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I1 -

 

 

 

,OiO

 

LIBRARY

MICthan State
niversity

 

 

 

This is to certify that the
dissertation entitled

HEMODYNAMIC MONITORING VIA IMPULSE RESPONSE
ESTIMATION

presented by

Da Xu

has been accepted towards fulfillment
of the requirements for the

Doctoral degree in Electrical Engineering

 

 

LkWL—

Major Professor’s Signature
3‘ / 2 a / l 0

Date

 

MSU is an Affirmative Action/Equal Opportunity Employer

 

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5/08 ICIProj/AcofiPres/ClRC/Dateoue.indd

 

HEMODYNAMIC MONITORING VIA IMPULSE
RESPONSE ESTIMATION

By

Da Xu

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Electrical Engineering

2010

ABSTRACT

HEMODYNAMIC MONITORING VIA IMPULSE RESPONSE
ESTIMATION
By

Da Xu

Hemodynamic monitoring is a highly valuable guidance during observation,
diagnosis, and treatment of cardiovascular diseases. While most hemodynamic
monitoring systems today entail routine measurement and display of blood pressure
or other arterial waveforms, more effective systems are demanded by a fast growth in
the proportion of the elderly population and a major shortage of clinical staff
projected over the next decade. To this end, novel techniques based on impulse
response estimation are presented in this dissertation to continuously monitor cardinal
hemodynamic variables by mathematical analysis of cardiovascular waveforms
measured with instrumentation already in use or available.

Techniques based on the Windkessel model were proposed to continuously
estimate cardiac output and left atrial pressure from peripheral arterial blood pressure,
pulmonary artery pressure, and right ventricular pressure waveforms respectively.
Long time interval analysis was applied in these techniques to circumvent the wave
reflections and inertial effects in the blood pressure waveforms. The techniques were
evaluated with animal/human experiments and showed application potential in

clinical practice. Efforts were further made to extend the long time interval analysis

technique to the photoplethysmography waveform and pilot results confirmed the
feasibility.

Techniques for robust estimation of the pulse wave velocity were developed in
order to achieve accurate arterial stiffness and cuff-less blood pressure monitoring.
System identification methods using both physiologic-based and black-box models
were employed to improve the robustness of the techniques. Preliminary results
obtained from animal/human experiments demonstrated potential clinical values of
the techniques.

With further evaluation, these techniques may ultimately be employed
conjunctively to arrive at continuous and effective hemodynamic monitoring systems

in various clinical settings.

To my wife

iv

ACKNOWLEDGEMENTS

It is a pleasure to thank those who made this dissertation possible. First of all, I
would like to express my deepest gratitude to my advisor Dr. Ramakrishna
Mukkamala for his professional guidance and persistent support to my research work.
His technical genius and continuous spirit of adventure in regard to research have
been motivating me throughout my Ph.D. study and will continuously benefit me in
my future research career.

I would like to address my sincere appreciation to my committee members Dr.
Bari Olivier, Dr. Selin Aviyente, and Dr. Shantanu Chakrabartty for their valuable
advices and guidance on my work. Dr. Bari Olivier is meanwhile my collaborator,
without whom none of the animal experiments in this dissertation would have been
completed.

My gratitude also extends to my other collaborators: Dr. Andrew Reisner in
Massachusetts General Hospital, Dr. Victor Convertino and Dr. Kathy Ryan in the
United States Army Institute of Surgical Research, and Dr. Caroline Richards in
University of Texas for their instructive opinions and suggestions regarding my
research projects. In addition, my special thanks to Mr. Gary Muniz, Mr. Joseph
Prinsen and Mr. Thoralf Hoelzer—Maddox for their great technical contributions to the
experimental data collection.

I would like to take this opportunity to thank my former advisor Dr. Yuanyuan

Wang in Fudan University, who introduced me into this exciting research area.

I am indebted to my colleagues for their generous help and the wonderful
experiences enjoyed with them: Xiaoxiao Chen, Gokul Swamy, Guanqun Zhang,
Federico Aletti, Soroor Soltani, Anton Khomyakov, Zhenwei Lu, Kabi Padhi, and
Mohsen Moslehpour.

Finally, I owe my greatest thanks to my family, especially my wife Fang Sun, to
whom I dedicate this dissertation. Without their unconditional support and

encouragement, I would never have accomplished anything on this way.

vi

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LIST OF TABLEs x
LIST OF FIGURES -- ........... -xi
ABBREVIATIONS _ xv
CHAPTER 1 INTRODUCTION 1
1.1 Background 1
1.2 Motivation and Objective ..... 2
1.3 Limitation of Convention Methods 2
1.4 Scope and Organization of the Dissertation 8
CHAPTER 2 BACKGROUND ...... 10
2.1 System Identification and Impulse Response 10
2.1.1 System identification 10
2.1.2 Impulse response 11

2.2 Black-Box Models and Least Squares Method 12
2.2.1 Autoregressive exogenous input model 12
2.2.2 Least squares method 13
2.2.3 Output error model 14

2.3 Receiver Operating Characteristic Curve ............ 14

 

CHAPTER 3 CARDIAC OUTPUT MONITORING BY PERIPHERAL ARTERIAL BLOOD

 

 

 

 

 

 

 

 

 

PRESSURE WAVEFORM ANALYSIS 17
3.1 Introduction __ __ 17
3.2 The Technique ............ 23
3.3 Methods ............... 26

3.3.1 Experimental procedures 26
3.3.2 Data analysis 28
3.4 Results 29
3.4.1 Detection of progressive hypovolemia 29
3.4.2 Discrimination between hypovolemia and its resuscitation .................... 34

3.4.3 Discrimination between high-tolerant and low-tolerant subjects ......... 34

3.5 Discussion

35

 

3.6 Technique Extension

40

 

41

 

3.6.1 CO monitoring by PPG waveform analysis

vii

3.6.2 Methods

 

3.6.3 Pilot results and discussion

41
43

 

CHAPTER 4 CARDIAC OUTPUT AND LEFT ATRIAL PRESSURE MONITORING BY

PULMONARY ARTERY PRESSURE WAVEFORM ANALYSIS

46

 

4.1 Introduction

46

 

4.2 The Technique

48

 

4.3 Methock

53

 

4.3.1 Experimental procedures

53

 

4.3.2 Data analysis

55

 

4.4 Results

 

4.5 Discussion

57
64

 

CHAPTER 5 CARDIAC OUTPUT AND LEFT ATRIAL PRESSURE MONITORING BY

RIGHT VENTRICULAR PRESSURE WAVEFORM ANALYSIS

71

 

5.1 Introduction

71
73

 

5.2 The Technique
5.3 Methods

77

 

5.3.1 Experimental procedures

77

 

5.3.2 Data analysis

78

 

5.4 Results ...............................

79

 

5.5 Discussion ............ ....................................

 

83

 

 

CHAPTER 6 ROBUST PULSE WAVE VELOCITY ESTIMATION BY SYSTEM
IDENTIFICATION _____

'86

 

6.1 Introduction ...... - .....

86
89

 

6.2 The Techniques ........
6.2.1 Arterial tube model-based technique

89

 

6.2.2 Black-box system identification technique

91

 

6.3 Methods

94

 

6.3.1 Arterial tube model-based technique

94

 

6.3.2 Black-box system identification technique

96

 

6.4 Results

98

 

98

 

6.4.1 Arterial tube model-based technique
6.4.2 Black-box system identification technique

100

 

6.5 Discussion ......

--101

 

CHAPTER 7 SUMMARY AND FUTURE WORK ......

104

 

7.1 Accomplishments and Summary

104

 

7.2 Future Work

105

 

viii

REFERENCES - -- 111

 

ix

LIST OF TABLES

Table 1.1 Conventional methods for measuring cardiac output, left
atrial pressure, and pulse wave velocity.

 

Table 3.1 Area under receiver Operating Characteristic curves with
standard errors for discrimination between different levels of lower

body negative pressure, using investigational cardiac output metrics. .............

Table 3.2 Area under receiver Operating characteristic curves with
standard errors for discrimination between different levels of lower

body negative pressure, using investigational stroke volume metrics. ..............

Table 3.3 Area under receiver operating characteristic curves with
standard errors for discrimination between high-tolerant and low-
tolerant subjects using cardiac output and stroke volume metrics at -60

 

mmI-Ig lower body negative pressure.

Table 4.1 Summary of hemodynamic range and results of the long time
interval analysis technique as well as the Classic end-diastolic pulmonary
artery pressure technique for each dog.

 

Table 5.1 Root-mean-squared-errors of the hemodynamic variables
estimated by the long time interval analysis technique of Fig. 5.1 for each

 

dog.

Table 5.2 Root-mean-squared-errors, Slopes, and intercepts of Bland-
Altman plots of the hemodynamic variables estimated by the long time
interval analysis technique of Fig. 5.1 and the previous techniques of Fig.
5.2 over all the dogs.

 

..... 31

..... 33

35

59

81

81

LIST OF FIGURES

Figure 1.1 Limitations of conventional blood pressure monitoring. ................

Figure 2.1 The concept of system identification.

 

Figure 2.2 Examples of receiver operating characteristic curves for
three discrimination metrics.

 

Figure 3.1 Previous technique for cardiac output monitoring by
analysis of the central arterial blood pressure waveform based on
Windkessel model.

 

Figure 3.2 The arterial blood pressure waveform becomes
progressively distorted from the central aorta to the peripheral arteries

 

due to wave reflections in the arterial tree. (Adapted from (99).)

Figure 3.3 Two arterial blood pressure waveforms simultaneously
measured from the central aorta and the radial artery. (Adapted from
(106).)

 

Figure 3.4 Long time interval analysis technique for monitoring relative
cardiac output Change from a peripheral arterial blood pressure
waveform.

 

Figure 3.5 Group means of subjects (n = 21) for the investigational
cardiac output metrics through progressive levels of lower body
negative pressure decompression, expressed as % of baseline
measurement. Vertical positions of data points were staggered to
display non-overlapping 95% confidence intervals.

 

Figure 3.6 Group means of subjects (n = 21) for the investigational
stroke volume metrics through progressive levels of lower body negative
pressure decompression, expressed as % of baseline measurement
Vertical positions of data points were staggered to display non-
overlapping 95% confidence intervals.

 

xi

........ 4

10

15

18

20

22

24

30

32

Figure 3.7 Excerpts of arterial blood pressure waveforms from one
subject during different levels of decompression. 38

 

Figure 3.8 Normalized cardiac output values estimated by the long time
interval analysis technique applied to calibrated photoplethysmography
waveforms compared with reference thermodilution measurements. .................. 45

Figure 4.1 A potential technique for continuous cardiac output and left
atrial pressure monitoring by intra-beat analysis of the pulmonary
artery pressure waveform. 49

 

Figure 4.2 Long time interval analysis technique for monitoring relative
cardiac output Change and left atrial pressure from a pulmonary artery
pressure waveform. 5 1

 

Figure 4.3 Sample segments of the pulmonary artery pressure

waveform and the measured aortic flow and left atrial pressure

waveform from dog 5 during baseline, phenylephrine, and hemorrhage
conditions. Note that pure exponential diastolic decays are not apparent

in the pulmonary artery pressure waveform segments. 58

 

Figure 4.4 Results of the long time interval analysis technique and the

classic end-diastolic pulmonary artery pressure technique in terms of

regression plots of the calibrated cardiac output and absolute left atrial

pressure estimates versus their corresponding reference aortic flow

probe cardiac output and left atrial pressure catheter values for each dog.

p is the correlation coefficient between the estimated and reference

values. 60

 

Figure 4.5 Results of the long time interval analysis technique and the

classic end-diastolic pulmonary artery pressure technique in terms of
Bland-Altman plots of the calibrated cardiac output and absolute left

atrial pressure errors versus the reference aortic flow probe cardiac

output and left atrial pressure catheter values pooled over all five dogs.

u is the bias error; 0', the precision error; and RMSE the root-mean-
squared-error (i.e., \l(p2+oz)). 62

 

xii

Figure 4.6 Results of the long time interval analysis technique and the
classic end-diastolic pulmonary artery pressure technique in terms of
Bland-Altman plots of the changes in the calibrated cardiac output and
absolute left atrial pressure estimates (with respect to their mean values
in each dog) versus the corresponding changes in their reference values
for the dobutamine, esmolol, phenylephrine, and nitroglycerin
interventions pooled over all five dogs.

 

Figure 5.1 Long time interval analysis technique for monitoring relative
cardiac output change, left atrial pressure, and mean pulmonary artery

 

pressure from a right ventricular pressure waveform.

Figure 5.2 The three previous techniques for monitoring relative
cardiac output change, left atrial pressure, and mean pulmonary artery
pressure by intra-beat analysis of the right ventricular pressure

waveform. P1st indicates the value of right ventricular pressure at the
time of the first zero crossing (from positive to negative) of the third
derivative of the waveform following the time of its maximal positive

 

first derivative. (Adapted from (71).)

Figure 5.3 Regression plots and Bland-Altman plots of the relative
cardiac output change and left atrial pressure estimated by the new
technique of Fig. 5.1 over all four dogs. [4 and 6 respectively indicate the
constant bias and precision error.

 

Figure 6.1 Typical plot of diastolic pressure versus proportional pulse
wave velocity. (Adapted from (97).)

 

Figure 6.2 Technique for robust estimation of pulse wave velocity from
central and peripheral (lower limb) arterial pressure waveforms (pc(t)
and pp(t)) based on an arterial tube model.

 

Figure 6.3 Black-box system identification technique for robust
estimation of pulse wave velocity from impedance cardiography and
peripheral arterial blood pressure waveforms.

 

xiii

63

74

80

82

87

90

92

Figure 6.4 Conventional detection method for estimation of pulse wave
velocity from impedance cardiography and peripheral arterial blood
pressure waveforms.

93

 

Figure 6.5 Sample segments of measured arterial pressure waveforms
before and after contamination with noise of varying amounts. SN R is
Signal-tO-noise ratio.

99

 

Figure 6.6 Root-mean-squared-error of the predicted diastolic pressure
and mean arterial pressure as a function of signal-to-noise ratio.

99

 

Figure 6.7 Diastolic pressure estimated via proportional pulse wave
velocity estimate versus measured diastolic pressure over all the
subjects.

 

Figure 7.1 Continuous and non-invasive monitoring system for cardiac
output and arterial stiffness by mathematical analysis of
ballistocardiography and peripheral arterial blood pressure waveforms.

 

(Reproduced in part from (1).)

Figure 7.2 Continuous, non-invasive, and low-cost monitoring system
for cardiac output and arterial stiffness by mathematical analysis of
ballistocardiography and photoplethysmography waveforms.
(Reproduced in part from (9).)

