Free access article

ESAIM: Proc., September 2005, Vol. 14, pp. 14-24
DOI: 10.1051/proc:2005002

Reduced models for blood flow in curved vessels

S. Balbis¹, L. Formaggia², G. Pontrelli³ and C. Guiot<sup>1

1</sup>  University of Torino, Neuroscience Dep., C.so Raffaello, 30, 10125 Torino, Italy.
²  MOX, Mathematics Department, Politecnico di Milano, Italy.
³  Istituto per le Applicazioni del Calcolo - CNR, Viale del Policlinico, 137, 00161 Roma, Italy.

Abstract
Flow in curved pipes has been intensively investigated and applications to arterial flow are relevant both in physiological and pathological conditions. A comprehensive survey of the work developed over almost one century from experimental and modelling point of view is carried out. Despite its complex nature, the 3D curved flow can be modeled, under reasonable assumptions, accounting only for 2, or even 1, geometrical dimensions. A couple of different reduced models are presented and discussed here. Results of numerical simulations demonstrate the role of curvature in the formation of the secondary flow patterns and in the asymmetry of wall shear stresses. Both the above features can have important haemodynamical effects and clinical diagnostic velocimeters should be equipped with correction algorithms for the measurement bias induced by vessel curvature.

Key words: Blood flow, Doppler ultrasound, Navier-Stokes equations, numerical methods


© EDP Sciences, ESAIM 2005

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