. Multiplying these
with 1.18, we obtain values 6.56:1.18 having a parallel resistance value of 1.
By connecting two resistors of similar proportions in series, between the
electrodes A and M, we find that their point of connection in real space is f.
Similarly the point g' divides the image space segment of line C'-E' in
the proportion 1.61:1. The parallel value of these is 0.62. The point h' divides
the segment of line g'-I' in the proportion 1:2.29. If we multiply this by 0.62,
we get 0.62:1.41. Now we have the relative resistor values 1.61, 1, and 1.41 to
electrodes C, E, and I, respectively. To adjust their parallel resistances to be
equal to 1, we multiply each by 2.32 and we obtain 3.74R, 2.32R,
and 3.72R. Now we have synthesized the lead vector x ;
relative to the assumed image space scale, it has a magnitude of 156 units..
Fig. 16.9 Determination of the foot-to-head component
(z-component) in the Frank lead system. The image space shown on the left
corresponds to the actual sagittal plane on the right.
Fig. 16.10 Determination of the back-to-front
component (x-component) in the Frank lead system. The image space shown on the
left corresponds to the actual transverse plane on the right.
Frank Lead Matrix
We have now determined all three lead vectors that form an
orthogonal lead system. This system must still be normalized. Therefore,
resistors 13.3R and 7.15R are connected between the leads of the
x- and y-components to attenuate these signals to the same level
as the z-lead signal. Now the Frank lead system is orthonormal. It should be
noted once again that the resistance of the resistor network connected to each
lead pair is unity. This choice results in a balanced load and increases the
common mode rejection ratio of the system. The absolute value of the lead matrix
resistances may be determined once the value of R is specified. For this
factor Frank recommended that it should be at least 25kW, and preferably 100 kW. Nowadays the lead signals are usually detected with a
high-impedance preamplifier, and the lead matrix function is performed by
operational amplifiers or digitally thereafter. Figure 16.11 illustrates the
complete Frank lead matrix. It is worth
mentioning that the Frank system is presently the most common of all clinical
VCG systems throughout the world. (However, VCG's represent less than 5% of the
electrocardiograms.).
Fig. 16.11 The lead matrix of the Frank VCG-system.
The electrodes are marked I, E, C, A, M, F, and H, and their anatomical
positions are shown. The resistor matrix results in the establishment of
normalized x-, y-, and z-component lead vectors, as described in
the text.
16.3.2 McFee-Parungao Lead System
PRECONDITIONS:SOURCE: Dipole moment of a volume
sourceCONDUCTOR: Finite, homogeneous
McFee and Parungao (1961) published a simple VCG lead system
called the axial system, based on a lead field theoretic approach. In
addition, the heart was modeled with a volume source and the thorax was assumed
to be homogeneous. The three
uniform lead fields were designed according to the principle discussed in
Section 11.6.10. To detect the three orthogonal components of the electric heart
vector, three pairs of (single or multiple) electrodes must be used on each
coordinate axis, one on either side of the heart. McFee and Parungao recognized
that the closer to the heart the electrodes are placed the more electrodes must
be used to achieve a homogeneous lead field within the heart's area.
Back-to-Front Component (x-Component)
McFee and Parungao felt that three anterior electrodes should
be assigned to the measurement of the back-to-front component of the VCG. This
would generate a lead field with sufficient homogeneity even though the heart is
close to the anterior wall of the thorax. They followed the method of
synthesizing ideal lead fields as discussed in Section 11.5.8. By connecting 100
kW resistances to each electrode,
the net lead impedance is 33 kW.
The
accurate location of the chest electrodes is found as follows: The electrodes
form an equilateral triangle so oriented that its base is nearest to the
subject's feet. The electrodes are at a distance of 6 cm from the center of the
triangle. The center of the triangle is in the fifth intercostal space, 2 cm to
the left of the sternal margin. This position should ensure that the chest
electrodes are located directly above the center of gravity of the ventricles.
(This is illustrated in Figure 16.12.) Because the
posterior wall of the thorax is more distant from the heart, only one electrode
is needed there. The back electrode lies directly behind the center of the chest
triangle. McFee and Parungao did not balance the lead system against common mode
noise. The authors suggest that if a 33 kW resistor were connected to the back electrode, the
balancing requirement, discussed earlier, would be fulfilled.
Right-to-Left Component (y-component)
For the y-component the same procedure as described
above was followed. McFee and Parungao placed two electrodes with 66 kW resistances on the left side and one
electrode on the right side of the thorax. The right electrode is located on the
same level as the center of the electrode triangle on the chest. It is placed on
the right side, one third of the way from the chest to the back. The electrodes
on the left side are also located one third of the way toward the back at
longitudinal levels 5.5 cm over and below the level of the center of the chest
triangle. The electrode spacing is therefore 11 cm. These produce reasonably
uniform right-to-left lead fields in the region of the heart. McFee and
Parungao did not balance the y-lead either. The authors suggest that
adding a 33 kW resistor to the
electrode on the right balances the lead against common mode noise.
