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BLOOD PRESSURE
BIOMEDICAL ENGINEERING2006200401
TAE_EUI, KIM
Invasive BP measurementInvasive BP measurement
CatheterDome Diaphragm
Strain gages (usually Four)
Pressure Sensor
Po should be same as Pi
“Fluid Mechanics”
What affect the quality of PoWhat affect the quality of Po
• Catheter length should be shorter but there is
• Viscosity of liquid
• Diameter
• Elastic material for catheter
• Diaphragm itself should be elastic
• No air bubble
Equivalent Circuit Method of Catheter Equivalent Circuit Method of Catheter – Sensor System– Sensor System
Electric Circuit Fluid Mechanics
Voltage , V [v] Pressure , P [pa]
Current , i [A] (Volume) Flow , f [m3/s]
Charge , q [c] Volume , V [m3]
R, L, C circuit Physics things
Equivalent Circuit Method of Catheter Equivalent Circuit Method of Catheter – Resistance– Resistance
V RiV L
Ri A
Electrical resistance :
Liquid resistance : p R f LR
A
If viscosity is too big?
Equivalent Circuit Method of Catheter Equivalent Circuit Method of Catheter – Capacitance or Compliance– Capacitance or Compliance
dPf C
dt ( AC flow )dv
i Cdt
AC
x Young's moduleC
The bigger Compliance, the bigger flow
Equivalent Circuit Method of Catheter Equivalent Circuit Method of Catheter – Inductance or Innertance– Inductance or Innertance
div L
dt
dfP L
dt
2
mL
A
Equivalent Circuit ModelEquivalent Circuit Model
1 2 ( radius difference)R R
1 2 1 R R R
Catheter
iP 1R 2R
oP
Sensor
Equivalent Circuit ModelEquivalent Circuit Model
i c c o
div R i L v
dt
2
2
we need equation between and
Second-Order ODE (ordinary differential euation)
od
o oo c d c d i
i v
dvi C
dt
dv d vv R C L C v
dt dt
Catheter & Sensor are rigid but not diaphragm
Equivalent Circuit ModelEquivalent Circuit Model
2
2
2
2
2 1 ( ) ( )
o oo c d c d i
o in n
dv d vv R C L C v
dt dt
D Dv t Kv t
W W
max
1
( 1)2
1 > ( max freq. of (t) )
c d
c
n i
c d
K
R C
L
W W vL C
21
2
2d
c
RC
LC
CRL
CR
L
Frequency Transfer FunctionFrequency Transfer Function
2
2
122 2
2
2 2
2
1( )
( ) 2 1
1 =
1 ( ) 2
21
= tan
11 4
1 = t
1 4
o
i
n n
n n
n
nn n
n n
vH j
j jv
j
1 2an
n
n
Magnitude ResponseMagnitude Response
nWW
H
2
1
1
2
0.25 (under damped)
0.5 (critical damped)
1 (over damped)
Phase ResponsePhase Response
nWW
H
2
If higher , Phase is linear but high frequency discarded in terms of Magnitude
Trade off
ReferenceReference2
2
2
2
2
2
( 1)
LC(j )
1 H(j )= ( )
( ) ( ) 1
( ) ( ) { ( )}
( ) ( ) { }
( )
o
o o o i
o i
o o o o i
oD j
i
j t
j t
j
d vLC RC
dt
LCD v RCDv v v
LCD RCD v v
v RCj v RCj v v v
vH D
v LC j RC j
v j v t e dt v t
dv t dv te dt
dt dtdv t e
dt
F
F
( )( ) ( )
( ){ ( ) ( ) }
( ) ( ) }
0 { }
t j t j t
j t j t j t
j t j t
dv te v t e j
dtdv t d
e dt v t e j v t e dtdt dt
dv t e dt j v t e dt
dtj j
F
Steady State Frequency ResponseSteady State Frequency Response
1
1
( ) sin(2 )
( ) sin(2 )4
i
o
v t A f t
v t KA f t
2
2
( ) sin(2 )
( ) 0.1 sin(2 1.9 )i
o
v t A f t
v t A f t
R L
C
H H
0.1
K4
1.9
21f 2f
1f 2f
Steady State Frequency ResponseSteady State Frequency Response
1 1 2 2
1 1 1 1 2 2 2 2
( ) sin(2 ) sin(2 )
( ) sin(2 ) sin(2 )i
o
P t A f t A f t
P t K A f t K A f t
; Principle of Superposition
Transient ResponseTransient Response
( ) sin(2 ) ( ) ; Signal generated from a specific timeiv t A ft u t
; Principle of Superposition
( )iv t
1A 1KA
( )ov tTransient Property!
Transient Property!