Complete Unsteady One-Dimensional Model of the Net Aortic Pressure Drop

A large amount of engineering and medical research has been devoted to the assessment of aortic valve stenosis severity in the past decades. The net transvalvular pressure drop has been recognized as one of the parameters that better reflect stenosis effects on left ventricle overload, and its adoption in clinical assessment of stenosis has been proposed. Flow unsteadiness has been shown to have a non-negligible impact on the net drop; however, a simple formulation for net drop calculation that includes not only flow pulsatility but also the effects of valve dynamics is still lacking.

The present contribution is hence aimed at developing a complete unsteady one-dimensional model of the net aortic transvalvular pressure drop that just requires non-invasive data to be implemented.

Transvalvular flow is described as a jet of incompressible viscous fluid through a circular orifice placed in a concentric rigid circular tube. The classical one-dimensional mass and total head conservation equations are applied. The effective orifice area and transvalvular flow rate are assumed to vary with time throughout the ejection period.

The model is found to capture pressure drop oscillations occurring when the valve opens/closes and/or leaflets flutter, thanks to the inclusion of valve dynamics effects. The model is also proposed as a numerical tool for the calculation of the instantaneous effective orifice area once net pressure drop and flow rate are known.

The model may contribute to the improvement of non-invasive aortic stenosis assessment.