Biomedical Engineering Reference
In-Depth Information
may be unknown, and is not of great concern as long as
the empirical procedure furnishes precise diagnostic re-
sults. All doctors world over are trained according to this
tradition (the interpretation of EEG waveforms is an-
other striking example of such a practice). For special
diagnostic problems the vector cardiograph has some
distinct advantages. For example, the vector display of
the QRS complex has a much better resolution than the
narrow QRS waveform obtained with a standard 12 lead
ECG. Also the vector cardiograph is valuable for training
purposes to obtain a better understanding of the spatial
distribution of the electrical activity of the heart.
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Frequency (Hz)
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4.1.1.6 Forward and inverse problem
0
The purpose of the ECG examination is to find the
electrical properties of the heart by measuring potential
differences on the skin surface. The EMFs of the heart
produce currents in the surrounding tissue. The anatomy
of the thorax and the conductivity distribution de-
termine how the current flow spreads and which po-
tential differences are to be found at the skin surface. It is
generally accepted that the thorax tissue is linear with
the usual endogenous current density/electrical field
amplitudes generated by the heart. The different con-
tributions of different myocard volumes can therefore
simply be added. On the other hand the tissue may be
anisotropic and the transfer impedance is frequency de-
pendent. A rough demonstration of that can be obtained
by measuring the transfer impedance between the arms
and a bipolar skin surface pick-up electrode pair posi-
tioned over the apex and the sternum (
Fig. 4.1-7
). Be-
cause of reciprocity the transfer impedance is the same if
the current is applied to the electrodes on the thorax and
the potential difference between the hands is measured.
From
Fig. 4.1-7
the frequency components of the P and T
waves are not much attenuated, but the frequency
components of the QRS above 50 Hz are attenuated by
a factor of about 10 or more.
To find the electrical properties of the heart is an
inverse
problem, and in principle it is unsolvable, as there
are infinitely many source configurations which may
result in the measured skin potentials.
We therefore start with the forward problem: from
heart models in a conductive medium to surface poten-
tials. Those problems are solvable, but it is difficult to
model the heart and it is difficult to model the signal
transmission from the heart up to the surface. The model
may be an infinite homogeneous volume or a torso filled
with saline or with a heterogeneous conductor mimicking
the conductivity distribution of a thorax.
The most basic electrical model of the heart is a bound
vector with the variable vector moment m
¼ i
L
cc
.
Plonsey (1966) showed that a model with more than one
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Frequency (Hz)
Figure 4.1-7 Transfer impedance between two chest surface
electrodes (apex-sternum) and two electrodes in each of the
hands.
dipole is of no use because it will not be possible from
surface measurements to determine the contribution
from each source. The only refinement is to let the single
bound dipole be extended to a multipole of higher terms
(e.g. with a quadrupole).
The Einthoven triangle was an early solution to the
inverse problem: how to characterize the source from
surface electrode derived data. It is astonishing how the
original Einthoven triangle still is the basis for standard
clinical ECG interpretations all over the world even if
many improvements have been proposed. Actually the
tradition of using a simple theoretical model with an ideal
dipole in an infinite, homogeneous volume conductor is
uninterrupted. The six limb leads have been heavily
attacked for their redundancy. There must be some
reason why they have endured all these attacks and
reached the overwhelming global spread and acceptance
they have today. The large amount of clinical data is one
reason; perhaps the value of these data is based on the
exceptional reproducibility of their lead vectors. The salt
bridge principle assures a well-defined coupling to the
shoulders and symphysis, and the position of the elec-
trodes on the limbs is totally uncritical. The chest elec-
trode positions are critical both for the precordial leads
and the vector cardiographical leads.
4.1.1.7 Technology
Signal amplitude, limb lead II
The
R
voltage amplitude is usually around 1 mV. Am-
plitudes
<
0.5 mV are characterized as ''low voltage''
