Mathematical Determination of Inspiratory Upper Airway Resistance Using a Polynomial Equation

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Abstract
We have previously shown that the pressure-flow relationship of the upper airway during nonrapid eye movement sleep can be characterized by a polynomial equation: F(P) = AP 3 + BP 2 + CP + D. On the basis of fluid mechanic principles, we hypothesized that we could objectively calculate upper airway resistance (RUA) using the polynomial equation. We manually measured RUA (mRUA) from the first linear portion of a pressure-flow loop in 544 breaths from 20 subjects and compared the mRUA to the RUA calculated from the polynomial equation (cRUA). Bland-Altman analysis showed that the mean difference between mRUA and cRUA was 0.0 cm H2O/L/s (95% CI, 0.1 to 0.1 cm H2O/L/s) with an upper limit of agreement of 2.0 cm H2O/L/s (95% CI, 1.9 to 2.1 cm H2O/L/s) and a lower limit of agreement −2.0 cm H2O/L/s (95% CI, −2.1 to −1.9 cm H2O/L/s). Additional Bland-Altman analyses showed that the agreement between the two measures was excellent for both inspiratory flow-limited and non-flow-limited breaths. We conclude that RUA can be measured in a simple, objective, and reproducible fashion from a polynomial function that characterizes the upper airway pressure-flow relationship.