doi:10.1016/j.ultrasmedbio.2004.09.007 ● Original Contribution CURVATURE AFFECTS DOPPLER INVESTIGATION OF VESSELS: IMPLICATIONS FOR CLINICAL PRACTICE S. BALBIS, † S. ROATTA,* and C. GUIOT* † *Department of Neuroscience, University of Torino, Torino, Italy; and † INFM, Torino, Italy (Received 25 May 2004; revised 12 September 2004; in final form 16 September 2004) Abstract—In clinical practice, blood velocity estimations from Doppler examination of curved vascular segments are normally different from those of nearby straight segments. The observed “accelerations,” sometimes considered as a sort of stochastic disturbances, can actually be related to very specific physical effects due to vessel curvature (i.e., the development of nonaxial velocity [NAV] components) and the spreading of the axial velocity direction in the Doppler sample volume with respect to the insonation axis. The relevant phenomena and their dependence on the radius of curvature of the vessels and on the insonation angle are investigated with a beam-vessel geometry as close as possible to clinical setting, with the simplifying assumptions of steady flow, mild vessel curvature, uniform ultrasonic beam and complete vessel insonation. The insonation angles that minimize the errors are provided on the basis of the study results. (Email:caterina.guiot@unito.it) © 2005 World Federation for Ultrasound in Medicine & Biology. Key Words: Curved vessels, Doppler, Blood velocity, Nonaxial velocity components, Modelling. INTRODUCTION Doppler ultrasound (US) is currently used to assess cir- culatory disorders in large blood vessels. Clinical indices and estimated velocities are extracted from Doppler spectra and are, therefore, affected by the measurement conditions, such as the geometry of the 3-D setting, the insonation procedure and the data-processing procedure of the equipment (Geoffrey and Thompson 1992; Guiot et al., 1999; Gill, 1985). The geometry of the vascular structures can signif- icantly affect clinical results (Janerot Sjoberg et al., 1993; Lees et al., 1999; Tortoli et al., 2002). This is well-known in the case of stenosed or aneuristic vessels, but the same occurs in the case of curved vessels. Many vessels, both in physiological and pathological situa- tions, exhibit nonnegligible curvatures: for instance, the aortic arch and the carotids are normally curved, but other cerebral vessels bend in disease (i.e., in case of cervical arthrosis) (see Fig. 1). Clinicians sometimes experience difficulties in in- vestigating curved segments, because sharp changes of velocity (“accelerations” of the blood flow) and whirling motions in the vessel bends are often observed. The current explanation they give (Hines et al. 2001; Pancera et al. 1998), similar to the case of stenosed vessels, is that turbulence develops and diffuse vorticosity is generated, affecting blood velocity in some unpredictable, stochas- tic way. For curved vessels, however, this is not the case. Two main reasons may account for abnormal blood velocity in curved vessels. First, axial flow direction is not constant, even in the short vessel segment crossed by the US beam. Therefore, within the sample volume, the axial flow directions actually spread in a certain range. Second, centrifugal forces develop and give rise to non- axial velocity (NAV) components that generate two re- circulating whirlpools (see Fig. 2); the process can be fully described in mathematical deterministic form (Dean 1927, 1928). In this paper, the 3-D geometry of the CW Doppler insonation of steady flow in a rigid curved tube is stud- ied, aiming at evaluating the impact of curvature in Doppler investigations. Results are valid for slightly curved veins only, because steady flows are considered and the assumption that the radius of curvature is much larger than the vessel radius is made. Work is in progress for extending the present investigation to arteries and to severe curvature. Address correspondence to: Caterina Guiot, Ph.D., Dip. Neuro- science, Università di Torino, Corso Raffaello 30, Torino 10125 Italy. E-mail: caterina.guiot@unito.it Ultrasound in Med. & Biol., Vol. 31, No. 1, pp. 65–77, 2005 Copyright © 2005 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/05/$–see front matter 65