local measurement of the pulse wave velocity using doppler

Local Measurement of the Pulse Wave Velocity using

Doppler Ultrasoundby

Minnan XuSubmitted to the Department of Electrical Engineering and

Computer Sciencein partial fulfillment of the requirements for the degree of

Bachelor of Science in Electrical Engineering and Computer Science andMaster 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 distributepublicly paper and electronic copies of this thesis and to grant others the

right to do so.

Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Department of Electrical Engineering and

Computer ScienceMay 24, 2002

Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .David Prater

VI-A Company Thesis SupervisorThesis Supervisor

Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Roger D. Kamm

Professor, Biological EngineeringThesis Supervisor

Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Arthur C. Smith

Chairman, Department Committee on Graduate Theses

Local Measurement of the Pulse Wave Velocity using Doppler

Ultrasound

by

Minnan Xu

Submitted to the Department of Electrical Engineering andComputer Science

on May 24, 2002, in partial fulfillment of therequirements for the degree of

Bachelor of Science in Electrical Engineering and Computer Science and Master ofEngineering in Electrical Engineering and Computer Science

Abstract

Cardiovascular disease is the leading cause of death in many developed countries. Arteries ofpeople 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 detect-ing the development of cardiovascular disease. Several methods focus on the measurement ofpulse wave velocity, the velocity at which the pressure wave propagates, because it is directlyrelated to arterial stiffness. The objective of this project is to investigate the feasibility ofmeasuring local pulse wave velocity from the blood flow waveforms acquired by Dopplerultrasound. The proposed method includes the following steps: first acquire flow waveformsby Doppler ultrasound at two locations within the same artery, next detect the delay ordifference in arrival time of the flow wave at the two arterial locations, and then calculatethe PWV by dividing the length of the arterial segment being imaged by the calculatedtime delay. Although at the conclusion of this study reliable pulse wave velocity detectionis not achieved, the study sheds light on many important issues surrounding this potentialapplication. The project explores how sources of variations such as radial postioning of theprobe and noise level affect the accuracy of the delay estimate.

Thesis Supervisor: David PraterTitle: VI-A Company Thesis Supervisor

Thesis Supervisor: Roger D. KammTitle: Professor, Biological Engineering

3

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

Contents

1 Introduction 15

1.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.2 Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 Background 17

2.1 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 29

3.1 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 Data Processing 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 49

5.1 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 63

6.1 Estimated PWV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.1.1 Simulated Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.1.2 Flow System Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.1.3 Physiological Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.2 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

6.4 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

6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

9

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



5-7 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




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

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 measure-

ment 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 (PWV ) 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

1Arteriosclerosis is a chronic disease characterized by abnormal thickening and hardening of the arterialwall.

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 avail-

able, 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 T2, 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 propa-

gating 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 de-

termine. 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 arte-

rial 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

2A proximal point is one located toward the center of the body.3A distal point is one located far from the center of the body.4Atherosclerosis is an arteriosclerosis characterized by the deposition of fatty substance in and fibrosis of

the inner layer of the arteries.

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,

W (r, t) =2B0

πR2

[1 −

( r

R

)2]

+N∑

n=1

Bn

πR2

1 − J0(αn

rR

i3/2)

J0(αni3/2)

1 − 2J1(αni3/2)

αni3/2(αni3/2)

einωt (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 re-

flected 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 =2ftv 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

Direction ofBlood Flow

θ

Ultrasonic Beam

v cos θ

v sin

θ

v

Figure 2-1: Ultrasound Beam and Artery The ultrasound beam intersects the artery at anangle θ. The component of the blood velocity vector −→v in the direction of the beam ismeasured. 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 mea-surement of blood velocity in the center of a common carotid artery. The vertical tick marksin the middle of the spectrum indicates a duration of one second. The vertical axis is propor-tional to the Doppler shift frequency and in this case has been converted to velocity (unitsof 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 PRF2

.

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 (2.5)

26

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).

Receive Pulse

Transmit Pulse

BloodMotion

fs

PhaserEstimate

Figure 2-3: Illustration of the Pulsed Doppler Principle Estimates of the blood velocity isderived from a series of phase shifts resulting from motion of blood. fs denotes the Dopplershifted frequency. This diagram is adopted from Hwang [10].

