Elementary complex number analysis of lung models

Formulae from the complex number method of network analysis are used by respiratory physiologists with increasing frequency. As yet, however, no elementary derivation of these has been found in physiological journals, the reader usually being referred to electronic texts: the derivations in these texts are not directed to respiratory problems and are generally more involved than required for respiratory purposes. The present presentation of the complex number analysis method is elementary, the necessary grounding in the field of complex numbers being given in an Appendix. The analysis is directed first to a one-compartment lung, then to a simple two-compartment lung (effectively the same method applying also to simple multiple-compartment lungs), and finally an indication is given of the analysis of more complex models that include air-compression effects. By gaining an understanding of the underlying principles the respiratory physiologist will improve the extent and depth of application of this powerful method of analysis. In particular, he will be in a position to analyse the body plethysmographic measurement of the non-uniform lung.