Estimation of viscosity from ultrasound measurements of velocity

Blood and plasma viscosity have recently been identified as independent risk factors for atherothrombotic vascular diseases. On the other hand, a monitoring of viscosity parameter is also required for the treatments of some cardiovascular diseases in order to control blood fluidity. This work suggests the use of ultrasound systems to achieve this monitoring in a non invasive manner, and proposes a method to estimate blood viscosity. The estimation procedure has been developed in a more general framework and computes simultaneously viscosity and pressure gradient from the knowledge of blood flow profiles. In a rigid tube, velocity profile shapes of a Newtonian fluid in a laminar flow are related to both viscosity and pressure gradient following Navier-Stokes equation. The idea of this paper is to use inverse problem approaches to estimate parameters of the flow that are not directly observable. Flow profiles are processed as an indirect observation of these quantities. To do so, N samples of velocity values taken along the tube radius are arbitrary chosen. An integration of Navier-Stokes equation over these N values leads to an N equations system. The contribution here is an inversion algorithm that uses a maximum likelihood estimator. The estimation process is tested on a fluid with measured viscosity that is placed in a flow phantom with a controlled flow rate