27

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 ultra-

sound 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

On-screenDisplay

Scannerboard

DDET board PVT card

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 incomingacoustic 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

FFT MagnitudeDetector FFT shift

TemporalSmoothingFilter

Interpolationto Display

Map Gainand Output

Time domaindoppler signal

DDET Processor B

Window

Figure 3-2: Diagram of Doppler Detector Board Doppler processor B is responsible forprocessing the incoming acoustic signal into Doppler spectra and prepares the spectra forvideo 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 wall-

filtering 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.



Interpolationto Display

Map Gainand OutputTime domain

doppler signal

Modified DDET Processor B

Window



Window

Figure 3-3: Diagram of the Modified Doppler Detector Board The modified DDET boardsplits the incoming acoustic signal into two paths and processes them separately producingtwo 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 windowin the upper right shows the B-mode image of the carotid artery. The circle designates oneof the sample volumes being imaged. The other sample volume, which is not drawn, lies atthe other end of the artery parallel to the first sample volume. The bottom display showsthe two spectra. The upper spectrum corresponds to the flow waveform captured at themarked sample volume. The lower spectrum corresponds to the flow waveform captured atthe 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 non-

duplex 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 accommo-

date 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 win-

dows 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) 33.61Doppler (A) 148.50Doppler (B) 148.50

Table 3.1: Modified Triggered Mode Frame Table The modified Triggered Mode frame tableallows 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 atthe appropriate focus. The Doppler line times depend on the PRF. The values given areonly a possible value.

Line Type Line Time (µs)2D Load Line (2D) 134.24Doppler Setup (SA) 34.01Doppler (A) 148.50Dop Setup (SB) 34.01Doppler B (B) 148.50

Table 3.2: Modified Duplex Mode Frame Table The modified Duplex Mode frame table allowstwo pulsed Doppler beams to be shot alternating from two ends of the transducer. The 2Dload line is one of the lines used to build the B-mode image. The 2D line has an associatedangle which changes with each repetition of the frame table. The Doppler setup lines loadsthe correct delay coefficients to receive the reflected signal at the appropriate focus. TheDoppler line times depend on the PRF. The values given are only a possible value.

34

S A B S A B S A B . . . . . .

33.61µs

1/PRF

A A A . . . . . . B B B . . . . . .

FFT

5 ms

Doppler Spectra Display Area

system delays

Repeat of Frame Table(Scanner Environment)

Acoustic signal in time(Doppler Detector Environment)

Spectral Display(PVT Environment.)

Figure 3-5: Doppler Signal Path in Non-duplex systems The scanner follows the frame tableshown in Table 3.1. S is the setup time during which the scanner loads the correct delaycoefficients to receive the reflected signal at the appropriate focus. A and B are Dopplerlines from the two ends of the transducer. The time between 2 Doppler lines from the sameaperture is 1/PRF. The system delay is the time between 2 Doppler lines from differentapertures. There are two possible system delay times: one after A is shot and before B isshot, the other after B is shot and before A is shot. Both the PRF and the system delaydepend on the time needed to shoot one Doppler line. This time is determined by the depthof 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/ccViscosity 1.66 centistokesParticle Size 30 µmParticle 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

Pump

Elastic Tube Tube Housing

One-Way Connector

Reservoirs

Apply flow resistance here

Probe

Drawing not to scale

Resistance

Tube

Figure 3-6: Flow System Setup A flow system was used to measure the pulse wave velocity ina more constrained environment.The flow system consists of two fluid reservoirs, one higherthan the other. When pressure is applied, fluid flows from the lower reservoir through theelastic tube and then to the higher reservoir. When pressure is released, fluid from the higherreservoir flows back to the lower reservoir without flowing through the elastic tube. A hardplastic housing holds the tube at two ends. When imaging, the entire housing and elastictube is submerged in water. The ultrasound probe is fixed about a half centimeter abovethe elastic tube with water in between the probe and the tube. The elastic tube is roughly14 cm long and 0.5 cm in diameter. The fluid used is a blood-mimicking fluid from ATSLaboratories. 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 theflow system illustrated in Figure 3-6. The quality of the image is highly dependent on theamount 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 inthe 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 win-

dowing. 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 islocated. The angle of measurement is away from the head in order to avoid the carotidbifurcation. The focus of the two beams are placed as close to the center of the artery aspossible. 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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

Time (Sec)

Vel

ocity

(cm

/s)

upstreamdownstream

Figure 4-2: Extracted Envelopes Maximum frequency followers are used to extract envelopesfrom Doppler spectra.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−10

0

10

20

30

40

50

60

Time (Sec)

Vel

ocity

(cm

/s)

Low pass filtered upstreamLow pass filtered downstream

Figure 4-3: Low-pass filtering of Envelopse Filtering introduced a delay size correspondingto 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.

