Local Measurement of the Pulse Wave Velocity using
Doppler Ultrasound
by
Minnan Xu
Submitted to the Department of Electrical Engineering and
Computer Science
in partial fulfillment of the requirements for the degree of
Bachelor of Science in Electrical Engineering and Computer Science and
Master of Engineering in Electrical Engineering and Computer Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 24, 2002
c 2002 Minnan Xu, All rights reserved.
The author hereby grants to M.I.T. permission to reproduce and distribute
publicly paper and electronic copies of this thesis and to grant others the
right to do so.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Electrical Engineering and
Computer Science
May 24, 2002
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
David Prater
VI-A Company Thesis Supervisor
Thesis Supervisor
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Roger D. Kamm
Professor, Biological Engineering
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arthur C. Smith
Chairman, Department Committee on Graduate Theses
2
Local Measurement of the Pulse Wave Velocity using Doppler
Ultrasound
by
Minnan Xu
Submitted to the Department of Electrical Engineering and
Computer Science
on May 24, 2002, in partial fulfillment of the
requirements for the degree of
Bachelor of Science in Electrical Engineering and Computer Science and Master of
Engineering in Electrical Engineering and Computer Science
Abstract
Cardiovascular disease is the leading cause of death in many developed countries. Arteries of
people suffering from this disease become stiff and blocked by fatty deposits. In recent years,
non-invasive imaging techniques have been playing an increasingly important role in detecting the development of cardiovascular disease. Several methods focus on the measurement of
pulse wave velocity, the velocity at which the pressure wave propagates, because it is directly
related to arterial stiffness. The objective of this project is to investigate the feasibility of
measuring local pulse wave velocity from the blood flow waveforms acquired by Doppler
ultrasound. The proposed method includes the following steps: first acquire flow waveforms
by Doppler ultrasound at two locations within the same artery, next detect the delay or
difference in arrival time of the flow wave at the two arterial locations, and then calculate
the PWV by dividing the length of the arterial segment being imaged by the calculated
time delay. Although at the conclusion of this study reliable pulse wave velocity detection
is not achieved, the study sheds light on many important issues surrounding this potential
application. The project explores how sources of variations such as radial postioning of the
probe and noise level affect the accuracy of the delay estimate.
Thesis Supervisor: David Prater
Title: VI-A Company Thesis Supervisor
Thesis Supervisor: Roger D. Kamm
Title: Professor, Biological Engineering
3
4
Acknowledgments
This thesis project has been a great academic and personal learning experience. I would like
to thank everyone who helped me through this thesis project. Here is a partial list of all those
who helped me learn. Dave Prater, with whom I have worked three summers and a term, is
the originator of this project idea. He has always inspired me with his energy and innovation.
Prof. Roger Kamm, my MIT advisor, who pointed me to so many useful resources. Guohao
Dai, who let me borrow his flow system. Andrew Davenport, who solved all my software
problems at work. Tony Vallance and the AQ group at Philips, who made me part of a team
at Philips. Jim Michner, who helped me with the PVT part of the project. Bill Fry, who
helped with modifications made to the Doppler board. Jodie Perry, McKee Poland, and Kim
Robertson who helped me with the ever confusing scanner part of the project. David Clark,
who help me understand Doppler ultrasound. Dr. Ivan Salgo, my neighbor at Philips, who
greeted me every morning and also shared his knowledge of the medical world. Tony Borges,
who helped me settle in from the very first day. Tony Brock-Fisher, who gave me some
hard to find Doppler ultrasound test fluid. Prof. Denny Freeman, who came to visit me in
Andover. Markus Zahn and Lydia Wereminski from the MIT 6A office, who were invaluable
in helping through the 6A and M.Eng programs. Raymond Chan and Dr. Robert Lees from
the Boston Heart Foundation, who offered great advice on this project and graduate school.
The volleyball group at work who made the end of every week a blast. My family, who
are supportive always. I would also like to thank my family for pushing me to work hard
before I knew any better. And last but not least, Kevin Wilson, my friend in every way. He
helped with every part of this project, from discussing ideas to providing moral support and
encouragements.
Thank you!
Minnan
5
6
Contents
1 Introduction
15
1.1
Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
1.2
Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
2 Background
2.1
17
Arterial Stiffness and Pulse Wave Velocity . . . . . . . . . . . . . . . . . . .
17
2.1.1
Existing Methods of Measuring Pulse Wave Velocity
. . . . . . . . .
18
2.1.2
Factors Influencing Pulse Wave Velocity . . . . . . . . . . . . . . . .
20
2.1.3
Other Uses of PWV measurement . . . . . . . . . . . . . . . . . . . .
21
2.2
Blood Flow in the Common Carotid Artery . . . . . . . . . . . . . . . . . .
21
2.3
Ultrasound in Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.4
Doppler Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
2.4.1
Doppler Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
2.4.2
Measuring Blood Flow with Doppler Ultrasound . . . . . . . . . . . .
24
2.5
Pulsed Doppler vs. Continuous Doppler . . . . . . . . . . . . . . . . . . . . .
24
2.6
Principles of Pulsed Doppler . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
3 Methodology
3.1
29
System Modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3.1.1
Scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3.1.2
Doppler Processor
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
3.1.3
Video Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
3.1.4
Timing Changes Due to System Modifications . . . . . . . . . . . . .
33
7
3.2
Flow System Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Data Processing
36
39
4.1
Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
4.2
Envelope Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4.2.1
Maximum Frequency Follower . . . . . . . . . . . . . . . . . . . . . .
41
4.2.2
Difficulties in Envelope Detection . . . . . . . . . . . . . . . . . . . .
41
4.3
Windowing the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
4.4
Delay Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
4.4.1
Correlation Based Techniques . . . . . . . . . . . . . . . . . . . . . .
45
4.4.2
Phase Difference Delay Estimation . . . . . . . . . . . . . . . . . . .
46
5 Results
5.1
49
Simulated Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
5.1.1
Variance of the Delay Estimates . . . . . . . . . . . . . . . . . . . . .
52
5.1.2
Random Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
5.2
Flow System Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
5.3
Physiological Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
6 Discussion
6.1
6.2
63
Estimated PWV
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
6.1.1
Simulated Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
6.1.2
Flow System Data . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
6.1.3
Physiological Data . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
High Variance in the Delay Estimate . . . . . . . . . . . . . . . . . . . . . .
65
6.2.1
Waveform Variation Due to Radial Position . . . . . . . . . . . . . .
65
6.2.2
Waveform Variation Due to Wave Dispersion . . . . . . . . . . . . . .
67
6.2.3
Variability Due to Scanning . . . . . . . . . . . . . . . . . . . . . . .
67
6.2.4
Physiological Variability . . . . . . . . . . . . . . . . . . . . . . . . .
68
6.2.5
Number of Heart Cycles Needed . . . . . . . . . . . . . . . . . . . . .
68
6.2.6
System Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
8
6.3
Variance Due to Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
6.3.1
Results of Simulated Noise . . . . . . . . . . . . . . . . . . . . . . . .
70
6.3.2
Noise in Physiological Data . . . . . . . . . . . . . . . . . . . . . . .
70
System Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
6.4.1
Dual Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
6.4.2
Resolution of Delay Estimate . . . . . . . . . . . . . . . . . . . . . .
72
6.4.3
Velocity Measurement Accuracy . . . . . . . . . . . . . . . . . . . . .
72
6.4.4
Small Image Buffer Size . . . . . . . . . . . . . . . . . . . . . . . . .
73
6.5
Delay Estimation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
6.6
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
6.6.1
System Modifications . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
6.6.2
User Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
6.6.3
Other Applications of Dual Beam Setup . . . . . . . . . . . . . . . .
75
6.6.4
Areas for Further Research . . . . . . . . . . . . . . . . . . . . . . . .
75
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
6.4
6.7
9
10
List of Figures
2-1 Ultrasound Beam and Artery . . . . . . . . . . . . . . . . . . . . . . . . . .
24
2-2 A Single Spectrum Acquired Using Doppler Ultrasound . . . . . . . . . . . .
25
2-3 Illustration of the Pulsed Doppler Principle . . . . . . . . . . . . . . . . . . .
27
3-1 General data path from acoustic signal to video display . . . . . . . . . . . .
30
3-2 Diagram of Doppler Detector Board . . . . . . . . . . . . . . . . . . . . . . .
31
3-3 Diagram of the Modified Doppler Detector Board . . . . . . . . . . . . . . .
31
3-4 Two Spectra Acquired Simultaneously Using Doppler Ultrasound . . . . . .
32
3-5 Doppler Signal Path in Non-Duplex Systems . . . . . . . . . . . . . . . . . .
35
3-6 Flow System Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
3-7 Video Display of Dual Beam Phantom Data . . . . . . . . . . . . . . . . . .
38
4-1 Acquisition of Dual Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4-2 Extracted Envelopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
4-3 Low-pass Filtering of Envelopes . . . . . . . . . . . . . . . . . . . . . . . . .
42
4-4 Windowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
4-5 The Delay Estimation Problem . . . . . . . . . . . . . . . . . . . . . . . . .
45
4-6 Average Phase differences . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
4-7 Variance of Phase differences . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
5-1 Simulated Envelope Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
5-2 Velocity Profile at Center of the Artery . . . . . . . . . . . . . . . . . . . . .
51
5-3 Delay Estimates From Different Radial Positions . . . . . . . . . . . . . . . .
53
5-4 Simulated Data with Noise of SNR = 74dB . . . . . . . . . . . . . . . . . . .
53
11
5-5 Simulated Data with Noise of SNR = 62dB . . . . . . . . . . . . . . . . . . .
54
5-6 Simulated Data with Noise of SNR = 47dB . . . . . . . . . . . . . . . . . . .
54
5-7 Phantom Flow Wave Envelopes . . . . . . . . . . . . . . . . . . . . . . . . .
55
5-8 Flow System Data Set 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
5-9 Flow System Data Set 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
5-10 Physiological Data Set A1 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
5-11 Physiological Data Set A2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
5-12 Physiological Data Set B1 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
5-13 Physiological Data Set B2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
5-14 Physiological Data Set B3 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
5-15 Physiological Data Set B4 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
6-1 Beam Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
12
List of Tables
3.1
Modified Triggered Mode Frame Table . . . . . . . . . . . . . . . . . . . . .
34
3.2
Modified Duplex Mode Frame Table . . . . . . . . . . . . . . . . . . . . . . .
34
3.3
Doppler Test Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
5.1
Summary of Simulated Data Sets . . . . . . . . . . . . . . . . . . . . . . . .
50
5.2
Simulated Data Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
5.3
Effect of Radial Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
5.4
Summary of Flow System Data Sets . . . . . . . . . . . . . . . . . . . . . . .
55
5.5
Summary of Physiological Data Sets . . . . . . . . . . . . . . . . . . . . . .
