Physiological basis of flow dependence of Gorlin formula valve area in aortic stenosis: analysis using an hydraulic model of pulsatile flow

J Heart Valve Dis. 2000 Nov;9(6):740-51.


Background and aim of the study: The study aim was to clarify the basis of the cardiac output dependence of aortic valve area calculated with the Gorlin formula which has been reported in patients with aortic stenosis. Clinical and experimental studies which have attempted to differentiate between a change in physical orifice area, versus a defect in the Gorlin formula as the cause of cardiac output related variations in Gorlin valve area in aortic stenosis have yielded conflicting results.

Methods: We employed a numerical model of pulsatile flow in which the total instantaneous transvalvular gradient was the sum of the convective and viscous pressure losses and pressure recovery beyond the stenosis. By analogy with other hydraulic devices, viscous losses due to stenosis were modeled by the term KfV(EXP), where V is flow velocity. Kf and EXP were determined for various orifices by adjusting these two parameters to obtain excellent fit between curves of the orifice discharge coefficient based upon the expression KfV(EXP), and empirically measured orifice discharge coefficient curves which have been published in the engineering literature. Mean systolic transvalvular gradient was calculated from the total instantaneous transvalvular gradient values for an assumed jet area, and an assumed systolic time-velocity flow profile. This mean gradient was substituted into the Gorlin equation to find the apparent Gorlin valve area at cardiac outputs varying from 0 to 10 l/min for a range of where V is assumed true areas between 0.5 and 2.0 cm2.

Results: For functional valve areas <1.5 cm2, viscous losses resulted in at most a 10-12% fall in apparent Gorlin valve area when cardiac output was decreased from 5 to 2.5 l/min. In addition, maximum viscous losses did not result in a pressure-flow relationship which was closer to linear than to quadratic. which the

Conclusion: Clinically significant changes in valve area with flow are due to orifice area changes rather than Gorlin formula flow variability. Moreover beyond the Gorlin valve area is preferred over valve 'resistance' for assessing stenosis severity. In low cardiac output states, output should be increased to the normal range before Gorlin valve area is measured.

MeSH terms

  • Aortic Valve / physiopathology*
  • Aortic Valve Stenosis / physiopathology*
  • Blood Flow Velocity
  • Cardiac Output
  • Humans
  • Models, Cardiovascular*
  • Models, Theoretical*
  • Pulsatile Flow
  • Rheology
  • Viscosity