Affiliations: [a] Department of Chemical Engineering, Physiological Transport Studies Laboratory, The Pennsylvania State University, 155 Fenske Laboratory, University Park, PA 16802, USA | [b] Department of Bioengineering, The Pennsylvania State University, 155 Fenske Laboratory, University Park, PA 16802, USA; Fax: 814-865-7846
Abstract: In vitro experiments were conducted to measure the oscillatory flow pressure gradient along an elastic tube in order to assess the recent nonlinear theory of Wang and Tarbell. According to this theory, in an elastic tube with oscillatory flow, the mean (time-averaged) pressure gradient cannot be calculated using Poiseuille’s law. The effect of wall motion creates a nonlinear convective acceleration, and an induced mean pressure gradient is required to balance the convective acceleration. The induced mean pressure gradient depends on the diameter variation over a cycle, the pulsatility and unsteadiness of the flow, and the phase difference between the pressure wave form and the flow wave form. The amplitude of the pressure gradient also depends on these parameters and may deviate significantly from Womersley’s rigid tube theory. A flow loop was constructed to produce oscillatory flow in an elastic tube. Flow wave forms were measured with an ultrasonic flow probe, and ultrasonic diameter crystals were used to measure wall movement. A special device for pressure drop measurement was constructed using Millar catheter tip transducers to obtain both forward and backward pressure drops that were then averaged. This averaging method eliminated the static error of the pressure transducers. The pressure-flow phase angle was varied by clamping a distal elastic section at various locations. Pressure gradients were obtained for a range of phase angles between -55° and +49°. The mean and amplitude of the measured pressure gradient were compared to theoretical values. Both positive and negative induced mean pressure gradients were measured over the range of phase angles. The measured pressure gradient amplitudes were always lower than predicted by Womersley’s rigid tube theory. The experimental means and amplitudes are in good agreement with the elastic tube theoretical values. Thus, the experiments verify the theory of Wang and Tarbell.
