Accurate information about fluid distribution in different compartments of the human body is very important in various areas of medicine like drug dosage, renal replacement therapy, nutritional support, coronary artery disease, colorectal cancer and HIV infection. The body impedance analysis method being simple, inexpensive, accurate and noninvasive is largely used to this end. Several models of the body impedance are presented in this chapter. The first is the Cole model, a linear, first-order RC circuit valid for a frequency range of two decades. Another model, developed by De Lorenzo, employs a fractional-order impedance whose parameters are identified using the frequency characteristics of the impedance module and can be used for a frequency range of three decades. In addition, two other models are presented, a ladder RC model valid for a frequency range of two decades and its extension to three decades, as well as a circuit containing multiple RC branches connected in parallel. These two models are obtained by approximating the measured body admittance modulus with a physically realizable circuit function followed by the circuit synthesis. The last model can be simplified, its simplest form being the Cole model. Allowing a better prediction of the intracellular and extracellular water volumes, this model can be viewed as an extension of the Cole model.
Part of the book: Electrochemical Impedance Spectroscopy
An electrical circuit containing at least one dynamic circuit element (inductor or capacitor) is an example of a dynamic system. The behavior of inductors and capacitors is described using differential equations in terms of voltages and currents. The resulting set of differential equations can be rewritten as state equations in normal form. The eigenvalues of the state matrix can be used to verify the stability of the circuit. The most fitted numerical methods to integrate electrical circuit differential equations are the Euler Method (Forward and Backward), the Trapezoidal Rule, and the Gear Method of second to sixth degree, for circuits having stiff equations. These methods are implemented, with adjustable time-step integration, in the majority of circuit simulation software, such as SPICE. The analytical solution can also be computed, for small-size circuits, applying the Laplace Transform. It is interesting to compare the graphical presentation of numerically and analytically obtained solutions. While the numerical methods can be used for both linear and nonlinear circuits, the Laplace Transform is mostly used for linear circuits. A method of using it for nonlinear circuits is also presented.
Part of the book: Qualitative and Computational Aspects of Dynamical Systems