MEDICAL INSTRUMENTATION

5 th 2005200444

정진웅

Invasive BP measurement

actually, using this way in hospital to measure patient’s BP

Catheter

Strain gage Blood vessel useles s Dome

Cable diaphragm it is very flexible when blood push the diaphragm

Invasive BP measurement

Invasive BP measurement

P in (t) pressure P in (t) same?

P out (t) pressure P out (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.

Length Diameter Air bubble in dome Material of catheter Viscosity of blood < factor > ① Length ☞ shorter length is better.

② Diameter ☞ shorter diameter is better.

③ ④ Viscosity of blood ☞ No viscosity is better.

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.

F= ma

< analogy>

Voltage, V, [V] → Pressure, P, [Pa] : effecter potential ※ Pa = [N/m 2 ] Current, I, [A] = [c/s] → moving flow, f, [m 3 /s] : volume flow Charge, q, [C] → Volume, v, [m 3 ] section A basic concept of equivalent circuit model of catheter-sensor system

Equivalent circuit model

P 1 it affects flow & resistance gap of height P 2 1) Voltage = gap of pressure (P 1 - P 2 ) 2) Current = F (moving flow through a waterway) It represents a gap of pressures. P 1 - P 2 (voltage in circuit)

Equivalent circuit model

3) Resistance

R

 

L A

(  :

vis

cos

ity

) why?

Electrical resistance

V



IR



R



V I

 

L A

A ρ ρ = resistivity L ( wire ) So, Liquid resistance is

R

 

P F

 

L A

(  :

vis

cos

ity

)

Equivalent circuit model

4) Capacitance ( = compliance )

i



C dv dt



f



C dP dt

※ 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 )

V



di L dt



P



L df dt L



M A

2 Mass Inductance M ∝ L That is, M↑ means inertance↑ 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

Voltage Current Charge

R



V I

 

L A

[

ohm

]

L



V dt C



I dI dt dv

Field mechanics

Pressure Flow Volume

R



P F L

  8  

r L

4 [

Pa



s P dt dI

  

r L

2 /

m

3 ]

C



young

'

s

mod

uls

Equivalent circuit model

So, using concept of the preceding part, catheter sensor

Transformation

RESISTANCE INDUCTOR input current CAPACITOR output

< Analogous electric system > RLC circuit

SECOND-ORDER INSTRUMENT Now, we analyze the RLC electronic circuit..



V I

RESISTANCE

R C

current INDUCTOR

L C

CAPACITOR

C D



V O

 

V I



R C



I



L C di



V O dt

Then, substitute

i



C D dV O dt V I



R C



C D dV O dt



L C C D d

2

V O dt

2 

V O

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 2 nd order system

And..

L C C D d

2

V O dt

2 

R C



C D dV O dt



V O



V I

 

D

2 

n

2  2 

D



n

  1  

V o

(

t

) 

K



V I

(

t

) can reduced to three new ones

K

 1  

D

2 

n

2  2 

D



n

  1  

V o

(

t

) 

K



V I

(

t

) 

n

 1

L C C D

  2

R C C D L C C D

 1

L C C D



R C

2 

L C C D L C

SECOND-ORDER INSTRUMENT ※ Meaning of terms

K

 1 = static sensitivity , output units divided by input units.



n

 1

L C C D

 1

L C C D

= undamped natural frequency , rad/s   2

R C C D L C C D



R C

 2

L C C D L C

= damping ratio , dimensionless

SECOND-ORDER INSTRUMENT Exponential function offer solution to this 2 nd order system.

 

D

2 

n

2  2 

D



n

  1  

V o

(

t

) 

K



V I

(

t

) 1 )

H

(

D

) 

V V I o

( (

D

)

D

) 

D

2 

n

2

K

(  1 )  2 

D



n

 1 : operational transfer function 2 )

H

(

j

 ) 

V o

(

V I

(

j

 )

j

 ) 

K

(  1 )  

j

 

n

  2  2 

j

 

n

 1  1     

n

1   2  2 

j

 

n

 1    1     

n

  2    2  4  2    

n

  2   ,        arctan  

n

2    

n

    transformer : frequency transfer function

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

Example 7.1

V o

(

V I

(

j

 )

j

 ) ( Magnitude frequency response ) No bubble 

n

 91

Hz

  0 .

033 bubble 

n

 22

Hz

  0 .

133 

n

 91

Hz



n

 22

Hz

 ζ<0, so, underdamped Magnitude is max At natural freq.

(reference page)

V o

(

V I

(

j

 )

j

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

n

 : log

scale

(reference page)

Standard output ζ=1, critically damped ζ>1, over damped ζ<1, under damped

Example 7.1



n

   91

Hz

0 .

033  1 0˚ -90˚ -180˚ 

n

( phase response)

(reference page)

 

n

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

Example 7.1

y

(

t

)

K

 1 ripple ( unit step response)

t

(reference page)

y

(

t

) ζ<1 ζ=1

K

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

t

(reference page)

overdamped, ζ>1 :

y

(

t

)    2    2 2  1

Ke

(     1  2  1 ) 

n t

  2    2 2  1

Ke

(     1  2  1 ) 

n t



K

  arcsin 1   2 Critically damped, ζ=1 :

y

(

t

)   ( 1  

n t

)

Ke

 

n t



K

  arcsin 1   2

Example 7.2

V o

(

V I

(

j

 )

j

 ) 

n

   1 29

Hz

( Magnitude frequency response ) 

n

ln(  )