0 0.2 0.4 0.6 0.80

20

40

60

80

100

Time (s)

Vel

ocity

(cm

/s)

upstreamwindow

0 0.2 0.4 0.6 0.80

20

40

60

80

100

Time (s)

Vel

ocity

(cm

/s)

downstreamwindow

0 0.2 0.4 0.6 0.80

20

40

60

80

100

Time (s)

Vel

ocity

(cm

/s)

Windowed Upstream

0 0.2 0.4 0.6 0.80

20

40

60

80

100

Time (s)

Vel

ocity

(cm

/s)

Windowed Downstream

Figure 4-4: Windowing The two plots on the left show the upstream and down streamflow waveforms with the window overlaid. The two plots on the right show the result ofwindowing. The wave front and the part of the cardiac cycle with high flow has beenextracted 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) = C1s(t) + n1(t) (4.1)

x2(t) = C2s(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 corre-

sponds to a delay of T ms. Thus time delay is related to sample delay by the following:

D̂ = sample delay × T (4.4)

44

Β Α

Artery

Α:

Β:

D

x (t)

x (t)

1

2

∆L

Probe

velo

city

(ar

bitr

ary)

velo

city

(ar

bitr

ary)

time

time

Figure 4-5: The Delay Estimation Problem The flow wave is acquired by Doppler Ultra-sound 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 wavevelocity is related to the difference in time of arrival of the pressure pulse at the two sites ofmeasurement. 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 (Rx1x2(τ)) to

estimate time delay between signals, where Rx1x2(τ) is given by

45

Rx1x2(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, Rx1x2 can only be estimated. An estimate of the cross correlation function

is given by

R̂x1x2(τ) =1

N

N∑k=1

x1(kT )x2(kT − τ)dt. (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 tech-

niques 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(e

jω), which are related by

X2(ejω) = X1(e

jω) e−jωD (4.7)

46

The phase difference between the two signals can be calculated by

∆φ(ω) = ∠X2(ejω) − ∠X1(e

jω) (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 4-

6 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 10 20 30 40 50 60 70 80 90 100−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Frequency (Hz)

Pha

se d

iffer

ence

(ra

dian

s)

Figure 4-6: This plot shows the phase differences averaged for individual frequencies across82 cardiac cycles (Data Set A1). For frequencies less than 5Hz, the average phase differencehas a well defined slope which is related to the group velocity.

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Frequency (Hz)

Var

ianc

e of

Pha

se d

iffer

ence

(ra

dian

s)

Figure 4-7: This plot shows the variance of the phase differences for individual frequenciescalculated across 82 cardiac cycles (Data Set A1). The lower frequencies show much lowervariance 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 Mean of Std ofSample Delay Sample Delay

1 Radial Position 11 radial positions - -

2 Noise 1 100 cardiac cycles 0.99358 0.10848SNR = 74 dB



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 rR

= 0.

Figure 5-2 shows the simulated velocity profile for all rR’s at the peak of the flow waveform.

0 1 2 3 4 5 61

1.5

2

2.5

3

3.5

cycle phase (radian)

velo

city

(ar

bitr

ary)

Simulated Envelope

Figure 5-1: Simulated Envelope Data from the Womersley’s model and the parameters inTable 5.2

50

Harmonic Frequency(ω) α |Bn| ∠Bn (degrees)0 - - 1.00 -1 1.03 3.9 0.33 742 2.05 5.5 0.24 793 3.08 6.8 0.24 1214 4.10 7.8 0.12 1465 5.13 8.7 0.11 1476 6.15 9.6 0.13 1797 7.18 10.3 0.06 2338 8.21 12.4 0.04 218

Table 5.2: Simulated Data Parameters (Reproduced from Evans 2000 [7]) Fourier com-ponents and corresponding values of the non-dimensional parameter α for flow waveformsrecorded 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 startingpoint.(diameter(estimated) = 6.0mm; heart rate = 62 bpm; viscosity = 0.038 St)