57
5.6
Time delays and Estimated PWV . . . . . . . . . . . . . . . . . . . . . . . .
61
13
14
Chapter 1
Introduction
Cardiovascular disease is the leading cause of death in many developed countries. Arteries
of people suffering from this disease become stiff and blocked by fatty deposits. In recent
years, non-invasive imaging techniques have been playing an increasingly important role in
detecting the development of cardiovascular disease. Several methods focus on the measurement of pulse wave velocity, the velocity at which the pressure wave propagates, because
it is directly related to arterial stiffness. The objective of this project is to investigate the
feasibility of measuring local pulse wave velocity from the blood flow waveforms acquired by
Doppler ultrasound. Although at the conclusion of this study reliable pulse wave velocity
detection is not achieved, the study still sheds light on many important issues surrounding
this potential application.
1.1
Problem Description
The proposed method is to acquire two blood flow waveforms using a single ultrasound probe
at two locations of an artery. The delay in the arrival time of the flow wave at the two points
of measurement divided by the distance between the two points gives the pulse wave velocity.
The distance of travel is determined by the separation of the two apertures at the two ends
of a linear transducer. The details of estimating the delay will be the main focus of the
study.
15
1.2
Overview of Thesis
This thesis is organized as follows: Chapter 2 begins with a brief overview of arterial stiffness,
pulse wave velocity, and Doppler ultrasound. Chapter 3 presents the experimental setup and
system modifications made for data acquisition. Chapter 4 develops the various steps and
algorithms involved in delay estimation. Chapter 5 shows the results from simulated data,
flow system data, and physiological data. Chapter 6 analyzes the results and the proposed
technique for the detection of pulse wave velocity.
16
Chapter 2
Background
This chapter presents a brief introduction to arterial stiffness, blood flow, pulse wave velocity,
ultrasound imaging, Doppler ultrasound, and the use of Doppler ultrasound to measure
blood flow. Section 2.1.1 presents current and representative methods of measuring pulse
wave velocity and their disadvantages that the proposed method addresses.
2.1
Arterial Stiffness and Pulse Wave Velocity
Pulse wave velocity has long been attractive as a diagnostic tool. It is generally agreed that
many cardiovascular disorders are associated with increasing rigidity of the arterial wall due
to arteriosclerosis
1
[1]. The relationship between the pulse wave velocity (P W V ) and the
elasticity of a thin-walled elastic tube filled with an incompressible fluid is expressed by the
Moens-Korteweg Equation (2.1).
PWV =
Eh
ρD
(2.1)
From this equation, we see that the PWV (m/s) is related to the square root of Young’s
modulus of elasticity (E). Therefore measuring the pulse wave velocity leads to an estimate
1
Arteriosclerosis is a chronic disease characterized by abnormal thickening and hardening of the arterial
wall.
17
of the stiffness of the tube. Higher velocity corresponds to higher arterial stiffness. The
blood density, ρ, of a person should stay fairly constant. The other two parameters h and
D may be estimated from the B-mode images of the artery [7].
2.1.1
Existing Methods of Measuring Pulse Wave Velocity
Pressure Wave or Flow Wave
There are existing methods which measure PWV by using Doppler ultrasound [26, 6, 14].
These methods use continuous Doppler and measure two sites very distant in the arterial
tree, so these methods have the problem of measuring an averaged value for the PWV. (The
problem with acquiring an average PWV value is discussed later.) However these methods
demonstrate that the flow wave measured by Doppler ultrasound can be used just as well as
the pressure wave for detecting the PWV [1].
Delay Detection
Many computer algorithms have been developed to detect the delay between the waves
captured at distant sites of the arterial tree [5]. Most of these algorithms rely on detecting
the PWV by first identifying characteristic points of the waveforms. The characteristic
points are usually chosen near the foot or the lowest point of the flow wave. The foot is
preferred because it is relatively free of arterial wave reflection so that error in the calculation
of the forward pulse wave velocity is minimized [16]. The technique of finding the time delay
between the feet of waveforms works well when the two points of measurement are far apart
in the arterial tree making the delay large. This technique would not work for measuring the
delay between two waveforms captured a few centimeters apart in the arterial tree. This is
because the error associated with locating the foot of the flow wave is around the sampling
interval (5 ms) which is on the order of the delay being detected in this application.
18
Sequential or Simultaneous Measurements
The standard method of measuring PWV is to record a proximal2 and a distal3 pressure
wave at two different sites on the arterial tree [1]. There are several variations that differ
in the choice of artery being measured and whether the measurement at the two sites is
sequential or simultaneous. Sequential recording is performed when only one probe is available, therefore simultaneous recording of two sites is not possible. The operator first records
the flow or pressure wave from the proximal site and then from the distal site. At both
sites, the ECG is also recorded. The time differences between the ECG signal and the flow
or pressure waveforms at the two sites, T1 and T 2, yields the time delay: ∆T = T2 − T1 .
The PWV measurement based on sequential methods is not based on the traveling speed of
the same wave generated by the same heartbeat, as is possible in simultaneous techniques.
Furthermore, sequential methods do not consider the variability between recordings at the
proximal and the distal sites.
The standard technique is the simultaneous measurement of the pressure wave propagating from the carotid artery to the femoral artery [6]. However, this method has several
problems. The distance the pulse wave travels from the carotid to the femoral is hard to determine. A non-invasive, superficial estimate of the traveled distance is the distance covered
by skin between the two transducers. It is known that PWV increases from near the heart
to the femoral artery. Thus, the PWV obtained from the popular carotid-femoral technique
shows their average value.
Local Measurement of the PWV is desired because of the local nature of arteriosclerosis.
In the early stage of arteriosclerosis, fibrous spots a few millimeters in diameter are scattered
on the arterial wall. In the final stage of arteriosclerosis, after these spots grow, the arterial wall becomes homogeneously hard [6]. Therefore it is important for early diagnosis to
measure the local hardness of the arterial wall. It has been shown that health of the certain
arteries, such as the carotid artery is highly correlated to atherosclerosis4 [2]. Therefore it
2
A proximal point is one located toward the center of the body.
A distal point is one located far from the center of the body.
4
Atherosclerosis is an arteriosclerosis characterized by the deposition of fatty substance in and fibrosis of
the inner layer of the arteries.
3
19
would be beneficial to measure arteries locally.
The proposed technique of simultaneously measuring two points in the same artery solves
the above problems. The distance of wave propagation is easier to determine since the
transducer length and the aperture size are known. The distance between the center of the
two apertures is the traveled distance. Measuring two points in the same artery ensures the
local measurement of PWV instead of an average value of PWV of two distant locations in
the arterial tree. Local PWV provides a measurement of local arterial properties, therefore
allowing possibly early diagnosis of arteriosclerosis.
Arterial Wall Motion Detection for PWV Measurement
As the pressure pulse travels through an arterial segment, the arterial radius at a fixed
location expands and contracts from its undisturbed size. Chubachi et al. [6] studies the
use of Doppler ultrasound to capture the motion of the arterial wall at two sites. The radio
frequency (RF) signal captured from the two sites are used to estimate the difference in
arterial wall vibration and hence the propagation delay of the pulse wave. This method
requires accurate tracking of the arterial wall from the B-mode ultrasound image, which
may be difficult since the arterial walls are very thin.
2.1.2
Factors Influencing Pulse Wave Velocity
Pulse wave velocity can change with many physiological parameters. Age and cardiovascular
health are two factors which are important for the basis of this project. As a person ages, his
arteries harden gradually and the PWV of an arterial segment increases gradually following a
relatively smooth curve. When a person develops cardiovascular problems, the PWV deviates
from the normal curve. The proposed technique for PWV measurement has the potential
to pick up deviations from the normal curve of PWV increase. The intention is that the
technique is simple enough to be used as part of a routine check-up. Each measurement can
be seen as a point on the curve of a person’s cardiovascular health. If a person’s arteries are
hardening normally with age, then there is not much reason for alarm. However if a person’s
arteries are hardening abnormally with disease, having a record of how the PWV is changing
20
may help to identify this health problem.
Other factors which influence the pulse wave velocity are shorter in time frame, which can
be problematic for the measurement of PWV. Studies have shown that the pulse wave velocity
varies with respiration [1]. PWV is slightly higher during expiration than inspiration, due to
the fact that blood pressure is slightly increased during the expiratory phase. The observed
differences of PWVs between the inspiration and expiration phases were less than 0.5 m/s
in normal subjects. Typical PWV for the common carotid is from 6.80 m/s to 8.30 m/s.
Studies have also shown that after a meal there is a significant increase of PWV in peripheral
vessels such as the carotid [11]. The reason for this change has not been established. These
factors should be taken into consideration when comparing PWV measurements taken at
different times.
Blood flow velocity (average of 0.25 m/s in the carotid artery) is small compared to
the pulse wave velocity. Therefore correction for the velocity of blood flow itself is small.
However any considerable increase in the velocity of the blood as a result of local or general
disturbances will cause an equal increase in the velocity of the pulse wave [1]. The study
pointed out that “any experimentally determined wave velocity must represent the velocity
of the wave relative to the blood, plus the velocity of the blood in the artery.”
2.1.3
Other Uses of PWV measurement
Aside from using PWV to diagnose the presence of cardiovascular disease, it can also be used
to monitor the effect of drugs. Asmar [1] discusses the use of PWV to monitor the effects
of antihypertensive drugs used to treat arteriosclerosis, the effect of hormone replacement
therapy on arterial properties, and the effect of other possible treatments such as specific
food intake and exercise on cardiovascular health.
2.2
Blood Flow in the Common Carotid Artery
The common carotid artery was chosen for this study for the following reasons. The carotid
artery is easily accessible since it is located close to the skin with no other major arteries
21
nearby. The common carotid is straight and can be approximated well by a large straight
elastic tube. Health of the carotid artery is important. It has been shown that carotid health
is highly correlated to atherosclerosis [2].
The diameter of the common carotid in adults range from 0.2 cm to 0.8 cm with an
average value of about 0.7 cm. Typical carotid pulse wave velocity in human ranges from
6.80 m/s to 8.30 m/s [1].
Like other main arteries, the common carotid has a flexible wall that is thin compared
to its diameter. The wall expands and contracts in response to pressure pulses. Blood flow
can be modeled as pulsatile flow in an elastic tube. Womerley’s model of pulsatile flow is
presented here. This model is used to generate simulated data (presented in Section 5.1).
Womersley’s model is for a fully developed pulsatile flow in a straight circular cylinder.
