Download Doctor’s Orders

MEDICAL
INSTRUMENTATION
5th 2005200444 정진웅
Invasive BP measurement
actually, using this way in hospital
to measure patient’s BP
Catheter
Strain
gage
Cable
Blood
vessel
useles
s
Dome
diaphragm
it is very flexible
<Catheter sensor >
when blood push
the diaphragm
Invasive BP measurement
Invasive BP measurement
pressure
Pin (t)
Pin (t)
pressure
Pout(t)
same?
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>
F= ma
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]
section A
basic concept of
equivalent circuit model of
catheter-sensor system
Equivalent circuit model
P1
it affects
flow & resistance
It represents a gap of
pressures.
P1 - P2
(voltage in circuit)
gap of height
P2
1) Voltage = gap of pressure (P1 - P2)
2) Current = F (moving flow through a waterway)
Equivalent circuit model
3) Resistance R  
L
( : vis cos ity )
A
why?
Electrical resistance V  IR  R  V   L
I
A
A
ρ
ρ = resistivity
L
( wire )
So,
P
L
R



( : vis cos ity )
Liquid resistance is
F
A
Equivalent circuit model
4) Capacitance ( = compliance )
dv
dP
iC
 f C
dt
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 L
di
df
PL
dt
dt
M
L 2
A
Mass
M∝L
That is,
M↑ means inertance↑
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
R
V
L
  [ohm]
I
A
dt
dI
dt
CI
dv
L V
R
P 8L
 4 [ Pa  s / m3 ]
F r
dt L
LP  2
dI r
C  young ' s mod uls
Equivalent circuit model
So, using concept of the preceding part,
catheter sensor
Transformation
RESISTANCE
input
current
INDUCTOR
CAPACITOR
< Analogous electric system >
RLC circuit
output
SECOND-ORDER INSTRUMENT
Now, we analyze the RLC electronic circuit..
RESISTANCE

RC
INDUCTOR
LC

VI
current
CAPACITOR
CD
VO


VI  RC  I  LC
di
 VO
dt
Then, substitute i  C D
dVO
d 2VO
VI  RC  CD
 LC CD
 VO
2
dt
dt
dVO
dt
We called it,
SECONDORDER
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..
d 2VO
dVO
LC CD

R

C
 VO  VI
C
D
2
dt
dt
 D 2 2D 
 1 Vo (t )  K VI (t )
 2


n
 n

can reduced to three new ones
 D 2 2D 
 1 Vo (t )  K VI (t )
 2


n
 n

K 1
n 
1

LC C D
1
LC C D
LC CD
RC C D
RC
 


2
LC
2 LC C D
SECOND-ORDER INSTRUMENT
※ Meaning of terms
K  1 = static sensitivity, output units divided by input units.
n 
1

LC C D
1
= undamped natural frequency, rad/s
LC C D
LC C D
RC C D
RC
= damping ratio, dimensionless
 


2
LC
2 LC C D
SECOND-ORDER INSTRUMENT
Exponential function offer solution to this 2nd order system.
 D 2 2D 
 1 Vo (t )  K VI (t )
 2


n
 n

1) H ( D) 
Vo ( D)
K ( 1)
 2
VI ( D) D 2D

1
2
n
2) H ( j ) 
: operational transfer function
n
transformer
Vo ( j )
K ( 1)
1


2
VI ( j )  j  2 2j
   2j

 
 1 1    


n
n
 n
 n 




1
2



 ,    arctan
2

 n 
2
   2 


2  

 
1      4  
n

  n  
 n 
: frequency
transfer function
From now on,
let us 2nd-order instrument more
specifically
with two example
Example 7.1
Vo ( j )
VI ( j )
No bubble
n  91Hz
  0.033
bubble
n  22 Hz
  0.133
n  91Hz
n  22Hz

( Magnitude frequency
response )
ζ<0,
so, underdamped
Magnitude is max
At natural freq.
(reference page)
Vo ( j )
VI ( j )
ζ=1,
so, critically
damped
ζ=2,
so,
overdampe
d
 : log scale
n
( Magnitude frequency
response )
(reference page)
Standard output
ζ=1,
critically damped
ζ>1,
over damped
ζ<1,
under damped
Example 7.1
n  91Hz
  0.033  1
0˚
-90˚
-180˚
n
( phase response)
(reference page)

Ζ<1
0˚
ζ=1
Ζ>1
-90˚
Ζ>1,
Linear,
-180˚
n
( phase response)
but
High frequency
is eliminated
Example 7.1
y (t )
rippl
e
K 1
t
( unit step response)
(reference page)
y (t )
ζ<1
ζ=1
K 1
ζ=2
t
( unit step response)
Very stable. Rise-time is most
slow
(reference page)
overdamped, ζ>1 :
y (t )  
   2 1
2  1
2
Ke
(    2 1 ) n t
  arcsin 1   2
Critically damped, ζ=1 :
y (t )  (1  nt ) Kent  K
  arcsin 1   2

   2 1
2  1
2
Ke
(    2 1 ) n t
K
Example 7.2
Vo ( j )
VI ( j )
n  29 Hz
 1
n
( Magnitude frequency
response )
ln(  )