Models with Any Geometry and Conductivity Distribution

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. 

If the system is reciprocal, the swapping of the recording and current carrying electrode pairs shall give the same transfer impedance. It is also possible to have the eleetrode system situated into the volume of interest, for example, as needles or catheters. Sueh volume calculation, for example, of cardiae output, is used in some implantable heart pacemaker designs (see Seetion 10.12.3). 

Conductivity may change as a function of time, for example, caused by flow. The special case of a changing conductivity with a general but constant geometry was analyzed by Geselowitz (1971) who developed an expression for AZ based upon the potential field. Lehr (1972) proposed to use current density instead of potential in the development. Using the nomenclature of our book and putting E = —VO and as J = aE in isotropic media, we have  

Sigman et al. (1937) were the first to report that the resistivity of blood is flow-dependent. They found that the resistivity fell about 7% when the blood velocity was increased from 10 to 40 cm/s. This is an application area for the Geselowitz (1971) equation, a change in measured conductance not related to volume and therefore not plethysmographic. It is a source of error in volume estimations, but not necessarily in flow estimations. 

---