Foot-to-Head Component (z-Component)
The electrodes designed to measure the z-component of
the VCG are so distant from the heart that McFee and Parungao used only one
electrode on the neck and one on the left foot. These electrodes may be equipped
with a 33 kW resistor for the
whole lead system to be balanced. The complete McFee-Parungao VCG lead system is
shown in Figure 16.12.
Fig. 16.12 McFee-Parungao VCG lead system.
16.3.3 SVEC III Lead System
PRECONDITIONS:SOURCE: Dipole moment of a volume
sourceCONDUCTOR: Finite, homogeneous
Otto H. Schmitt and Ernst Simonson developed many versions of
vectorcardiographic lead systems, calling them
stereovectorelectrocardiography (SVEC). The third version, SVEC III, was
published in 1955 (Schmitt and Simonson, 1955). It requires a total of 14
electrodes and creates a lead field in the thorax which is very symmetric in
relation to the sagittal plane. The lead system is described in Figure 16.13.
In the
SVEC III lead system, the electrodes are located on the thorax in the following
way: The torso is divided angularly into 30° symmetric sectors about a central
vertical axis so that, starting with 1 at the front, Arabic numerals up to 12
divide the torso vertically. Roman numerals refer to interspaces at the sternum
and are carried around horizontally on a flat panel so that a grid is
established on which a location such as V 7 would mean a location at the
vertical level of the fifth interspace and at the middle of the back.
Back-to-Front Component (x-Component)
The back-to-front component, the x-component, is formed
from four electrodes on the back and four electrodes on the chest. The back
electrodes are located at the grid points III 6, III 8, VI 6, and VI 8. Each of
these electrodes is connected with a 100 kW resistor to the common back terminal (-X). The
chest electrodes are located at grid points III 12, III 2, VI 2, and VI 12. A 70
kW resistor is connected from the
first one (III 12), and 100 kW
resistors are connected from the others to the common chest terminal
(+X).
Right-to-Left Component (y-Component)
The right terminal (-Y) is obtained by connecting 100
kW resistors to the right arm and
to the grid point V 11. The left terminal (+Y) is formed similarly by
connecting 100 k resistors to the left arm and to the grid point V 3. To
normalize the lead, the gain is adjusted to the 75% level.
Foot-to-Head Component (z-Component)
The z-component is obtained simply by placing electrodes
to the left foot and to the head. Again, to normalize the lead, the gain is
adjusted to the 71% level.
Fig. 16.13 SVEC III VCG lead system.
16.3.4 Fischmann-Barber-Weiss Lead System
PRECONDITIONS:SOURCE: Dipole moment of a volume source
with moving (optimal) locationCONDUCTOR: Finite, homogeneous
E. J. Fischmann, M. R. Barber, and G. H. Weiss (1971)
constructed a VCG lead system that measures the equivalent electric dipole
according to the Gabor-Nelson theorem. Their equipment
consisted of a matrix of 7 × 8 electrodes on the back of the patient and 11 × 12
on the chest. The latter were fixed on rods that could move along their axes.
Similar electrode matrices with 7 × 7 electrodes were also placed on the sides
of the patient. When the moving-rod electrodes are pressed against the surface
of the thorax, their movement gives information about the thorax shape. This
information is needed in the solution of the Gabor-Nelson equation. This lead
system was not intended for clinical use but rather for the demonstration of the
Gabor-Nelson theory in the measurement of the vectorcardiogram.
16.3.5 Nelson Lead System
PRECONDITIONS:SOURCE: Dipole moment of a volume source
with moving (optimal) locationCONDUCTOR: Finite, homogeneous
In 1971 Clifford V. Nelson and his collaborators published a
lead system suitable for clinical use based on the Gabor-Nelson theorem (Nelson
et al., 1971). The lead system includes electrodes placed on three levels of the
thorax with eight on each level, one electrode on the head, and one on the left
leg. The electrode rows are designated A, B, and C, as shown in Figure 16.14.
The levels are determined by measuring the distance H' between the
suprasternal notch and umbilicus. This distance is divided by 8, and the rows
are placed at 1/8 H', 4/8 H', and 7/8 H' from either notch
or umbilicus. As shown in Figure 16.14, electrodes 1 and 5 are placed at center-back
and midsternal line, respectively. Electrodes 2, 3, and 4 are equally spaced on
the right side, and electrodes 6, 7, and 8 are equally spaced on the left side.
