When should doppler-determined valve area be better than the Gorlin formula?: Variation in hydraulic constants in low flow states

Abstract

In low flow states, underestimation errors occur when the Gorlin formula is used to calculate valve area. A model of valvular stenosis designed to examine changes in the hydraulic discharge coefficient (Cd) and coefficient of orifice contraction (Cc) may explain these errors. Unsteady flow was examined in a pulsatile pump model and in a dog model. Valve areas were calculated from pressure and flow data using: a modified form of the Gorlin formula (assuming constant values for Cd and Cc) and a corrected formula (with values of Cd and Cc obtained from steady state data). Valve area was also calculated using the continuity equation with velocity and flow data (constant Cc). Flow velocities were measured using a newly designed ultrasound Doppler catheter capable of resolving flow velocities of up to 5.5 m/s. Both the corrected formula and continuity equation were highly predictive of actual valve area (r = 0.99, slope or M = 0.96 and r = 0.99, M = 1.06, respectively). The modified Gorlin equation was less accurate and tended to underestimate valve areas (r = 0.87, M = 0.83). This underestimation was most notable at low rates of flow (Gorlin: r = 0.94, M = 0.53; continuity: r = 0.93, M = 0.81 and r = 0.94, M = 0.89, respectively) more accurately than the modified Gorlin formula (r = 0.69, M = 0.49). In patients with low cardiac output, hemodynamic formulas, such as the Gorlin formula, which assume a constant value for the hydraulic discharge coefficient (Cd), may be less accurate than formulas using either a corrected value of Cd or Doppler-determined flow velocity and mean systolic flow.