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## Blood Pressure and Sound (2)

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**Dept. of Biomedical Engineering**2003200449 YOUNHO HONG Blood Pressure and Sound (2)**IBP ( Invasive BP ) measurement**diaphragm catheter Blood vessel cable Pi Po pill up with some liquid (ex.saline) strain gages Po Pi If we choose sticky and dense liquid, We can’t get the signal of Pi just like the graph. To get the signal, We should concern with distance, diameter of a catheter and liquid, air- bubble inside a catheter. t t**IBP ( Invasive BP ) measurement**# Equivalent Circuit Model Of Catheter-Sensor System (1) Resistance L A resistivity P1 R P2 viscosity**IBP ( Invasive BP ) measurement**(2) Capacitance or Compliance (3) Inductance or Inertance**IBP ( Invasive BP ) measurement**multi physics Electric Circuit Fluid Mechanics voltage current charge pressure flow volume**Equivalent Circuit Model of IBP**diaphragm Po catheter cable Pi strain gages liquid + Vo - Vi i Compliance of diaphragm damping ratio natural frequency**Equivalent Circuit Model of IBP**(1) Frequency Transfer Function**Equivalent Circuit Model of IBP**|H| w Wn ∠H w -π/2 -π**Equivalent Circuit Model of IBP**Methods to solve 2nd order ODE**Steady State Freq. Response**f1 f2 ∠H |H| -4/π K 0.5 -1.8π f1 f2 f**Unit Step Response**In reality, We need a unit step function for a starting point. For example, should be underdamping input signal overdamping critical damping**Transient Step Response**balloon Po P bulb saline overdamping critical damping underdamping**Example**(7.1) A 5mm-long air bubble has formed in the rigid-walled catheter to a Statham P23Dd sensor. The catheter is 1m long, 6 French diameter, and filled with water at 20 ℃. Plot the frequency-response curve of the system with and without the bubble. 1.34 1.95 log f**Example**(7.2) By changing only the radius of the catheter, redesign the (no-bubble) catheter of Figure 7.9 to achieve the damping ratio ζ=1. Calculate the resulting natiral frequency fn. 1.46 log f