 

Figure 7.3 Continuous cardiac output and left atrial pressure monitoring
systems by mathematical analysis of pulmonary artery pressure or right

ventricular pressure waveforms. (Reproduced in part from (7, 10).) ...............

xiv

100

107

108

..110

AC

AUC

BCG

BP

CO

DP

ECG

FDA

HR

ICG

ICU

LAP

LBNP

LTIA

LVFP

MDL

OE

PAC

ABBREVIATIONS

Arterial Blood Pressure

Arterial Compliance
Autoregressive Exogenous Input
Area Under Curve
Ballistocardiography

Blood Pressure

Cardiac Output

Diastolic Pressure
Electrocardiography

Food and Drug Administration
Heart Rate

Impedance Cardiography
Intensive Care Unit

Left Atrial Pressure

Lower Body Negative Pressure
Long Time Interval Analysis
Left Ventricular Filling Pressure
Mean Arterial Pressure
Minimum Description Length
Output Error

Pulmonary Arterial Compliance

XV

PAP

PAR

PCWP

PP

PPG

PWV

RMSE

RMSNE

ROC

RVP

SNR

SP

SV

TPR

Pulmonary Artery Pressure
Puhnonary Arterial Resistance
Pulmonary Capillary Wedge Pressure
Pulse Pressure
Photoplethysmography

Pulse Wave Velocity
Root-Mean-Squared-Error
Root-Mean-Squared-Normalized-Error
Receiver Operating Characteristic
Right Ventricular Pressure
Signal-to-Noise Ratio

Systolic Pressure

Stroke Volume

Total Peripheral Resistance

xvi

CHAPTER 1

INTRODUCTION

1.1 Background

The function of the cardiovascular circulation is to serve the needs of body
tissues by transporting essential substances to the tissues, removing waste products of
metabolism, conducting hormones from one part of the body to another, and
maintaining an appropriate environment in the tissue fluids of the body (52). The
cardiovascular circulation is divided into the systemic circulation and the pulmonary
circulation. Systemic circulation transports oxygenated blood from the heart to the
body tissues and returns oxygen-deprived blood back to the heart, while pulmonary
circulation propels oxygen-depleted blood into the lung for exchange of oxygen and
carbon dioxide and circulates the now oxygen-rich blood to the heart. Each of the
circulation systems contains a pump (the heart), a series of tubes for transportation
(arteries or veins), and thin tubes for exchanging substances between the blood and
the interstitial fluid (capillaries).

Physical quantities can be measured inside or outside the cardiovascular
circulation to record electrical activity of the heart (e.g., electrocardiography (ECG)),
pressure in the heart or blood vessel (e.g., blood pressure (BP)), volume change in
blood vessel (e.g., photoplethysmography (PPG)), flow rate in blood vessel, body

resistance change induced by the circulation (e.g., impedance cardiography (ICG)),

and recoil to the force generated by the pumping heart (e.g., ballistocardiography
(BCG)). Continuous measurements of these quantities result in hemodynamic

waveforms.

1.2 Motivation and Objective

Hemodynamic monitoring is extremely useful in diagnosis and therapy guidance
of cardiovascular disease, which is one of the leading causes of mortality in the
United States. In addition, the growth in the proportion of elderly population and
shortage of clinical staff (8, 145) imply the urgent need for continuous (i.e.,
automated) and effective hemodynamic monitoring systems. The Objective of this
dissertation is to investigate new techniques based on impulse response estimation in
an attempt to ultimately build continuous, less invasive, and more effective

hemodynamic monitoring systems.

1.3 Limitation of Convention Methock

Today, hemodynamic monitoring in clinical settings mostly involves continuous
measurement and display of BP waveforms. Minimally invasive catheters are
employed at intensive care unit (ICU) to measure a peripheral arterial BP (ABP)
waveform from typically the radial artery (2, 74). Moreover, non-invasive systems
for measurement of a peripheral BP waveform are now commercially available (1 , 5).
Invasive catheters are also used in critically ill patients to measure BP waveforms
from the pulmonary artery and right heart (95, 115). Recently, a well-tested and safe

implantable device has also been developed for chronic ambulatory monitoring of the

right ventricular pressure (RVP) waveform for congestive heart failure patients (92,
111, 112). In addition to BP monitoring, the PPG technique, which measures blood
volume change in the microvascular bed of tissue, also has widespread applications in
clinical hemodynamic monitoring (12, 24).

Although these waveform monitoring systems are used in clinical settings,
critical information in the waveforms has not been fully revealed yet. The PPG
waveform is not fully understood and issues such as calibration and motion artifact
during measurement also hinder its clinical applications. Perhaps, as a result,
successful applications of PPG technique today are limited (i.e., the monitoring of the
blood oxygen saturation, rather than the waveform itself, through pulse oxirneter (12,
14)). Furthermore, although BP waveforms are more intensively studied and provide
continuous and safe measurements for clinical use, they are not able to provide
precise and sufficient information to indicate the circulatory status.

One limitation of BP monitoring is that BP does not provide an early indicator of
changes in circulatory status because of the cardiovascular control system (e.g., the
autonomic nervous system) which tends to maintain the BP levels within a narrow
range (52). For example, as illustrated in Fig. 1.1a, BP is maintained in the early
stage of hemorrhage while other hemodynamic variables (e.g., cardiac output (CO),
the total blood flow rate in the circulation) change Significantly (16). In the sense of
hemodynamic monitoring, the maintained BP could be misleading and allow
insufficient time for interventions before the frank hypotension eventually occurs (see
Fig. 1.1a). On the other hand, CO provides an earlier indicator of circulatory changes

and may permit adequate time for successful therapy.

(a) (b)

 

 

 

 

 

5' so
:1: U E. 40
E E I.I.l Lu / \
I! I— 0 20 100 '- -—-
Ear 9% _
SE 5 0 80 E '5 sepsis? hypovolemia?
a n
2 _20 _ 60 g _. cardiac
120 - dysfunction?

O. Venesection

3.3 10° 1080 com I“

g E 80 1: 72:?“ lat} '9 77/” g ABPVL

!- 12 <0

g: E- 60 g E T/ \ ¢

0) 2 CO CO

'E' 4° E 2
Eg a 6 g E sepsis LAPT LAPI
< D 0 I g
0 o g 4' . ‘ . < / \
=- o 4 8 12 16 5 cardiac hypovolemla
MINUTES dysfunction

Figure 1.1 Limitations of conventional blood pressure (BP) monitoring. (a) In the
early stages of hemorrhage, BP is maintained even while cardiac output (CO) is
falling due to the cardiovascular control system. Thus, BP does not provide an early
indicator of harmful changes in circulatory status and, as a result, may not provide
enough time for effective therapy. (Adapted from (16).) (b) BP is not sufficiently
Specific to permit diagnosis and guide therapy. However, a differential diagnosis may
be obtained by also monitoring CO and left atrial pressure (LAP).

Another limitation is that BP could be affected by multiple physiologic factors.
Therefore, diagnosis and therapy are only possible when additional hemodynarrric
variables other than BP are available. For example, when decrease of BP is observed,
CO and left atrial pressure (LAP, which indicates the filling pressure or preload of the
left ventricle) or other measures of left ventricular filling pressure (LVFP) must also

be monitored so as to distinguish different possible causes (sepsis, cardiac

dysfunction, or hypovolemia) (72, 118) (see Fig. 1.1b).

As shown above, hemodynamic variables such as CO and LAP are more
clinically valuable than BP. In addition, pulse wave velocity (PWV, which is the
Speed of energy wave propagation in the arteries) is another cardinal cardiovascular
parameter. PWV increases with decreasing arterial compliance (AC) and is perhaps
the most common index of arterial stiffness (15). Further, since AC varies inversely
with BP, PWV and BP Show strong, positive correlation. PWV may, in fact, represent
the only viable means at present for achieving continuous, non-invasive, and cuff-less
monitoring of BP. Several methods are currently available for measuring CO, LAP,
and PWV (see Table 1.1).

Table 1.] Conventional methods for measuring cardiac output (CO), left atrial
pressure (LAP), and pulse wave velocity (PWV).

 

 

 

 

 

Her‘nxzplaemrc Method Advantages Disadvantages
aortic flow probe (43) contrnuousagigtaeutomated); thoracotomy
bolus thermodilution relatively Simple; p :figtfiiyzagzy

(43) inexpensive ’
operator
. continuous pulmo .3 . .)
contmuous ri ht ventricular e'ection cathetenzatron,
thermodilution (43) g fraction (153 1" 63) less accurate than bolus
C0 ’ thermodilution (164)
oxygen fick (43) . accurate; two catheterrzatrons;
mexpensrve operator
impedance continuous; Inaccurate m the.
. . . presence of lung flurds
cardiography (43, 86) non-mvasrve (3 5)
ultrasound non-invasive expert operator;
(e.g., Doppler (43, 86)) expensive
left atrial catheter (133) c::::::;8; too invasive and risky
LAP '
pulmonary capillary relatively simple; ”mm af‘ery
wedge pressure (120, inex ensive catheterrzatron;
143) p operator
PWV foot-to-foot time delay relatively simple; susceptible to

(27)

non-invasive

measurement artifact

 

The most accurate methods measuring CO and LAP involve placing an ultrasonic
flow probe around the ascending aorta (43) and directly catheterizing the left atrium
(133). While these methods afford continuous monitoring, they are rarely performed
in clinical practice due to high level of invasiveness and associated risk of blood clot
formation and embolization (e. g., stroke).

In clinical setting, the standard methods for monitoring CO and LAP both
involve the use of the less risky pulmonary artery catheter (95, 143). CO is
Specifically estimated by the bolus thermodilution method. This method involves
injecting a bolus of cold saline in the right atrium via a proximal catheter port,
measuring temperature downstream in the pulmonary artery with a thermistor near the
distal catheter end, and computing the average CO based on conservation laws. LAP
is estimated through the pulmonary capillary wedge pressure (PCWP) method. This
method involves advancing the catheter into a branch of the pulmonary artery,
inflating a balloon at the catheter tip, and measuring the distal steady-state pressure.
In theory, the resulting PCWP should approximately equal LAP, as flow has ceased
through the branch.

Despite their use in critically ill patients, the thermodilution and PCWP methods
have significant limitations. The main limitation is that these methods require an
operator to make each individual measurement. Consequently, thermodilution and
PCWP measurements are typically made infrequently. Indeed, in 775 critically ill
patients instrumented with pulmonary artery catheters, only 0.83 thermodilution and
0.15 PCWP measurements were made on average per day (8). Another limitation is

that several technical problems must be overcome in making valid PCWP

measurements. These problems include partial wedging and balloon over-inflation
(82, 104), dependence of the measurement on the wedge catheter position (58, 68),
and proper interpretation of phasic PCWP (49, 62). Even the developers of the PCWP
method reported that they could properly measure PCWP only about 75% of the time
in the cardiac catheterization laboratory (120). Similarly, technical problems are also
encountered in making thermodilution measurements in which variations in inj ectate
volume, rate, and temperature introduce significant error in the measurement (83, 102,
138). A third limitation is that the injection of fluid and balloon inflation poses risk
(e.g., air emoblization) (43, 73, 88). Perhaps due in part to infrequent use (126, 146)
and misuse (80, 118, 125, 146) of the PCWP and thermodilution methods, the
potential benefit of CO and LAP monitoring in guiding clinical decision-making may
not, in general, be sufficiently attained through the thermodilution and PCWP
methods to exceed the upfront risk of using the invasive catheter.

CO is also non-invasively measured using ICG (36, 43, 77, 78, 86) technique.
This technique is based on the resistance change in the thorax to a low-intensity, high-
frequency alternating current applied to the thorax by two surface electrodes placed at
the root of the neck and two surface electrodes placed at the xiphoid process at the
midaxillary line. Stroke volume (SV) is computed according to the Kubicek equation
(78) and CO is taken as the product of SV and heart rate (HR). Although this
technique achieves non-invasive monitoring of CO, the measurement involves
electrode placement on the neck and chest, which is sometimes precluded by surgical
wounds. In addition, ICG may not perform as well in critically ill patients as healthy

subjects (65) because of errors associated with abnormal thoracic anatomy (e.g., post-

pneumonectomy) or intra-thoracic fluid (e.g., pleural effusions, pulmonary edema,
ARDS) (20, 35, 36).

PWV is conventionally measured through the time delay between the onsets of
upstroke of proximal and distal arterial waveforms (i.e., foot-to-foot time delay) (27,
48). Sometimes, this parameter is more conveniently approximated through the time
delay between the R-wave of an ECG waveform and the foot of a distal arterial
waveform. But, this convenience comes at the significant price of confounding the
time delay with the pre-ejection period (48, 113). Despite its simplicity, this
conventional method to determine PWV is susceptible to measurement noise

especially the motion artifact.

1.4 Scope and Organization of the Dissertation

This dissertation aims to bridge the readily available continuous measurements
(e.g., BP, PPG, ICG, and BCG) to clinically more significant hemodynamic variables
(e.g., CO, LAP, and PWV) via mathematical analysis techniques so as to make the
hemodynamic monitoring both effective (i.e., tracking the key variables needed to
direct therapy) and easy-to-use (i.e., continuous and less invasive or non-invasive). In
each technique, an impulse response is identified from available measurements and
the hemodynamic variable is estimated from the impulse response (i.e., impulse
response estimation).

This dissertation is organized as follows: Chapter 1 includes a brief background
of the cardiovascular circulation, the motivation of the work, and the limitations of

current hemodynamic monitoring systems. Chapter 2 describes background

knowledge and concepts used in following chapters. Chapter 3 reviews a previously
developed technique for monitoring CO from peripheral ABP waveform and
evaluates the technique with new human data. In addition, the proof-of—concept of
extending this technique to PPG waveform is demonstrated as well. Chapter 4 and
Chapter 5 formulate two extended techniques for monitoring CO and LAP from
puhnonary artery pressure (PAP) and RVP waveforms respectively. Chapter 6
introduces robust PWV estimation techniques by application of system identification
to proximal and distal arterial waveforms. Chapter 7 summarizes major contributions

of the dissertation and proposes future work.

CHAPTER 2

BACKGROUND

In this chapter, important background knowledge and concepts using in

following chapters are briefly introduced.

2.1 System Identification and Impulse Response

2.1.1 System identification

The cardiovascular circulation or part of it can be considered as a dynamic
system and the hemodynamic measurements are the input (i.e., stimulus) and output
(i.e., response) of the system. The approach to identify the dynamic system from
observed input and output signals is called system identification, which is the basis of

signal processing techniques used in this dissertation (see Fig. 2.1) (89).

 

 

 

Input I) Output

) F

 

 

 

Figure 2.1 The concept of system identification.

The real-life complicated system is characterized by mathematical models in
order to make the system identification applicable. These mathematical models are

divided into gray-box and black-box models in terms of the availability of pre-

10

knowledge about the system. The gray-box model assumes that partial knowledge of
the system is understood (e.g., the structure of the cardiovascular system can be
obtained based on physical or physiological properties but the parameters in the
model are unknown). Gray-box model identification is helpful to better understand
the dynamic system as the model parameters generally have specific physical
meanings. On the other hand, the black-box model assumes no prior knowledge
about the system to be identified, that is, both the system structure and model
parameters are unknown. Some standard model structures are used to represent the
system in this case. While the black-box model provides less insight into the true
system, the model structure is more flexible than that of the gray-box model. Both

models are used in this dissertation.
2.1.2 Impulse response

Consider a system with input signal x(t) and output y(t) (t indicates discrete time
here and hereafter in the dissertation). Intuitively, output y(t) is the response of the
system to input x(t). For a linear, time-invariant system, when the input is a unit
impulse function 5(t) (which has the value zero everywhere except at t = 0 where its
value is infinitely large in such a way that its total integral is one), the corresponding
output h(t) is called the impulse response (89). The impulse response is a complete
characterization of the dynamic system and the system response y(t) to any input x(t)
can be computed as follows:

y(t): Zh(k)x(t—k> (2.1)

k=—oo

11

Therefore, system identification can also be viewed as the identification of the system

impulse response.

