Accuracy of the inverse Womersley method for the calculation of hemodynamic variables

We have studied the accuracy of the inverse Womersley method, a linear theory for the calculation of hemodynamic variables from measured volumetric flow rate or centerline velocity, for two canine arteries with different degrees of arterial wall motion and taper. The results from the linear theory are compared with the estimates from the nonlinear theory of Ling and Atabek for a canine thoracic aorta and femoral artery. For the thoracic aorta, the linear theory underestimates the mean wall shear stress by as much as 77%, when compared with the nonlinear theory. For the femoral artery, on the other hand, the mean wall shear stress value is underestimated by as much as 23%. Estimates of other hemodynamic variables show similar discrepancies between the nonlinear and linear theories. Thus, the inverse Womersley method does not give accurate estimates of hemodynamic quantities. This failure results from the neglect of convective accelerations due to arterial wall motion and taper, with the neglect of arterial taper leading to the largest errors.