Biomedical Engineering Reference
In-Depth Information
I
II
III
aVR
aVL
aVF
Figure 4.1-1 The six limb leads derived from three limb electrodes (both arms and LL). Here 'a' (e.g. in aVR) means augmented.
following relationship between the scalar lead voltages:
u
II
¼ u
I
þ u
III
.
Figure 4.1-2
shows an example of a typical
ECG waveform.
Cabrera sequence. The text box in
Fig. 4.1-3
contains a set
of data extracted from the six ECG lead waveforms.
Einthoven triangle and the lead vector
Einthoven (1913) proposed an equilateral triangle model
with center in the heart center (
Fig. 4.1-4
). Each side of
the triangle corresponded to each of the three bipolar
leads I, II and III. He proposed the heart modeled as
a bound dipole vector (he did not use that expression),
and that a lead voltage was the projection of the heart
vector on a corresponding triangle side (actually a dot
product). He proposed that his model could be used for
determining the heart vector axis. This means that he
saw a solution to the inverse problem: from measured
lead voltages to the heart vector, from measured surface
potentials to source characterization. He regarded the
triangle apexes as corresponding to right and left shoul-
der and the symphysis. The triangle is in the frontal plane
of the patient, and the heart vector has no component
perpendicular to the frontal plane. He considered the
heart vector to be very short.
Burger and Milan (1946) formalized Einthoven's idea
and introduced the concept of the
lead vector
. The lead
vectors H of the I, II and III leads correspond to the sides
of the Einthoven triangle with corners corresponding to
the anatomy: the shoulders and the symphysis. The
measured lead voltage
u
(volt) is a scalar and
u ¼
H$m so
that
u
is the projection of m in the direction of a lead
vector H (
Fig. 4.1-4
). H [
U
/meter] for each lead is
The three unipolar limb leads: aVR, aVL, aVF
In the days of the first publications of Einthoven
1
no am-
plification tube had yet been invented, and the signal from
the electrodes had to drive a galvanometer directly. Later
the
unipolar augmented
leads were invented; they were
called augmented because the signal amplitudes were
higher. A ''reference'' voltage was obtained by summing
the voltage from two of the limb electrodes (
Fig. 4.1-1
).
More important, these vector leads have the interesting
property of interlacing the vector lead angles of I, II and III
(0
,60
and 120
) so that each 30
is covered. This is
shown in
Fig. 4.1-6
, where both an example of the heart
vector m and the six lead directions are shown.
Figure
4.1-3
shows the six limb leads arranged in a so-called
R
R
T
P
T
P
Q
S
Q
S
Figure 4.1-2 ECG waveform lead II. Dashed line is zero voltage
determined by the electronic circuit high-pass filter functioning
so that the negative and positive areas become equal.
1
Willem Einthoven (1860-1927), Dutch physician. Nobel prize laureate in medicine 1924 (on ECG).
