title: A comparison of valve resistance, the continuity equation, and the Gorlin formula against directly observed orifice area in bioprosthetic valves in the mitral position: an in vitro study.
abstract: OBJECTIVE
  There is no consensus over how to describe forward flow through valves in the mitral position. There are three main candidate hydraulic formulae; resistance, the Gorlin formula and the continuity equation. However, virtually no work has been performed to validate resistance and the continuity equation for valves in the mitral position. The aim of this study, therefore, was to compare the three formulae against an independent standard provided by directly observed orifice areas.
  
  
  METHODS
  Five bioprosthetic valves with orifice areas between 0.14 cm2 and 2.33 cm2 were studied in a pulse simulator at up to 20 different stroke volume/rate combinations using quasi-physiologic flow curves. Orifice areas were measured using a video camera, pressure difference using strain gauge transducers and Doppler signals using a 1.9 MHz Pedoff probe with a Vingmed SD50 system.
  
  
  RESULTS
  The Gorlin ratio (flow/square root of mean delta P) had a direct curvilinear relationship with the orifice area (log(y) = 0.31 + 0.36x; r = 0.94, SEE 0.08 cm2, p < 0.0001). Resistance (mean delta P/flow) had an indirect curvilinear relationship (log(y) = 0.19 - 0.55x, r = -0.93, SEE 0.13 cm2, p < 0.0001). The continuity equation was directly related to observed orifice area although with high scatter (y = 1.13 + 0.79x; r = 0.90, SEE 0.23 cm2, p < 0.0001). Although both the Gorlin ratio and resistance changed with flow, there was also a tendency for observed orifice areas to increase with flow. Empirical effective orifice areas calculated using the regression equations closely resembled observed orifice areas and agreement was reasonable, with 95% limits of -0.33 cm2 to +0.33 cm2 (Gorlin), -0.41 cm2 to +0.42 cm2 (resistance) and -0.40 cm2 to +0.48 cm2 (continuity).
  
  
  CONCLUSIONS
  In conclusion, no single formula adequately predicted all observed orifice areas although resistance and the Gorlin formula gave useful predictions after empirical correction.
authors.affiliation: Department of Cardiology, Guy's Hospital, London, United Kingdom.
authors.forename: J B
authors.initials: JB
authors.lastname: Chambers
authors.forename: Z
authors.initials: Z
authors.lastname: Wang
authors.forename: R A
authors.initials: RA
authors.lastname: Cooke
authors.forename: M M
authors.initials: MM
authors.lastname: Black
mesh_terms: D001705:Bioprosthesis; D001794:Blood Pressure; D015150:Echocardiography, Doppler; D006349:Heart Valve Diseases / Q000503:physiopathology / Q000601:surgery; D006350:Heart Valve Prosthesis; D006801:Humans; D008943:Mitral Valve / Q000503:physiopathology / Q000601:surgery; D008955:Models, Cardiovascular; D011474:Prosthesis Design; D013318:Stroke Volume; D014655:Vascular Resistance