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Blood Pressure and Sound (2)
Dept. of Biomedical Engineering2003200449
YOUNHO HONG
IBP ( Invasive BP ) measurement
t
Pi
catheterBloodvessel
Pi
pill up withsome liquid(ex.saline)
diaphragm
strain gages
cablePo
t
Po
If we choose sticky and dense liquid, We can’t get the signal of Pi just like the graph.To get the signal, We should concern with distance, diameter of a catheter and liquid, air-bubble inside a catheter.
IBP ( Invasive BP ) measurement
# Equivalent Circuit Model Of Catheter-Sensor System
(1) Resistance
AL
A
LVRRiV
, : resistance Electrical
resistivity
P1
P2
)21( PPF R
FRop : resistance Liquid
A
LR
viscosity
IBP ( Invasive BP ) measurement
(2) Capacitance or Compliance
x
AC
dt
dvCi ,
dt
dpCf modulus sYoung'
YC
(3) Inductance or Inertance
dt
diLV
2 ,
A
mL
dt
dfLP
IBP ( Invasive BP ) measurement
multiphysics Electric Circuit Fluid Mechanics
voltagecurrentcharge
pressure flow volume
dtdVI
C
dtdIV
L
A
L
I
VR
)( ][
modulus sYoung'
)(
)8
( ][
2
43
C
r
L
dtdFP
L
r
Lm
sPaF
R
Equivalent Circuit Model of IBP
catheterPi
liquid
diaphragm
strain gages
cablePo
L c
C d
R c
Vi
Compliance of diaphragm
+Vo -
i
ODEorder 2nd :
20
20
0
00
dt
VdCL
dt
dVCRVV
dt
dVCiV
dt
diLiRV
dcdci
dcci
)()(]12
[
operator :
2
2
tKVtVW
D
W
D
dt
dD
ionn
dc
n
c
dc
CLW
L
CRK
1
2 ,1
dampingratio
naturalfrequency
Equivalent Circuit Model of IBP
(1) Frequency Transfer Function
nnnn
i
o
Ww
jWw
Wjw
WjwjwV
jwVjwH
2)(1
1
12)(
1
)(
)()(
22
)2
(tan
)(4])(1[
1
))(1
2
(tan
)(4])(1[
1)(
1
2222
2
1
2222
w
W
Ww
Ww
Ww
WwWw
Ww
Ww
jwH
n
nnn
n
n
nn
Equivalent Circuit Model of IBP
w
|H|
Wn
)dunderdampe( 5.0
)damped critically( 1
)overdamped( 2
w
-π
-π/2
∠H)dunderdampe( 5.0
)damped critically( 1
)overdamped( 2
Equivalent Circuit Model of IBP
Methods to solve 2nd order ODE io VV
dt
dVRC
dt
VdLC 0
20
2
function transfer loperationa : 1
1)(
dt
d )1(
)1(
2
2
2
RCDLCDV
VDH
DVVRCDLCD
VVRCDVVLCD
i
o
io
iooo
jwD
i
o
iooo
DH
jwRCjwLCV
VjwH
VVRCjwVVjwLC
)(
1)()(
1)(
)( )2(
2
2
Steady State Freq. Response
)4
2sin()(
)2sin()(
1
1
tfKAtV
tfAtV
o
i
|H|
ff1 f2
K
0.5
)8.12sin(5.0)(
)2sin()(
2
2
tfAtV
tfAtV
o
i
f2f1
-4/π
-1.8π
∠H
Unit Step ResponseIn reality, We need a unit step function for a starting point.
For example, should be )()2sin()( 1 tutfAtVi )2sin()( 1tfAtVi
input signal
underdamping
critical damping
overdamping
Transient Step Response
Pbulb
balloon
saline
Po
underdamping
critical damping
overdamping
Example(7.1) A 5mm-long air bubble has formed in the rigid-walled catheter to a Statham P23Dd sensor. The catheter is 1m long, 6 French diameter, and filled with water at 20 ℃. Plot the frequency-response curve of the system with and without the bubble.
033.0)(4
91)1
(2
21
3
21
P
VL
r
HzL
P
L
rfn
137.0
22,
bub
bubn Hzf
log f1.34 1.95
Example(7.2) By changing only the radius of the catheter, redesign the (no-bubble) catheter of Figure 7.9 to achieve the damping ratio ζ=1. Calculate the resulting natiral frequency fn.
Hzf
rrff
r
r
rr
n
nn
29
147.0
0032.0
00
3
03
03
log f1.46
Thank you.