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

dimensionless distance from axis (r/R)

axia

l vel

ocity

(ar

bitr

ary)

Simulated Velocity Profile

Figure 5-2: Velocity profile according to Womersley’s model of pulsatile blood flow. Theparameters used to generate this data are from other people’s experiments. They are listedin 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 esti-

mate 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.

rR

% of Vmax Delay Estimate0 100.0000 1.0000

0.1000 99.5741 0.95970.2000 98.2771 0.83650.3000 96.0350 0.62330.4000 92.6645 0.30470.5000 87.7748 -0.14630.6000 80.6295 -0.77080.7000 70.0167 -1.61950.8000 54.2347 -2.74080.9000 31.3629 -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 samplecorresponds 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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−10

−8

−6

−4

−2

0

2

r/R

dela

y es

timat

e (d

imen

sion

less

sam

ples

)

Figure 5-3: Delay Estimates From Different Radial Positions The simulated data had anartificial delay of 1 sample. One sample corresponds to a time delay of 5 ms.

0 1 2 3 4 5 6

1.5

2

2.5

3

3.5


velo

city

(ar

bitr

ary)

Simulated Upstream

0 1 2 3 4 5 6

1.5

2

2.5

3


velo

city

(ar

bitr

ary)

Simulated Downstream

−5 −4 −3 −2 −1 0 1 2 3 4 50

5

10

15

20

25

30

35

40

Delay Estimate (dimensionless samples)

Num

ber

of o

ccur

ence

s

Total # of Occurences = 100

mean = 0.99358

std = 0.10848

Figure 5-4: Simulated Data with Noise of SNR = 74dBA downstream data has a simulated delay of 1 sample or 5 ms.

53

0 1 2 3 4 5 6

1.5

2

2.5

3

3.5


velo

city

(ar

bitr

ary)

Simulated Upstream

0 1 2 3 4 5 6

1.5

2

2.5

3

3.5


velo

city

(ar

bitr

ary)


−5 −4 −3 −2 −1 0 1 2 3 4 50

2

4

6

8

10

12

14

16

18

20


Num

ber

of o

ccur

ence

s


mean = 1.0017

std = 0.20355


0 1 2 3 4 5 6

1.5

2

2.5

3

3.5


velo

city

(ar

bitr

ary)

Simulated Upstream

0 1 2 3 4 5 6

1.5

2

2.5

3

3.5


velo

city

(ar

bitr

ary)


−5 −4 −3 −2 −1 0 1 2 3 4 50

2

4

6

8

10

12


Num

ber

of o

ccur

ence

s


mean = 1.0405

std = 0.51097


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 Mean of Std ofSample Delay Sample Delay

1 34 cycles 0.49471 0.522612 21 cycles 0.32286 0.55016

Table 5.4: Summary of Flow System Data SetsThe estimated delays are in terms of samples, with one sample equal to a time delay of 5ms.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

20

40

60

80

100

120

Time (sec)

Vel

ocity

(cm

/s)

Upstream

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

20

40

60

80

100

120

Time (sec)

Vel

ocity

(cm

/s)

Downstream

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

20

40

60

80

100

120

Time (sec)

Vel

ocity

(cm

/s)

Upstream

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

20

40

60

80

100

120

Time (sec)

Vel

ocity

(cm

/s)

Downstream

Figure 5-7: Phantom Flow Wave Envelopes The left side shows the envelopes extractedfrom imaging the flow system. The right side shows the low pass filtered version of the flowwave.

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.

−5 −4 −3 −2 −1 0 1 2 3 4 50

2

4

6

8

10

12

14


Num

ber

of o

ccur

ence

sTotal # of Occurences = 34

mean = 0.49471

std = 0.52261

Figure 5-8: Flow System Data Set 1 Delay estimates are in terms of samples, with onesample equal to a time delay of 5 ms.