This model assumes that the flow is at a location sufficiently distant from the inlet, where
the radial and circumferential components of velocity and pressure vanish [22]. The solution,
under the above assumption, is shown in Equation 2.2,



r 3/2
J0 (αn R
i )
N 

1
−
2
r
2B0
Bn 
J0 (αn i3/2 )

1
−
+
W (r, t) =
einωt
2
2J1 (αn i3 /2)


πR2
R
πR
1 − αn i3/2 (αn i3/2 )
n=1
(2.2)
W (r, t) is the velocity profile. R is the radius of the cylinder, J0 and J1 are Bessel functions
of the first kind of order 0 and 1, respectively. αn = R (nω)/ν where ν is the kinematic
viscosity. The non-dimensional parameter α = R ω/ν is known as the Womersley number.
Section 5.1 shows plots of waveforms generated by using this model.
2.3
Ultrasound in Medicine
In recent years, non-invasive imaging techniques such as ultrasound have been playing an
increasingly important role in clinical settings [4]. Ultrasound imaging’s moderate cost and
capability to acquire data sets over both space and time make it the modality of choice for
many diagnostic applications.
22
The ultrasound B-mode image is generated by the use of a ultrasonic transducer held
up to the body. The transducer transmits ultrasound pulses into the body and receives reflected echoes. As the transmitted signal travels through the body and encounters structural
boundaries, part of the signal is reflected. The amount of the ultrasound signal reflected is
proportional to the difference in the tissue’s acoustic densities. An example of a B-mode
image is the small image of the carotid artery at the upper right corner in Figure 2-2.
2.4
Doppler Ultrasound
Doppler ultrasound is a technique for making non-invasive velocity measurements of blood
flow. The transmitter sends out ultrasound pulses. The receiver, instead of measuring how
much energy is reflected back by structures in the body, listens for how the signal has changed
in frequency.
2.4.1
Doppler Principle
The Doppler principle is utilized by transmitting a signal into the body and observing the
changes in frequency that occur when it is reflected or scattered from the targets [7]. When
a known frequency is sent out, a moving target returns that frequency shifted by an amount
proportional to its velocity. The frequency shift occurs only for the motion that is in the
direction of the ultrasound beam. The equation for the Doppler shift is
fs =
2ft v cos(θ)
c
(2.3)
where ft is the frequency transmitted, fs is the frequency shift, v is the velocity of the target,
c is the velocity of sound in tissue, and θ is the angle between the blood velocity vector and
the direction of wave propagation as shown in Figure 2-1. The term cos(θ) shows that only
the component of the velocity in the direction of ultrasound propagation is measured.
23
θ
sin
Direction of
Blood Flow
v
v
v
co
θ
s
θ
a
ltr
U
so
m
ea
cB
ni
Figure 2-1: Ultrasound Beam and Artery The ultrasound beam intersects the artery at an
→
angle θ. The component of the blood velocity vector −
v in the direction of the beam is
measured. As the angle increases, the Doppler shift frequency decreases.
2.4.2
Measuring Blood Flow with Doppler Ultrasound
In Figure 2-2, a typical Doppler spectrum of the carotid flow shows the distribution of
frequency shifts of velocities of the scatterers in the blood. The spectrum changes with time
since blood flow is pulsatile. The shape of the spectrum gives an idea of how blood flow
changes temporally.
Doppler assessment of blood flow has become routine in many diagnostic ultrasound
exams [20]. The use of Doppler today ranges from assessing blood flow in the fetus and
umbilical cord, to flow patterns through valves in the heart or monitoring of blood flow to
the brain [7]. A variety of instruments are available, ranging from simple pocket-size versions
that give an audio output, to very expensive imaging systems that integrate blood velocity
measurements with images of anatomy [20].
2.5
Pulsed Doppler vs. Continuous Doppler
There are two modes of operation for Doppler ultrasound, continuous wave (CW) and pulse
wave (PW) ultrasound. In CW mode, the transducer has the transmitter and receiver
24
Figure 2-2: A Single Spectrum Acquired Using Doppler Ultrasound Spectral Doppler measurement of blood velocity in the center of a common carotid artery. The vertical tick marks
in the middle of the spectrum indicates a duration of one second. The vertical axis is proportional to the Doppler shift frequency and in this case has been converted to velocity (units
of cm/s).
mounted side by side. The transmitter continuously sends out a beam of ultrasound and
the receiver is continuously receiving the returned ultrasound signal. In PW mode, a short
burst of ultrasound is transmitted at a repetition frequency of fr . The returned signal is
received with the same transducer at a time delay of Td after the transmission of the pulse.
Td is determined by the range of interest.
For PWV measurements, continuous wave (CW) Doppler is traditionally used because of
its economic advantage. However, CW Doppler has one major drawback; there is no range
resolution. This is because the beam is continually transmitted and received, so the blood
motion along the entire beam is being observed. In the PW mode, only the blood motion in
the range of interest is observed. In this project, PW is used for its range resolution and also
25
because it is easier to make the system changes necessary to acquire two Doppler spectra.
2.6
Principles of Pulsed Doppler
Pulsed Doppler provides localized velocity measurements. The instrument transmits a pulse
that can vary from a single pulse to 40 cycles long [20], depending on the desired length of the
sample volume. The returned signal contains both amplitude and phase information. The
phase information can be extracted by coherent demodulation by comparing the received
pulses to the reference signal which is oscillating at the frequency sent out. This process
is illustrated in Figure 2-3. Short bursts of ultrasound are transmitted at regular intervals,
the pulse repetition frequency (PRF), toward a moving target. As the target moves away
from the transducer, the returning echoes gradually shift in phase relative to the reference
wave. The pulsed Doppler system is sampling this phase shift at the PRF. When the target
is moving too fast, or the phase shift occurs too fast, the frequency shift is aliased. Thus,
the highest frequency shift pulsed Doppler systems can detect is
P RF
.
2
The PW sample volume depends on the combination of the transmitted pulse length and
the length of the gated range [7]. The width of the sample volume is determined by the
width of the beam at the position of the range gate. However, PW sample volumes have not
been studied in detail [7].
The distance from the transducer to the beginning of the range cell, Z1 , is given by:
Z1 = c(td − tp )/2
(2.4)
where c is the velocity of the ultrasound in tissue, tp the pulse length, and td the time delay
between the start of transmission and the moment at which the receiver gate opens. The
distance from the transducer to the end of the range cell, Z2 , is given by:
Z2 = c(td + tp )/2
26
(2.5)
where tp is the period for which the gate is open. The length of the range cell Zr , may
therefore be written as the following:
Zr = Z2 − Z1 = c(tg + tp )2
(2.6)
The sample volume is an important consideration for the maximum frequency envelope and
the effect of radial positioning of the probe (Section 6.2.1).
Transmit Pulse
Phaser
Estimate
Receive Pulse
Blood
Motion
fs
Figure 2-3: Illustration of the Pulsed Doppler Principle Estimates of the blood velocity is
derived from a series of phase shifts resulting from motion of blood. fs denotes the Doppler
shifted frequency. This diagram is adopted from Hwang [10].
27
28
Chapter 3
Methodology
This chapter presents the system modifications made to acquire flow waves at two locations
in an artery and the flow system set up for simulating pulsatile blood flow.
3.1
System Modifications
The underlying system used in this study is the SONOS 5500 from Philips Medical Systems
Cardiac Monitoring Group (previously part of Agilent Technologies and which was previously
part of Hewlett-Packard.) To make the dual spectrum measurement, the system was modified
in several ways. The modifications allow the acquisition of blood flow information from two
locations within the artery, then process the incoming Doppler signal as signals from two
locations instead of one. Figure 3-1 shows the overall diagram of the data path. Each of the
three blocks will be explained in more detail in the following sections. Figure 3-5 shows the
data path in a more pictorial format.
3.1.1
Scanner
The scanner environment sets up the the transducer for transmitting and receiving ultrasound pulses. The transducer has 288 piezoelectric elements at its surface (spanning 5 cm).
Before every ultrasound beam is shot, only the relevant elements are activated. The correct
delay coefficients are also put in place to receive the reflected signal at the appropriate focus.
29
Time domain
acoustic data
Scanner
board
DDET board
PVT card
On-screen
Display
Figure 3-1: General data path from acoustic signal to video display The scanner board,
Doppler detector board (DDET) and the PVT card were modified to process the incoming
acoustic data captured from two apertures instead of one.
For this study, the scanner environment is modified to transmit two pulses, one at each
end of the linear transducer. Aperture sizes of 128 elements at each end of the linear probe
are used to send out the two pulses. The two pulses are identical (in frequency, direction,
and depth) except for their aperture positions. The center of the apertures are separated by
a distance of approximately 3 cm. A side effect of alternating between two pulses is that the
pulse repetition frequency has been cut by half. Thus the highest frequency shift or velocity
detected is decreased by a factor of two.
3.1.2
Doppler Processor
The Doppler processor processes the incoming acoustic signal. The Doppler board consists
of three processors: A, B, and C. Processor A wall-filters the acoustic signal to remove
low frequencies associated with slow motions of the arterial walls and other nearby tissues.
Processor B calculates the spectrum from the acoustic signal and further processes it for
video display and audio output. Processor C holds the image and audio data for retrieval.
Figure 3-2 shows the data path in the Doppler processor B. The incoming data stream is first
windowed by a 128-point Hamming window, then fast Fourier transformed (FFT) to give the
the frequency content of the acoustic signal. The spectrum is then FFT shifted so that the
the spectrum is ordered by increasing frequency. Next, the spectrum undergoes temporal
smoothing. Finally the spectrum is interpolated and gain corrected for video display.
The modifications made to the Doppler processor occurs for most of the steps outlined
30
DDET Processor B
Time domain
doppler signal
Window
FFT
Magnitude
Detector
FFT shift
Temporal
Smoothing
Filter
Interpolation
to Display
Map Gain
and Output
Figure 3-2: Diagram of Doppler Detector Board Doppler processor B is responsible for
processing the incoming acoustic signal into Doppler spectra and prepares the spectra for
video display.
above. The input data is assumed to be interlaced, with values alternating from the two
side of the transducer. The interlaced data is split into two streams before undergoing wallfiltering in Doppler processor A. The result of the wall-filter is interlaced again so that the
input to Doppler processor B is of the same format as in the unmodified system. The data
stream is again split into two in Doppler processor B before undergoing windowing, FFT,
etc. Figure 3-3 shows the modified Doppler processor B. The two streams are put side by side
before the interpolation step, with data from one side of the probe on top and data from the
other side of the probe on the bottom. This concatenation ensures the correct interpolation
to fit the video display area. The FFT size has been changed from the previous value of 128
to 64.
Modified DDET Processor B
Window
FFT
Magnitude
Detector
FFT shift
Temporal
Smoothing
Filter
Time domain
doppler signal
Interpolation
to Display
Window
FFT
Magnitude
Detector
FFT shift
Map Gain
and Output
Temporal
Smoothing
Filter
Figure 3-3: Diagram of the Modified Doppler Detector Board The modified DDET board
splits the incoming acoustic signal into two paths and processes them separately producing
two Doppler spectral displays.
