A dual-port catheter can simultaneously measure pressure in an artery at two dif

Question

A dual-port catheter can simultaneously measure pressure in an artery at two different locations, or “taps.” Idealized measurements from one such catheter are shown in Fig. 4.34. It is known that there is a bifurcation distal to the measurement locations.
(a) If the two ports are 4 cm apart, estimate the wave speed in the artery containing the catheter. Explain your logic.

(b) If the ratio of parent:daughter artery cross-sections at the distal bifurcation is 3:1, estimate the wave speed in the daughter arteries. Hint: first estimate the reflection coefficient at the bifurcation.

140 Distal Pressure Tap 120 6100 80 60 40 20 0.01 0.02 0.03 0.04 0.05 Time (sec) 140 Proximal Pressure Tap 120 100 80 60 40 20 0.01 0.02 0.03 0.04 0.05 Time (sec) Figure 4.34 For Problem 4.10

Explanation / Answer

A) Ans : because It will depend on the elastic properties of the tube, as well as on the inertia of the fluid. the tube’s elastic properties by its distensibility where A is the tube cross-sectional area, D is the tube diameter, p is the transmural pressure, and we have assumed that the tube cross-section remains circular and is proportional to the fractional change in tube diameter induced by a unit change in transmural pressure.the pulse wave speed c depends on artery distensibility and fluid density.

B)Ans: Reflection coefficients at the bifurcation.

Every time a pressure wave encounters a change in mechanical or geometrical properties of the vessel, a part of the forward pressure wave is reflected and backward propagating waves are generated. Although diffused reflections arise everywhere, bifurcations are the main source of reflections. In this regard, the bifurcation reflection coefficient can be assessed as :           

                            

where is the bifurcation-specific reflection coefficient and subscripts in and out refer to bifurcation inlet and the outlet sections.A positive (negative) reflection coefficient means that part of the forward pressure wave is reflected as a compression (expansion) wave, so that the backward pressure wave adds (subtracts) to the incident wave.

The characteristic impedance of the daughter arteries will in general be different from that of the parent artery, since c and A will differ from daughter to parent. This means that the ratio of the pressure pulse amplitude to the flow pulse amplitude must change as the pulse wave passes through the junction.the arteries and junction are treated as a one dimensional system in which pressure is uniform across the artery at each axial station, while pressure and flow rate vary axially.

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