2.2 Black-Box Models and Least Squares Method

2.2.1 Autoregressive exogenous input model

One of the most widely used black-box models is the autoregressive exogenous
input (ARX) model (89), which is also frequently employed in this dissertation. The
basic relationship between input and output in this model is formulated by the
following linear difference equation:

y(t)=a1y(t—1)+...+am y(t—m)+b1x(t—l)+...+bn x(t—n)+e(t)

m n (2.2)
= Zak y(t—k)+ Zbk x(t—k)+e(t)
k=1 k=1

where e(t) is an unobserved, white noise that is uncorrelated with x(t). Unknown

parameters {ak} and {bk} are referred to as autoregressive and exogenous coefficients

respectively. The constants m and n are called model orders. By introducing the

vectors

8=[a1...am b1...bn]T

(2.3)
(p(t)=[y(t—l)...y(t—m) x(t—l)...x(t—n)]T,

Eq. 2.2 can be rewritten as

y(t) = «9109+ e(t) (2.4)
where T indicates the transposition of the vector. The ARX model can be expressed

in Z-domain as well by the following equation:

12

 

 

B(z) X(z) +

Ya) = 1— A(z) 1— A(z)

B(z) (2.5)

where A(z) = alz-l+a22'2+. . .+amz'm, B(z) = b1z'1+b22'2+. . .+bnz-n, and B(z) is the Z
transform of e(t).
2.2.2 Least squares method

In order to estimate the parameters in ARX model (i.e., 9), certain criterions are
needed to define the optimal 6 of the model. One of the most popular criterions is the
least squares method, that is, 8 is selected to minimize the mean square of the

prediction error (i.e., e(t)) (89), which is denoted as follows:

6 = arg nrin V(8,t) (2.6)
9

where
1 N 2 1 N r 2 1 N 2
WW) =—Zty(t)—y(t)1 =—Z[y(t)—<p (091 =—Ze (t) (2.7)
Nt=l N =1 N =1
In Eq. 2.7, N is the number of samples of observed input and output and hat indicates
estimated values.
Since V(6,t) is quadratic in 0, the minimum value can be found by setting the

derivative to zero:

(I 2 N T
0=EV(9,t)=§§¢(t)[y(t)-v (091

which gives the optimal 6 in the least squares sense

13

t=1 t=l

. N ‘1 N
9=[Z<P(t)<pT(t)] Z¢(t)y(t) (2-8)

2.2.3 Output error model

Another commonly employed black-box model is the output error (OE) model
with the Z-domain form as follows:

B(z)

Y”) = 1— A(z)

 

X(z) + B(z) (2.9)

While the ARX model minimizes the one-step prediction error, the OE model tries to
minimize the full prediction error. However, the OE model can not be implemented
linearly as the ARX model. Instead, nonlinear optimization methods such as

numerical search are employed to identify the OE model.

2.3 Receiver Operating Characteristic Curve

Receiver operating characteristic (ROC) curve (60, 103) is remarkably useful in
medical decision-making. To demonstrate the basic concept of the ROC curve, a
specific illustration is helpful. In a binary decision-making scheme (e.g., to decide
whether a patient has a certain cardiovascular disease), generally a discrimination
metric is measured from the patient and compared to a threshold. For example, a
resulting metric greater than the threshold indicates the presence of the disease (i.e.,
positive outcome), otherwise, the outcome is negative. The test outcome is then
compared to the gold standard that indicates whether the patient really has the disease

in order to evaluate the metric. If the test outcome is positive and the patient does

14

have the disease, it is defined as a true positive. Similarly, false positive means that
positive outcome appears on patient without disease. Further, true negative and false
negative can likewise be introduced.

The ROC curve is a graphical plot of the true positive rate versus false positive
rate as the threshold is varied. In this example, the true positive rate is the number of
true positives divide by the number of ill patients, while the false positive rate is
computed by dividing the number of false positives with the number of patients

without the disease. Fig. 2.2 Shows examples of the ROC curves.

 

 

 

 

True Posi ive Rate
O
01

 

 

 

 

 

// ./ — Metric ‘l
/ _ / - — — Metric 2
./ —-—- lMetric3
0 I
0 0.5 1

False Positive Rate

Figure 2.2 Examples of receiver operating characteristic (ROC) curves for three
discrimination metrics.

15

According to the definition of true positive rate and false positive rate, metric 1 is
the best discriminator and metric 3 is the poorest one in Fig. 2.2. Indeed, metric 3
Shows no capability of discrimination at all.

Intuitively, the area under ROC curve (ROC AUC) could be used to assess the
discrimination metric quantitatively. More details about the meaning and applications

of the ROC AUC are described in (54, 55).

16

CHAPTER 3

CARDIAC OUTPUT MONITORING BY PERIPHERAL ARTERIAL

BLOOD PRESSURE WAVEFORM ANALYSIS

3.1 Introduction

Numerous investigators have proposed analysis techniques to monitor CO from
ABP waveforms over the last century. Frank first suggested that CO could be
estimated from ABP waveforms (47). Erlanger et al. proposed the first such
technique in 1904 (46). Their technique involved detecting pulse pressure (PP) from
the central ABP waveform, which was observed to be positively correlated to SV (i.e.,
SV-PP), and multiplying it by HR to determine CO for each beat within constant scale
factors (i.e., CO-PP°HR). In this way, the technique is able to track the relative
changes of CO or the absolute CO values after calibration with an absolute CO
measurement. (Note that, in the context of continuous monitoring in the acute setting
to direct therapy or detect a hemodynamic event, changes would be most relevant.)
However, this technique assumes that cardiac ejection occurs instantaneously when,
in actuality, it occurs over finite time in which a portion of the ejected blood passes
through the aorta.

Bourgeois et al. proposed one of the most compelling techniques (21, 22) among
the numerous ensuing studies of Erlanger et al.’s work (87, 98, 121, 136, 147, 149).

Their technique represents the arterial tree with a Windkessel model accounting for

17

the lumped compliance of the large arteries (arterial compliance, AC) and the total

peripheral resistance (TPR) of the small arteries (108) (see Fig. 3.1a).

 

 

 

 

    

 

 

 

(a) (b)
20 CO
co = HR . sv ABP E
o———-> g
1 1:5 2 215 S
...... ..., Central ABP
AC TPR In 140 T
E 120
Z 100
‘3 8° . . . ,
° 9- 1 1.5 2 2.5 3
T = TPR - AC Time [sec]
Pa“)
at
CO I

Figure 3.1 Previous technique for CO monitoring by analysis of the central arterial
blood pressure (ABP) waveform based on Windkessel model (22). (a) Electrical
analog of the Windkessel model of the arterial tree. This model predicts that ABP
Should decay like a pure exponential during each diastolic interval with a time
constant (1) equal to the total peripheral resistance (TPR) times the nearly constant
arterial compliance (AC). (b) Based on this model, an exponential is fitted to each
diastolic interval of the ABP waveform to estimate 1.‘ and then proportional CO is
computed via Ohm’s law.

According to this model, ABP should decay like a pure exponential during each
diastolic interval with a time constant (I) equal to the product of TPR and AC. Since
AC is relatively constant over a wide pressure range and on the time scale Of months
to years (53), CO could then be estimated to within a constant scale factor by dividing

the time-average of ABP with t (i.e., similar to invoking Ohm’s law) (see Fig. 3.1b).

18

Thus, their technique involved fitting an exponential to each diastolic interval of the
ABP waveform in order to estimate 1. Wesseling et al. proposed a more intricate
“Modelflow” technique by representing the arterial system with a nonlinear three-
element Windkessel model (150).

Bourgeois et al. were able to validate their technique when applied to central
ABP waveforms, whose diastolic intervals can resemble pure exponential decays
following incisura (see Fig. 3.1b). However, central ABP waveforms are rarely
measured for routine monitoring due to its high level of invasiveness carrying the
risks of thrombo-embolism (e. g., stroke). Furthermore, in readily available peripheral
ABP waveforms, exponential diastolic decays are usually not apparent due to the
high-frequency arterial wave reflections. That is, when the heart ejects blood,
pressure and flow waves are initiated and propagate through the arterial tree.
Whenever the waves reach a site of impedance mismatch, especially the high
resistance arterial termination points (99, 108, 152), they are in part reflected back
towards the heart. The long and varying distances between the aorta and arterial
termination points result in forward and backward waves in the aorta with large
phasic differences (108). SO, waves with relatively Short wavelengths (i.e., high
frequency), which constructively add in the peripheral ABP waveforms because of the
close proximity to the reflection sites, destructively interfere in the aorta and rrritigate
their cumulative effects on the central ABP waveform. On the other hand, waves with
longer wavelengths (i.e., low frequency) constructively add and are felt by the aorta

(108). As a result, the ABP waveform becomes progressively distorted with

19

increasing distance from the heart (see Fig. 3.2) (99, 109). Most notably, PP and
systolic pressure (SP) become increasingly amplified, while exponential diastolic

decays become less apparent.

 

 

  

 

 

 

I ~ ----- .
.— 100 \\
g M \
E . so \\
-—- . ~‘——— \
l L... . \ \
5" 60 -- . , \\\‘

' Central J, Peripheral
Aorta Artery

 

Figure 3.2 The ABP waveform becomes progressively distorted from the central
aorta to the peripheral arteries due to wave reflections in the arterial tree. (Adapted

from (99).)

Thus, the peripheral ABP generally cannot be adequately represented with the
Windkessel model. AS a result, the technique of Bourgeois et a1. is not successful
when applied to peripheral ABP waveforms. Indeed, the confounding (i.e., high.
frequency) arterial wave reflection has been an Obstacle of all previous techniques for
monitoring CO from peripheral ABP waveforms (33, 39, 117). One important reason
is that these techniques are applied over short time scales within a cardiac cycle,
where the confounding wave reflections dominate. Even so, two PP-based techniques
and a Windkessel-type technique are now commercially available for continuous and
rrrinimally invasive CO monitoring (39). While these techniques have Shown overall
accuracies good enough for the Food and Drug Administration (FDA), they can

markedly overestimate CO during strong vasoconstriction states such as hypovolemia

20

(33, 39, 117). This overestimation may at least be partly attributed to the
augmentation of wave reflections, which bufi‘ers the decrease in peripheral PP via SV.

Fortunately, the corruptive effects of these high frequency reflections diminish
and would not complicate the waveform with increasing time scale (108). This
important concept is demonstrated in Fig. 3.3, which illustrates two ABP waveforms
measured at the same time but at different sites in the arterial tree. The short time
scale (within one beat) variations are different because the complex wave reflections
at the two measurement sites differ from each other. However, the Slow (beat-to-beat)
variations are much more Similar as the confounding effects of the wave reflections
diminish over long time scale. The key point is that, as the wavelengths of the
propagating waves increase, the pressures at the various arterial Sites converge to the
same level such that the arterial tree behaves more like a single reservoir. Therefore,
the Windkessel model becomes a more valid representation of the arterial tree over
longer time scales. For example, if pulsatile activity abruptly ceased, then peripheral
ABP would eventually decay like a pure exponential once the faster wave reflections
vanish. Based on this fact, a new technique was introduced for continuously
monitoring changes in CO by analyzing a peripheral ABP waveform over long time
intervals so as to circumvent the confounding wave reflections and was evaluated on
animal and human data sets (57, 90, 105, 106).

AS discussed in Chapter 1, CO could be a more precise indicator of progressive
hemorrhage, which is a serious cause of hypotension and shock, causing morbidity
and mortality in diverse patient populations (including trauma casualties, surgical

patients, and patients treated with anticoagulation). Indeed, the earlier hypovolemia is

21

detected, the greater the Opportunity exists for caregivers to administer volume
replacement or perform a hemostatic intervention. Moreover, it is important to assess
the efficacy of volume resuscitation, for example, to discriminate between patients
with successful volume therapy and may even be at risk for over-resuscitation and

those who may need operative as a result of failed volume therapy (50).

 

 

o.
n. 100' m 100
2 8 / < a /
_ :I: so E a: so
g E 3 E
5 £- 5° .gé, 60
U
6490 6500 6510 g 6490 6500 6510
Time [see] Time [see]

Figure 3.3 Two ABP waveforms simultaneously measured from the central aorta and
the radial artery. (Adapted from (106).)

In this chapter, the aforementioned long time interval analysis (LTIA) technique
was reviewed and evaluated in 21 healthy humans subjected to lower body negative
pressure (LBNP), which is a safe human hemorrhage model. The technique was then
compared with other available techniques in terms of the ability to I) detect
progressive hypovolemia; 2) discriminate between hypovolemia and its resuscitation;
3) discriminate between high-tolerant and low-tolerant subjects (122). Further, the
LTIA technique was investigated through a pilot study where the technique was
applied to the PPG waveform to monitor CO change in two canine experiments in

which controlled progressive hemorrhage was induced and followed by resuscitation.

22

3.2 The Technique

The technique analyzes the peripheral ABP waveform over long time intervals
(seconds to minutes) in order to determine the pure exponential decay which would
eventually result if pulsatile activity abruptly ceased. More Specifically, the ABP
response to a Single, solitary cardiac contraction is eStimated by optimal fitting of a
segment of ABP waveform (see impulse response h(t) in Fig. 3.4). Then the
Windkessel time constant I is measured by fitting an exponential to the tail end of h(t)
once the faster wave reflections have vanished (see Fig. 3.4). Finally, proportional
CO is computed via Ohm’s law. (Thus, the technique accounts for the faster wave
effects in the ABP waveform through the estimated impulse response but does not
attempt to physically model them, as there is no need in the context of estimating
average proportional CO). The technique, as is illustrated in Fig. 3.4, is specifically
implemented in four mathematical steps as follows.

First, a cardiac contractions signal (x(t)) is derived from the measured ABP
waveform segment (y(t)) based on the well-known impulse ejection model (46, 96).
That is, as indicated in Fig. 3.4, x(t) is formed as an impulse train in which each
impulse is located at the onset of upstroke of an ABP pulse (R) and has an area equal
to the ensuing pulse pressure (PP).

Second, the relationship between x(t) and y(t) is characterized by estimating an
impulse response (h(t)) which when convolved with x(t) best fits y(t) in the least
squares sense. The estimated h(t) represents the ABP response to a single cardiac

contraction. The impulse response h(t) is specifically estimated with the following

23

ARX structure (also see Section 2.2):
m I1
y(t): Zak y(t—k)+ Zbk x(t—k)+e(t) (3.1)
k=l k=1

where e(t) is the unmeasured residual error, {ak, bk} are sets of unknown parameters,

and m and n represent the unknown model order limiting the number of parameters
(89). For a fixed model order, the parameters are estimated from x(t) and y(t) in
closed-form through the least squares minimization of e(t) (89). The model order is

determined by minimizing the minimum description length (MDL) criterion (89).

