Mathematical Determination of Inspiratory Upper Airway Resistance Using a Polynomial Equation

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 (R_UA) using the polynomial equation. We manually measured RUA (mR_UA) from the first linear portion of a pressure-flow loop in 544 breaths from 20 subjects and compared the mRUA to the R_UA calculated from the polynomial equation (cRUA). Bland-Altman analysis showed that the mean difference between mR_UA 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 R_UA can be measured in a simple, objective, and reproducible fashion from a polynomial function that characterizes the upper airway pressure-flow relationship.

KEYWORDS

Upper airway resistance - pressure-flow relationship - polynomial equation

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