Non-linear analysis of the arterial pulsatile flow: assessment of a model allowing a non-invasive ultrasonic functional exploration

Ultrasonic measurements and modelling of blood flow in large vessels allows non-invasive evaluation of clinically interesting hemodynamic variables. To this aim, a non-linear mathematical model for the pulsatile arterial flow is proposed using the approximation of “local flow” theory. The model requires only measurements of instantaneous radius and centre-line blood velocity, and the knowledge of the tube distensibility to calculate blood velocity profiles, pressure gradient and wall shear stress. Evaluation of the proposed model using experimental data obtained from the literature proved that it can provide reliable results. In addition, as shown by assessing significance of various non-linear terms, results did not significantly change when a linear pressure–radius relationship was used instead of a non-linear relationship. Also, the model was found to be moderately sensitive to arterial tapering. Thus, the proposed model is suitable for a non-invasive clinical arterial exploration since it only requires three measurements which can be easily and precisely obtained in vivo using ultrasonic methods: the instantaneous radius, the centre-line velocity and the mean pulse wave velocity, this last variable characterizing the tube distensibility when assuming a linear pressure–radius relationship.