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

Peripheral ABP
60 , h(t) 1201 PP .1
1 I ; j ij PPj+1
E, 40 PPj-1 ppj PPJ+1 I :5 30
I l
E I E R-
.E. ' —> 05% —>£ 11 RI Rm
3: 20 T g 40}
7 l > ~.
R14 RI RI+1 , o — J
o o 1 2 ° . 3 5 o o 1 2
_ Trme[sec] ,
Time [sec] __ Time [sec]
t
COOC?

Figure 3.4 Long time interval analysis (LTIA) technique for monitoring relative CO
change from a peripheral ABP waveform (90, 106). First, a cardiac contractions
signal (x(t)) is constructed from a peripheral ABP waveform segment (y(t)). Second,
the ABP response (impulse response) to a single cardiac contraction (h(t)) is estimated
SO as to optimally fit y(t) when convolved with x(t). Then, the Windkessel time
constant I is determined by fitting an exponential to the tail end of h(t) once the faster
wave reflections vanish. Finally, proportional CO is computed via Ohm’s law so as to
monitor the relative change in CO.

24

With the estimated parameters, h(t) is computed as follows:
m {1 .
h(t) = Zak h(t — k) + Zbk 5(1— k) (3.2)
k=l k=l
where hat indicates estimated parameters, and 6(t) is the unit impulse function.
Third, I is determined over the interval of h(t) ranging fi'om two to four seconds

after the time of its maximum value based on the following exponential equation:

h(t) = Ae_% + w(t) (3.3)
The unknown parameters A and 1: here are estimated through least squares
minimization of the unmeasured residual error w(t). This optimization is achieved in
closed-form using linear least squares estimation after log transformation of h(t) (89).
In principle, reliable determination of r is achieved by virtue of accurately fitting the
long time scale variations in the ABP waveform segment y(t).

Finally, average proportional CO is computed to within a constant scale factor

equal to l/AC as follows:

co oc 1:9 (3.4)

where overbar indicates time average. This technique represents the first attempt to
monitor CO by circumventing the wave reflections in a peripheral ABP waveform.
Note that AC is assumed to be constant here. Indeed, AC is mainly due to the
aorta, which is relatively sparse in smooth muscle (23, 100). So, changes in
vasomotor tone should only have a small effect on AC. Further, AC is not very

sensitive to ABP changes, as wave propagation delay time, which is inversely related

25

to AC, varies only modestly with large ABP changes (119). Thus, the well-known
inverse relationship between AC and ABP (53) may only become a major factor
during extreme ABP perturbations. Consequently, and more precisely, AC is
approximately constant over a wide ABP range and on the time scale of months to
years. On the other hand, small variations in AC do represent a source of the CO
error. Therefore, further investigation of the LTIA technique accounting for AC

changes (e. g. via estimation of PWV (see Chapter 6)) is warranted.

3.3 Methork

3.3.1 Experimental procedures

The study was approved by the Institutional Review Board for the use of human
subjects at the Brooke Army Medical Center at Fort Sam Houston, Texas. 21 healthy,
normotensive subjects aged 27-52 years with no chronic cardiopulmonary medical
condition underwent the investigational protocol. In addition, female subjects
underwent an initial urine test prior to experimentation to ensure that they were not
pregnant. Subjects maintained their normal sleep pattern, refrained from exercise,
and abstained from caffeine and other autonomic stimulants. During an orientation
session that preceded each experiment, all subjects received a verbal briefing and a
written description of all procedures and risks associated with the experiments, and
were made familiar with the laboratory, the protocol, and procedures. Subjects gave
written informed voluntary consent to participate in the experiments.

LBNP was applied in the present investigation, which is a highly-reproducible

experimental tool to simulate loss of central blood volume (e.g., hemorrhage) in

26

humans (30, 32). Subjects were placed in the supine position and secured in the
LBNP chamber using a neoprene skirt designed to form an airtight seal between the
subject and the chamber. The application of negative pressure to the lower body
(below the iliac crest) results in a redistribution of blood away from the upper body to
the lower extremities and abdomen. Subjects underwent an LBNP protocol consisting
of a 5-min baseline period, followed by sequential exposure to -15, -30, -45, -60, -70,
-80, -90 and -100 mmHg decompression for 5 minutes each. Not all subjects were
exposed to all levels of LBNP. Termination of LBNP was based on a precipitous fall
in SP of more than 15 mmHg coincident with presyncopal symptoms such as nausea,
dizziness, or lightheadedness. Upon the presence of these signs and symptoms (i.e.,
hemodynamic decompensation), LBNP was released and the pressure within the
chamber immediately returned to atmospheric pressure (0 mmHg). After cessation of
LBNP and a S-min transition interval (to allow for a return of fluid sequestered in the
lower body), data were collected for an additional 5 minutes (“recovery”), which
simulated complete volume resuscitation of hypovolemic patients.

Continuous HR was measured with a four-lead ECG with lead 11 configuration.
Beat-to-beat SV was measured non-invasively using ICG technique (HIC-2000 Bio-
Electric Impedance Cardiograph, Bio-impedance Technology, Chapel Hill, NC). SV
was computed according to the Kubicek equation (78) (SV—ICG) and CO was taken
as the product of SV and HR (CO-ICG). CO-ICG and SV-ICG were taken as the
reference in this study. Continuous non-invasive peripheral ABP was measured using
the F inometer (Finapres Medical Systems, Amsterdam, the Netherlands) which

employs the volume clamp method of Penaz (63). All continuous waveform data

27

were sampled at 500 Hz and were recorded directly to computer with commercial
hardware and software (DataQ Instruments, Akron, OH). The Finometer also
automatically outputs SV (SV—MF) and CO (CO-MF) estimated from the ABP
waveform using the Modelflow technique (67, 150). These data were recorded

directly to a data acquisition system on a beat-to-beat basis.
3.3.2 Data analysis

The technique was applied to up to 5-min (90 seconds at least) ABP waveforms
in each level of decompression as well as the recovery stage to estimate CO changes
(CO-LTIA). Proportional SV was also computed by dividing the estimated CO with
HR (SV-LTIA). For comparison, beat-to-beat COS computed by Modelflow, ICG, and
PP-HR methods were averaged over the same segments analyzed by the LTIA
technique. Each of the four metrics (CO-ICG, CO-MF, CO-LTIA, CO-PP-HR) was
normalized by its baseline value for each subject. The reported metrics therefore
represent relative or percent (%) values with respect to baseline. Group means (%)
were computed for each metric, using the average of all subjects’ values, for each
level of decompression, and the recovery. Pair-wise correlation coefficient analysis
was performed for all the metrics in order to quantify the relationships between
investigational measures of different techniques.

We compared how well the metrics could distinguish between any two levels of
LBNP. Specifically, for every combination of LBNP levels for which there were data
for all subjects (i.e., -15 mmHg, -30 mmHg, -45 mmHg, -60 mmHg, and recovery),

ROC curve (60, 103) (see Section 2.3) was computed and the ROC AUC with

28

standard error was calculated (54). The AUC quantifies how well two different LBNP
levels were distinguished by an investigational metric. For example, if all the CO
measurements at -30 mmHg, across all subjects, were lower than those from -15
mmHg, then that hypothetical metric would yield an AUC of 1.0 (indicating a perfect
ability to discriminate between the two levels). Conversely, if the distribution of CO
measurements from -30 mmHg LBNP was perfectly overlapped with that from -15
mmHg LBNP, then that metric would yield an AUC of 0.5 (indicating no utility for
discrimination). The level of statistical significance of the difference between two
AUCS was determined by the Hanley-McNeil method for paired data (5 5).

All subjects tolerated LBNP to -60 mmHg for at least 90 seconds. 13 out of 21
subjects were able to withstand LBNP of -70 mmHg for at least 90 seconds and were
termed the “high-tolerant” subjects. The remaining eight subjects were termed the
“low-tolerant” subjects. We tested if the investigational metrics, as measured at -60
mmHg, would discriminate between high-tolerant and low-tolerant subjects. ROC
AUCS with standard errors were likewise calculated and tested for statistical
differences using the Hanley-McNeil method (54, 55).

The SV metrics (SV-ICG, SV-MF, SV-LTIA, SV-PP) were similarly analyzed.

3.4 Results
3.4.1 Detection Of progressive hypovolemia _

The group means of CO-ICG, CO-MF, CO-LTIA, and CO-PP-HR are shown in
Fig. 3.5. CO-PP-HR did not decline with increasing LBNP. Indeed, on average, CO-

PP-HR increased even as LBNP progressed to -60 mmHg. Because CO-PP-HR failed

29

to provide the most rudimentary indication of progressive central hypovolemia, this
metric is excluded in further results. CO-ICG, CO-MF, and CO-LTIA tracked LBNP
during progressive decompression. These methods were statistically similar in
distinguishing between levels of -15, -30, -45, and -60 mmHg, as determined by ROC

AUC analysis (see Table 3.1).

 

 

 

 

 

 

 

 

120 - .. —~- ~ -« - -—~ -~ -------------- -——~ -
110
2.3
.- 100
:3
D.
H
a
O
.8 9°
'5
5
cs
0
80
---8— Long Time Interval Analysis _‘
-¢— ModeIrow
7° ” —6- Impedance Cardiography
—6— Pulse Pressure- Heart Rate . . _ _ j ;_ _> . ,
0 -15 -30 -45 -60 0
Baseline LBNP Level [mmHg] Recovery

Figure 3.5 Group means of subjects (n = 21) for the investigational CO metrics
through progressive levels of lower body negative pressure (LBNP) decompression,
expressed as % of baseline measurement. Vertical positions of data points were
staggered to display non-overlapping 95% confidence intervals.

30

Table 3.1 Area under receiver operating characteristic curves (ROC AUCS) with
standard errors for discrimination between different levels of lower body negative
pressure (LBNP), using investigational CO metrics.

 

 

 

 

 

 

~15mmHg -30 mmHg 45 mmHg -60mmHg
CO-LTIA 0.46i0.09 O.66i0.08 0.76:b0.07 0.80:t0.07
Recovery CO-MF 0.221007" 04110.09" 0.573009” 0.61:0.091’
CO-ICG 0.494.009 0.67:0.08 0.75:t0.08 0.794007
CO-LTIA 0.924004 0.772t0.07 0641:009
-60 mmHg CO-MF 0.842E0.06 0.75:t0.08 0.604009
CO-ICG 0.79:1:0.07 0.69:1:008 0.6ld:0.09
co-LTIA 0.91E005 0.69i0.08
-45 mmHg CO-MF 0.91:1:0.05 O.74:t0.08
CO-ICG 0752:0086 0.62:1:0.09
CO-LTIA 0.82i0.07
-30 mmHg CO-MF O.77i0.07
CO-ICG 06710.08

 

CO-LTIA is CO by long time interval analysis (LTIA) technique; CO-MF, CO by Modelflow
method; and CO-ICG, CO by impedance cardiography (ICG).

a AUC of CO-MF significantly less than those of CO-LT IA @<0. 001 ) and CO-ICG (p<0. 001);
b AUC ofCO-MF significantly less than those of CO-LT IA @<0.01) and CO-ICG (p<0. 05);
c AUC of CO-ICG Significantly less than that of C O-MF (p<0.05).

The group means of SV-ICG, SV-MF, SV-LTIA, and SV—PP are shown in Fig. 3.6.
SV—ICG, SV-MF, and SV-LTIA also tracked LBNP during progressive decompression.
These methods were statistically similar in distinguishing between decompression
levels of -15, -30, -45, and -60 mmHg, as determined by ROC AUC analysis (see
Table 3.2). SV-PP also declined, but not as reliably, and it yielded less AUCS than the

other metrics.

31

110 -

100

70l-

Stroke Volume [%]
8

 

-8— Long Time Interval Analysis
—+- Modelflow

50 - —9— Impedance Cardiography
—6— Pulse Pressure ‘

0 -15 -30 -45 -60 0

 

 

 

 

 

 

Baseline LBNP LeveI [mmHg] Recovery

Figure 3.6 Group means of subjects (n = 21) for the investigational stroke volume
(SV) metrics through progressive levels of LBNP decompression, expressed as % of
baseline measurement. Vertical positions of data points were staggered to display
non-overlapping 95% confidence intervals.

The correlation coefficients (with 95% confidence intervals) between
investigational techniques and the reference ICG technique for CO metrics were 0.64
(0.51-0.74) (LTIA:ICG) and 0.52 (0.36-0.65) (MleCG). The correlation coefficients
(with 95% confidence intervals) for SV metrics were 0.83 (0.76-0.88) (LTIA:ICG),
0.77 (0.69-0.85) (MleCG), and 0.60 (0.46-0.71) (PP:ICG). (Note that a greater range

of SV metrics was observed than the range in CO, as seen in Fig. 3.5 and 3.6.

Accordingly, correlations between SV metrics tended to be greater than CO metrics.)

32

Table 3.2 ROC AUCS with standard errors for discrimination between different
levels of LBNP, using investigational stroke volume (SV) metrics.

 

 

 

 

 

 

-15 mmHg -30 mmHg -45 mmHg -60 mmHg
SV-LTIA 06390.09 08890.05 0.959003 0.989002
SV-MF 0.379009" 0.749008" 0.949004 0.989002
Recovery
sv-rco 0.669008 0.919005 0.969003 0.999001
SV-PP 0.1590066 0.389009“ 0.5990096 0.819007"
SV-LTIA 1 09890.02 08490.06
SV-MF 1 09790.03 08290.07
'60 Mg SV-ICG 09890.02 09190.05 07590.08
SV-PP 0.989002 0.399005" 0.769007
SV-LTIA 0.999001 0.869006
SV-MF 09990.01 08890.05
'45 mmHg SV-ICG 09390.04 07990.07
SV-PP 09290.04 07190.08f
SV-LTIA 0.869006
_30 mmHg SV-MF 0.879006
sv-rco 0.789007
SV-PP 08390.06

 

SV-LTIA is SV by LTIA technique; SV-MF, SV by Modelflow method; SV-ICG, SV by ICG
technique; and SV-PP, SV estimated from pulse pressure (PP).

a AUC of S V-MF significantly less than those of S V-LTIA (p<0. 0001) and S V-ICG @<0.01);
b
AUC of S V-MF significantly less than those of S V-LTYA @<0.01) and S V-ICG @<0.05),°

c AUC of S V-PP significantly less than those of S V-LTIA (p<0.0001), S V-MF 07<0.01), and S V-
ICG (p<0. 0001);

d
AUC of S V-PP significantly less than those of S V—LTIA 0K0. 01), S V-MF @<0.01), and S V-IC G

(p<0.01),-
e A UC ofSV-PP significantly less than that ofSV-LTIA @<0.05),~

fA UC of S V-PP significantly less than those of SV-LTIA 07<0.05) and S V-MF @<0.05).

33

3.4.2 Discrimination between hypovolemia and its resuscitation

CO-LTIA and CO-ICG tracked decompression and returned to a near baseline
level during recovery (see Fig. 3.5). CO-MF tracked decompression but, during
recovery, returned to only 87% of baseline, which was comparable to the average CO-
MF measured between -30 and -45 mmHg of LBNP.

