Use of Fourier Series for the Analysis of Biological Systems

In an attempt to quantitate the physical behavior of biological systems, Fourier analysis has been applied to the respiratory and circulatory systems by a number of investigators. The validity of this application has been questioned on the basis that these systems are nonlinear and not strictly periodic. If these objections were valid much of the more recent work in this field would have to be re-evaluated. The applicability of Fourier analysis to these two systems was therefore investigated, both theoretically and experimentally, using on-line analysis on a LINC (laboratory instrument computer) digital computer. In normal anesthetized dogs errors introduced by deviations from periodicity and linearity were found to be within the range of measurement errors. In sinusoidally perfused aortas the amount of second harmonic produced by the vessel was less than 5%. In addition, the magnitude of errors due to faulty determination of cycle length, sampling techniques, aliasing, and A-D (analogue to digital) conversion were evaluated and found to be within the noise level of the measuring equipment when appropriate techniques were employed. Utmost care has to be used in the coupling between a transducer and the system to be measured, and dynamic calibration before each experiment is a prerequisite for successful analysis. With presently available equipment the static measurement errors can be reduced to +/-0.2 cm H(2)O for pressure transducers, 0.1 cm(3)/sec for electromagnetic flowmeters, and 5 x 10(-4) cm for measurement of radius changes. The frequency response of this equipment once properly coupled to the system is flat to at least 20 cycle/sec.