31
3.1.3
Video Display
The video display step is responsible for updating the Doppler spectrum on the monitor and
drawing the accessory information such as the spectral base line and various markers. The
video display is changed to be able to show both spectra (Figure 3-4), each one half the size
as the normal single spectrum. Two base lines are drawn instead of one to designate the
place of zero frequency shift. More work is needed to make the velocity or frequency shift
scales correct for the two spectra. The current velocity scale shows the correct velocity range
for one of the two spectra. The B-mode image in the upper right shows one gate for the
beam corresponding to one end of the probe. Due to time constraints, the software changes
necessary for displaying the other gate was not implemented.
Figure 3-4: Two spectra acquired simultaneously using Doppler ultrasound The small window
in the upper right shows the B-mode image of the carotid artery. The circle designates one
of the sample volumes being imaged. The other sample volume, which is not drawn, lies at
the other end of the artery parallel to the first sample volume. The bottom display shows
the two spectra. The upper spectrum corresponds to the flow waveform captured at the
marked sample volume. The lower spectrum corresponds to the flow waveform captured at
the unmarked sample volume.
32
3.1.4
Timing Changes Due to System Modifications
There are two modes of operation in the PW system: non-duplex and duplex. The nonduplex or Triggered Mode continuously updates the Doppler waveform. The B-mode image
at the upper right of the video display is not updated until the user requests B-mode imaging.
Thus at a given time only one of the two displays (Doppler or B-mode) is active. When the
Doppler display is active, the part of the frame table (shown in Table 3.1) is repeated until an
interrupt occurs. The interrupt brings the system to another part of the frame table where
only 2D lines are shot. The Duplex Mode keeps both the Doppler display and the B-mode
image active. The frame table consists of repeats of the fragment shown in Table 3.2.
The frame table of both the Triggered Mode and Duplex Mode are modified to accommodate two Doppler lines shot from different aperture settings. Tables 3.1 and 3.2 shows the
altered versions. The Doppler line time of 148.50µs is only one possible value. The Doppler
line time depends on the gate depth and other system parameters. Figure 3-5 shows how
how the non-duplex frame table is repeated to give the Doppler acoustic signal. The Doppler
signal is continuously windowed. Each window results in one spectral line. Since the windows are overlapping, each FFT carries redundant information. This redundancy ensures
that the Doppler spectrum appears relatively smooth in time. The number of new acoustic
samples captured by each window changes with the PRF, allowing the window length, FFT
length, and display size to remain constant.
33
Line Type
Line Time (µs)
Doppler Setup (S)
33.61
Doppler (A)
148.50
Doppler (B)
148.50
Table 3.1: Modified Triggered Mode Frame Table The modified Triggered Mode frame table
allows two pulsed Doppler beams to be shot alternating from two ends of the transducer.
The Doppler setup line loads the correct delay coefficients to receive the reflected signal at
the appropriate focus. The Doppler line times depend on the PRF. The values given are
only a possible value.
Line Type
Line Time (µs)
2D Load Line (2D)
134.24
Doppler Setup (SA )
34.01
Doppler (A)
148.50
Dop Setup (SB )
34.01
Doppler B (B)
148.50
Table 3.2: Modified Duplex Mode Frame Table The modified Duplex Mode frame table allows
two pulsed Doppler beams to be shot alternating from two ends of the transducer. The 2D
load line is one of the lines used to build the B-mode image. The 2D line has an associated
angle which changes with each repetition of the frame table. The Doppler setup lines loads
the correct delay coefficients to receive the reflected signal at the appropriate focus. The
Doppler line times depend on the PRF. The values given are only a possible value.
34
system delays
1/PRF
33.61µs
S
A
B
S
A A A ... ...
A
B
S
A
B
... ...
B B B ... ...
Repeat of Frame Table
(Scanner Environment)
Acoustic signal in time
(Doppler Detector
Environment)
T
FF
Doppler Spectra Display Area
Spectral Display
(PVT Environment.)
5 ms
Figure 3-5: Doppler Signal Path in Non-duplex systems The scanner follows the frame table
shown in Table 3.1. S is the setup time during which the scanner loads the correct delay
coefficients to receive the reflected signal at the appropriate focus. A and B are Doppler
lines from the two ends of the transducer. The time between 2 Doppler lines from the same
aperture is 1/PRF. The system delay is the time between 2 Doppler lines from different
apertures. There are two possible system delay times: one after A is shot and before B is
shot, the other after B is shot and before A is shot. Both the PRF and the system delay
depend on the time needed to shoot one Doppler line. This time is determined by the depth
of the gate and other system parameters.
35
3.2
Flow System Setup
A flow system or flow phantom was used to measure the pulse wave velocity in a more
constrained environment. An elastic tube was hooked up to a bicycle pump. An illustration
of the setup is shown in Figure 3-6. The flow system was used to test the feasibility of
detecting delays, and how velocity profiles change with radial positions. The flow system
consists of two fluid reservoirs, one higher than the other. When pressure is applied, fluid
flows from the lower reservoir through the elastic tube and then to the higher reservoir. When
pressure is released, fluid from the higher reservoir flows back to the lower reservoir without
flowing through the elastic tube. A hard plastic housing holds the tube at two ends. When
imaging, the entire housing and the elastic tube are submerged in water. The ultrasound
probe is fixed about a half centimeter above the elastic tube with water in between the
probe and the tube. The elastic tube is roughly 14 cm in length and 0.5 cm in diameter.
The fluid used is a blood-mimicking fluid from ATS Laboratories. Table 3.3 shows the fluid
specifications. A bicycle pump provides the pressure required to drive the fluid through
the flow system. Resistance to the flow system is accomplished by a screw mechanism. At
maximum resistance, the tube can be completely blocked of flow.
Density
1.04 g/cc
1.66 centistokes
Viscosity
30 µm
Particle Size
Particle Concentration
1.7 per cc
Table 3.3: Composition of the Doppler test fluid used in the flow system.
An example of the signal captured from the flow system is shown in Figure 3-7. The
signal quality depends much on the scatterers in the test fluid. To achieve better signal
quality, it is important to shake up the test fluid before using to make sure enough particles
are in the fluid to scatter the ultrasound pulses.
36
Reservoirs
One-Way Connector
Apply flow resistance here
Probe
Tube
Elastic Tube
Tube Housing
Resistance
Drawing not to scale
Pump
Figure 3-6: Flow System Setup A flow system was used to measure the pulse wave velocity in
a more constrained environment.The flow system consists of two fluid reservoirs, one higher
than the other. When pressure is applied, fluid flows from the lower reservoir through the
elastic tube and then to the higher reservoir. When pressure is released, fluid from the higher
reservoir flows back to the lower reservoir without flowing through the elastic tube. A hard
plastic housing holds the tube at two ends. When imaging, the entire housing and elastic
tube is submerged in water. The ultrasound probe is fixed about a half centimeter above
the elastic tube with water in between the probe and the tube. The elastic tube is roughly
14 cm long and 0.5 cm in diameter. The fluid used is a blood-mimicking fluid from ATS
Laboratories. Resistance to the flow system is accomplished by a screw mechanism.
37
Figure 3-7: Video Display of Dual Beam Phantom Data The data is acquired by imaging the
flow system illustrated in Figure 3-6. The quality of the image is highly dependent on the
amount of scatterers suspended in the Doppler test fluid. To achieve better signal quality,
it is important to shake up the test fluid before using to make sure enough particles are in
the fluid to scatter the ultrasound pulses.
38
Chapter 4
Data Processing
Once the data has been brought off-line, it undergoes many data processing steps before
producing a PWV estimate. First the maximum frequency envelope is extracted from the
Doppler spectra. Then the more representative part of the envelope is extracted by windowing. Next the delay between the upstream and downstream envelopes are calculated.
This delay is then converted to a PWV estimate. For each step, there are many methods
available. This section will present the method chosen for each step and why they are more
suitable than other methods for this application.
4.1
Data Acquisition
Data is acquired with the modified Doppler ultrasound system. Section 3.1 describes the
modifications. The acquired data has two flow spectra as seen in Figure 3-4. For each
subject, over 40 cardiac cycles are acquired. Image data such as shown in Figure 3-4 is
captured and then brought off-line for analysis. Image data is the easiest to acquire. Ideally
one should try to access the raw acoustic data.
The linear probe is placed on the neck over the carotid artery. The center of the two
beams are placed in the middle of the artery, or as close to the center as possible. This is
because flow velocities vary with radial position (Figure 4-1). The human subject should be
at rest for about 5 minutes prior to measurement to establish steady flow rate [26].
39
The SONOS 5500 has enough buffer size to store roughly 8 cardiac cycles. Each time
the buffer is filled up, data acquisition is stopped to store the content of the buffer to disk.
After the image data is stored, measurement is resumed. Therefore the data acquired is not
from consecutive cardiac cycles, but from sets of 8 cardiac cycles.
Probe
Figure 4-1: The linear probe is held up to the neck close to where the carotid artery is
located. The angle of measurement is away from the head in order to avoid the carotid
bifurcation. The focus of the two beams are placed as close to the center of the artery as
possible. the arrow shows the direction of blood flow.
4.2
Envelope Detection
The Doppler ultrasound signal from blood flow contains a spectrum of frequencies whose
amplitude is related to the velocities of blood within the sample volume. Estimating the
delay directly from a 2D image is computationally intensive. A one-dimensional signal is
more suitable for delay estimation. There are many ways to extract a meaningful 1D signal
to capture how the signal is changing with time. Commonly, the highest frequency present
in the Doppler signal at a particular time is used to represent the Doppler signal. Studies
40
have shown that the maximum frequency envelope is relatively insensitive to changes in
beam-vessel geometry [8]. Other possibilities include the mean frequency envelope and the
median frequency envelope.
4.2.1
Maximum Frequency Follower
There are various methods of extracting the maximum frequency envelope. In theory, the
maximum frequency simply corresponds to a maximum velocity present in the volume of
blood flow being imaged. This seemingly simple task is complicated by intrinsic spectral
broadening and noise [7]. A number of approaches have been developed to deal with these
difficulties. For this project, the threshold-crossing method adaptive to background noise is
used [8]. A threshold is determined based on the estimated noise level. The magnitude of
each bin of the spectrum (scanning from high to low frequency bins) is compared with the
threshold. When in a sequence of r successive bins there are at least m bins which exceed
the threshold, then the highest bin frequency in that sequence is assigned as the maximum
frequency. Figure 4-2 shows the extracted envelopes from one cardiac cycle. The two spectra
correspond to the upstream and downstream locations in the artery.
4.2.2
Difficulties in Envelope Detection
The extracted maximum frequency envelope is very noisy. This is due to several factors.
