Use of the Blasius resistance formula to estimate the effective diameter of endotracheal tubes

Abstract

To early detect mucus deposition in endotracheal tubes (ETT), we propose using a geometric, flow-independent parameter, i.e., diameter of the ETT, based on a precise knowledge of ETT flow regime, instead of using the classic flow-dependent ETT resistance based on the empirical, nonlinear Rohrer equation. From the estimated slope of -0.24 derived from Moody diagrams characterizing the pressure-flow relationship in ETT of various inner diameters (D), we first assessed that the Blasius resistance formula slope of -0.25 could be applied to adult-size ETT, meaning that flow remains fully developed, turbulent, and hydraulically smooth (0.5 L/s less than or equal to V less than or equal to 1.4 L/s). Insertion into the ETT of a pressure catheter (external diameter: d) to stimulate in vivo measurements did not modify these results, provided the hydraulic diameter, D* = D - d, was substituted for D in the Blasius formula. The Blasius formula was then used to determine, from in vitro pressure and flow measurements in ETT before intubation and in ETT lined with dry mucus secretions, the effective diameter, shown here to be highly correlated to the actual diameter measured by volumetric water displacement. The effective ETT diameter was measured in eight patients at different stages after oral or nasal intubation. Compared with the actual ETT diameter measured before insertion, the effective diameter was slightly reduced (2.6 +/- 2.5%) during the first week of intubation and was strongly reduced (12.2 +/- 2.8%) during the second week.(ABSTRACT TRUNCATED AT 250 WORDS)