For discrimination between LBNP and recovery, CO-LTIA was quite similar to
CO-ICG in terms of AUCS (see Table 3.1). Both CO-LTIA and CO-ICG were
superior to CO-MF for discriminating between hypovolemia and euvolemia (i.e.,
termination of LBNP, which was our simulation of complete resuscitation). The
difference was statistically significant for any level of LBNP (see Table 3.1).

The SV metric was more discriminatory (i.e., higher AUC) than the
corresponding CO metric in all comparisons. SV-LTIA and SV—ICG were similar in
terms of AUCS (see Table 3.2) and both superior to SV-MF for discriminating
between hypovolemia and euvolemia (see Table 3.2). SV—LTIA and SV—ICG were

superior to SV-PP at almost any two LBNP levels.
3.4.3 Discrimination between high-tolerant and low-tolerant subjects

By assessing which subjects had the largest reductions in CO (or SV) at -60
mmHg, it was possible to discriminate, to some degree, between high-tolerant and
low-tolerant subjects (i.e., which subjects were most at-risk of cardiovascular collapse
with any additional LBNP). ROC analysis of CO-LTIA yielded an AUC of 0.66
(where preservation of CO-LTIA was associated with high-tolerant subjects and

reduced CO-LTIA was associated with low-tolerant subjects), and was significantly

34

greater than CO-MF (see Table 3.3). CO-MF yielded a ROC AUC of 0.40 which
means that preservation of CO-MF was paradoxically associated with low-tolerant
subjects. SV metrics yield higher AUCS than corresponding CO metrics and the best
discriminator between high-tolerant and low-tolerant subjects was SV—LTIA with
AUC of 0.86, which was significantly greater than SV-ICG and SV-MF, though non-
significantly better than SV—PP (see Table 3.3).

Table 3.3 ROC AUCS with standard errors for discrimination between high-tolerant
and low-tolerant subjects using CO and SV metrics at -60 rman LBNP.

 

 

 

LTIA MF ICG may
co 06690.13 0.409013" 0.499013 0.559013
sv 0.869009 0.549013" 0.6190136 0.79901 1

 

“ A UC of CO-MF significantly less than that of CO-LTIA p<0 05),-

b AUC of S V-MF significantly less than that of S V-LTIA (p<0. 01);

c AUC of S V-ICG significantly less than that of S V-LTIA (p<0. 05).

3.5 Discussion

In this study, we evaluated the LTIA technique for monitoring CO and SV from a
peripheral ABP waveform on 21 healthy humans subjected to LBNP, which is a
carefully-controlled laboratory procedure to induce, then resolve, a standardized
circulatory disturbance. The technique was compared with other three non-invasive
CO and SV measurement modalities (i.e., Modelflow, ICG and PP(-HR)) in term of
the diagnostic capabilities. The ICG technique was taken as the reference.

LTIA and ICG methods, based on waveform analysis and thoracic bioimpedance,

35

respectively, yielded similar ROC AUCS for both CO and SV metrics. Throughout
progressive hypovolemia, Modelflow was diagnostically similar to both LTIA and
ICG SV—PP also declined, but not as reliably, during progressive hypovolemia and it
trended towards lower AUCs than the other SV metrics. The reduction in PP
underestimated the actual reduction of SV, which was evidenced by the finding that
CO-PP°HR paradoxically increased during progressive LBNP. With simulated
resuscitation, (i.e., termination of LBNP), CO-MF, SV-MF, and SV-PP remained
reduced, with inferior ability to discriminate between hypovolemia and euvolemia
(see Table 3.1 and Table 3.2).

It appears that both ICG and LTIA methods would be preferable for monitoring
subjects who receive resuscitation for their hypovolemia. In terms of practical
requirements, ICG technique suffers from several problems as discussed in Chapter 1.
The LTIA technique, on the other hand, requires a peripheral ABP waveform, which
can be measured via an indwelling arterial catheter or a non-invasive finger-cuff
apparatus, e. g., the Finometer used in this study.

Clinically, it would be most useful to monitor a circulatory metric that is an
accurate indicator of impending cardiovascular collapse. Therefore, all the metrics
were assessed in terms of the ability to indicate which subjects would prove unable to
tolerate additional LBNP. The results showed that protection of SV-LTIA at -60
mmHg LBNP was a strong predictor (AUC 0.86) of high tolerance to the deepest
levels of LBNP. The AUC of SV—LTIA was significantly greater than SV-ICG (AUC
0.61) and SV-MF (AUC 0.54). In general, SV metrics were more predictive of

tolerance than CO metrics. Paradoxically, CO-MF yielded an AUC less than 0.50,

36

meaning that the biggest reductions in CO-MF at -60 mmHg LBNP were associated
with the most tolerant subjects, which is counter-intuitive and also inconsistent with
prior findings (31, 130). Overall, the superior ability of SV-LTIA to identify between
high-tolerant and low-tolerant subjects suggests it may be a more valid assessment of
circulatory status compared with the alternatives.

While the Modelflow technique performed similarly to both LTIA and ICG
methods during progressive hypovolemia, it showed inferior ability to discriminate
between hypovolemia and its resolution. Although the Modelflow technique employs
an intricate three-element Windkessel model, it analyzes the waveform over short
time scale (single cardiac cycle) and is expected to suffer from the confounding wave
reflections as discussed above. Remaining reduced CO-MF and SV-MF during
recovery implied that the technique may not be reliable when CO and SV were
restored. During different levels of decompression, TPR is significantly changed in
order to maintain the BP level. Therefore, the contour of ABP waveforms at different
LBNP levels exhibited large differences even at the same measurement site due to
varying wave reflections (see Fig. 3.7). We speculate that perhaps the Modelflow
method was not flexible enough to account for these contour changes caused by fast
waves, which was not a dominant factor in the LTIA technique (108). (In Fig. 3.7, the
waveform shape during recovery is notably different from that from baseline, which
may explain why the estimates from recovery by Modelflow technique failed to return

to the baseline level.)

37

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Baseline -30 mmHg -60 mmHg Recovery

_ 14° 13o « 135 140
3‘? 120 « 120
E 110 . 120
E, 100
g 90 < 10° ‘ 100 l
< so 1 l

o 6.5 1 70o 015 1 80o 6.5 80o 6.5 3

Time [see]

Figure 3.7 Excerpts of ABP waveforms from one subject during different levels of
decompression.

PP has value in the diagnosis of progressive hypovolemia (see Table 3.2), though
it was consistently less diagnostic than SV-LTIA and SV-ICG PP and SV were found
to be correlated, which has been previously noted in other reports (e.g., high
correlation of variability of PP and SV during major abdominal surgery (42).) At the
same time, it is important to appreciate that the magnitude of reduction in SV was
underestimated by PP. This is highlighted by the fact that CO-PP-HR paradoxically
increased throughout progressive LBNP. These results suggest that any algorithm that
assumes PP is a quantitative surrogate for SV (e. g., the FloTrac method (4)) will need
to offer substantial compensation, and these findings may also explain why certain
PP-based algorithms have shown inconsistent reliability in some clinical reports (44).
A variation of CO-PP-HR proposed by Liljestrand and Zander, in which PP-HR was
scaled by (SP+diastolic pressure (DP)) to adjust for arterial compliance (85), was
reported by Sun et al. to be well performed in an ICU population consisting of older
patients with relatively less dynamic changes in TPR (140). However, in our dataset,

PP-HR/(SP+DP) failed to decline with progressive LBNP.

38

In terms of the validity of the experimental model, the results (see Fig. 3.5) were
consistent, on average, with prior reports involving LBNP to reduce CO. Using
echocardiography, Kimmerly et al. found that CO had fallen to 79% at —40 mmHg of
LBNP (75), while Chang et al. reported that CO had fallen to 65% at -45mmHg of
LBNP using C02 rebreathing (25). We found that subjects returned to near their
baseline circulatory state (e.g., CO-ICG values were 95i7% of their baseline values)
5-10 minutes after cessation of LBNP, which is consistent with a prior finding that
intravascular fluid sequestered by LBNP is immediately returned upon cessation of
LBNP, and most edema is resorbed within minutes after cessation of LBNP (91). In
light of our trends for CO-ICG and CO-LTIA, and in light of the LBNP literature, we
conclude that CO in this study declined as a function of LBNP as expected, and that
the recovery interval was physiologically similar to euvolemia.

There are several limitations to this study. First, the study of healthy subjects in
laboratory conditions may not be strictly equivalent to clinical use. For instance,
there may be more measurement error in actual clinical use, or other confounding
factors, such as vasopressor infusion. However, this study design provided
unambiguous outcomes impossible to accomplish through clinical trials, so such
controlled laboratory studies may be quite complimentary to clinical “real world”
investigations. Second, the peripheral ABP was measured using the Finometer. It is
possible that ABP waveform analysis using an indwelling arterial catheter might yield
different results. Therefore, these results may not necessarily generalize to subjects
with an indwelling ABP measurement. On the other hand, the Finometer has been

shown to provide a valid measurement of ABP (51). Moreover, a non-invasive

39

method of CO monitoring could be useful in the management of the majority of
hospitalized patients without invasive arterial lines.

In conclusion, we found that CO and SV estimated by LTIA, ICG, and
Modelflow techniques, all tracked progressive hypovolemia. SV-PP also declined,
but CO-PP-HR was not a suitable quantitative surrogate for CO, as it erroneously
increased during progressive LBNP. After restoration of circulating volume, CO and
SV by LTIA and ICG were able to distinguish between ongoing hypovolenria and
resuscitation, while the metrics by Modelflow and PP(-HR) were significantly less
discriminatory. Protection of SV-LTIA was the strongest predictor of high tolerance
to the deepest levels of LBNP. In all instances, SV metrics were more discriminatory
than CO metrics. These results have implications for the utility of non-invasive CO

and SV measurements to track progressive bleeding and effective fluid resuscitation.

3.6 Technique Extension

As discussed in Chapter 1, despite the simplicity and low cost of PPG technique,
the PPG waveform is not fully understood and its clinical applications are limited.
On the other hand, monitoring of critical hemodynamic variables such as CO based
on the PPG waveform would be valuable for developing non-invasive, low-cost, and
easy-to-use hemodynarrric monitoring systems. To this end, we conducted a pilot
study to investigate the feasibility of CO monitoring from the PPG waveform by the

LTIA technique.

40

3.6.1 CO monitoring by PPG waveform analysis

The peripheral ABP waveform represents the pulsatile BP in peripheral vascular
bed while the PPG waveform indicates corresponding blood volume change. The
“pressure-to—volume” relationship may be characterized by a low pass filter (13),
according to which most low fi'equency components of the peripheral ABP waveform
would be preserved in the PPG waveform. As discussed above, in the LTIA
technique, the low frequency information in the waveform is much more crucial than
the high frequency components to determine CO. Therefore, the LTIA technique, in
principle, should be applicable to the PPG waveform as well. However, in order to
estimate the correct impulse response and time constant T, the PPG waveform has to
be first calibrated to BP levels (i.e., DP, SP, and mean arterial pressure (MAP)) during
the period of measurement. The oscillometry (i.e., the cuff) measurements or other
BP monitoring techniques (e.g. non-invasive and cuff-less BP monitoring via PWV

estimation (see Chapter 6)) could be employed for the calibration.
3.6.2 Methods

To evaluate this extension of the technique, we performed canine experiments
with protocol inducing controlled progressive hemorrhage and followed volume
resuscitation, which is approved by the MSU All-University Committee on Animal
Use and Care.

Experiments were performed in two normal adult beagles (9.6-10.4 kg). Briefly,
general anesthesia was induced and mechanical ventilation was instituted. A

micromanometer-tipped catheter was positioned at the pulmonary artery for reference

41

thermodilution CO measurement. A fluid-filled catheter was placed at ascending
aorta via a femoral artery for aortic pressure waveform and another fluid—filled
catheter at carpal or dorsal pedal artery for peripheral ABP waveform. Surface
electrodes were placed for standard ECG waveform. The measurements were then
recorded at a sampling rate of 1000 Hz. The PPG waveform was collected with a
separate device by placing a PPG sensor at the tongue. ECG waveform was also
measured by the device and the measurements were recorded at a sampling rate of
250 Hz. Synchronization between the two sets of measurements was achieved by
aligning marks in two ECG waveforms induced by electrical muscle stimulation
during the experiments.

All measurements were recorded during a 10-min baseline period followed by
five 20-min fixed-volume hemorrhage and a 25-min retransfusion period. During
each hemorrhage, 60 ml blood was removed over 5-min followed by S-min
equilibration and 10-min steady period. All shed blood was then retransfused over
10-min followed by 5-min equilibration and 10-min steady period. During the 10-
min steady period of each of the seven conditions, the following measurements were
made: three cuff measurements (each of which included DP, SP, and MAP values) at
0-min, S-min, and 10-min marks respectively and two thermodilution CO
measurements right after the second cuff record (one or two more thermodilution if
initial two measurements did not agree).

Clean l-min segments were selected from the 10-min steady records during each
of the seven conditions for analysis. Cuff BP measurements, which were intended to

be used to calibrate the PPG waveform, did not agree well with BP measured by

42

fluid-filled catheters. Therefore, to prove the concept, BP levels averaged from the
peripheral ABP waveforms during the same l—min segments of analysis were utilized
to calibrate the PPG waveform. The LTIA technique was then applied to the
calibrated PPG waveforms and the estimated CO values were normalized by the
baseline value for each dog and compared with the likewise normalized reference
thermodilution CO. (Note that the reference C0 of each condition was averaged over

the thermodilution measurements made during that condition.)
3.6.3 Pilot results and discussion

Fig. 3.8 shows the results of applying the LTIA technique to calibrated PPG
waveforms as well as the reference thermodilution measurements for each dog. The
estimated CO by LTIA technique corresponded well to the reference measurements
during progressive hemorrhage and retransfusion.

The preliminary results demonstrate the feasibility of extending the LTIA
technique to the calibrated PPG waveform. However, there are two limitations in the
study.

First, the anesthesia in the first experiment blunted the cardiovascular reflexes in
the dog. Hence, BP decreased and HR barely changed during hemorrhage (results not
shown) while, in reality, BP is maintained and HR increases before the cardiovascular
control system eventually collapses (see Fig. 1.1). Nevertheless, BP decreased not as
much as both reference and estimated CO during progressive hemorrhage and did not
return to the reference CO during retransfusion, which, to some degree, reveals the

advantage of the new technique. A different anesthesia procedure was used in the

43

second experiment in an attempt to maintain BP during the bleed. The BP was
maintained effectively until the middle stages of the bleed (120 and 180 ml blood
loss), when serious problems occurred with the experimental preparation due to the
anesthesia. These problems caused 1) the isolated time point reference CO
measurement to be unreliable during 120 ml; 2) the reference CO measurement to
actually increase during 180 m1; and 3) a reduced ability to maintain BP towards the
end stages of the hemorrhage. Therefore, the unreliable data at 120 ml blood loss and
the counter-intuitive data at 180 ml blood loss were excluded in dog 2 of Fig. 3.8.

Another limitation is that invasive peripheral ABP was used to calibrate the PPG
waveforms instead of cuff measurements, which is not applicable in practice where
ABP waveform is not available. Therefore, if further investigation confirms that the
cuff measurement is not accurate enough for calibration, alternative cuff-less and non-
invasive BP estimation techniques are required.