The Fourier transform-based spectrum analyzer exhibits a characteristic granular pattern
called Doppler speckle which causes large random fluctuations of the instantaneous spectral
amplitude from the true amplitude. The size of the deviation from the true amplitude is
comparable to the true amplitude [8]. Other sources of fluctuations are electronic noise
and interference from anatomical structures near the artery. The envelope goes through
low-pass filtering to remove high frequencies which are considered to be mostly noise. This
assumption is explained later in Section 4.4.2. Figure 4-3 shows the envelopes of Figure 4-2
after filtering. Filtering introduced a delay corresponding to the filter length. The delay
caused by the filter will not affect the accuracy of the propagation delay estimation, since
the filter introduces equal amount of delay to both the upstream and the downstream signal.
41
80
upstream
downstream
70
60
Velocity (cm/s)
50
40
30
20
10
0
0
0.1
0.2
0.3
0.4
0.5
Time (Sec)
0.6
0.7
0.8
0.9
1
Figure 4-2: Extracted Envelopes Maximum frequency followers are used to extract envelopes
from Doppler spectra.
60
50
Velocity (cm/s)
40
30
20
10
Low pass filtered upstream
Low pass filtered downstream
0
−10
0
0.1
0.2
0.3
0.4
0.5
Time (Sec)
0.6
0.7
0.8
0.9
1
Figure 4-3: Low-pass filtering of Envelopse Filtering introduced a delay size corresponding
to the length of the low-pass filter.
42
4.3
Windowing the Data
The rising edge or wave front of the pulse wave is the smoothest and most consistent of
each pulse. This part of the wave suffers the least from reflected waves that the pulse wave
creates [16]. The maximum frequency envelope is smoothest and most consistent at the
rising edge of each pulse [7]. In this implementation, only the segment of data surrounding
the peak of each cardiac cycle is extracted for delay estimation. Because of the finite length
of the extracted segment, it is important to apply a window. Application of the window
eliminates the problems caused by rapid changes in the signal at the edges of the window.
These problems include misrepresentation of the high frequency information.
The window used is a Blackman window with a stretch of ones filled in at the top.
Figure 4-4 shows the effect of windowing on the signal. The wave front and the part of the
cardiac cycle with high flow has been extracted for analysis.
Windowed Upstream
100
100
upstream
window
80
Velocity (cm/s)
Velocity (cm/s)
80
60
40
20
0
60
40
20
0
0.2
0.4
0.6
Time (s)
0
0.8
0
0.2
0.4
0.6
Time (s)
0.8
Windowed Downstream
100
100
downstream
window
80
Velocity (cm/s)
Velocity (cm/s)
80
60
40
20
0
60
40
20
0
0.2
0.4
0.6
Time (s)
0
0.8
0
0.2
0.4
0.6
Time (s)
0.8
Figure 4-4: Windowing The two plots on the left show the upstream and down stream
flow waveforms with the window overlaid. The two plots on the right show the result of
windowing. The wave front and the part of the cardiac cycle with high flow has been
extracted for analysis.
43
4.4
Delay Estimation
The objective of time delay estimation is to determine the delay between two scaled versions
of the same signal, s(t), in the presence of noise, n(t) [15]. This involves sampling and
processing two continuous time signals x1 (t) and x2 (t) given by
x1 (t) = C1 s(t) + n1 (t)
(4.1)
x2 (t) = C2 s(t − D) + n2 (t)
(4.2)
In a discrete time sampled data system, with sampling period T , the estimation problem
reduces to determining an estimate D̂ of the true time delay D using a finite set of measured
samples, x1 (kT ) and x2 (kT ), of the signals x1 (t) and x2 (t).
Delay estimation for this application is performed on the maximum frequency envelopes
of two Doppler spectra of the same cardiac cycle (Figure 4-5). The signals x1 (kT ) and
x2 (kT ) are sampled from the continuous time upstream and downstream maximum frequency
envelopes respectively. The delay estimate D̂ can then be mapped to an estimate of PWV
by the following relation:
PWV =
∆L
D̂
(4.3)
where ∆L is the distance of travel or the distance between the two apertures of the probe.
The results of Chapter 5 present delay estimates in terms of samples. Each sample corresponds to a delay of T ms. Thus time delay is related to sample delay by the following:
D̂ = sample delay × T
44
(4.4)
Probe
∆L
Artery
Β
Α
velocity (arbitrary)
Α: x1 (t)
time
D
velocity (arbitrary)
Β: x2 (t)
time
Figure 4-5: The Delay Estimation Problem The flow wave is acquired by Doppler Ultrasound at two locations in an artery, one upstream and one downstream. x1 (t) and x2 (t)
are the envelopes of the upstream and downstream spectra respectively. The pulse wave
velocity is related to the difference in time of arrival of the pressure pulse at the two sites of
measurement. Thus this project aims to detect the delay D.
4.4.1
Correlation Based Techniques
Much research has been done on computing the cross correlation function (Rx1 x2 (τ )) to
estimate time delay between signals, where Rx1 x2 (τ ) is given by
45
Rx1 x2 (τ ) = E [x1 (kT )x2 (kT − τ )] .
(4.5)
The variable τ that maximizes Equation 4.5 is an estimate of the delay. Due to the finite
observation time, Rx1 x2 can only be estimated. An estimate of the cross correlation function
is given by
N
1 R̂x1 x2 (τ ) =
x1 (kT )x2 (kT − τ )dt.
N k=1
(4.6)
x1 (t) and x2 (t) can be prefiltered by H1 (f ) and H2 (f ) respectively to improve the accuracy
of the delay estimate. When H1 (f ) = H2 (f ) = 1 for all frequencies, the delay estimate is
simply the peak of the cross-correlation function. Knapp and Carter [12] presents a number
of possible prefilters under the generalized correlation method.
Since the time-domain cross-correlation delay estimator can only resolve the delay to a
resolution equal to the sampling interval T (5 ms for this application), it is necessary to use
some form of interpolation to resolve the delay to a finer resolution [15]. One common techniques is to interpolate the signals x1 (kT ) and x2 (kT ). Another variation is to approximate
a parabola in the neighborhood of the maximum of Equation 4.6. The delay estimator of
this project interpolates the input signals x1 (kT ) and x2 (kT ) by a factor of 100. Thus the
resolution of this delay estimator becomes 0.05 ms.
4.4.2
Phase Difference Delay Estimation
A delay in time translates into a linear phase difference in frequency [3, 18]. Thus one can
estimate the time delay by evaluating the phase shift for one or a set of frequencies. The
Fourier transform of x1 (t) and x2 (t) are X1 (ejω ) and X2 (ejω ), which are related by
X2 (ejω ) = X1 (ejω ) e−jωD
46
(4.7)
The phase difference between the two signals can be calculated by
∆φ(ω) = ∠X2 (ejω ) − ∠X1 (ejω )
(4.8)
The group delay, the delay of interest, of a system is defined as
D(ω) =
d∆φ(ω)
dω
(4.9)
For this application, only the low frequencies of the envelope are seen as the underlying
flow wave signal. The high frequencies are seen as noise. Figure 4-7 shows the variance of the
phase difference calculated for a data set of 82 cardiac cycles (Data Set A1 of Section 5). The
variance of the phase difference is low for lower frequencies but high for higher frequencies.
The useful low frequencies are averaged to give the slope for those frequencies. Figure 46 shows the phase difference averaged over many cardiac cycles. The phase difference for
frequencies less than 5 Hz is assumed to be linear. Therefore the phase delay for those
frequencies are averaged to give the group delay D. This group delay can then be translated
to the PWV by the following relation:
PWV =
∆L
D
(4.10)
The delay estimates of Chapter 5 are given in terms of sample delays. The sample delay
is related to the phase delay by:
sample delay =
∆L
PWV × T
(4.11)
The frequency based method has the advantage that the envelope does not need to be
interpolated. This is because the slope of the phase difference (the group delay) is not
restricted to integer values. This can potentially save on computation time.
47
0.5
0.4
0.3
Phase difference (radians)
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0
10
20
30
40
50
60
Frequency (Hz)
70
80
90
100
Figure 4-6: This plot shows the phase differences averaged for individual frequencies across
82 cardiac cycles (Data Set A1 ). For frequencies less than 5Hz, the average phase difference
has a well defined slope which is related to the group velocity.
4.5
4
Variance of Phase difference (radians)
3.5
3
2.5
2
1.5
1
0.5
0
0
10
20
30
40
50
60
Frequency (Hz)
70
80
90
100
Figure 4-7: This plot shows the variance of the phase differences for individual frequencies
calculated across 82 cardiac cycles (Data Set A1 ). The lower frequencies show much lower
variance than the higher frequencies.
48
Chapter 5
Results
This chapter contains the experimental results used to assess the method of using flow
waves captured by Doppler ultrasound to measure pulse wave velocity. Data from three
sources are listed: data simulated from using Womersley’s model of pulsatile flow, data from
a flow system which models blood flow through an elastic tube, and data from imaging
carotid arteries of human subjects. Simulated data illustrates problems with position of the
ultrasound beam and the effect of noise on delay estimation. Data from the flow system
helps to assess the system’s performance under more constrained conditions than imaging
real arteries. The effect of beam position is also explored with flow system data. Physiological
data helps assess the systems performance on humans. For all three data types, waveforms
from a number of cardiac cycles were acquired to form a data set. Each data set is then
averaged to give the delay estimate. The delay estimate is given in terms of sample to better
show the result of sub-sample delay estimation. A delay of one sample corresponds to a time
delay of 5 ms. The standard deviation of the data set gives a measure of the amount of
variability in the data set.
5.1
Simulated Data
A few sets of simulated data were generated to study various sources of variation in real
physiological data. The effects studied are radial positions of the ultrasound beam inside
49
the artery, noise, and propagation of waves. Table 5.1 summarizes the simulated data sets.
Data Set
Variable
Description
2
Noise 1
3
Noise 2
4
Noise 3
100 cardiac cycles
SNR = 74 dB
100 cardiac cycles
SNR = 62 dB
100 cardiac cycles
SNR = 47 dB
1
Mean of
Sample Delay
Radial Position 11 radial positions
-
Std of
Sample Delay
-
0.99358
0.10848
1.0017
0.20355
1.0405
0.51097
Table 5.1: Summary of Simulated Data Sets
To simulate a carotid waveform, Womersley’s model as presented in Section 2.2 is used.
The parameters used to simulate one cycle of the carotid waveform are shown in Table 5.2.
These parameters are taken from McDickens and Evans’s Chapter 2 [7]. The parameters
were derived from waveforms of mean velocity blood flow acquired by Doppler ultrasound.
Figure 5-1 shows the simulated velocity profile at the center of the artery where
Figure 5-2 shows the simulated velocity profile for all
r
’s
R
r
R
= 0.
at the peak of the flow waveform.
