title: Beyond Bernoulli: Improving the Accuracy and Precision of Noninvasive Estimation of Peak Pressure Drops.
abstract: BACKGROUND
  Transvalvular peak pressure drops are routinely assessed noninvasively by echocardiography using the Bernoulli principle. However, the Bernoulli principle relies on several approximations that may not be appropriate, including that the majority of the pressure drop is because of the spatial acceleration of the blood flow, and the ejection jet is a single streamline (single peak velocity value).
  
  
  RESULTS
  We assessed the accuracy of the Bernoulli principle to estimate the peak pressure drop at the aortic valve using 3-dimensional cardiovascular magnetic resonance flow data in 32 subjects. Reference pressure drops were computed from the flow field, accounting for the principles of physics (ie, the Navier-Stokes equations). Analysis of the pressure components confirmed that the spatial acceleration of the blood jet through the valve is most significant (accounting for 99% of the total drop in stenotic subjects). However, the Bernoulli formulation demonstrated a consistent overestimation of the transvalvular pressure (average of 54%, range 5%-136%) resulting from the use of a single peak velocity value, which neglects the velocity distribution across the aortic valve plane. This assumption was a source of uncontrolled variability.
  
  
  CONCLUSIONS
  The application of the Bernoulli formulation results in a clinically significant overestimation of peak pressure drops because of approximation of blood flow as a single streamline. A corrected formulation that accounts for the cross-sectional profile of the blood flow is proposed and adapted to both cardiovascular magnetic resonance and echocardiographic data.
authors.affiliation: From the King's College London, Division of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, The Rayne Institute, United Kingdom (F.D., N.P.S., D.A.N., P.L.); Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, United Kingdom (S.M., M.M.B., S.N.); University of Auckland, New Zealand (N.P.S.); and Department of Non Invasive Cardiology, King's College Hospital, London, United Kingdom (M.J.M.).
authors.forename: Fabrizio
authors.initials: F
authors.lastname: Donati
authors.affiliation: From the King's College London, Division of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, The Rayne Institute, United Kingdom (F.D., N.P.S., D.A.N., P.L.); Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, United Kingdom (S.M., M.M.B., S.N.); University of Auckland, New Zealand (N.P.S.); and Department of Non Invasive Cardiology, King's College Hospital, London, United Kingdom (M.J.M.).
authors.forename: Saul
authors.initials: S
authors.lastname: Myerson
authors.affiliation: From the King's College London, Division of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, The Rayne Institute, United Kingdom (F.D., N.P.S., D.A.N., P.L.); Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, United Kingdom (S.M., M.M.B., S.N.); University of Auckland, New Zealand (N.P.S.); and Department of Non Invasive Cardiology, King's College Hospital, London, United Kingdom (M.J.M.).
authors.forename: Malenka M
authors.initials: MM
authors.lastname: Bissell
authors.affiliation: From the King's College London, Division of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, The Rayne Institute, United Kingdom (F.D., N.P.S., D.A.N., P.L.); Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, United Kingdom (S.M., M.M.B., S.N.); University of Auckland, New Zealand (N.P.S.); and Department of Non Invasive Cardiology, King's College Hospital, London, United Kingdom (M.J.M.).
authors.forename: Nicolas P
authors.initials: NP
authors.lastname: Smith
authors.affiliation: From the King's College London, Division of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, The Rayne Institute, United Kingdom (F.D., N.P.S., D.A.N., P.L.); Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, United Kingdom (S.M., M.M.B., S.N.); University of Auckland, New Zealand (N.P.S.); and Department of Non Invasive Cardiology, King's College Hospital, London, United Kingdom (M.J.M.).
authors.forename: Stefan
authors.initials: S
authors.lastname: Neubauer
authors.affiliation: From the King's College London, Division of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, The Rayne Institute, United Kingdom (F.D., N.P.S., D.A.N., P.L.); Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, United Kingdom (S.M., M.M.B., S.N.); University of Auckland, New Zealand (N.P.S.); and Department of Non Invasive Cardiology, King's College Hospital, London, United Kingdom (M.J.M.).
authors.forename: Mark J
authors.initials: MJ
authors.lastname: Monaghan
authors.affiliation: From the King's College London, Division of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, The Rayne Institute, United Kingdom (F.D., N.P.S., D.A.N., P.L.); Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, United Kingdom (S.M., M.M.B., S.N.); University of Auckland, New Zealand (N.P.S.); and Department of Non Invasive Cardiology, King's College Hospital, London, United Kingdom (M.J.M.).
authors.forename: David A
authors.initials: DA
authors.lastname: Nordsletten
authors.affiliation: From the King's College London, Division of Biomedical Engineering and Imaging Sciences, St. Thomas' Hospital, The Rayne Institute, United Kingdom (F.D., N.P.S., D.A.N., P.L.); Division of Cardiovascular Medicine, Radcliffe Department of Medicine, University of Oxford, United Kingdom (S.M., M.M.B., S.N.); University of Auckland, New Zealand (N.P.S.); and Department of Non Invasive Cardiology, King's College Hospital, London, United Kingdom (M.J.M.). Pablo.Lamata@kcl.ac.uk.
authors.forename: Pablo
authors.initials: P
authors.lastname: Lamata
mesh_terms: D000293:Adolescent; D000328:Adult; D001021:Aortic Valve / Q000002:abnormalities* / Q000000981:diagnostic imaging* / Q000503:physiopathology; D001024:Aortic Valve Stenosis / Q000000981:diagnostic imaging* / Q000209:etiology / Q000503:physiopathology; D000082882:Bicuspid Aortic Valve Disease; D001783:Blood Flow Velocity; D001794:Blood Pressure; D015150:Echocardiography, Doppler; D005260:Female; D006349:Heart Valve Diseases / Q000150:complications / Q000000981:diagnostic imaging* / Q000503:physiopathology; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008297:Male; D008875:Middle Aged; D008955:Models, Cardiovascular; D011237:Predictive Value of Tests; D012039:Regional Blood Flow; D015203:Reproducibility of Results; D055815:Young Adult
keywords: Bernoulli principle; biomarker; blood pressure; hemodynamics; stenosis; valve