5th 2005200444 정진웅

MEDICAL MEDICAL INSTRUMENTATIONINSTRUMENTATION

Invasive BP measurement

actually, using this way in hospitalto measure patient’s BP

Blood vessel

Cable

CatheterCatheter

Dome

Straingage

diaphragmit is very flexible

<Catheter sensor ><Catheter sensor >when blood push the diaphragm

useless

Invasive BP measurement

Invasive BP measurement

pressure Pout(t)

pressure Pin

(t)same?

`

Pout(t)Pin (t)

Maybe, they are not same each other. So we need to know about property of a catheter sensor.

Invasive BP measurementWhy Output is different?We have to overcome some factor.

Length

Diameter

Viscosity of blood

Material of catheter

Air bubble in dome

< 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.

section A

F= ma< 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]

basic concept of equivalent circuit model of catheter-sensor system

Equivalent circuit model

gap of height

P1

P2

it affectsflow & resistance

It represents a gap of pressures. P1 - P2

(voltage in circuit)

1) Voltage = gap of pressure (P1 - P2)2) Current = F (moving flow through a waterway)

Equivalent circuit model

3) Resistance

why?

)cos:( ityvisA

LR

Electrical resistanceA

L

I

VRIRV

A ρ

L( wire )

ρ = resistivity

So,Liquid resistance is )cos:( ityvis

A

L

F

PR

Equivalent circuit model

4) Capacitance ( = compliance )

dt

dPCf

dt

dvCi

※ meaning of complianceThe 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 )

dt

dfLP

dt

diLV

2A

ML

Inductance

Mass

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.

M ∝ LThat is, M↑ means inertance↑

Equivalent circuit model

Electric circuit Field mechanics

Voltage Pressure

Current Flow

Charge Volume

ArrangementArrangement

][ohmA

L

I

VR

dI

dtVL

dv

dtIC

]/[8 3

4msPa

r

L

F

PR

2r

L

dI

dtPL

syoungC ' ulsmod

Equivalent circuit model

So, using concept of the preceding part,

catheter sensor

R E S I S TA N C E I N D U C TO R

C A P A C I TO R

TransformationTransformation

current output

< Analogous electric system >RLC circuit

input

SECOND-ORDER INSTRUMENT

R E S I S TA N C E I N D U C TO R

C A P A C I TO R

CR CL

OV

DCIV

Now, we analyze the RLC electronic circuit..

current

OCCI Vdt

diLIRV

dt

dVCi O

D

OO

DCO

DCI Vdt

VdCL

dt

dVCRV

2

2

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..

IOO

DCO

DC VVdt

dVCR

dt

VdCL

2

2

)()(12

2

2

tVKtVDD

Ionn

can reduced to three new ones

C

DCC

DC

DC

DCDCn

L

CLR

CL

CR

CLCL

K

22

11

1

)()(1

22

2

tVKtVDD

Ionn

SECOND-ORDER INSTRUMENT

※ Meaning of terms

C

DCC

DC

DC

DCDCn

L

CLR

CL

CR

CLCL

K

22

11

1

= 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.

)()(12

2

2

tVKtVDD

Ionn

12

)1(

)(

)()()1

2

2

nn

I

o

DD

K

DV

DVDH

nnnn

I

o

jjj

K

jV

jVjH

2

1

1

12

)1(

)(

)()()2 22

n

n

nn

2arctan,

41

1

2

2

22

: operational transfer function

: frequency transfer function

transformer

From now on,

let us 2nd-order instrument more specifically

with two example

Example 7.1

( Magnitude frequency response )

No bubble

033.0

91

Hzn

bubble

133.0

22

Hzn

Hzn 91

Hzn 22 ζ<0,so, underdamped

Magnitude is maxAt natural freq.

)(

)(

jV

jV

I

o

(reference page)

n

ζ=1,so, critically

dampedζ=2,so,

overdamped

scalelog:

)(

)(

jV

jV

I

o

( Magnitude frequency response )

(reference page)

ζ=1, critically

damped

ζ>1, over damped

ζ<1, under damped

Standard output

Example 7.1

n

( phase response)

0˚

-180˚

-90˚

1033.0

91

Hzn

(reference page)

n

0˚

-180˚

-90˚

( phase response)

ζ=1

Ζ<1

Ζ>1

Ζ>1,

Linear,

butHigh frequencyis eliminated

Example 7.1

)(ty

t

1K

( unit step response)

ripple

(reference page))(ty

t

1K

( unit step response)

ζ=1

ζ=2

Very stable. Rise-time is most slow

ζ<1

(reference page)overdamped, ζ>1 :

2

)1(

2

2)1(

2

2

1arcsin

12

1

12

1)(

22

KKeKety tt nn

Critically damped, ζ=1 :

21arcsin

)1()(

KKetty tn

n

Example 7.2

( Magnitude frequency response )

)ln(

1

29

Hzn

)(

)(

jV

jV

I

o

n