title: Effects of valve characteristics on the accuracy of the Bernoulli equation: a survey of data submitted to the U.S. FDA.
abstract: OBJECTIVE
  In 1988, valve manufacturers petitioned the U. S. Food & Drug Administration (FDA) to replace catheter with Doppler ultrasound measurements of pressure gradient (delta P) in clinical studies. Manufactures agreed to submit bench data validating the Bernoulli equation used to calculate delta P = delta P = K(Vd2 - Vp2), where K = constant, Vd = distal Doppler velocity, and Vp = proximal Doppler velocity. Previous studies suggest that K may vary from the idealized 4.0, which could lead to incorrect valve assessment and clinical errors.
  
  
  METHODS
  Variation in K-values in marketing application data submitted to the FDA was assessed. Pulse duplicator data included four bileaflet valves, two stented bioprostheses, and seven stentless bioprostheses, sized from 19 to 33 mm. Effects of valve type, valve size, blood-mimicking fluid used, and distal pressure tap position (DPTP) were evaluated via an analysis of variance.
  
  
  RESULTS
  K-values varied from 2.50 to 7.40 (n = 90). K was found to be dependent on valve type (p < 0.0001), blood-mimicking fluid (p < 0.0001) and DPTP (p < 0.0001), but not valve size. At DPTP = 30 mm, K = 3.43 +/- 0.56, 5.15 +/- 0.81, and 4.81 +/- 1.02, for bileaflet, stented and stentless valves, respectively. K averaged 10% less using the 100-mm DPTP, due to pressure recovery. Variations due to blood-mimicking fluid were likely related to the fluid density.
  
  
  CONCLUSIONS
  Variations due to DPTP and fluid used are consistent with physical mechanisms of pressure recovery and fluid density. Results from previous studies have suggested that effects of valve type on K are also real. The magnitude of these effects appeared to be +/- 25%. Extrapolation to patients is difficult, but clinicians should be aware that Doppler measurements may vary by similar amounts. Doppler pressure gradients should be interpreted qualitatively and moderated by other diagnostic measures of valve performance.
authors.affiliation: Office of Science and Engineering Laboratories, Food and Drug Administration, 9200 Corporate Blvd. (HFZ-132), Rockville, MD 20850, USA. sxs@cdrh.fda.gov
authors.forename: Sandy F
authors.initials: SF
authors.lastname: Stewart
authors.forename: Bruce A
authors.initials: BA
authors.lastname: Herman
authors.forename: Diane M
authors.initials: DM
authors.lastname: Nell
authors.forename: Stephen M
authors.initials: SM
authors.lastname: Retta
mesh_terms: D000704:Analysis of Variance; D001705:Bioprosthesis; D001783:Blood Flow Velocity; D001794:Blood Pressure; D003625:Data Collection; D018795:Device Approval; D015150:Echocardiography, Doppler; D006350:Heart Valve Prosthesis; D006351:Heart Valves / Q000000981:diagnostic imaging / Q000503:physiopathology*; D018056:Hemorheology; D006801:Humans; D008955:Models, Cardiovascular; D008962:Models, Theoretical; D011474:Prosthesis Design; D012039:Regional Blood Flow; D015203:Reproducibility of Results; D014481:United States