In summary, the feasibility of the new LTIA technique based on the calibrated
PPG waveform is demonstrated. However, to complete this study, proper anesthesia
procedure without compromising the cardiovascular control system is needed and
accurate BP estimation techniques should be developed (e.g., via PWV estimation

(see Chapter 6)).

44

0091

120-

100

80*

 

 

 

 

 

o 1 1 r I l J
3 6 0 60 120 180 240 300 0
8 0092
120-
100
80-
6° 0 60 240 360 40
Baseline Blood Loss [ml] Retransfusion

 

1+ Thermodilution
+ Long Time Interval Analysis

 

Figure 3.8 Normalized CO values estimated by the LTIA technique applied to
calibrated photoplethysmography (PPG) waveforms compared with reference
thermodilution measurements.

45

CHAPTER 4

CARDIAC OUTPUT AND LEFT ATRIAL PRESSURE MONITORING

BY PULMONARY ARTERY PRESSURE WAVEFORM ANALYSIS

4.1 Introduction

As discussed in Chapter 1, both CO and LAP are critical variables as they can
facilitate the diagnosis, monitoring, and treatment of various disease processes such
as left ventricular failure, mitral valve disease, and shock of any cause. For example,
a decrease in CO while LAP is rising would indicate an insult to the heart, whereas a
decrease in CO while LAP is falling would indicate a vascular anomaly or a reduction
in effective circulating blood volume.

In critically ill patients, the standard methods for monitoring CO and LAP (i.e.,
thermodilution and PCWP, respectively) both involve the use of the pulmonary artery
catheter. While these techniques suffer from major limitations (see details in Chapter
1), the pulmonary artery catheter, on the other hand, also permits continuous
monitoring of the PAP waveform. Since CO and LAP are both significant
determinants of PAP, we considered that it could be possible to continuously monitor
these two critical hemodynamic variables by mathematical analysis of the PAP
waveform.

A few investigative teams have proposed techniques for monitoring CO by PAP

waveform analysis (29, 40, 144, 161, 162). This set of papers describes a total of five

46

different techniques that analyzed each individual beat of the PAP waveform to
compute CO to within a proportionality constant. However, similar to the peripheral
ABP waveform, confounding waves as well as inertial effects in the low-resistance
pulmonary circulation are prominent in the PAP waveform over the short time scales
within a beat (108). Perhaps, as a result, the success of the techniques was, in general,
shown to be limited.

Far fewer techniques have been introduced for estimating LAP from even
general BP waveforms. Over half a century ago, Cournand helped establish the
classic technique of monitoring LAP through the end-diastolic PAP (34, 56) that is
sometimes used in clinical practice (95). However, end-diastolic PAP is not as
accurate as PCWP (61) and is contraindicated for following LAP during puhnonary
hypertension (59, 95). Within the past two decades, some investigators have
proposed techniques to predict LAP from a BP waveform through formula derived
from a training dataset of LVFP measures and BP waveforms. In particular, McIntyre
led the development of a technique to monitor left ventricular end-diastolic pressure
from the peripheral ABP response to a Valsalva maneuver (101, 133). This technique
is now available on the market with FDA clearance (3). Marik and others formulated
a technique to monitor PCWP from peripheral SP variations induced by mechanical
ventilation (94, 157). Most recently, deBoisblanc et al. conceived a technique to
predict PCWP from the PAP waveform specifically using a neural network (38). The
former two techniques, which extract LVFP information from the induced
intrathoracic pressure variations, provide an attractive minimally invasive or non-

invasive means to sensitively monitor LAP but do require a hemodynamic

47

perturbation. On the other hand, the latter, more invasive technique is continuous and
may be more specific, as PAP is directly determined by LAP whereas ABP is not. For
all of these techniques, accuracy is dependent on the availability of comprehensive
training datasets.

In short, there is a paucity of techniques in the literature for monitoring CO or
LAP from the PAP waveform. Moreover, amongst the few previous techniques, none
simultaneously estimate both CO and LAP. In this chapter, we developed a new
technique to continuously monitor both CO and LAP by mathematical analysis of the
PAP waveform (156). The technique is notable in that it 1) analyzes inter-beat (i.e.,
long time scale) variations in the PAP waveform in which confounding waves and
inertial effects cease to be major factors (108); 2) is not based on training data and
may therefore be generally applicable; and 3) jointly estimates CO and LAP. We then
performed experiments in five dogs in order to evaluate the technique with respect to
the most accurate available reference methods during commonly employed

hemodynamic interventions.

4.2 The Technique

The technique for continuous CO and LAP monitoring by PAP waveform
analysis represents an extension of the LTIA technique introduced in Chapter 3 for
monitoring CO by analysis of a peripheral ABP waveform (90, 106).

The technique arises fiom the Windkessel model of the pulmonary circulation
shown in Fig. 4.1a. This model predicts that PAP should decay like a pure

exponential function during each diastolic interval with a time constant (1:) equal to

48

the product of the pulmonary arterial resistance (PAR) and the pulmonary arterial
compliance (PAC). The model further predicts that the exponential pressure decay

should equilibrate towards LAP rather than zero pressure.

(a) (b)

 

 

 

 

 

 

1'
co PAP 330 l
H E
20
PAR E. ‘~‘_
PAc —— & 10"-"""—""T.AP
LAP 0. o . r . r r
10 11 12 13 14 15
° Time [sec]
T=PAR°PAC PA—P-LAP
00C 1:

Figure 4.1 A potential technique for continuous CO and LAP monitoring by intra-
beat analysis of the pulmonary artery pressure (PAP) waveform. (a) The Windkessel
model of the pulmonary circulation. (b) The model suggests that a time constant I,
which is equal to the product of the pulmonary arterial resistance (PAR) and the
pulmonary arterial compliance (PAC), and average LAP may be determined from the
PAP waveform by fitting an exponential plus a constant term to each of its diastolic
intervals. Moreover, assuming PAC is relatively constant, proportional CO may then
be determined similar to invoking Ohm’s law.

Thus, as illustrated in Fig. 4.1b, the Windkessel model suggests that both I and
average LAP may be determined from the PAP waveform by fitting a single
exponential function plus a constant term to each of its diastolic intervals. Moreover,
assuming PAC is relatively constant over a monitoring period, proportional CO may

then be determined by subtracting LAP from the time average of PAP and dividing

49

this difference by t (i.e., similar to invoking Ohm’s law).

However, pure exponential diastolic decays are generally not apparent in
experimental PAP waveforms (144) (see Fig. 4.3) due to complex wave reflections
and inertial effects in the puhnonary circulation (108). On the other hand, as we and
other researchers have previously noted, such phenomena may only complicate the
PAP waveform over short time scales (i.e., high frequencies) (90, 106, 108). For
example, as the time scale increases (i.e., the frequency decreases), the wavelengths
of the propagating waves become larger with respect to the dimension of the
pulmonary circulation such that the circulation appears more lumped, and inertial
effects, which are proportional to the time derivative of the flow rate, become more
attenuated. Thus, the Windkessel model of Fig. 4.1a may be a more valid
representation of the long time scale or beat-to-beat (i.e., low fiequency) dynamics of
the PAP waveform. So, for example, if pulsatile activity abruptly ceased, then PAP
may eventually decay like a pure exponential function and equilibrate to LAP once
the faster confounding dynamics vanish.

Similar to the previous LTIA technique (see Chapter 3), this technique analyzes
the PAP waveform over long time intervals in order to determine the pure exponential
decay and equilibrium pressure that would eventually result once pulsatile activity
suddenly ceased. More specifically, average LAP and the PAP-LAP response to a
single, solitary cardiac contraction (see impulse response h(t) in Fig. 4.2) are
simultaneously estimated by optimal prediction of a 6-min segment of the PAP

waveform. Then, 1.‘ is determined by fitting a single exponential function to the tail

50

end of h(t) once the faster wave and inertial effects have vanished (see Fig. 4.2).
Finally, average proportional CO is computed similar to invoking Ohm’s law and
calibrated with a single absolute CO measurement. The technique is likewise

implemented in four steps as follows.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PAP
. h(t) PP-
25 25FPPj-1 PP] 1+1
_ 20 1- ... 20
E E’
E 15’"’"""j PPj+1 E 15-
E I 05L —> E
: 1o- - I C : 1N R Rj+1
37 5. L l T T; S'Rj—1 J
R-. R- R- - LAP
o 11- J - 1+1 00 1 —2 o _ - -
o 0.5 1 1.5 . o 0.5 1 1.5
Time [see] I Time [see] Time [sec]
—T-LAP
co 0c 1%}—

Figure 4.2 LTIA technique for monitoring relative CO change and LAP fiom a PAP
waveform. First, a cardiac contractions signal (x(t)) is constructed from a PAP
waveform segment (y(t)). Second, y(t) is fitted according to the sum of a constant
term with the convolution between x(t) and an impulse response (h(t)). That is, the
constant term and h(t) are estimated so as to optimally fit y(t). Next, the time constant
1.‘ of the Windkessel model of Fig. 4.1 is determined by fitting an exponential to the
tail end of h(t) once the faster wave and inertial effects vanish. Finally, average
proportional CO is determined similar to invoking Ohm’s law.

First, a cardiac contractions signal (x(t)) is constructed through the formation of
an impulse train in which each impulse is located at the time of end-diastolic PAP (R)
and has an area equal to the subsequent pulse pressure (PP) (46, 96).

Second, y(t) is fitted according to the sum of an unknown constant term with the

convolution between the known x(t) and an unknown impulse response (h(t)). That is,

51

the constant term and h(t) are estimated so as to permit the best fit or prediction of y(t)
in the least squares sense. The estimated constant term represents the average LAP,
while, by mathematical definition, the estimated h(t) represents the PAP-LAP

response to a single cardiac contraction. The impulse response h(t) and average LAP
are specifically estimated with the following ARX structure with constant term a0:
m n
y(t) = a0 + Zak y(t — k) + Zbk x(t — k) + e(t) (4.1)
k=1 k=1
where e(t) is the unmeasured residual error; {ak, bk}, sets of unknown parameters; m

and 11, unknown model order (89). For a fixed model order, the parameters are
estimated from x(t) and y(t) through regularized least squares minimization of e(t).
This optimization is achieved in closed-form using linear least squares estimation
with Tikonov regularization (89). The model order is determined by minimizing the
MDL criterion (89) over a range of l S m, n S 15. With the estimated parameters,

average LAP and h(t) are computed as follows:

LAP = 5(/ [1 — Zak] (4.2)
k=1

h(t) = Zak h(t - k) + 26k 5(t — k) (4.3)
k=l k=1

where hat indicates estimated parameters, and 5(t) is the unit impulse function.
Third, I is determined, based on Eq. 3.3, over the interval of h(t) ranging from
one to two seconds following the time of its maximum value. In theory, accurate

determination of ‘L' as well as average LAP is achieved by virtue of h(t) coupling the

52

long time scale or beat-to-beat variations in x(t) to y(t).
Finally, average proportional CO is computed to within a constant scale factor

equal to 1/PAC as follows:

Om—fiT)—LAP
T

C (4.4)

where overbar indicates time average. The proportional CO estimate may then be
conveniently calibrated to absolute CO with a readily available thermodilution

measurement.

4.3 Methock

We conducted canine experiments to evaluate the PAP waveform LTIA
technique and to compare it to competing intra-beat analysis techniques. We outline

our methods for experimental procedures and data analysis below.
4.3.1 Experimental procedures

Experiments were performed in five normal adult dogs (10-26 kg), either beagles
or mongrels. Each dog was studied on two separate experimental days under a
protocol approved by the MSU All-University Committee on Animal Use and Care.

On the first experimental day, chronic instrumentation was installed in the dog
for data recording using a sterile procedure as follows. General anesthesia was
induced with an intravenous injection of propofol (2.2-6.6 mg/kg) and maintained
with inhaled isoflorane (1.5-2.5%), and mechanical ventilation was instituted. A left
lateral thorocotomy was performed. An ultrasonic flow probe was placed around the

ascending aorta for reference CO (A-series, Transonic Systems, Ithaca, NY). (After

53

chronic implantation of this flow probe to ensure acoustic coupling, the error in
measuring relative CO changes, which is all that is needed to evaluate the technique
for estimating proportional CO, is reported to be 2% (6, 11). One source of this error
is changes to coronary blood flow (4-5% of the CO (52)), which is not captured by
the flow probe.) A tygon catheter was placed in the left atrial appendage for reference
LAP (Norton, Akron, OH). The chest was evacuated and closed in layers, with the
cable and catheter tunneled subcutaneously and exteriorized between the scapulae.
The dog was then allowed 10-14 days for recovery during which the catheter was
irrigated daily with a heparinized saline solution.

On the second experimental day, additional transient instrumentation was
achieved as follows. General anesthesia was induced and maintained as previously
described. Mechanical ventilation was instituted at a rate of 12 breaths/min and a
tidal volume of 20-25 ml/kg (in three of the dogs). A micromanometer-tipped
catheter was inserted into a jugular vein and positioned under fluoroscopic guidance
in the main pulmonary artery for the PAP waveform (Millar Instruments, Houston,
TX). Another micromanometer-tipped catheter was similarly inserted and positioned
for the RVP waveform (in four of the dogs). A third micromanometer—tipped catheter
was placed in the descending thoracic aorta via femoral artery access in conjunction
with fluoroscopic guidance for an ABP waveform (in three of the degs). A catheter
was inserted into a cephalic vein for drug and isotonic fluid administration, and
surface electrodes were positioned for two frontal ECG leads. All of the analog
transducer outputs were interfaced to a personal computer through an A/D conversion

system (DataQ Instruments, Akron, OH). The cardiovascular measurements were

54

then recorded in each dog at a sampling rate of 500-1000 Hz over the course of 100-
230 minutes during a subset of the following common hemodynamic interventions:
infusions of dobutamine, isoproterenol, esmolol, phenylephrine, nitroglycerin, and
volume as well as hemorrhage. Various infusion rates were employed followed by

recovery periods.
4.3.2 Data analysis

The technique was applied off-line to 6-min non-overlapping segments of the
PAP waveforms resampled to 90 Hz so as to estimate proportional CO and absolute
LAP trends for each dog. (When the 6—min segment included a step PAP change due
to bolus drug infusion, the technique was applied to the longest steady interval of the
waveform within the segment.) The corresponding absolute reference CO and LAP
trends were established by averaging the aortic flow probe and LAP catheter
measurements over the identical time segments. To compare an estimated
proportional CO trend with the absolute reference CO trend, the former trend was first
scaled to have the same mean value as the latter trend in each dog. The estimated,
calibrated CO and absolute LAP trends were then evaluated against their
corresponding reference trends through 1) classic regression analysis to
comprehensively illustrate the estimated values versus the reference values and
provide the correlation coefficient (p) between these values; 2) Bland-Altman
analysis (19) (which has become the standard for comparing two clinical
measurement methods) to comprehensively illustrate the estimation errors versus the

highly accurate reference values (rather than the average of the estimated and

55

reference values) and indicate the bias [1 and precision o of the estimation errors; and
3) the root-mean—square of the estimation errors (RMSE = \/(u2+oz)) to succinctly
indicate the overall error size. Both absolute and relative estimation errors were
assessed, with relative CO estimation errors in units of percent and absolute LAP
estimation errors in units of mmHg emphasized for congruence with previous, related
studies (e.g., (37)). (Note that the CO RMSE here, when expressed in percent, is
equivalent to the CO root-mean-squared-normalized-error (RMSNE) that we have
reported in previous studies (90, 106, 141).) In addition, the changes in the estimated,
calibrated CO and absolute LAP trends with respect to their mean values in each dog
were evaluated against the corresponding changes in the reference trends for some of
the hemodynamic interventions through Bland-Altman analysis.

