Models, Descriptive and Explanatory

We will see in Section 9.2.3 that, when measuring on a parallel circuit with controlled voltage, the real part of the resulting current will he proportional to the conductance and the imaginary part will he proportional to the susceptance. And furthermore, that if the physical reality is a series circuit, this simple proportionality will he absent, and the values must be mathematically calculated in each case. The same proportionality is also present for controlled current measurements on a series circuit. Values for conductance and susceptance of the skin are thus always related to an opinion on whether these phenomena electrically exist in series or parallel. 

The problem when trying to make an electrical model of the physical or chemical processes in tissue is often that it is not possible to mimic the electrical behavior with ordinary lumped, physically realisable components such as resistors (R), capacitors (C), inductors, semiconductor components, and batteries. Let us mention three examples 1) The constant phase element (CPE), not realizable with a finite number of ideal resistors and capacitors. 2) The double layer in the electrolyte in contact with a metal surface. Such a layer has capacitive properties, but perhaps with a capacitance that is voltage or frequency dependent. 3) Diffusion-controlled processes (see Section 2.4). Distributed components such as a CPE can be considered composed of an infinite number of lumped components, even if the mathematical expression for a CPE is simple. 

In this section, we will use electrical models for human skin as examples in a general discussion on the use of electrical models. An electrical model of the skin with only two components will obviously not be able to simulate the frequency response measured on skin—it is certainly too simple compared with the complex anatomy of human skin. 

We suggest three solutions to this problem, which would result in the following archetypes  

Model 1 (explanatory)-. One solution is to make a complete distinction between the different structures of the skin and hence make an electrical model as complex as the skin itself. Lipid membranes would then typically be replaced by capacitors, electrolytes by resistors, and semipermeable membranes by voltage sources. The model will, without compromise on the cellular level, aim to reflect the electrical properties of the various microanatomical structures. 

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