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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