1. Chapter 7 Blood Pressure and Sound

2. Blood pressure measurement
(Ideal) Target:
Blood pressure
@ the heart chambers
@ the peripheral vascular system
Purpose:
to help the physician to determine the functional integrity (完整) of the cardiovascular system
Methods:
Direct (invasive) techniques
2. Indirect (noninvasive) techniques

3. 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

4. 組織
大動脈
下大靜脈 肺 肺 組織
Figure 7.1 The left ventricle ejects blood into the systemic circulatory system. The right ventricle ejects blood into the pulmonary circulatory system.

5. Valve: 瓣膜

6. 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

7. Armature
Strain-gage wires A D
(a) C B
Diaphragm
(b) c b d a R4
D uo ui R3 R2 Ry Ri Rx R1

8. Armature
Strain-gage wires A D
(a) C B
Diaphragm
(b) c b d a R4
D uo ui R3 R2 Ry Ri Rx R1
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.

9. Figure 2.2 Armature Strain-gage wires A D (a) C B Diaphragm (b) c b d
D uo ui R3 R2 Ry Ri Rx R1
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.

10. Armature
Strain-gage wires A D
(a) C B
Diaphragm
(b) c b d a R4
D uo ui R3 R2 Ry Ri Rx R1
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.

11. 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.

12. 7.3 Dynamic properties of the pressure sensor
Static pressure
Blood pressure
(dynamic)

13. Models of liquid-filled catheter sensor:
Distributed-parameter model:
More accurate;
More complicated;
Lumped-parameter model:
Acceptable accuracy;
Easier to work with;

14. 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
(順從性)
Electric capacitance (C )
Pressure (P), pascal = N/m2
Voluminal flow rate (F), m3/s
Liquid volume, m3
Voltage (V), V
Current (I), C/s = A
Electric charge, coulomb

15. △P I ＋△V－  F  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
F  △P I 
＋△V－

16. Compliance vs capacitance

18. Physical model & Analogous electrical model
Analogous (adj.) 類似的
Analog (adj.) 類比式的
Diaphragm
Sensor Ls Lc Rs Rc P Cc C
d = Cs DV DP
Liquid
Catheter
(a)
(b)
Incremental
length
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.

19. Rc
Poiseuille equation： a physical law that describes slow viscous incompressible flow through a constant circular cross-section

22. Lc

23. Cd
>, =, <
Compliance:
Ball
Clay
Elasticity:

24. Diaphragm Sensor Ls Lc Rs Rc P Cc C d = Cs DV DP Liquid Catheter (a)
(b)
Incremental
length
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.

25. Physical model & Analogous electrical model
Analogous (adj.) 類似的
Analog (adj.) 類比式的
Diaphragm
Sensor Ls Lc Rs Rc P Cc C
d = Cs DV DP
Liquid
Catheter
(a)
(b)
Incremental
length
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.

26. Catheter liquid inertia Catheter liquid resistance Sensor diaphragm
compliance
(a) Lc Rc
Lcd
Rcd
ui (t) C Cd
uo (t) b
(b) Lc Rc
ui (t) 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.

27. Example 7.1 Pin (real) Pout (measured) Diaphragm Sensor Ls Lc Rs Rc PCc C
d = Cs DV DP
Liquid
Catheter
(a)
(b)
Incremental
length
Pin (real)
Pout (measured)

35. fn = 91 Hz  = 0.033 10 fn = 22 Hz  = 0.137 1.0 No bubble uo (jw)
0.01
0.1
1.0 10
0.91
f / fn
Bubble
fn = 91 Hz
 = 0.033
fn = 22 Hz
 = 0.137
No bubble
uo (jw)
ui (jw)
0.02
0.04
0.06
0.22
0.4
0.6 1 2 4 6 8
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 to with the bubble present.

36. Diaphragm
Sensor Ls Lc Rs Rc P Cc C
d = Cs DV DP
Liquid
Catheter
(a)
(b)
Incremental
length

37. Surgical
glove
Three-
way
stopcock
Match
O-ring
Air
Saline
Rubber
washer
Sphygmomanometer
bulb
Figure 7.10 Transient-response technique for testing a pressure-sensor-catheter-sensor system.

38. Figure 7.11 Pressure-sensor transient response Negative-step input pressure is recorded on the top channel; the bottom channel is sensor response for a Statham P23Gb sensor connected to a 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.)

39. Pressure sensor "Ideal“ sensor Catheter Saline Underwater speaker
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
Saline
Underwater
speaker
Low-frequency
sine generator

40. 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.

41. 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

42. 7.13 Indirect Measurements of Blood Pressure

43. 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
A mercury  for detection of pressure

44. 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., Philadelphia: W. B. Saunders Co. Used with permission.)

45. Normal blood pressure values