Simulated Envelope
3.5
velocity (arbitrary)
3
2.5
2
1.5
1
0
1
2
3
cycle phase (radian)
4
5
6
Figure 5-1: Simulated Envelope Data from the Womersley’s model and the parameters in
Table 5.2
50
Harmonic
0
1
2
3
4
5
6
7
8
Frequency(ω)
1.03
2.05
3.08
4.10
5.13
6.15
7.18
8.21
α
|Bn | ∠Bn (degrees)
1.00
3.9 0.33
74
5.5 0.24
79
6.8 0.24
121
7.8 0.12
146
8.7 0.11
147
9.6 0.13
179
10.3 0.06
233
12.4 0.04
218
Table 5.2: Simulated Data Parameters (Reproduced from Evans 2000 [7]) Fourier components and corresponding values of the non-dimensional parameter α for flow waveforms
recorded from the common carotid arteries of a healthy young subject. The values of Bn
have been normalized to B0 , and the angle ∠Bn is given in degrees from an arbitrary starting
point.
(diameter(estimated) = 6.0mm; heart rate = 62 bpm; viscosity = 0.038 St)
Simulated Velocity Profile
3.5
3
axial velocity (arbitrary)
2.5
2
1.5
1
0.5
0
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
dimensionless distance from axis (r/R)
0.6
0.8
1
Figure 5-2: Velocity profile according to Womersley’s model of pulsatile blood flow. The
parameters used to generate this data are from other people’s experiments. They are listed
in Table 5.2
51
5.1.1
Variance of the Delay Estimates
Many factors contribute to the high variance seen in the delay estimate. (We will see later
that the variance of delay estimates from physiological data is higher than that of simulated
data. This section attempts to pinpoint some of the sources of variation through simulation.
When two waveforms from different radial positions are used for delay estimation, the estimate can be very different. Table 5.3 and Figure 5-3 show the result of a study of the effects
of radial position on the delay estimate. In this study, the upstream waveform is assumed to
be located at the center of the artery. The downstream waveform is allowed to vary in radial
position. The downstream waveform has an artificial delay of one sample which corresponds
to a time delay of 5 ms.
r
R
0
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000
% of Vmax
100.0000
99.5741
98.2771
96.0350
92.6645
87.7748
80.6295
70.0167
54.2347
31.3629
Delay Estimate
1.0000
0.9597
0.8365
0.6233
0.3047
-0.1463
-0.7708
-1.6195
-2.7408
-4.1705
Table 5.3: Effect of Radial Positioning. Assumptions: Vmax occurs at the center of the artery.
The upstream beam is at the center of the artery. Simulated delay = 1 sample. One sample
corresponds to a time delay of 5 ms.
5.1.2
Random Noise
Different amounts of uniform white noise were added to the canonical waveform (shown in
Figure 5-1) to see the effect of noise on the delay estimate. Figures 5-4, 5-5, and 5-6 show the
simulated data with various amounts of additive noise. Next to an example of the waveform
with added noise is the histogram of the estimated delays with best-fit Gaussian probability
density functions (PDFs) overlaid.
52
2
delay estimate (dimensionless samples)
0
−2
−4
−6
−8
−10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
r/R
Figure 5-3: Delay Estimates From Different Radial Positions The simulated data had an
artificial delay of 1 sample. One sample corresponds to a time delay of 5 ms.
Simulated Upstream
40
35
3
std = 0.10848
30
2
1.5
0
1
2
3
cycle phase (radian)
4
5
6
Simulated Downstream
velocity (arbitrary)
Total # of Occurences = 100
mean = 0.99358
2.5
Number of occurences
velocity (arbitrary)
3.5
25
20
15
3
10
2.5
5
2
1.5
0
1
2
3
cycle phase (radian)
4
5
0
−5
6
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
Figure 5-4: Simulated Data with Noise of SNR = 74dB
A downstream data has a simulated delay of 1 sample or 5 ms.
53
3
4
5
Simulated Upstream
20
3.5
std = 0.20355
14
2
1.5
0
1
2
3
cycle phase (radian)
4
5
6
Simulated Downstream
3.5
velocity (arbitrary)
Total # of Occurences = 100
mean = 1.0017
16
2.5
Number of occurences
velocity (arbitrary)
18
3
12
10
8
3
6
2.5
4
2
2
1.5
0
1
2
3
cycle phase (radian)
4
5
0
−5
6
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
3
4
5
3
4
5
Figure 5-5: Simulated Data with Noise of SNR = 62dB
A downstream data has a simulated delay of 1 sample or 5 ms.
Simulated Upstream
12
3.5
mean = 1.0405
10
std = 0.51097
2.5
2
8
1.5
0
1
2
3
cycle phase (radian)
4
5
6
Simulated Downstream
3.5
Number of occurences
velocity (arbitrary)
Total # of Occurences = 100
3
6
velocity (arbitrary)
4
3
2.5
2
2
1.5
0
1
2
3
cycle phase (radian)
4
5
0
−5
6
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
Figure 5-6: Simulated Data with Noise of SNR = 47dB
A downstream data has a simulated delay of 1 sample or 5 ms.
54
5.2
Flow System Data
A few sets of phantom data were acquired using the procedure described in Section 3.2. An
example of the waveform acquired using the flow system is shown in Figure 5-7. The left
side shows the envelopes extracted from the Doppler spectra acquired by imaging the flow
system. The right side shows the low pass filtered version of the flow wave. The general
shape of the smoothed version share some characteristics with the filtered and windowed
version of the real physiological data. It has a fast rising edge and a slower delay. However
a major difference is that the width of the pulse is approximately double that of the real
physiological pulse. Table 5.4 summarizes the flow system data sets.
Data Set Number of Cycles
1
2
34 cycles
21 cycles
Mean of
Sample Delay
0.49471
0.32286
Std of
Sample Delay
0.52261
0.55016
Table 5.4: Summary of Flow System Data Sets
The estimated delays are in terms of samples, with one sample equal to a time delay of 5
ms.
Upstream
120
100
100
Velocity (cm/s)
Velocity (cm/s)
Upstream
120
80
60
40
20
0
80
60
40
20
0
0.2
0.4
0.6
0.8
1
Time (sec)
1.2
1.4
1.6
1.8
0
2
0
0.2
0.4
0.6
0.8
120
100
100
80
60
40
20
0
1.2
1.4
1.6
1.8
2
1.2
1.4
1.6
1.8
2
Downstream
120
Velocity (cm/s)
Velocity (cm/s)
Downstream
1
Time (sec)
80
60
40
20
0
0.2
0.4
0.6
0.8
1
Time (sec)
1.2
1.4
1.6
1.8
0
2
0
0.2
0.4
0.6
0.8
1
Time (sec)
Figure 5-7: Phantom Flow Wave Envelopes The left side shows the envelopes extracted
from imaging the flow system. The right side shows the low pass filtered version of the flow
wave.
55
Figures 5-8 and Figure 5-9 shows the histograms of the estimated delays from the flow
system data with best-fit Gaussian PDFs overlaid. During acquisition of the flow system
Data Set 2, the radial positions were intentionally varied. However no significant difference
in the wave form shape or the variance of the delay estimate can be seen.
14
12
Total # of Occurences = 34
mean = 0.49471
std = 0.52261
Number of occurences
10
8
6
4
2
0
−5
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
3
4
5
Figure 5-8: Flow System Data Set 1 Delay estimates are in terms of samples, with one
sample equal to a time delay of 5 ms.
8
7
Number of occurences
6
Total # of Occurences = 21
mean = 0.32286
std = 0.55016
5
4
3
2
1
0
−5
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
3
4
5
Figure 5-9: Flow System Data Set 2 The radial positions were intentionally varied in this
data set. However no significant difference in the wave form shape or the variance of the
delay estimate can be seen. Delay estimates are in terms of samples, with one sample equal
to a time delay of 5 ms.
56
5.3
Physiological Data
To see the system’s performance on human subjects, a few sets of physiological data were
take from two healthy volunteers. One volunteer is a healthy 22-year-old female and the
second is a healthy 25-year-old male. These two volunteers are not expected to have any
heart disease, therefore their PWV should appear normal. The procedures for acquiring data
are described in Section 4.1. Table 5.5 summarizes the physiological data sets. Figures 5-10
through 5-15 show the histograms of the delay estimates of physiological data with best-fit
Gaussian PDFs overlaid.
Data Set
Date
Subject
A1
A2
B1
B2
B3
B4
12/15/2001
02/02/2002
12/06/2001
12/07/2001
12/15/2001
02/02/2002
A
A
B
B
B
B
Number of
Cardiac Cycles
82
208
48
99
119
57
Mean of
Sample Delay
1.2727
1.0136
1.1425
1.3958
0.6758
0.59789
Std of
Sample Delay
0.78273
0.54677
1.1325
0.95784
0.51977
1.1508
Table 5.5: Summary of Physiological Data Sets Subject A is a healthy 25-year-old male.
Subject B is a healthy 22-year-old female. The mean and standard deviations of the sample
delay are results of applying the correlation based delay estimation method. Delay estimates
are in terms of samples, with one sample equal to a time delay of 5 ms.
Table 5.6 shows the sample delay estimates from physiological data converted to time
delays in milliseconds and PWV. To convert sample delay to time delay, one simply multiplies
the sample delay by 5 ms (the sampling interval T) as implied by the relationship shown
in Equation 4.4. The conversion from sample delay to PWV is stated in Equation 4.11.
However this relation presents infinite PWV estimates when the delay estimate in samples
in zero. To avoid unrealistically high PWV values, sample delays within 0.2 sample of zero
are ignored. This threshold restricts PWV values to have an absolute value of 30 m/s. Given
that the normal PWV in the common carotid is between 6.80 m/s and 8.30 m/s, this cutoff
seems acceptable. The column titled Number of Cardiac Cycles in Table 5.6 shows the actual
number of cardiac cycles used to produce the PWV estimates.
57
25
Number of occurences
20
Total # of Occurences = 82
mean = 1.2727
std = 0.78273
15
10
5
0
−5
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
3
4
5
Figure 5-10: Physiological Data Set A1 Delay estimates are in terms of samples, with one
sample equal to a time delay of 5 ms.
80
Total # of Occurences = 206
70
mean = 1.0137
std = 0.54934
Number of occurences
60
50
40
30
20
10
0
−5
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
Figure 5-11: Physiological Data Set A2
sample equal to a time delay of 5 ms.
3
4
5
Delay estimates are in terms of samples, with one
58
12
Total # of Occurences = 48
mean = 1.1425
10
std = 1.1325
Number of occurences
8
6
4
2
0
−5
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
Figure 5-12: Physiological Data Set B1
sample equal to a time delay of 5 ms.
3
4
5
Delay estimates are in terms of samples, with one
25
Total # of Occurences = 99
mean = 1.3958
Number of occurences
20
std = 0.95784
15
10
5
0
−5
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
Figure 5-13: Physiological Data Set B2
sample equal to a time delay of 5 ms.
