Biomedical Engineering Reference
In-Depth Information
Experimental validation studies for inverse imaging solutions can involve animal prepara-
tions, completely synthetic physical materials, or even a combination of the two in order to
simulate the ideal conditions of biopotential sources inside a human body. Because of the
technical challenges of measuring source parameters and geometry from animal models, most
validation studies for inverse problems use synthetic electrical sources embedded in conduct-
ing media as a way to obtain controlled physical models of the source organ and body.
Early modeling of the heart for inverse electrocardiography experiments used a current
bipole to simulate the source because it is a direct equivalent of the single heart dipole vec-
tor that still serves as the basis of much of clinical electrocardiography. A
potentiostat-
galvanostat
is a general-purpose instrument that may be used for controlling either the
potential di
erence between the electrodes of the bipole source (potentiostatic operation)
or the current between them (galvanostatic operation).
Figure 6.31 shows the circuit for a potentiostat-galvanostat. When the potentiostat-
galvanostat switch (SW1) is set for potentiostatic (constant-voltage) operation, the poten-
tial di
ff
er
IC1, where it is compared against the control voltage. Any error existing between these
two potentials will be ampli
ff
erence between the “active” and “reference” electrodes is fed into the error ampli
fi
ow
between the active and reference electrodes. This imposed current will force the potential
di
fi
ed by IC1 and bu
ff
ered by IC2, causing a current to
fl
erence between the electrodes to move in a direction so as to reduce the error between
it and the control voltage. In a very short time (~1 ms) a steady state will be achieved in
which the current is just su
ff
cient to maintain a very small error voltage.
With the potentiostat-galvanostat select switch set for galvanostatic operation, the volt-
age from current-sensing resistor R1 is ampli
er
IC1, where it is compared against the control voltage. As described above, the error
ampli
fi
fed by IC4 and fed into the error ampli
fi
er will amplify any error existing between the two voltages, causing some addi-
tional current to
fi
flow between the electrodes so as to reduce the error voltage. A steady
state is achieved when the error becomes very small. However, in this case it is the current,
not the electrode potential, which is maintained at the desired value.
The control voltage can be dc or ac. With the component values shown in Figure 6.31,
the electrode potential di
fl
erence or electrode current will track the control voltage as long
as the input signal is limited to the range dc to 300 Hz. IC5A and IC6A bu
ff
er the electrode
voltage and current signals from the outputs of IC3 and IC4. These can be monitored
through an oscilloscope to evaluate the dc or ac impedance of the electrodes.
Probably the simplest physical models used to shed light on the inverse problem in elec-
trocardiography were two-dimensional models. Grayzel and Lizzi [1967] used conductive
paper (Teledeltos) to create two-dimensional inhomogeneous models of the human thorax,
to which they attached current source-sink pairs (bipoles) to represent the heart. Teledeltos
paper is a resistive paper that has uniform resistance. As shown in Figure 6.32, Teledeltos
paper can simply be cut, after suitable scaling, to the shape of the body region to be inves-
tigated. Then electrodes are painted on the paper with conductive silver ink so that sources
(voltage and current sources, and sinks or loads) can be attached to the paper at the appro-
priate places to set up an analog of the boundary conditions desired. The extent and value
of inhomogeneities are controlled by means of perforations or silver spots applied to the
conductive paper. The ratio of hole diameter to hole spacing determines the relative
increase in resistivity of the area punched. The ratio of silver-dot diameter to center spac-
ing determines the relative decrease in resistivity.
To
ff
field intensity values by using a sharp-tipped
voltmeter probe applied to the paper at any point that
fi
find solutions, one simply reads out the
fi
field intensity is desired. Thus, a very
simple laboratory setup can be used to solve sets of complicated partial di
fi
ff
erential equa-
tions empirically without the user even knowing what partial di
ff
erential equations he or
she is actually solving!
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