An inverse method for non-invasive viscosity measurements

¹ Service de Biophysique, Laboratoires Innothera, 7–9 Av. F.V. Raspail, 94110 Arcueil, France
² Matière et Systèmes Complexes, Université Paris 7, France
³ Laboratoire de Modélisation en Mécanique, Université Paris 6, France

Corresponding author: jose-maria.fullana@innothera.com

Received: 24 July 2006
Accepted: 19 December 2006
Published online: 14 March 2007

Abstract

A procedure is presented which allows to compute in a non-invasive manner, blood viscosity through flow measurements obtained at a fixed vessel cross-section. The data set is made of measurements (artery radius and spatially discrete velocity profiles) performed at given time intervals for which the signal to noise ratio is typical of U.S. Doppler velocimetry in clinical situation. This identification approach is based on the minimization, through a backpropagation algorithm, of a cost function quantifying the distance between numerical data obtained through Navier-Stokes simulations and experimental measurements. Since this cost function implicitly depends on the value of viscosity used in numerical simulations, its minimization determines an effective viscosity which is shown to be robust to measurement errors and sampling time. Such an approach is shown to work in an in vitro experiment, and seems to be suitable for in vivo measurements of viscosity by the atraumatic techniques of Doppler echography.