3
4
5
Delay estimates are in terms of samples, with one
59
50
45
Total # of Occurences = 119
mean = 0.6758
40
std = 0.51977
Number of occurences
35
30
25
20
15
10
5
0
−5
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
Figure 5-14: Physiological Data Set B3
sample equal to a time delay of 5 ms.
3
4
5
Delay estimates are in terms of samples, with one
12
10
Total # of Occurences = 57
mean = 0.59789
std = 1.1508
Number of occurences
8
6
4
2
0
−5
−4
−3
−2
−1
0
1
2
Delay Estimate (dimensionless samples)
Figure 5-15: Physiological Data Set B4
sample equal to a time delay of 5 ms.
3
4
5
Delay estimates are in terms of samples, with one
60
Data Set Time Delay
Number of
(ms)
Cardiac Cycles
A1
6.3635
76/82
5.0680
191/208
A2
B1
5.7125
39/48
6.9790
94/99
B2
3.3790
95/119
B3
2.9895
47/57
B4
Estimated
PWV (m/s)
5.6615
6.5313
7.3750
5.7477
7.3140
2.6382
Standard Deviation
of PWV Estimate
4.16
4.75
7.61
6.82
8.87
9.54
Table 5.6: Time delays and Estimated PWV This table shows the sample delays converted
to time delays in milliseconds and PWV. To convert sample delay to time delay, one simply
multiplies the sample delay by 5 ms (the sampling interval T) as implied by the relationship
shown in Equation 4.4. The conversion from sample delay to PWV is stated in Equation 4.11.
However this relation presents infinite PWV estimates when the delay estimate in samples in
zero. To avoid unrealistically high PWV values, sample delays within 0.2 sample of zero are
ignored. This threshold restricts PWV values to have an absolute value of 30 m/s. Given
that the normal PWV in the common carotid is between 6.80 m/s and 8.30 m/s, this cutoff
seems acceptable. The column titled Number of Cardiac Cycles shows the actual number of
cardiac cycles used to produce the PWV estimates.
61
62
Chapter 6
Discussion
This chapter includes a summary and interpretation of the results in Chapter 5. This
summary is followed by suggestions of future work. This chapter closes with a general
conclusion on the thesis.
6.1
Estimated PWV
This section briefly looks at the delay estimates from the three different data sources.
6.1.1
Simulated Data
Simulated data allowed the study of the effect of radial positioning and the effect of additive
white noise. With varying radial positions, the estimated delay degraded fast from the
simulated delay of 1 sample or 5 ms. Section 6.2.1 will discuss more in depth the effect of
varying beam position in the artery. Additive noise, at different amounts, all produced delay
estimates close to the simulated delay of 1 sample or 5 ms. Section 6.3 will discuss further
what the simulated data tells about possible sources of noise in the system.
6.1.2
Flow System Data
The flow system was supposed to provide a more constrained environment for the measurement of PWV. The probe is kept still and at a constant position relative to the elastic tube
63
(Data Set 1). It was hoped that the flow system would produce delay estimates with very
little variation. However even under more constrained setting, the estimated delay exhibits
large variance similar to physiological data.
Despite the lack of success with the flow system, its data still provides some valuable
insights. Section 6.2.1 discusses how flow system data suggests that radial positioning does
not affect the delay estimate in practice as drastically as expected from theory. The variance
in flow system data is comparable to the variance seen in physiological data. This implies
that many sources of variability are not caused by physiological factors. Instead variability
is most likely caused by noise (further discussed in Section 6.3).
The delay estimates from the flow system are on average lower than that of physiological
data. This suggests that the PWV of the elastic tube used is faster than that of the common
carotid.
6.1.3
Physiological Data
From the results presented in Chapter 5. The estimated PWV can be calculated from the
estimated sample delays with Equation 4.11. Table 5.6 summarizes this analysis. Most of
the estimated values for PWV are within the range of possible carotid pulse wave velocities.
Therefore although not accurate, the implementation presented in this study can detect a
probable delay from the Doppler flow waves.
Even though the proposed method can detect a valid delay, the estimates are far from
ideal. As seen from the histograms of Section 5, the delay estimates have very wide distributions. Even for the data from the same person, the means of the estimated delays can change
drastically from session to session. Another problem is the resolution of the delay estimates.
The time between samples of the envelope is 5 ms. The delay we are trying to detect is
on the scale of 1 or 2 samples. Sub-sample accuracy is needed to achieve delay estimates
of finer resolution. Interpolation is a reasonable way to get sub-sample accuracy. A higher
sampling rate would help by reducing the effective amount of noise, since there would be
more samples for the same period of time. The important issues for delay estimation are the
signal to noise ratio (SNR) and the bandwidth of the signal, not necessarily the sampling
64
rate. Therefore, even though a higher sampling rate can help, the problem of the proposed
method is more attributed to the various sources of error. What follows is a analysis of the
different sources of variability.
For physiological data, there is no gold standard for the PWV of the human subjects.
The variance of the data sets provide some measure of the error, but it does not show if the
estimate has some overall bias.
6.2
High Variance in the Delay Estimate
The results of this study show that the present implementation can detect a delay in the
blood flow waveforms. However, the detected delay has very high variance. This variance
has many sources.
6.2.1
Waveform Variation Due to Radial Position
Because the two beams cannot be placed at the same distance from the center of the artery
and because there is not necessarily radial symmetry in the artery, some of the variation
is due to flow differences at different radial positions. According to Womersley’s model
of pulsatile flow (Equation 2.2), the velocity profile of blood flow is dependent on radial
position. Therefore it it expected that radial positioning will contribute to the error in delay
estimation.
It is very hard to place both beams at the center of the arterial cross sections. This difficulty is compounded by the fact that the B-mode image which can help guide the placement
of the beams only shows one dimension of the artery. Even when the beam looks centered
in one plane, they may be off-center in the other plane (Figure 6-1).
Table 5.3 shows that if the two beams are not placed at the center of the artery, the delay
estimate can be drastically affected. The delay estimate can change drastically as the ratio
r/R deviates from 0. In practice, this effect of radial positioning is not as clear. Both beams
are unlikely to be at the center. In reality, arteries are not perfect cylinders. The artery can
also curve and taper so that there may not be a clear center.
65
e of
Plan
nd
asou
s
beam
ultr
x
Artery
x
Figure 6-1: Beam Plane X marks the focus of the beams. It is very hard to place both
beams at the center of the arterial cross sections. This difficulty is compounded by the fact
that the B-mode image which can help guide the placement of the beams only shows one
dimension of the artery. Even when the beam looks centered in one plane, they may be
off-center in the other plane.
In practice, the effect of variable radial positioning is not large. The ultrasound beam is
imaging a volume of blood. At the smallest setting, the volume’s diameter (if approximated
by a sphere) can be from 1/4 to a 1/3 of the arterial diameter. Therefore, having the beam
slightly off-center with a r/R of 0.5 will still include the blood scatterers at the center of
the artery. Blood at the center of the artery is assumed to have the maximum velocity. The
Doppler spectrum is the envelope detected by a maximum frequency follower. As long as
the center of the artery is included in the sample volume, the same maximum frequency
envelope will result. Therefore, the flow waveform in practice does not change as fast with
radial position as the simulated flow waveform.
Data acquired from the flow system supports the idea that varying the radial position
does not affect the delay estimate as much as theorized. For Data Set 1 from the flow system,
the probe was kept very still and the beam focus were placed at the axis of the elastic tubes.
For Data Set 2, the beam focused were altered drastically from next the the tube wall to the
tube axis. Since the tube diameter is small (0.5 cm), no matter where the focus is placed
66
inside the tube, the sample volume is likely to cover some area of maximum flow velocity.
The maximum frequency envelopes from Data Set 2 did not look very different from those
of Data Set 1. The delay estimate from Data Set 2 is smaller than that of Data Set 1. This
makes intuitive sense because if the beam focus is placed on the axis some of the time and
off axis for some of the time, then the average delay should be smaller. Flow further from
the axis differs in phase from the flow on the axis. The standard deviations from the two
data sets did not change too much.
6.2.2
Waveform Variation Due to Wave Dispersion
The pulse wave disperses as it travels down the artery due to frequency dependence of the
arterial wave speed [17, 24]. Pressure waves measured further down the arterial tree are
higher in peak pressure, but lower in mean pressure [16]. Dispersion causes the waveform
shape to change, which may present problems for correlation based estimation techniques.
For a distance of 3 to 4 centimeters, the blood flow waveform is not expected to change very
much. However since the time delay being measured is a small phenomenon, even small
changes in shape may affect the accuracy of the estimate. Due to time constraints, the affect
of wave dispersion on delay estimation was not studied as part of this project.
6.2.3
Variability Due to Scanning
For the data acquired for this project, subject B scanned herself. It is very difficult to keep
the probe steady while playing with the knobs on the control panel. It would help to have
different people scanning and manipulating the control panel. In the case of subject A, the
two tasks are separated. The higher quality of the data for subject A may be attributed to
this difference.
To see if there was any difference between my scanning and that of a real sonographer, an
expert was consulted to acquire a few very short data sets. Preliminary results (not shown
in this report) demonstrate that the sonographer’s data do not provide less variance than
my data.
67
6.2.4
Physiological Variability
Section 2.1.2 lists some factors, both long term and short term, which can change the PWV.
The short term factors, such as blood velocity, food intake, and exercise, may contribute to
the error in this study.
People’s arteries have different geometries. Even over a distance of 3 to 4 centimeters, the
artery’s shape can change dramatically, which can affect the flow wave. In a healthy person,
where the artery is not expected to have any abnormal flow, the PWV should be easier to
measure. For a person with heart disease, where the artery may be partially occluded, the
flow waves will be turbulent and even harder to measure PWV.
6.2.5
Number of Heart Cycles Needed
All of these different sources of variability result in delay estimates with a wide distribution.
The next question is then how many heart cycles to average to achieve an acceptable variance
on the delay estimate. (Each heart cycle results in one delay estimate.)
Before beginning the analysis, here are a few definitions to simplify the notation. Let dn
indicate the delay estimate from some heart cycle, and let D indicate the estimate of the
delay distribution formed by averaging the delay estimates from single heart cycles:
N
1 dn .
D=
N n=1
(6.1)
The delay estimates dn from single heart cycles can be viewed as a random variable with
the probability density function (PDF) dX (x). D, which is the average of N realizations of
dX (x) can also be viewed as a random variable whose probability density function (PDF) is
a Gaussian with a mean of µ and standard deviation σ. Let PX (x) denote the PDF of N
averaged delays. Let D also denote the delay estimator.
