“…In the past, researchers have been using a series of simplified equations, either empirical or derived from fluid mechanics theory, for the non-invasive clinical estimation of the pressure gradient in cardiovascular stenosis (including in heart valves, [ 4 1 _ T D $ D I F F ] atherosclerosis, and AoCo). In these simplified models, flow velocity and the geometry of the flow channel in the stenosis were estimated from either Doppler echocardiography [10][11][12][13][14][15][16][17][18][19][20] or magnetic resonance imaging (MRI) [21][22][23] measurements. This non-invasive procedure seemed to achieve fair agreement in the diagnosis of stenosis in heart valves and [ 4 1 _ T D $ D I F F ] atherosclerosis, and has been extended to analyze other vascular diseases [24,25].…”