Design of New Reliable CFD-Based Estimation of Flow Rate: Early in-Vivo Results R Ponzini 1 , C Vergara 2 , A Veneziani 4 , A Redaelli 3 1 CILEA (Consorzio Interuniversitario), Segrate (MI), Italy 2 Universit di Bergamo, Bergamo, Italy 3 Politecnico di Milano, Milano, Italy 4 Emory University, Atlanta, Georgia, USA Abstract In the present work a new approach for the blood flow rate estimate is discussed together with the performances results on both Computational Fluid Dynamics and in vivo datasets. In the mean time the comparison of this new method against the standard one used in clinics during catheterization in Doppler based flow rate estimate is provided showing important limitation of the latter and possible concrete enhancements using the new one proposed herein. 1. Introduction The correct knowledge of the blood flow rate (Q) is a major issue in clinical practice. the elective approach for blood flow analysis is based on the Doppler technique which cannot measure directly the flow rate. The latter has to be indirectly estimated starting from the value of the maximum velocity (V m ) and the value of the area of the vessel (A). In particular from [1] an a-priori profile is usually assumed: Q D = A V m /2 (1) This equation involves a parabolic spatial profile for the velocity; in this sense this method has been also associated to a quasi-static hypothesis which can hardly hold true for blood. By means of about 200 computational fluid dynamics (CFD) simulations we designed a new formulation for the flow-rate estimate based on the Womersley number (W): a dimensionless index used for quantifying the pulsatility of the flow (see [2]). In what follows we present how the new formula has been obtained and how it has been validated in a wide range of CFD models and under a wide range of fluid- dynamics physiological conditions (see [2] and [3]). Finally, the first possible approach to in-vivo validations of the new formula, as suggested and fully described in [4], is presented together with the very early results. 2. Methods The general form of the new formulation is: Q = g(V m , W) (2) establishing a link between the mean velocity and V m as a function of the Womersley number W. Parameters calibration have been performed using estimates of data in the form (V m , W) obtained solving the Navier-Stokes equations, prescribing the flow rate boundary conditions without choosing a priori the velocity profile and thus avoiding any bias on the computed flow fields (see [5]), under a wide range of flow conditions in the range of W: 2.7< W < 15. The resulting formula, that will be named Womersley-based approach, can be written in the form: Q W =      ≤ < ≤ < - + ≤ . 15 1 . 3 1 . 3 7 . 2 ) 1 ( 7 . 2 2 2 1 1 W g W g w wg W g (3) Where: g 1 (V M ,W) =0.5 × A × V M × (1+a 1 W b1 ); g 2 (V M ,W) =0.5 × A × V M × b 2 arctan(a 2 W); and a1=0.00417, b1=2.95272, a2=1.00241, b2=0.94973, w=(W-2.7)/(W-2.7)-(3.1-2.7). The performances of the new Womersley-based approach for blood volume estimate was tested and fully validated using again CFD in realistic geometries and under a wide range of physiological conditions (see [2] and [3]). In each case, we compared the percentage error on the flow- rate estimate using these two approaches (eqn. 1 and eqn. 3 respectively) given by Q D and Q W ,. Recently in vivo acquisitions of 2D phase contrast MRI of the descending abdominal aorta in an healthy young volunteer have been performed. As fully discussed in [4] the richness of the PCMRI data can be used twofold: in one hand to compute the effective value of the flow rate as integral of the velocity field across the vessel and on the other hand to evaluate the two estimate formula (eqn 1 and 3) by mimicking the Doppler acquisition and dataset. In figure ISSN 0276-6574 953 Computers in Cardiology 2008;35:953-955.