If the arms intervene on level C, electrodes 3 and 7 are placed on the right arm
and left arm, respectively. The angle q is the angle between the surface of the thorax and the
frontal plane. Resistors of 500 kW
(R) are connected to the electrodes on rows A, B, and C (see Figure
16.15). From these resistors, on each three levels four (Rx
and Ry) are variable and are adjusted according to the shape
of the thorax of the patient to obey the Gabor-Nelson theory. The adjustment is
made so that
Rx /R = sin q
(16.1)
Ry /R = cos q
where q = the
angle between the surface normal and the sagittal plane
Nelson and
co-workers claim that on the basis of their measurements this VCG lead system is
much more accurate than the McFee or Frank lead systems. Furthermore, this
system should be very insensitive to electrode misplacement.
Fig. 16.14 The electrode locations in the Nelson lead system.
Fig. 16.15 Electrode matrix in the Nelson VCG lead system.
16.4 DISCUSSION ON VECTORCARDIOGRAPHIC LEADS
16.4.1 The Interchangeability of Vectorcardiographic
Systems
The purpose of the vectorcardiographic systems is to detect the
equivalent dipole of the heart. If various systems make this measurement
accurately, the measurement results should be identical. This is, however, not
the case. In practice, each vectorcardiographic system gives a little different
measurement result. There have been
attempts to develop transformation coefficients from one system to another in
order to make the various systems commensurable. If the various systems are
orthogonal, these transformations should, in principle, also be orthogonal.
Horan,
Flowers, and Brody (1965) made a careful study on the transformation
coefficients between Frank, McFee-Parungao (axial-), and SVEC III lead systems
for 35 normal young men. In this study it was found that the transformations
between these lead systems were not orthogonal, indicating that at least two of
the vectorcardiographic systems are not truly orthogonal. They also came to the
conclusion that the practical interchangeability of quantitative information
obtained from one lead system into that obtained by another is seriously limited
because of the wide range of biologic variation in transformation
characteristics.
16.4.2 Properties of Various Vectorcardiographic Lead
Systems
The previously discussed lead systems have been examined using
computer models of the thorax to determine the extent to which they satisfy the
fundamental conditions for corrected orthogonal leads. Under uniform,
homogeneous, and bounded conditions, Brody and Arzbaecher (1964) evaluated the
lead fields for several VCG systems and compared the degree of uniformity. They
found that the Frank, SVEC III, and McFee-Parungao lead systems introduced a
degree of distortion. However, the Grishman cube and Wilson tetrahedron lead
systems were considerably worse. The McFee- Parungao system was found to have
the best orthogonality of all systems, but the strength of the leads was found
to be unequal. Macfarlane (1969) introduced a modification that equalized the
lead strengths. The effect of inhomogeneities on the lead vector field has been
considered by Milan Horá ek (1989). This examination was conducted by a computer
simulation in which the influence of inhomogeneities on the image surface was
evaluated. The effect of the intracavitary blood mass tends to counteract that of
the lungs. The blood mass decreases tangential dipoles and enhances normal
dipoles. The effect of lung conductivity on lead vectors was studied by Stanley,
Pilkington, and Morrow (1986). Using a realistic canine torso model, they showed
that the z (foot-to-head) dipole moment decreased monotonically as the lung
conductivity increased. On the other hand, the y (right-to-left) and
x (back-to-front) dipole moment have a bellshaped behavior, with low
values for both high and low lung conductivities. They found that the lung
conductivity, nevertheless, has relatively little effect on the overall torso
volume conductor properties. The inhomogeneity that, in their study, has a
significant effect is the skeletal muscle layer. These results are reasonably
consistent with those of Gulrajani and Mailloux (1983) and Rudy and Plonsey
(1980). Jari Hyttinen analyzed the properties of Frank, axial, and SVEC III
lead systems with his computer model called the hybrid model (Hyttinen, 1989).
He analyzed the magnitude and the direction of the lead vectors in various
regions of the heart in an inhomogeneous thorax model. He also conducted studies
on the sensitivities of the leads to sources in radial and tangential directions
(in relation to the heart), which has certain clinical implications. In his study of
the ideal VCG lead, Hyttinen found that in all of the studied lead systems, the
lead vectors of the x-leads are directed downward in the upper posterior
part of the heart. The blood masses in and above the heart in the great vessels
are mainly responsible for this behavior of the lead vectors. The x-lead,
which is closest to ideal, is in the axial system. The total sensitivity in the
x-direction is a little lower than that of the SVEC III x-lead,
but the homogeneity of the lead is much better. The locations of the chest
electrodes are good and the proximity effect is weaker in the axial
x-lead compared to the other lead systems. For the
y-leads, the SVEC III y-lead has the best properties. The SVEC III
and the axial y-leads have equal sensitivity in the y-direction,
but the differences in the spatial sensitivity distribution - that is, the
homogeneity of the sensitivity - is better in the SVEC III system. The proximity
effect is not so pronounced because of the use of lead I as a part of the SVEC
III y-lead. In the
z-leads, the inhomogeneities are the main reasons for distortion of the
spatial sensitivity. This can be seen especially in the septal area. The leads
are, however, very similar with the Frank z-lead, having slightly better
spatial sensitivity properties than the other lead systems..
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