1. MEDICAL INSTRUMENTATION
5th 정진웅

2. 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 >

3. Invasive BP measurement

4. 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.

5. 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

6. 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

7. Equivalent circuit modelP1
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)

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

9. 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.

10. 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.

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

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

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

14. 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

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

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

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

18. 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 )

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

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

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

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

23. Example 7.1
ripple
( unit step response)

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

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

26. Example 7.2
( Magnitude frequency response )