Chapter 7 Blood Pressure
and Sound
Blood pressure measurement
Target:
Blood pressure
@ the heart chambers
@ the peripheral vascular system
Purpose:
to help the physician to determine the functional integrity of the
cardiovascular system
Methods:
1. Direct (invasive) techniques
2. Indirect (noninvasive) techniques
Phonocardiography
The sources of heart sounds:
the variations set up by the accelerations and deccelerations of blood
Function of blood circulation:
 oxygen, nutrient  Tissues
 metabolic waste 
Tissues
Figure 7.1 The left ventricle ejects blood into the systemic circulatory system. The right ventricle ejects blood into the pulmonary circulatory system.
7.1 Direct Measurements
Blood pressure sensors:
Type 1) Extravascular pressure sensors
Type 2) intravascular pressure sensors
Types of sensor elements:
Strain gage, linear-variable differential transformer, variable
inductance, variable capacitance, optoelectronic,
piezoelectric, semiconductor
Diaphragm
A
c
B
R2
Armature
Rx
ui
C
b
a
Ry
D
(a)
R1
R4
R3
Strain-gage wires
d
(b)
D uo
Ri
Diaphragm
A
c
B
R2
Armature
Rx
ui
C
b
a
Ry
D
(a)
R1
R4
R3
Strain-gage wires
d
(b)
D uo
Ri
Figure 2.2 (a) Unbonded strain-gage pressure sensor. The diaphragm is directly coupled by an armature to an unbonded strain-gage system.
With increasing pressure, the strain on gage pair B and C is increased, while that on gage pair A and D is decreased. (b) Wheatstone bridge
with four active elements. R1 = A, R2 = B, R3 = D, and R4 = C when the unbonded strain gage is connected for translation motion.
Resistor Ry and potentiometer Rx are used to initially balance the bridge. vi is the applied voltage and Dv0 is the output voltage on a voltmeter
or similar device with an internal resistance of Ri.
Figure
2.2
Diaphragm
A
c
B
R2
Armature
Rx
ui
C
b
a
Ry
D
(a)
R1
R4
R3
Strain-gage wires
d
(b)
D uo
Ri
Figure 2.2 (a) Unbonded strain-gage pressure sensor. The diaphragm is directly coupled by an armature to an unbonded strain-gage system.
With increasing pressure, the strain on gage pair B and C is increased, while that on gage pair A and D is decreased. (b) Wheatstone bridge
with four active elements. R1 = A, R2 = B, R3 = D, and R4 = C when the unbonded strain gage is connected for translation motion.
Resistor Ry and potentiometer Rx are used to initially balance the bridge. vi is the applied voltage and Dv0 is the output voltage on a voltmeter
or similar device with an internal resistance of Ri.
Diaphragm
A
c
B
R2
Armature
Rx
ui
C
b
a
Ry
D
(a)
R1
R4
R3
Strain-gage wires
d
(b)
D uo
Ri
Figure 2.2 (a) Unbonded strain-gage pressure sensor. The diaphragm is directly coupled by an armature to an unbonded strain-gage system.
With increasing pressure, the strain on gage pair B and C is increased, while that on gage pair A and D is decreased. (b) Wheatstone bridge
with four active elements. R1 = A, R2 = B, R3 = D, and R4 = C when the unbonded strain gage is connected for translation motion.
Resistor Ry and potentiometer Rx are used to initially balance the bridge. vi is the applied voltage and Dv0 is the output voltage on a voltmeter
or similar device with an internal resistance of Ri.
Flush solution under pressure
Sensing
port
Sample and transducer
zero stopcock
Roller clamp
Electrical connector
Disposable pressure transducer with an integral flush device
Figure 7.3 Extravascular pressure-sensor system A catheter couples a flush solution (heparinized saline) through a disposable pressure sensor with an integral flush device
to the sensing port. The three-way stopcock is used to take blood samples and zero the pressure sensor.
7.3 Dynamic properties of the pressure sensor
Static pressure
Blood pressure
(dynamic)
Models of liquid-filled catheter sensor:
Distributed-parameter model:
More accurate;
More complicated;
Lumped-parameter model:
Acceptable accuracy;
Easier to work with;
Properties of liquid-filled catheter sensor:
Property
Hydraulic quantity
Electric analog
Inertia
(慣性)
Inertance
Electric inductance (L)
Friction
(摩擦力 )
Resistance
Electric resistance (R )
Elasticity
(彈性 )
Compliance
Electric capacitance (C )
(順從性)
Pressure (P), pascal = N/m2
Voltage (V), V
Voluminal flow rate (F), m3/s
Current (I), C/s = A
Liquid volume, m3
Electric charge, coulomb
Hydraulic quantity
Electric analog
Pressure (P), pascal = N/m2
Voltage (V), V
Voluminal flow rate (F), m3/s
Current (I), C/s = A
Liquid volume, m3
Electric charge, coulomb
△P
F
I ＋△V－

