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Frequency analysis of carbon dioxide regulation of the respiratory system relationship between end tidal and sinusoidally varying inspired carbon dioxide

, : Frequency analysis of carbon dioxide regulation of the respiratory system relationship between end tidal and sinusoidally varying inspired carbon dioxide. Japanese Journal of Anesthesiology 34(1): 51-58

A dynamic relationship between endtidal and sinusoidally varying inspired CO2 was analyzed. First, a mathematical relationship of respiratory variables which participate in pulmonary CO2 exchange was derived, taking into account breath-by-breath changes of the respiratory variables. The equation derived was non-linear and it was linearized at the input-driving frequency: (As + B)FA(s) - CFi(s) + DVA(s) = 0 (1) where A, B, C and D are constants. Next, in 13 resting subjects, a frequency-response curve was determined for the approximately linear operating region of the human respiratory control system. A closed-loop transfer function was found adequate to fit the experimental data: FET(s)/Fi(s) = K.cntdot.e-std.cntdot.}(.tau.4s + 1)(.tau.5s+1){/}(.tau.1s+1)(.tau.s+1)(.tau.3s+1){ (2) where K and .tau.1 .apprx. .tau.s are constants and td is the time delay. An open-loop gain for the respiratory control system, calculated from equations (2) and (3), was 3.08 and the time constant and the time delay of the pulmonary element for inspired CO2 were .apprx. 9 s and 4 s, respectively.


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