Biomedical Engineering Reference
In-Depth Information
90°
60°
120°
aVL
aVR
10
70
150°
30°
x
60
20
180°
I
50
30
+150°
30°
+120°
40 ms
60°
90°
Figure 4.1-5 Locus of the heart vector m given each 10 ms in
the QRS diastole. Derived from the Einthoven triangle ( Fig. 4.1-4 ).
The graph is in the frontal plane and the x-axis has the direction
of the lead vector H 1 ( a ¼ 0).
m
III
II
aVF
Figure 4.1-6 Myocard of left (thick) and right (thin) ventricles,
the Einthoven triangle in the frontal plane. QRS heart vector m,
normal angle values are between -30
and þ90 .
isotropic media proportional and simply related by
equation J ¼ sE. Einthoven did not use the vector
concept nor the dipole concept. He referred to the
direction of maximum potential difference, and this is in
accordance with the Maxwell equation E ¼VF .
The Einthoven triangle gained more and more accep-
tance, but was also heavily criticized. In particular four
aspects have been attacked:
1. Redundancy: Of course u I þ u II þ u III ¼ 0 (Kirchhoff's
law) in a linear system. Because the two input wires of
the amplifier of lead II are swapped, lead II has
changed sign so that: u III ¼ u II - u I . Theoretically
a third lead contains no new information, in practice
however, it represents quality control and eases rapid
waveform interpretations.
2. It is not a great surprise that an equivalent to
the electrical activity of the whole myocard, the
transmission from the sources to the different lead
electrodes included, can not be modeled as one
bound dipole vector alone. The surprise is that the
accordance is so good. Refinements can only include
expansion with spherical harmonic multipoles
such as a quadrupole, not with moving dipoles,
electromotive surfaces or multiple dipoles.
3. Lack of 3D data: The Einthoven triangle is flat as if all
electrical activities in the heart occur in a thin vertical
sheet. An additional back electrode would, for
instance, represent a first primitive approach to
a lead perpendicular to the classical Einthoven
triangle.
4. The triangle is actually based on a model with two
ideal dipoles. This presumption is broken because (1)
the distance between the dipoles is not very much
longer than the dipole lengths; (2) the medium is not
infinite and homogeneous.
Torso models were built filled with electrolytes and
with an artificial heart in the natural heart position. Burger
and Milan in 1946 used two copper plates 2 cm in di-
ameter and 2 cmapart with twowires supplying current as
an artificial heart. The dipole concept was not used but the
lead vector and an oblique triangle instead of the equi-
lateral Einthoven triangle. The direction of the heart
vector was defined as the direction in which a heart
propagates the current flow; the dimension was given as
[Vcm 2 ]. It is still easy tomix the dimensions, in Figs. 4.1-2
and 4.1-4 it is easy to believe that the heart vector is some
strange voltage vector created by projections of the lead
voltages. But the heart vector is a dipole vector according
to m ¼ i L cc [Am]. The direction of the vector is the
electrical axis of the heart, and this is clinically used. The
split components of m: the dipole current i and the dis-
tance vector L cc are not used clinically.
Table 4.1-1 shows time intervals and heart vector axis
is shown in Fig. 4.1-6
4.1.1.2 Six chest electrodes
(six unipolar precordial leads)
A larger signal with higher information content is
obtained by placing surface electrodes as near to the
Table 4.1-1 Normal values of time intervals and direction of the
heart vector
Normal values
-30 < QRS axis
< þ90
0.12 seconds <
PQ < 0.25
QRS < 0.12 seconds
seconds
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