Physical model & Analogous electrical model
Analogous (adj.) 類似的
Analog (adj.) 類比式的
Sensor
(a)
P
Diaphragm
Catheter
Liquid
Rc
Lc
Incremental
length
Rc
Lc
Rc
DV
Lc
Rs
Ls
(b)
Cc
Cc
Cc
Cs
C
d=
DV
DP
Figure 7.7 (a) Physical model of a catheter-sensor system. (b) Analogous electric system for this catheter-sensor system. Each segment of the catheter has its own resistance
Rc, inertance Lc, and compliance Cc. In addition, the sensor has resistor Rs, inertance, Ls, and
compliance Cs. The compliance of the diaphragm is Cd.
Rc
Liquid
Rc 
resistance
ΔP
Electric
of the catheter :
ΔP

F
Rc 
uA
P : pressure difference
across the segment,
A : cross - sectional
:
ΔV
I
Δ V : potential
difference
m/s
area, m
2
Poiseuille equation： a physical law that describes slow viscous
incompressible flow through a constant circular cross-section
Poiseuille
' s equation
(for laminar
RC 
or Poiseuille
flow)
8 L
 r
across the component,
I : electric current, A (  C/s)
3
F : flow rate, m /s
u : average velocity,
Pa
resistance
4
L : catheter length,
m
r : catheter radius, m
 : liquid viscosity , pascal - second
V
Lc
Liquid
Lc 
inertance
ΔP
of the catheter :

ΔP
dF / dt

aA
m
A
Δ P : pressure difference
2

L
 r
2
across the segment,
Pa
3
F : flow rate, m /s
a : accelerati on, m/s
m : mass of liquid,
2
kg
 : density of liquid, kg/m
3
Electric
L 
inductance
:
ΔV
dI / dt
Δ P : electric
potential
I : current flowing
difference
through t
across the component,
he component,
A (  C/s)
V
Cd
Electric
C 
capacitanc e :
Q
ΔV
Q : electric charge stored in the component,
ΔV : electric
Compliance
Cd 
ΔV
ΔP
of the diaphragm

