Tetrapolar electrode system

FIGURE 10.11 Volume sensitivity field of a biomaterial with a tetrapolar electrode system with two CC electrodes and two PU electrodes. Two homogeneous biomaterial regions, the vertical slice has 5 times the resistivity of the surrounding medium. 

Swapping the PU and CC pairs does not change the transfer impedance as long as the system is electrically linear (reciprocity). This is valid for both tripolar and tetrapolar electrode systems. 

Figure 10.12 shows a dynamic system in a vessel where, for example, a hlood holus volume on its passage leads to a temporal local volume increase during heart systole. The measured zone in the inner cylinder is filled with blood (inflow phase). Later, during the diastole, the blood is transported further (outflow phase), but also returned via the venous system. Figure 10.12 shows a tetrapolar electrode system for the measurement of G. 

In general a tetrapolar system is preferable it may then be somewhat easier to conflne the measured tissue volume to the zone of volume increase. The sensitivity for bolus detection with a tetrapolar electrode system will be dependent on the bolus lengfli wifli respect to the measured length. 

To analyze the situation with a tetrapolar electrode system in contact with, for example, a human body, we must leave our simplified models and turn to lead field theory (see Section 6.4). The total measured transfer impedance measured is the ratio of recorded voltage to injected current according to Eq. 6.39. The impedance is the sum of the impedance contributions from each small volume dv in the measured volume. In each small volume, the resistance contribution is the resistivity multiplied by the vector dot product of the space vectors (the local current density from a unit reciprocal current applied to the recording electrodes) and (the local current density from a unit current applied to the true current carrying electrodes). With disk-formed surface electrodes, the constrictional resistance increase from the proximal zone of the electrodes may reduce sensitivity considerably. A prerequisite for two-electrode methods is therefore large band electrodes with minimal current constriction. 

Figure 10.12 Tetrapolar electrode system and the effect of a bolus of blood passing the...

One of the first to introduce the method was Thomasset (1965), using a two-electrode method and 1 kHz signal frequency. With just two electrodes, it is important to use large-area band electrodes to reduce the contribution from the current constrictional zones near the electrodes. With a tetrapolar electrode system, it is easier to select the preferred... 

Note that sensitivity is not dependent on voxel resistivity. These equations demonstrate the reciprocal nature of tetrapolar systems (or any other electrode system where this theory applies) under linear conditions, the CC electrodes and PU electrodes can be interchanged without any change in measured values. 

The four-electrode tetrapolar system of Figure 10.10 is very different from the two-electrode mono-and bipolar systems (Grimnes and Martinsen 2007). It measures transfer impedance because the potential is recorded at a separate PU port and not at the CC port. If the two ports are far apart, no signal will be transferred from the CC to the PU port and the transfer impedance will be virtually 0 2. 

Figure 6.22 Illustration showing current paths and sensitivity in a simulation of a tetrapolar impedance measurement system. Four electrodes on top of the model and a spherical object in the center of the model below the electrodes (a) Current paths for the two current-carrying electrodes are the dark lines to the left, and the current paths for the reciprocal currents are the gray to the right, (b) Sensitivity distribution in a slice through the model in the same level as a spherical object inside the model. The darkest regions indicate negative sensitivity. Courte of Fred Johan...

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