• C E Hahn.
• Nuffield Department of Anaesthetics, Radcliffe Infirmary, University of Oxford, United Kingdom.
• J. Appl. Physiol. 1996 Aug 1; 81 (2): 985-97.

AbstractA sinusoidal forcing function inert-gas-exchange model (C. E. W. Hahn, A. M. S. Black, S. A. Barton, and I. Scott. J. Appl. Physiol. 75: 1863-1876, 1993) is modified by replacing the inspired inert gas with oxygen, which then behaves mathematically in the gas phase as if it were an inert gas. A simple perturbation theory is developed that relates the ratios of the amplitudes of the inspired, end-expired, and mixed-expired oxygen sine-wave oscillations to the airways' dead space volume and lung alveolar volume. These relationships are independent of oxygen consumption, the gas-exchange ratio, and the mean fractional inspired (FIO2) and expired oxygen partial pressures. The model also predicts that blood flow shunt fraction (Qs/QT) is directly related to the oxygen sine-wave amplitude perturbations transmitted to end-expired air and arterial and mixed-venous blood through two simple equations. When the mean FIO2 is sufficiently high for arterial hemoglobin to be fully saturated, oxygen behaves mathematically in the blood like a low-solubility inert gas, and the amplitudes of the arterial and end-expired sine-wave perturbations are directly related to Qs/QT. This relationship is independent of the mean arterial and mixed-venous oxygen partial pressures and is also free from mixed-venous perturbation effects at high forcing frequencies. When arterial blood is not fully saturated, the theory predicts that QS/QT is directly related to the ratio of the amplitudes of the induced-saturation sinusoids in arterial and mixed-venous blood. The model therefore predicts that 1) on-line calculation of airway dead space and end-expired lung volume can be made by the addition of an oxygen sine-wave perturbation component to the mean FIO2; and (2) QS/QT can be measured from the resultant oxygen perturbation sine-wave amplitudes in the expired gas and in arterial and mixed-venous blood and is independent of the mean blood oxygen partial pressure and oxyhemoglobin saturation values. These calculations can be updated at the sine-wave forcing period, typically 2-4 min.

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