Reliable CFD-based estimation of flow rate in haemodynamics measures.

Physically useful measures in current clinical practice refer often to the blood flow rate, that is related to the mean velocity. However, the direct measurement of the latter is currently not possible using a Doppler velocimetry technique. Therefore, the usual approach to calculate the flow rate with this technique consists in measuring the maximum velocity and in estimating the mean velocity, making the hypothesis of parabolic profile that in realistic situations results in strongly inaccurate estimates. In this paper, we propose a different way for estimating the flow rate regarded as a function of maximum velocity and Womersley number. This relation is obtained by fixing a parametrised representation and by evaluating the parameters by means of a least-square approach working on the numerical results of CFD simulations (about 200). Numerical simulations are carried out by prescribing the flow rate, not the velocity profile. In this way, no bias is implicitly induced in prescribing boundary conditions. Validation tests based on numerical simulations show that the proposed relation improves the flow rate estimation.

[1]  K W Johnston,et al.  Three-dimensional display of calculated velocity profiles for physiological flow waveforms. , 1993, Journal of vascular surgery.

[2]  Fabio Nobile,et al.  Numerical approximation of fluid-structure interaction problems with application to haemodynamics , 2001 .

[3]  R. Wells.  Syndromes of hyperviscosity. , 1970, The New England journal of medicine.

[4]  F. White.  Viscous Fluid Flow , 1974 .

[5]  H. M. Payne,et al.  Validation of A Doppler Guide Wire for Intravascular Measurement of Coronary Artery Flow Velocity , 1992, Circulation.

[6]  R Fumero,et al.  Blood flow through the ductus venosus in human fetus: calculation using Doppler velocimetry and computational findings. , 1998, Ultrasound in medicine & biology.

[7]  Alberto Redaelli,et al.  Doppler derived quantitative flow estimate in coronary artery bypass graft: a computational multiscale model for the evaluation of the current clinical procedure. , 2008, Medical engineering & physics.

[8]  David N. Ku,et al.  Simple calculation of the velocity profiles for pulsatile flow in a blood vessel using mathematica , 2006, Annals of Biomedical Engineering.

[9]  Gianni Pedrizzetti,et al.  Cardiovascular fluid mechanics , 2003 .

[10]  A. Beckett,et al.  AKUFO AND IBARAPA. , 1965, Lancet.

[11]  O. Alfieri,et al.  Flow dynamics of the St Jude Medical Symmetry aortic connector vein graft anastomosis do not contribute to the risk of acute thrombosis. , 2004, The Journal of thoracic and cardiovascular surgery.

[12]  B. Kuban,et al.  Validated computation of physiologic flow in a realistic coronary artery branch. , 1997, Journal of biomechanics.

[13]  D. Altman,et al.  STATISTICAL METHODS FOR ASSESSING AGREEMENT BETWEEN TWO METHODS OF CLINICAL MEASUREMENT , 1986, The Lancet.

[14]  V. Froelicher,et al.  The Response of Healthy Men to Treadmill Exercise , 1977, Circulation.

[15]  S. Savader,et al.  Volumetric evaluation of blood flow in normal renal arteries with a Doppler flow wire: a feasibility study. , 1997, Journal of vascular and interventional radiology : JVIR.

[16]  P. Kaufmann,et al.  In vitro validation of volumetric blood flow measurement using Doppler flow wire. , 2000, Ultrasound in medicine & biology.

[17]  A. Viedma,et al.  Extended Willis circle model to explain clinical observations in periorbital arterial flow. , 1997, Journal of biomechanics.

[18]  Christian Vergara,et al.  An approximate method for solving incompressible Navier–Stokes problems with flow rate conditions , 2007 .

[19]  J D Meindl,et al.  Blood flow measurement using the attenuation-compensated volume flowmeter. , 1979, Ultrasonic imaging.

[20]  L. Brush,et al.  McDonaldʼs Blood Flow in Arteries , 1991 .

[21]  S Tsangaris,et al.  Assessment of coronary stenoses by Doppler wires: a validation study using in vitro modeling and computer simulations. , 1999, Ultrasound in medicine & biology.

[22]  D. Steinman,et al.  The effect of wall distensibility on flow in a two-dimensional end-to-side anastomosis. , 1994, Journal of biomechanical engineering.

[23]  A. Quarteroni,et al.  Numerical Approximation of Partial Differential Equations , 2008 .

[24]  F. Migliavacca,et al.  Computational fluid dynamics simulations in realistic 3-D geometries of the total cavopulmonary anastomosis: the influence of the inferior caval anastomosis. , 2003, Journal of biomechanical engineering.

[25]  C. Vergara,et al.  Flow rate defective boundary conditions in haemodynamics simulations , 2005 .

[26]  M. Olufsen,et al.  Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions , 2000, Annals of Biomedical Engineering.

[27]  J M Bland,et al.  Statistical methods for assessing agreement between two methods of clinical measurement , 1986 .

[28]  C. F. Hottinger,et al.  Blood Flow Measurement Using the Attenuation-Compensated Volume Flowmeter , 1979 .

[29]  J. Womersley,et al.  Velocity profiles of oscillating arterial flow, with some calculations of viscous drag and the Reynolds number , 1955, The Journal of physiology.

[30]  Ian Marshall,et al.  Flow in Elliptical Vessels Calculated for a Physiological Waveform , 2001, Journal of Vascular Research.

[31]  Felix Matthews,et al.  A novel in vivo procedure for volumetric flow measurements. , 2004, Ultrasound in medicine & biology.

[32]  G Pennati,et al.  Computational analysis of the ductus venosus fluid dynamics based on Doppler measurements. , 1996, Ultrasound in Medicine and Biology.

[33]  Rolf Rannacher,et al.  ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER–STOKES EQUATIONS , 1996 .

[34]  A. Redaelli,et al.  The assignment of velocity profiles in finite element simulations of pulsatile flow in arteries. , 1997, Computers in biology and medicine.

[35]  Karl Perktold,et al.  Computational Models of Arterial Flow and Mass Transport , 2003 .

[36]  W. Nichols.  McDonald's Blood Flow in Arteries , 1996 .

[37]  J. Womersley.  Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known , 1955, The Journal of physiology.

[38]  D. Maki,et al.  Hyperviscosity syndromes associated with immunoglobulin abnormalities. , 1973, Seminars in hematology.

[39]  Alfio Quarteroni,et al.  Numerical Treatment of Defective Boundary Conditions for the Navier-Stokes Equations , 2002, SIAM J. Numer. Anal..

[40]  Hans Petter Langtangen,et al.  Python scripting for computational science , 2004 .