potential
diffeence
:
1
Ed
Δ P : pressure difference
across the segment,
Pa
ΔV :
E d : volume
modulus
of elasticity
of the sensor diaphragm
>, =, <
Compliance:
Ball
Clay
Elasticity:
Ball
Clay
C
across the component,
V
Sensor
(a)
P
Diaphragm
Catheter
Liquid
Rc
Lc
Incremental
length
Rc
Lc
Rc
DV
Lc
Rs
Ls
(b)
Cc
Cc
Cc
Cs
C
DV
d=
DP
Figure 7.7 (a) Physical model of a catheter-sensor system. (b) Analogous electric system for this catheter-sensor system. Each segment of the catheter has its own resistance
Rc, inertance Lc, and compliance Cc. In addition, the sensor has resistor Rs, inertance, Ls, and
compliance Cs. The compliance of the diaphragm is Cd.
Physical model & Analogous electrical model
Analogous (adj.) 類似的
Analog (adj.) 類比式的
Sensor
(a)
P
Diaphragm
Catheter
Liquid
Rc
Lc
Incremental
length
Rc
Lc
Rc
DV
Lc
Rs
Ls
(b)
Cc
Cc
Cc
Cs
C
d=
DV
DP
Figure 7.7 (a) Physical model of a catheter-sensor system. (b) Analogous electric system for this catheter-sensor system. Each segment of the catheter has its own resistance
Rc, inertance Lc, and compliance Cc. In addition, the sensor has resistor Rs, inertance, Ls, and
compliance Cs. The compliance of the diaphragm is Cd.
Catheter
liquid inertia
Catheter
liquid resistance
Sensor
diaphragm
compliance
(a)
Lc
Rc
Lcd
ui (t)
Cb
Rcd
Cd
uo (t)
(b)
Lc
ui (t)
Rc
Cb
Cd
uo (t)
(c)
Figure 7.8 (a) Simplified analogous circuit. Compliance of the sensor diaphragm is larger than compliance of catheter or sensor cavity for a bubble-free, noncompliant
catheter. The resistance and inertance of the catheter are larger than those of the sensor, because the catheter has longer length and smaller diameter. (b) Analogous circuit for
catheter-sensor system with a bubble in the catheter. Catheter properties proximal to the bubble are inertance Lc and resistance Rc. Catheter properties distal to the bubble are
Lcd and Rcd. Compliance of the diaphragm is Cd; Compliance of the bubble is Cb. (c) Simplified analogous circuit for catheter-sensor system with a bubble in the catheter,
assuming that Lcd and Rcd are negligible with respect to Rc and Lc.
Pout
Example 7.1
?
Pin
Sensor
Pin (real)
(a)
Pout (measured)
P
Diaphragm
Catheter
Liquid
Rc
Lc
Incremental
length
Rc
Lc
Rc
DV
Lc
Rs
Ls
(b)
Cc
Cc
Cc
Cs
C
d=
DV
DP
fn = 91 Hz
 = 0.033
10
fn = 22 Hz
 = 0.137
uo (jw)
ui (jw)
1.0
No bubble
Bubble
0.1
0.01
0.01
0.02
0.04 0.06 0.1
0.22 0.4 0.6
f / fn
1
2
4
6 8 10
0.91
Figure 7.9 Frequency-response curves for catheter-sensor system with and without bubbles. Natural frequency decreases from 91 Hz to 22 Hz and damping ratio increases
from 0.033 to 0.137 with the bubble present.
Sensor
(a)
P
Diaphragm
Catheter
Liquid
Rc
Lc
Incremental
length
Rc
Lc
Rc
DV
Lc
Rs
Ls
(b)
Cc
Cc
Cc
Cs
C
d=
DV
DP
Threeway
stopcock
Surgical
glove
Match
O-ring
Air
Saline
Rubber
washer
Sphygmomanometer
bulb
Figure 7.10 Transient-response technique for testing a
pressure-sensor-catheter-sensor system.
31-cm needle (0.495 mm ID). (From I. T. Gabe, "Pressure
Measurement in Experimental Physiology," in D. H. Bergel, ed.,
Cardiovascular Fluid Dynamics, vol I, New York: Academic Press,
1972.)
Figure 7.12 A sinusoidal pressure-generator test system A low-frequency sine generator drives an underwater-speaker system
that is coupled to the catheter of the pressure sensor under test. An "ideal" pressure sensor, with a frequency response from 0 to 100
Hz, is connected directly to the test chamber housing and monitors input pressure.
Pressure sensor
"Ideal“
sensor
Catheter
Underwater
speaker
Saline
Low-frequency
sine generator
7.6 Bandwidth requirements for measuring blood pressure
May ignore harmonics of the blood pressure
waveform higher than the tenth.
e.g.: 20 Hz bandwidth would be enough for a heart
rate of 120 bpm (or 2 Hz)
Measurements of the derivative of the pressure signal
increase the bandwidth requirements.
7.7 Typical pressure-waveform distortion
Overdamping: due to air bubbles or blood clots
due to pinching the catheter
Catheter whip (猛然挪動): The catheter is bent and
whipped in a region of high pulsatile flow
7.13 Indirect Measurements of Blood Pressure
7.13 Indirect Measurements of Blood Pressure
A rubber bulb  for inflation of the cuff
(橡膠球)
(充氣)
An inflatable cuff  for occlusion of the blood vessel
(橡膠球)
(充氣)
A mercury  for detection of pressure
(橡膠球)
(充氣)
Figure 7.20 Typical indirect blood-pressure measurement system The sphygmomanometer cuff is inflated by a hand bulb to pressures above the systolic level. Pressure is
then slowly released, and blood flow under the cuff is monitored by a microphone or stethoscope placed over a downstream artery. The first Korotkoff sound detected indicates
systolic pressure, whereas the transition from muffling to silence brackets diastolic pressure. (From R. F. Rushmer, Cardiovascular Dynamics, 3rd ed., 1970. Philadelphia: W.
B. Saunders Co. Used with permission.)
Normal blood pressure values