−5 −4 −3 −2 −1 0 1 2 3 4 50

1

2

3

4

5

6

7

8


Num

ber

of o

ccur

ence

s

Total # of Occurences = 21mean = 0.32286std = 0.55016

Figure 5-9: Flow System Data Set 2 The radial positions were intentionally varied in thisdata set. However no significant difference in the wave form shape or the variance of thedelay estimate can be seen. Delay estimates are in terms of samples, with one sample equalto 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 Number of Mean of Std ofCardiac Cycles Sample Delay Sample Delay

A1 12/15/2001 A 82 1.2727 0.78273A2 02/02/2002 A 208 1.0136 0.54677B1 12/06/2001 B 48 1.1425 1.1325B2 12/07/2001 B 99 1.3958 0.95784B3 12/15/2001 B 119 0.6758 0.51977B4 02/02/2002 B 57 0.59789 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 sampledelay are results of applying the correlation based delay estimation method. Delay estimatesare 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

−5 −4 −3 −2 −1 0 1 2 3 4 50

5

10

15

20

25


Num

ber

of o

ccur

ence

s

Total # of Occurences = 82mean = 1.2727std = 0.78273

Figure 5-10: Physiological Data Set A1 Delay estimates are in terms of samples, with onesample equal to a time delay of 5 ms.

−5 −4 −3 −2 −1 0 1 2 3 4 50

10

20

30

40

50

60

70

80


Num

ber

of o

ccur

ence

s


mean = 1.0137

std = 0.54934

Figure 5-11: Physiological Data Set A2 Delay estimates are in terms of samples, with onesample equal to a time delay of 5 ms.

58

−5 −4 −3 −2 −1 0 1 2 3 4 50

2

4

6

8

10

12


Num

ber

of o

ccur

ence

s


mean = 1.1425

std = 1.1325

Figure 5-12: Physiological Data Set B1 Delay estimates are in terms of samples, with onesample equal to a time delay of 5 ms.

−5 −4 −3 −2 −1 0 1 2 3 4 50

5

10

15

20

25


Num

ber

of o

ccur

ence

s


mean = 1.3958

std = 0.95784


59

−5 −4 −3 −2 −1 0 1 2 3 4 50

5

10

15

20

25

30

35

40

45

50


Num

ber

of o

ccur

ence

s


mean = 0.6758

std = 0.51977


−5 −4 −3 −2 −1 0 1 2 3 4 50

2

4

6

8

10

12


Num

ber

of o

ccur

ence

s


mean = 0.59789

std = 1.1508


60

Data Set Time Delay Number of Estimated Standard Deviation(ms) Cardiac Cycles PWV (m/s) of PWV Estimate

A1 6.3635 76/82 5.6615 4.16A2 5.0680 191/208 6.5313 4.75B1 5.7125 39/48 7.3750 7.61B2 6.9790 94/99 5.7477 6.82B3 3.3790 95/119 7.3140 8.87B4 2.9895 47/57 2.6382 9.54

Table 5.6: Time delays and Estimated PWV This table shows the sample delays convertedto time delays in milliseconds and PWV. To convert sample delay to time delay, one simplymultiplies the sample delay by 5 ms (the sampling interval T) as implied by the relationshipshown 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 inzero. To avoid unrealistically high PWV values, sample delays within 0.2 sample of zero areignored. This threshold restricts PWV values to have an absolute value of 30 m/s. Giventhat the normal PWV in the common carotid is between 6.80 m/s and 8.30 m/s, this cutoffseems acceptable. The column titled Number of Cardiac Cycles shows the actual number ofcardiac cycles used to produce the PWV estimates.

61

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 measure-

ment 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 distribu-

tions. 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 diffi-

culty 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

x

x

Artery

Plane of ultrasound beams

Figure 6-1: Beam Plane X marks the focus of the beams. It is very hard to place bothbeams at the center of the arterial cross sections. This difficulty is compounded by the factthat the B-mode image which can help guide the placement of the beams only shows onedimension of the artery. Even when the beam looks centered in one plane, they may beoff-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:

D =1

N

N∑n=1

dn. (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,

Pr[|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 measure-

ments, 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,

Pr[|D − µD| ≤ 1.65σD] = 90% (6.3)

Combining the above two equations yields

1.65σD = 0.1µD. (6.4)

1.65

(1√Nσd

)= 0.1µD. (6.5)

N =272.25σ2

d

µ2D

; (6.6)

69

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 Variance Due to Noise

6.3.1 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 sonog-

raphy [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 wave-

lengths 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

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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 mea-

surement 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 con-

tinuous 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 esti-

mation. 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

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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 ex-

ample, 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 re-

moves 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 con-

secutive 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

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envelopes, correlation of the 2D Doppler images, and manual matching of maximum fre-

quency 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.

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local measurement of the pulse wave velocity using doppler

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