For comparison, three competing intra—beat analysis techniques were also applied
to the measured PAP waveforms. The first technique was the classic end-diastolic
PAP estimate of LAP. The second technique, which is illustrated in Fig. 4.1, involved
fitting a single exponential and constant term to each diastolic interval (approximated
as the downstroke from peak systolic pressure to end—diastolic pressure) of the PAP
waveform so as to estimate 1: and LAP, and then computing proportional CO by
subtracting LAP from the time average of PAP and dividing this difference by t. The

third technique involved 1) fitting multiple complex exponentials and a constant term

to each diastolic interval of the PAP waveform (via a numerical search) to account for
confounding wave reflections and inertial effects in addition to 1: and LAP; 2)

extrapolating the exponentials to low pressure and fitting a single exponential to the

56

extrapolated values so as to determine T; and 3) likewise computing proportional CO
with the estimated LAP and I. These single and multiple exponential fitting
techniques may have neither been tested nor proposed before. However, the two
techniques do represent adaptations to a technique previously proposed by Engelberg
et al. in which 1." is estimated by directly fitting a single exponential to each diastolic
interval of the PAP waveform minus the LAP waveform (45).

To make a fair comparison, the beat-to-beat 1: and LAP estimated by the intra-
beat analysis techniques were averaged over the same 6-min time segments analyzed
by the LTIA technique so as to compute analogous proportional CO and absolute LAP
trends. The LAP trends estimated by the classic end-diastolic PAP technique were
then comprehensively evaluated as described for the LTIA technique, whereas the
proportional CO and absolute LAP trends estimated by the two new exponential

fitting techniques were assessed only through the RMSE for the sake of brevity.

4.4 Results

Fig. 4.3 illustrates sample segments of the PAP waveform as well as the
measured aortic flow (CO) and LAP waveforms from one of the dogs during baseline,
phenylephrine, and hemorrhage interventions. Relative to baseline, CO decreased
and LAP increased during phenylephrine due to enhanced cardiac afterload, while CO
and LAP both decreased during hemorrhage due to diminished venous return. As
exemplified in Fig. 4.3, pure exponential diastolic decays were generally not apparent

in the measured PAP waveforms throughout the experiments.

57

Baseline Phenylephrine Hemorrhage

 

 

 

 

 

 

 

 

 

 

 

 

3 30
:5
E 20W W
l
< 1° . , - . r
n.
.... 20
.E
E .
o 0
o . a n m
E”
E 15
g 10
S 5
15 16 7407 7408 I 9119 9120
Time[see]

Figure 4.3 Sample segments of the PAP waveform and the measured aortic flow (CO)
and LAP waveform from dog 5 during baseline, phenylephrine, and hemorrhage
conditions. Note that pure exponential diastolic decays are not apparent in the PAP
waveform segments.

Table 4.1 and Figs. 4.4-4.6 show the results of applying the new LTIA technique
as well as the classic end-diastolic PAP technique to the measured PAP waveforms.
In particular, Table 4.1 lists the hemodynamic range and calibrated CO and absolute
LAP RMSEs for each dog. Fig. 4.4 illustrates regression plots of the calibrated CO
and absolute LAP estimates for each dog, while Fig. 4.5 shows Bland-Altman plots of
these estimates pooled over all five dogs. Fig. 4.6 illustrates Bland-Altman plots of
the changes in the calibrated CO and absolute LAP estimates (with respect to their

mean values in each dog) for the dobutamine, esmolol, phenylephrine, and

nitroglycerin interventions pooled over all five dogs. (Note that similar plots for the

58

other employed interventions included significantly fewer data points and therefore

did not provide as interesting of an assessment.)

Table 4.1 Summary of hemodynamic range and results of the LTIA technique as well
as the classic end-diastolic pulmonary artery pressure (PAP) technique for each dog.

 

 

 

Mean LAP LAP via
CO LAP Mean PAP ABP HR CO RMSE RMSE EDPAP
Dog Range Range Range Range Range [%] [mmH g] RMSE
[IJmin] [mmHg] [mmHg] mmH [bpm] ([Uminj) 1y [mmHg]
[ g] ([ °]) ([%1)
5.6 1.5 2.0
l 0.9—2.4 6.6—16.4 17.4-26.1 N/A 101—139 (0.09) (12.2) (23.8)
21.6 1.7 7.5
18.7 2.4 7.3
3 2.0—6.5 8.2—31.5 15.1—36.3 75—170 115—155 (0.40) (18.2) (80.1)
13.0 0.9 2.0
4 3.1—6.0 4.5—11.2 10.2—15.6 67—95 129—148 (0.53) (13.7) (3“)
13.5 2.2 3.2
5 1.9—7.4 5.1—29.7 11.3—30.9 58-165 117—164 g (0.50) (27.3) (48.3)
15.2 1.7 4.7
TOTAL 0.9—7.4 4.5—31.5 10.2-36.3 58-170 101—168 (0.47) (18 .3) (56.0)

 

ABP is arterial blood pressure; HR, heart rate; EDPAP, end-diastolic PAP, and RMSE, root-mean-
squared-error.

CO ranged from about 75% to 200% of its baseline value on average in each dog,
whereas LAP generally ranged from about 4.5 to 17 mmHg in the dogs and briefly
reached higher values up to 31.5 mmHg. Mean PAP varied by 15 mmHg on average
in each dog, while mean ABP changed over a much larger range of up to 106 mmHg
in one dog. HR varied over a range of about 70 bpm over all the dogs but did not

reach values below 100 bpm.

59

Dog1

Dog 2

Dog 3

Dog 4

Dog 5

Estimated 8. Calibrated CO [lein]

p=0.98
y=1.06 x - 0.09

 

l

l .

/
/
/

0
N
p=o.69
y=1.35 x - 0.95

/

p=0.94
=0.87 x + 0.47

 

p=0.76

y=0.50 x + 1.93

 

?

K

 

p=0.96
y=0.78 x + 0.88

 

4 6 8

Aortic Flow Probe

co [lein]

Estlmated LAP [mmHg]

35’

25»

15

35'

25

15*

35

    
 

 

 

 

 

35 ‘
25»

15'

    
 

y=0.62 x + 10.82

 

 

35

25*

15’

   
 

25. /
/
/
15. o
O
a: p=0.93 /Q p=0.9o
y=1.11 x—1.69 5 » y=0.63x+ 5.52
35’
o/
/o
. 25» o
/ /
/
/ 15 o I
/ p=0.94 p=0.91
y=0.64x+2.41 '3; 5/ y=1.75x+0.12
A A 4‘ I ’ A A 4‘
E 35
E.
g 25’ ° 9
a I
.2 15 éf
-" t
o .9 / o
p=0.92 ,3 p=0.76
9
'D
I:
at

 

 

35‘

25

15

 

Direct Catheterization

y=0.92 x + 1.55 5 .
35
25 -
15’
=o.95
y=0.91 x + 1.36 5
I
a/
/ 25
/
o 15
p=0.90
y=0.92 x + 0.52 5

 

5 15 25 35

LAP [mmHg]

/
/
/
/

p=0.96
y=0.66 x + 4.50

L

 

/

9'
/

p=0.87

 

t y=0.73 x + 4.67

 

515 25 35

Direct Catheterization

LAP [mmHg]

Figure 4.4 Results of the LTIA technique and the classic end-diastolic PAP technique
in terms of regression plots of the calibrated CO and absolute LAP estimates versus
their corresponding reference aortic flow probe CO and LAP catheter values for each
dog. p is the correlation coefficient between the estimated and reference values.

60

The correlation coefficient p between the estimated and reference CO values was
0.87:1:0.06 (meaniSE) over all the dogs and ranged from 0.69 to 0.98 for each dog,
while the calibrated CO RMSE was 15.2% (0.47 L/min) over all the dogs and ranged
from 5.6% (0.09 L/min) to 21.6% (0.58 L/min) for each dog. Amongst the three large
calibrated CO error outliers (> 40%; see Fig. 4.5), two were obtained between
interventions (recovery period) from dog 2 and the other was obtained during the
phenyleprhine intervention in dog 3. If these outliers were ignored, the overall
calibrated CO RMSE would reduce to 11.8%. The calibrated CO RMSE was almost
entirely due to precision error merely as a result of the manner in which the
proportional CO estimates were calibrated. The calibrated CO errors showed a mild,
negative correlation with the reference CO values (p = -0.26), with the calibrated CO
estimates being systematically underestimated at high reference CO values (> 4.5
L/min). This underestimation occurred only when HR and SV were both high (results
not shown). However, the absolute value of the calibrated CO errors was virtually
uncorrelated with the reference CO values (p = -0.07). The errors in the changes in
the calibrated CO estimates appeared roughly of the same magnitude for the four
illustrated interventions (if the single large positive outlier in the phenylephrine
intervention were ignored).

The correlation coefficient p between the LAP values estimated by the new
technique and the reference LAP values was 0.93i0.01 over all the dogs and ranged
from 0.90 to 0.95 for each dog, while the LAP RMSE was 1.7 mmHg (18.3%) over

all the dogs and ranged from 0.9 mmHg (12.2%) to 2.4 mmHg (27.3%) for each dog.

61

The overall RMSE of the estimated LAP, which was un-calibrated, had essentially no
bias error component. The LAP errors and their absolute values were likewise only
modestly related to the reference LAP values (p = -0.22 and 0.31), with no obvious
systematic overestimation or underestimation over any reference LAP range.
Similarly, the errors in the changes in the LAP estimates appeared approximately of
the same magnitude for the four illustrated interventions (if the single large negative

outlier in the phenylephrine intervention were ignored).

CO RMSE=15.2°/o
O

80-

 

 

 

Callbrated CO Error [%]

 

0 1 2 3 4 5 6 7 3
Aortic Flow Probe CO [lein]

 

 

 

 

 

 

 

 

20 LAP RMSE=1.7 mmHg 0 20. LAP RMSE=4.7 mmHg
3 5’ g 15» o
I a .—
E 10 j 4, 310-
E. .5 e
3 5 l 00 no a g 5
t _ _ _____ +0 ._
W o L- T u- '- 9—p t 31' o
‘L r- - '5 ‘9 9' ——————— p-O 9 ‘1
5 0°: 0 ° 0 o o m
-5 . n- -5.
o <
_10 r r r r t r r _| '10 L A r 1 1 r s
0 5 10 15 20 25 30 35 0 5 1O 15 20 25 30 35
Direct Catheterization LAP [mmHg] Direct Catheterization LAP [mmHg]

Figure 4.5 Results of the LTIA technique and the classic end-diastolic PAP technique
in terms of Bland-Altman plots of the calibrated CO and absolute LAP errors versus
the reference aortic flow probe CO and LAP catheter values pooled over all five dogs.
p is the bias error; 0, the precision error; and RMSE the root-mean-squared-error (i.e.,

V(uz+62)).

62

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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z a 5 _ _ 3.93: _ _ _ ‘5
-2 0 2 0 10 20 0 10 20
Aortic Flow Probe Direct Catheterization Direct Catheterization
ACO [Umin] ALAP [mmHg] ALAP [mmHg]

Figure 4.6 Results of the LTIA technique and the classic end-diastolic PAP technique
in terms of Bland-Altman plots of the changes in the calibrated CO and absolute LAP
estimates (with respect to their mean values in each dog) versus the corresponding
changes in their reference values for the dobutamine, esmolol, phenylephrine, and
nitroglycerin interventions pooled over all five dogs.

The correlation coefficient p between the LAP values estimated by the classic
end-diastolic PAP technique and the reference LAP values was 0.88i0.03 over all the
dogs and ranged from 0.76 to 0.96 for each dog, while the overall LAP RMSE was
4.7 mmHg (56.0%) over all the dogs and ranged from 2.0 mmHg (23.8%) to 7.5

mmHg (83.7%) for each dog. This overall LAP RMSE was due to a bias error of 3.3

63

mmHg and a precision error of 3.5 mmHg. The LAP errors and their absolute values
were also hardly correlated to the reference LAP values (p = -0.12 and -0.04). Finally,
the errors in the changes in these LAP estimates were about the same as the changes
in the LAP values estimated by the new technique for the esmolol and phenyleprhine
interventions but much larger for the dobutarrrine and nitroglycerin interventions.

As further comparison, the overall calibrated CO and absolute LAP RMSEs were
20.2% (0.58 L/min) and 4.5 mmHg (53.7%) for the single exponential fitting
technique and 18.0% (0.58 L/min) and 2.8 mmHg (31.9%) for the multiple
exponential fitting technique employing three complex exponentials (detailed results
not shown in the table or figures). Note that we were unable to reduce the latter
RMSEs by using more exponentials or performing the fit over the actual diastolic

intervals as established with the simultaneously measured RVP waveforms.

4.5 Discussion

Previously, we developed and validated a LTIA technique to monitor relative
changes in CO by analyzing a peripheral ABP waveform (57, 90, 105, 106, 122),
which effectively fits a Windkessel model of the systemic arterial tree to the ABP
variations occurring over time scales greater than a cardiac cycle wherein
confounding wave reflections cease to be a major factor (see Chapter 3). Here, we
extended the LTIA technique to the PAP waveform so as to monitor LAP in addition
to CO. The extension amounts to the inclusion of a constant term in the analysis to
account for average LAP (see Figs. 4.1, Fig. 4.2, and Eq. 4.1). That is, an additive

constant term is estimated along with the impulse response so as to optimally fit the

64

PAP waveform segment. Note that this extension is actually necessary for reliable
fitting, as LAP is a major determinant of PAP due to the small PAR in pulmonary
circulation. Then, the Windkessel time constant of the pulmonary arterial tree (I =
PAR-PAC) is similarly determined fi'om the tail end of the impulse response, and
average proportional CO is computed by subtracting average LAP fi'om the time
average of PAP and dividing this difference by 1: (thereby implicitly assuming a linear
PAR and constant PAC). In principle, this extension may likewise be applied to an
ABP waveform so as to monitor venous pressure as well as proportional CO.
However, venous pressure is usually much smaller than ABP due to the large TPR and
may therefore be neglected or difficult to estimate. While the technique in Chapter 3
may permit continuous and minimally invasive or even non-invasive monitoring of
relative changes in CO, the more invasive technique here should be preferred when
LAP monitoring is also indicated. Furthermore, the proportional CO estimates may
be conveniently calibrated to absolute CO with a thermodilution measurement.

The extended LTIA technique is unique to the few aforementioned, related PAP
waveform analysis techniques in that 1) it analyzes PAP variations over time scales
greater than a cardiac cycle in which wave reflections and inertial effects are
attenuated; and 2) it jointly estimates both CO and LAP.

