MEDICAL INSTRUMENTATION 5th 2005200444 정진웅

Invasive BP measurement actually, using this way in hospital to measure patient’s BP Catheter Strain gage Cable useless Dome Blood vessel diaphragm it is very flexible when blood push the diaphragm <Catheter sensor >

Invasive BP measurement

Invasive BP measurement pressure Pin (t) same? pressure Pout(t) Pin (t) Pout(t) ` Maybe, they are not same each other. So we need to know about property of a catheter sensor.

Invasive BP measurement Why Output is different? We have to overcome some factor. Air bubble in dome Length Diameter Material of catheter Viscosity of blood < factor > ① Length ☞ shorter length is better. ② Diameter ☞ shorter diameter is better. ③ Viscosity of blood ☞ No viscosity is better. ④ Material of catheter ☞ Not rigid is better. ⑤ Air bubble ☞ No air-bubble is better

Invasive BP measurement At this point, we know that catheter sensor can be changed to analogous electric system. < analogy> Voltage, V, [V] → Pressure, P, [Pa] : effecter potential ※ Pa = [N/m2] Current, I, [A] = [c/s] → moving flow, f, [m3/s] : volume flow Charge, q, [C] → Volume, v, [m3] F= ma basic concept of equivalent circuit model of catheter-sensor system section A

Equivalent circuit model P1 It represents a gap of pressures. P1 - P2 (voltage in circuit) it affects flow & resistance gap of height P2 Voltage = gap of pressure (P1 - P2) Current = F (moving flow through a waterway)

Equivalent circuit model 3) Resistance why? Electrical resistance ρ ρ = resistivity A L ( wire ) So, Liquid resistance is

Equivalent circuit model 4) Capacitance ( = compliance ) ※ meaning of compliance The terms elastic and compliance are of particular significance in cardiovascular physiology and respiratory physiology. Specifically, the tendency of the arteries and veins to stretch in response to pressure has a large effect on perfusion and blood pressure. Compliance is calculated using the following equation, where ΔV is the change in volume, and ΔP is the change in pressure. Compliance is like a balloon. Pressure is getting higher and compliance is getting higher, too.

Equivalent circuit model 5) Inductance ( = inertance ) M ∝ L That is, M↑ means inertance↑ Mass Inductance Mass is getting heavier, and inertia is getting higher, too. So, Once, materials with heavy mass go into dome, it’s hard to push away.

Equivalent circuit model Arrangement Electric circuit Field mechanics Voltage Pressure Current Flow Charge Volume

Equivalent circuit model So, using concept of the preceding part, catheter sensor Transformation input current output < Analogous electric system > RLC circuit

SECOND-ORDER INSTRUMENT Now, we analyze the RLC electronic circuit.. current Then, substitute We called it, SECOND-ORDER INSTRUMENT

SECOND-ORDER INSTRUMENT Now, we analyze SECOND-ORDER INSTRUMENT Many medical instruments are second order or higher, and low pass. And many higher-order instruments can be approximated by 2nd order system And.. can reduced to three new ones

SECOND-ORDER INSTRUMENT ※ Meaning of terms = static sensitivity, output units divided by input units. = undamped natural frequency, rad/s = damping ratio, dimensionless

SECOND-ORDER INSTRUMENT Exponential function offer solution to this 2nd order system. : operational transfer function transformer : frequency transfer function

From now on, let us 2nd-order instrument more specifically with two example

Example 7.1 ζ<0, so, underdamped Magnitude is max At natural freq. No bubble bubble ζ<0, so, underdamped Magnitude is max At natural freq. ( Magnitude frequency response )

(reference page) ζ=1, so, critically damped ζ=2, so, overdamped ( Magnitude frequency response )

(reference page) Standard output ζ=1, critically damped ζ>1, over damped ζ<1, under damped

Example 7.1 0˚ -90˚ -180˚ ( phase response)

(reference page) Ζ<1 0˚ ζ=1 Ζ>1 Ζ>1, -90˚ Linear, but High frequency is eliminated -90˚ -180˚ ( phase response)

Example 7.1 ripple ( unit step response)

(reference page) ζ<1 ζ=1 ζ=2 ( unit step response) Very stable. Rise-time is most slow

(reference page) overdamped, ζ>1 : Critically damped, ζ=1 :

Example 7.2 ( Magnitude frequency response )