Application of Womersley Model to Reconstruct Pulsatile Flow From Doppler Ultrasound Measurements

A Womersley model-based assessment of pulsatile rigid-tube flow is presented. Multigate Doppler ultrasound was used to measure axial velocities at many radial locations along a single interrogation beam going through the center of a stiff tube. However, a large impediment to Doppler ultrasound diagnostics and resolution close to the wall is considerable noise due to the presence of the wall-fluid interface as well as many other effects, such as spectral broadening, coherent scattering, time resolution, and Doppler angle uncertainty. Thus, our confidence in measured signals is questionable, especially in the wall vicinity where the important oscillatory shear stresses occur. In order to alleviate known biases and shortcomings of the pulsed Doppler ultrasound measurements we have applied Womersley's laminar axisymmetric rigid-tube approximation to reconstruct velocity profiles over the entire flow domain and specifically close to wall, enabling unambiguous determination of the shear stresses. We employ harmonic analysis of the measured velocity profiles at all or selected trusted tube radial locations over one or more periods. Each of estimated Fourier coefficients has a unique counterpart in the respective pressure gradient component. From ensemble-averaged cross-sectional pressure gradient components we compute velocity profiles, volume flow rate, wall shear stress, and other flow parameters. Estimation of the pressure gradients from spatially resolved pulsed Doppler ultrasound velocity measurements is an added benefit of our reconstruction method. Multigate pulsed Doppler ultrasound scanners offer powerful capabilities to noninvasively and nonintrusively measure velocity profiles for hemodynamic and other fluid flow applications. This flow reconstruction method can also be tailored for use with other flow diagnostic modalities, such as magnetic resonance imaging (MRI) and a wide class of optical methods.