The principles of pressure drop in long segment stenosis

With Doppler echocardiography, determination of pressure gradients at the region of valvular stenoses with the aid of the modified Bernoulli equation has been shown feasible in clinical and experimental studies. The Bernoulli equation neglects frictional losses and prerequisites laminar flow across the stenosis such that it would not appear applicable for long segment stenoses in the cardiovascular system. To evaluate pressure drop in a long segment stenosis, the full form of the energy balance equation, encompassing frictional losses and localized velocity profile, must be taken into consideration. Frictional losses occur in the region of flow contraction, the stenosis itself and at the expansion area. Assuming a reasonably square edge at the contraction and expansion, losses in these areas, and, employing the Fanning friction factor, losses in the stenosis can be calculated. Investigation of the theoretically-derived frictional loss equation in an in vitro model of a long segment stenosis with various stenosis lengths and diameters showed a good correlation between manometrically determined pressure gradients and those calculated according to the Bernoulli equation and the frictional loss equation. On use of the frictional loss equation, the pressure gradients, however, were only slightly underestimated while those rendered by the Bernoulli equation were clearly underestimated. In vitro data suggest that a long segment stenosis existed when the obstructive length was greater than twice the obstructive diameter for each 10,000 Reynolds numbers.