By choosing a suitably large number N of realizations of dX (x), it will be possible to
reduce the percent error variance of D to acceptably small levels. One way to choose a
suitably large N is to set a limit on how far individual measurements of D deviates from the
68
expected value of D over a certain percentage of time. For example, suppose the criteria on
D were as follows: “The probability that an experimental value of D falls within ±10% of
its expected value equals 90%.” This statement can be expressed mathematically as,
P r[|D − µD | ≤ 0.1µD ] = 90%.
(6.2)
In terms of PWV (assuming a true PWV of 7 m/s), the above statement can be stated
as the probability that the PWV estimated from averaging N hearty cycles falls between 6.3
m/s and 7.7m/s 90% of the time.
Since D is assumed to be an average of a number of individual and independent measurements, the PDF of the random variable D closely approximates a Gaussian PDF. Therefore,
using existing tables for the cumulative distribution function (CDF) of the Gaussian PDF,
it can be shown that,
P r[|D − µD | ≤ 1.65σD ] = 90%
(6.3)
Combining the above two equations yields
1.65σD = 0.1µD .
1.65
1
√ σd
N
N=
(6.4)
= 0.1µD .
272.25σd2
;
µ2D
69
(6.5)
(6.6)
For the physiological data sets, N is calculated to be on the order of 200. This many
cardiac cycles would require 2-4 minutes of continuous data acquisition. This is hard to
achieve in practice, especially in the current implementation where data acquisition is not
consecutive. One must stop every 4 or 5 cardiac cycles to save the buffer to memory.
6.2.6
System Delays
Since the two beams are not sent out at precisely the same time, there exists a small delay
between the two beams. However, this delay is determined to be negligible compared to
other sources of delay. As seen in Section 3.1.4, the delay introduced is on the scale of a few
hundred microseconds. This is a factor of 100 less than the delay being estimated.
6.3
6.3.1
Variance Due to Noise
Results of Simulated Noise
The results of simulating different noise levels demonstrate that even with relatively high
level of noise, the delay estimate is not affected too much. This may be because the simulated
noise is independent of the signal, therefore signal and noise can be separated successfully
with simple filtering. In the real setting, noise is likely to be dependent on the signal. For
example, the speckle noise relates to the blood scatterers. The physiological noise is poorly
understood. To better characterize the effect of noise on delay estimation, one needs to
better understand the noise in the physiological data.
6.3.2
Noise in Physiological Data
Simulated noise showed that noise can certainly have an affect on delay estimation, although
not drastically. This demonstrates that the simulated white noise, is different from the noise
occurring with physiological data. The exact nature and composition of this noise is difficult
to determine. However one can speculate on the sources of noise.
70
Speckle
One salient feature of Doppler ultrasound images is that the spectra exhibit a characteristic
granular pattern called Doppler speckle. Doppler speckle causes large random fluctuations of
the instantaneous spectral amplitude from the true amplitude [8]. The size of this deviation
of speckle is comparable to the true amplitudes.
The speckle observed in Doppler spectra has a quality similar to that observed in sonography [13] (B-mode images). Speckle in sonography is the interference pattern which arises
from the coherent summation of signals from scatterers with sizes smaller than the wavelengths of ultrasound. The speckle pattern does not directly represent individual scatterers
but rather represents an interference pattern of the scatterer distribution scanned.
Doppler speckle affects the accuracy of maximum frequency follower. Since speckle exists
for both flow system data and physiological data, this helps explain why flow system did
not provide high quality data as expected. The size of speckle can range from one sample
to several in diameter, which is on the same order as the delay being detected. If the delay
we are trying to detect is much longer than the size of the speckle, then speckle would not
be such a big source of variation in delay estimation.
System Noise
When the Doppler signal strength is low due to, for example, attenuation by over lying
tissue or small vessel size, the Doppler amplifier gain must be increased in order to display
the spectrum. At high gains the spectrum exhibits a background noise associated with
electronic noise from the amplifier. Interference can also come from nearby blood vessels or
movements of the probe on the surface of the skin [8]. All of these factors contribute to the
difficulty of calculating an accurate maximum frequency envelope.
6.4
System Limitations
The data acquisition system presents sources of errors as well. The current implementation is
not elegant. It was put together with the bare minimum amount of functionality to capture
71
the data needed. Many modifications can potentially make the technique more accurate and
user friendly.
6.4.1
Dual Beam
One important limitation of the present implementation is the two Doppler ultrasound beams
are not independent. The beams’ depths and angles cannot be independently controlled.
This severely limits where the two points of measurements may be located in the artery.
Ideally, the two beams should both be placed at the center of the artery. The center of an
artery is assumed to have the maximum velocity scatterers.
The human anatomy very rarely offers straight carotid arteries. The carotid artery is
relatively straight in some individuals and very curved in others. To make this PWV measurement tool usable across the population, we must be able to measure people with different
anatomy. Two independently controlled beams would allow placement of beams in the center
of arteries.
6.4.2
Resolution of Delay Estimate
Another limitation of the system is that the time between two samples is 5 ms. One can argue
that faster sampling of the underlying continuous time signal is needed for finer resolution.
However, as mentioned in Section 4.4.1, this limitation can be remedied by interpolation. As
long as the sampled signal has enough bandwidth to accurately reconstruct the underlying
continuous time signal, interpolation is just as good as faster sampling of the original continuous time signal for finer resolution. Thus, although it would be nice to have a smaller
sampling period than 5 ms, the sampling rate does not limit the accuracy of the delay estimation. What does affect the accuracy of the delay estimates is the amount of noise in the
system.
6.4.3
Velocity Measurement Accuracy
Since the proposed method of measuring PWV depends on the blood velocity waveforms
acquired by Doppler ultrasound, it is important to know how accurate Doppler ultrasound
72
is in acquiring velocity information. Daniel Ricky [19] studied this problem. His results
showed that the velocity accuracy of Doppler instruments could be quite good, i.e. within a
few percent of the true velocities. However, the accuracy of Doppler velocity measurements
can be adversely affected by the instrument’s design and the patient’s physiology. For example, Hoskins and McDicken [9] showed that the measured velocities will be affected by
the use of a linear array transducer. The actual measured velocity depends on whether the
ultrasound beam is transmitted from the center of the array or from either end. However,
this source of error should not affect the results of this study even though a linear array is
used. Both apertures used for this study are from the same distance away from the edge
of the transducers. Willemetz et al. [25] showed that the design of the wall filter, which removes the signal component corresponding to the vessel wall and surrounding tissue, can also
affect the accuracy. Accuracy can also be affected by fundamental limitations such as the
frequency dependence of the attenuation coefficient (Holland et al. [21]). In this case, higher
frequencies are preferentially attenuated, which biases the Doppler measurements toward
lower velocities. These effects,along with others, such as frequency-dependent backscatter
from the blood (Newhouse et al. [23]), affect the measured Doppler velocity.
6.4.4
Small Image Buffer Size
The video capture buffer is very small. This means that the user can only capture 5 consecutive frames of data. This only captures around 10 heart cycles. The operator must
stop imaging and save the content of the buffer to disk before continuing to scan. During
this pause, the probe is very likely to move with respect to the carotid. This creates a
discontinuity in the data.
6.5
Delay Estimation Methods
Correlation-based and phase difference methods of delay estimation were tried to detect
the delay for this project. Variations of the correlation-based methods did not affect the
accuracy of the delay estimate. Variations include correlation of the maximum frequency
73
envelopes, correlation of the 2D Doppler images, and manual matching of maximum frequency envelopes. The results in Chapter 5 were calculated based on correlating interpolated
maximum frequency envelopes. Correlation of 2D Doppler spectra without extracting the
envelopes gave similar results. Since 2D correlation is much more computationally intensive,
it was not used. I also tried manual matching of maximum frequency envelopes to see if the
human eye can pick out features of the signal that can more accurately detect the delay.
From this experiment, I see that even a human observer, deemed better than machines in
many situations, could not detect a more accurate delay.
The phase difference method has the advantage that no interpolation is required for
estimating sub-sample delay. However just finding the phase change between the upstream
and downstream envelope and estimating the delay from that without considering frequency
weighting does not yield accurate results. If using the correct frequency weighting, the phase
difference method would give the same delay estimate. However the correlation method is
used because it inherently weighs the important frequencies more.
6.6
Future Work
The work completed for this project only began to explore the possibility of using flow waves
to measure pulse wave velocity. Many issues deserve to be explored further. The system can
be made more user friendly and robust. This study poses a few immediate areas of study
such as better understanding of the noise in the signal.
6.6.1
System Modifications
The two limitations of the system should be remedied. Independent control of the two beams
is not a hard task. However, given the time limitation of this study, this feature was not
implemented. Independent control is desired so that the focus of the two beams can be
placed as close to the center of the artery as possible.
Stable spectral display would mean the upstream spectrum is always displayed at the top
and the downstream spectrum is always displayed at the bottom of the screen. At the current
74
stage, the upstream and downstream spectra can switch positions in video display. This is
probably due to asynchronous communication among the system environments. Different
environments run on different processors with different clock frequencies.
6.6.2
User Feedback
To be useful in the clinical setting, the system should also provide user feedback. As the
user positions the probe for imaging, the system can continuously monitor if the position of
the probe is good for acquiring flow waveforms at two locations in the artery. This feature
is needed since the placement of ultrasound beams is important for this technique. If the
system is confident in its delay estimate, it should inform the user so that the user can try
to keep the probe in that position.
6.6.3
Other Applications of Dual Beam Setup
The dual beam setup of this experiment may be useful for other applications for monitoring
blood flow. One immediate use comes to mind. One can position the two beams before and
after a region of occlusion or plaque. One can then simultaneous observe the Doppler flow
wave from two sites to see how blood flow changes. This application would be more usable
if the two beams can be controlled independently in depth and angle.
6.6.4
Areas for Further Research
Due to time constraint of this project, there were a few areas I did not have time to research,
but are nonetheless very important. I suspect that speckle noise is a big contributor to
the error of measuring PWV. Studies exist in how to filter out speckles. For this project, I
applied a simple low pass filter to the maximum frequency envelopes. Better methods should
be used to filter out the speckle first before envelope detection.
I also stated that wave dispersion may contribute to the error in PWV estimates. However
I did not study what this effect would be. Given more time, I would have tried to simulate
how the waveform changes as it travels down a few centimeters of an artery to see how the
change in shape due to wave propagation can affect the delay estimation.
75
In order to extract the relevant part of the waveform for analysis, a window was used.
However, the window may introduce a small bias to the delay estimate [3]. This bias may
be negligible if certain windows are used. Further research should be done on finding the
best window for this application.
6.7
Conclusion
This thesis project explored the feasibility of using the flow wave captured by Doppler
ultrasound to measure the local propagation velocity of the flow wave. Although this project
has not resulted in a clinical product, many of the issues surrounding the measurement of
local pulse wave velocity has been elucidated. More work is needed to make this technique
a marketable technology.
76
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