The results of this study indicate that the new technique agreed well with
reference aortic flow probe CO and LAP catheter measurements from five dogs
during commonly employed hemodynamics interventions (see Table 4.1 and Figs.

4.4-4.6). That is, the overall calibrated CO and absolute LAP RMSEs of the

65

technique were 15.2% and 1.7 mmHg, respectively. These RMSEs compare
favorably to the 17% error reported for clinical thermodilution measurements (66, 138)
and the 1-2 mmHg error found in valid PCWP measurements (61, 81). (Note that
larger PCWP errors may be expected in clinical practice, as PCWP measurements are
often made incorrectly as discussed in Chapter 1.) The calibrated CO RMSE here is
also similar to that obtained with our original LTIA technique in six swine (106). The
study results also show that the new technique was in better agreement with the
reference methods than three competing intra-beat analysis techniques, namely the
classic end-diastolic PAP technique and the two exponential fitting techniques
proposed herein. In particular, the LTIA technique estimated LAP with hardly any
bias, unlike the end-diastolic PAP technique, and less than half the precision error of
this classic technique. The multiple exponential fitting technique did provide lower
calibrated CO and absolute LAP RMSEs than the other two intra-beat analysis
techniques by accounting for the wave reflections and inertial effects with complex
exponentials. However, these RMSEs, especially pertaining to LAP, were still larger
than those of the LTIA technique, which captured information embedded in the beat-
to-beat PAP variations.

We were not able to achieve a HR lower than 100 bpm in our canine experiments
with the employed interventions. Thus, our study is limited in that it does not address
the validity of the technique over this lower HR range. However, theoretically, our
technique should perform more accurately as HR decreases, because the Windkessel
model of Fig. 4.1 becomes a more valid representation of the PAP waveform with

decreasing frequency. For example, if the HR were sufficiently low, a pure

66

exponential decay may be visually apparent towards the end of the longer diastolic
interval (i.e., the fast confounding dynamics will have had enough time to vanish).

An assumption of the new technique is that PAC is constant within a subject over
a monitoring period. This assumption is specifically needed to be able to estimate
relative changes in CO. (The estimation of absolute LAP is not at all reliant on this
assumption.) However, some previous studies suggest that PAC may, on the contrary,
decrease with increasing pressure (79, 123, 129, 132). If PAC varied widely within
each of our dogs, then the estimation of proportional CO would be unreliable, with
the CO error showing substantial, positive correlation to mean PAP. However,
proportional CO was well estimated as we have discussed, and the CO error was only
modestly correlated with mean PAP (p = 0.20). Thus, PAC may have been at least
approximately constant over a mean PAP range of up to 21 mmHg within a dog here.
The relative constancy of PAC that we observed here contradicts the aforesaid studies
but is consistent with other studies (76, 134). The contrasting results could be due to
differences in the technique for estimating PAC and the experimental conditions (e. g.,
mean PAP range). While larger changes in mean PAP within a given subject could
certainly elicit more significant changes in PAC, in such circumstances, the
proportional CO estimates could always be recalibrated to the new PAC value with a
readily available thermodilution measurement. Note that the small changes in PAC
that likely occurred in our experiments do represent a source of the CO error of the
technique.

Another potential source of the errors is that the technique did not account for all

67

of the major mechanisms of respiratory variability in the PAP waveform. That is, the
external reference pressure of the pulmonary circulation is in actuality intrathoracic
pressure rather than the zero pressure indicated by the Windkessel model of Fig. 4.1.
Thus, the technique cannot account for respiratory-induced changes in intrathoracic
pressure that are directly transmitted to PAP. However, note that the technique is able
to account for the respiratory-induced variations in intrathoracic pressure that
modulate venous return to the right heart and the respiratory sinus arrhythmia
phenomenon (131) through the cardiac contractions signal.

On the other hand, nonlinearity of PAR due to recruitment and distension
phenomena probably did not represent a major source of the errors here. Since the
dogs were in the supine posture and average LAP was never less than 4.5 mmHg (see
Table 4.1), all of the collapsible pulmonary capillaries may have been open (i.e., zone
3 pulmonary blood flow) throughout the study (52, 114). Thus, PAR may have
always been operating in its linear regime. However, note that even when some of the
pulmonary capillaries are collapsed (i.e., zone 1 pulmonary blood flow) and some are
exhibiting the vascular waterfall effect (i.e., zone 2 pulmonary blood flow) (52, 114),
the linear PAR assumption may not be grossly violated as PAR is specifically
assumed to be linear only over each 6-min segment of analysis (i.e., piece-wise linear).

Like intra-beat analysis techniques, the LTIA technique can be implemented in
real time on a home personal computer. Its main disadvantage with respect to the
conventional techniques is that it cannot identify very rapid CO and LAP changes.
However, we believe that the temporal resolution afforded by our LTIA technique (on

the order of a few minutes) will be sufficient to successfully guide many therapeutic

68

interventions as well as detect most deleterious hemodynamic events, with rapid
catastrophic events (e.g., ventricular arrhythmias) being easily detected with standard
modalities (e.g., surface ECG leads). Another disadvantage of the LT IA technique is
that PAP waveform artifact observed in the critical care setting may be a more
significant problem. That is, the new technique requires a contiguous segment of
relatively artifact-free PAP waveform on order of minutes for analysis, while the
conventional techniques require just a beat. However, note that PAP waveform
artifact was a non-factor in the present controlled laboratory experiments.

It should be noted that the continuous thermodilution method, which was
introduced sometime after the standard bolus thermodilution method and is gaining
popularity (116, 158-160), is also able to provide continuous CO monitoring with a
temporal resolution on order of minutes through use of the pulmonary artery catheter
(with a thermal filament proximal to the catheter end for automatic heating of blood).
However, the signal-to-noise ratio of this method is small compared to standard
thermodilution (43), which may render the continuous method to be less accurate
(164). Moreover, in contrast to the PAP waveform analysis technique here, the
continuous thermodilution method is unable to provide continuous LAP monitoring.

There are several other methods currently available for measuring CO (43).
Ultrasound methods are perhaps the most notable, as they are non-invasive and also
provide measurements of left atrial dimensions. However, a major disadvantage of
these methods is that they require a well-trained operator to make each measurement.
Another important disadvantage is that left atrial dimensions, unlike LAP, do not

permit tracking of pulmonary edema and differentiation between cardiac dysfunction

69

and hypovolemia (118). Our technique would therefore be preferred when the
invasiveness of the pulmonary artery catheter is permissible.

Upon future successful testing in humans over a wide hemodynamic range
(including a lower HR range than that studied herein), our new LTIA technique on
PAP waveform may ultimately be employed for continuous CO and LAP monitoring
in critically ill patients instrumented with pulmonary artery catheters. Such
continuous monitoring capabilities would offer considerable advantages over the
standard, operator-required thermodilution and PCWP methods. These advantages
include: 1) circumventing the infrequent use, misuse, and added risk of the standard
methods (see Chapter 1); 2) saving precious time in the busy critical care environment
(43); 3) obtaining an early indication of deleterious hemodynamic events so as to
provide enough time for successful therapy; 4) being able to assess in real-time the
effects of fluid and drug interventions for optimal therapy (e.g., targeting diuretic
dosage in heart failure patients to minimize LAP without significantly compromising
CO); and 5) permitting remote critical care monitoring (127). We therefore believe
that the new technique, in conjunction with specific pulmonary artery catheter
management protocols as called for in recent editorials (26, 80, 118, 126), may
ultimately allow the pulmonary artery catheter to reveal a clinical benefit in a wide

variety of critically ill patient populations.

70

CHAPTER 5
CARDIAC OUTPUT AND LEFT ATRIAL PRESSURE MONITORING

BY RIGHT VENTRICULAR PRESSURE WAVEFORM ANALYSIS

5.1 Introduction

In addition to hemodynamic monitoring systems based on invasive catheters or
non-invasive commercial devices as discussed in Chapter 3 and Chapter 4,
ambulatory hemodynamic monitoring systems are also being developed recently. For
example, a fully implantable device for chronic measurement of the RVP waveform,
with a configuration similar to a standard single lead pacemaker, has been developed
and verified (92, 111, 112), which allows long-term hemodynamic monitoring of
congestive heart failure patients and potentially permit optimal day—to-day care,
reduce hospital admissions, and eliminate repeated central catheterizations. Although
the RVP waveform provides relevant clinical information, it is well appreciated that
CO and LAP are more useful for assessing cardiac function and managing volume
status (see Chapter 1). If these two cardinal hemodynanric variables could be
mathematically derived from the RVP waveform, then the potential of long-term
hemodynamic monitoring may be fully realized with an established device.

A few techniques have been proposed to estimate CO or LAP by analysis of the
RVP waveform. Bennett and co-workers were recently able to show that end-

diastolic PAP may be well estimated from the value of RVP at the time of its maximal

71

positive derivative (“ePAD”) over each beat (28, 110, 124) and may therefore be used
to approximate LAP. However, as demonstrated by other investigators as well as our
study (see Chapter 4), end-diastolic PAP is not as accurate as PCWP when estimating
LAP (59, 61, 95, 156). More recently, Bennett and co-workers have also proposed a
technique to track relative CO change through a portion of the systolic RVP area of
each beat (70, 71). However, to our knowledge, techniques for deriving CO or LAP
from the RVP waveform are otherwise lacking.

In this chapter, we developed a new technique based on impulse response
estimation to monitor CO and LAP by RVP waveform analysis (155). In contrast to
the two aforesaid intra-beat analysis techniques, our technique seeks to estimate LAP
itself rather than the end-diastolic PAP, and jointly estimates relative CO change.
Further, similar to the LTIA techniques introduced in Chapter 3 and Chapter 4, the
new technique examines the slow beat-to-beat variations in the RVP waveform
wherein simple Windkessel behavior dominates (108) in an attempt to augment the
estimation accuracy of the average over the beats, while the previous techniques only
analyze the fast changes in the waveform within an individual beat in which
complicating wave reflections and inertial effects are known to be prominent. To
demonstrate feasibility, we evaluated the new LTIA technique and compared it to the
previously pr0posed intra-beat analysis techniques based on four chronic canine
experiments in which the RVP waveform and accurate reference measurements were

simultaneously recorded during common hemodynamic interventions.

72

5.2 The Technique

We previously developed and verified LTIA techniques to estimate the relative
change in CO from a peripheral ABP waveform (90, 106) (see Chapter 3) and CO and
LAP from a PAP waveform (156) (see Chapter 4). This new technique for estimating
relative CO change and LAP from the RVP waveform directly arises from the latter
technique by exploiting the fact that RVP is nearly equal to PAP during the ejection
intervals provided that puhnonic valve stenosis is absent.

The technique is illustrated in Fig. 5.1. This technique is applied to continuous
segments (on order of minutes) of a digitized RVP waveform in six steps.

First, the ejection intervals of the RVP waveform segment (y(t)) are identified so
as to establish an “incomplete” PAP waveform segment that is specifically missing

diastolic intervals. In particular, the ejection interval for each beat is detected from

the time of the maximal positive derivative (tMpD) according to the previous ePAD

technique to the time of peak systolic pressure (Psys) plus a conservative time interval

comprising three samples (see Discussion).
Second, a cardiac contractions signal (x(t)) is constructed fi'om the ejection

intervals of y(t) based on the impulse ejection model (46, 96). That is, x(t) is formed

as an impulse train in which each impulse is located at tMpD of each beat and has an

area equal to the ensuing PP approximated as PSys minus y(tMpD) (i.e., ePAD). Note

that x(t) represents a “complete” cardiac contractions signal, as the sample values

between the impulses are defined to be zero.

73

 

(a)

 

   

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RVP
1+1
25 ppl-1 PPj PP
20L r
25» h(t) E” 1
... 20. E 15’ '.\
or
. I—I i.
E 15»PP"1 PPJ ij+1 3 1°
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310' s s s
x 5. oll'lifiil 7511"
1-1 1 1+1 gtMPogtMPo :tMPo
0 ”‘9'? ”W “"30 '5' Derivative ofERVP
0 0.5 1 1.5 . a 500 o o 0
Time [see] Time [sec] :1: o . -
E
E -500 e -
... 0 0.5 1 1.5
Time [sec]
0))
25' "(1) 25, PAP
20. 1’ _, 20
B _1 g
IE: 15-PPJ PPJ PP1+1 E 15’
E 10’ 0-5’ 1 E 10
i" . 1 Ti ,
5 1-1 1 1+1 ‘ LAP 5
1MP? *MPI? WED ' 09 - - - -
° * * 0 1 2 0
0 0.5 1 1.5 w 0 0.5 1 1.5
Time [sec] Time [390] Time [sec]
fi-LAP
cowl??—

Figure 5.1 LTIA technique for monitoring relative CO change, LAP, and mean PAP
from a right ventricular pressure (RVP) waveform. (a) First, the ejection intervals of
the RVP waveform (y(t)) are identified to produce an incomplete PAP waveform.
Specifically, as indicated with dots, the ejection interval of each beat (j) is detected

from the time of the maximal positive derivative (tMpD) to shortly after the peak
systolic pressure. Second, a complete cardiac contractions signal (x(t)) is constructed
from y(t). Third, average LAP and the impulse response (h(t)) are estimated so as to
optimally couple x(t) to y(t) only over the ejection intervals. Fourth, the Windkessel
time constant (I) is determined by fitting an exponential to the tail end of h(t) once the
faster wave reflections and inertial effects vanish. (b) Fifth, a complete PAP
waveform (z(t)) is constructed from average LAP, h(t), and x(t) to establish mean PAP.
Finally, proportional CO is computed similar to invoking Ohm’s law.

74

Third, an impulse response (h(t)) and an additive constant term are estimated so
as to optimally couple the complete “input” x(t) to the “output” y(t) over its ejection
intervals only. The estimated constant term represents average LAP, while the
estimated h(t) represents the PAP-LAP response to a single, solitary cardiac
contraction. Since a large number of parameters cannot be reliably estimated from
the limited information in the ejection intervals of y(t), h(t) is represented with a low
order model capable of yielding a physiologic appearing single contraction PAP-LAP
response. More specifically, h(t) and average LAP are estimated with the following

third-order OE structure with constant term:

y(t)=1b1e—t/all + b2 e—t/“12 cos(a3t) + b3 e—t/a2 sin(a3t))u(t2®x(t) + LAP + h(t) (5.1)
h(t)

 

where {ak, bk, k = 1-3}, which define h(t), are unknown parameters, u(t) is the unit

step function, ‘8 is the convolution operation, and n(t) is the unmeasured residual
error (89). (Note that Eq. 5.1 is an equivalent form of Eq. 2.9 in time-domain with
model orders m = n = 3.) The seven unknown parameters including the constant term
LAP are estimated from x(t) and y(t) via minimization of the mean square of u(t) over

the ejection intervals. This optimization is achieved by numerically searching over a

range of the nonlinear parameters {ak, k = 1-3} and estimating the linear parameters,

{bk, k = 1-3} and LAP, for each {ab k = 1-3} in closed-form with the linear least

squares solution (89). If an average LAP greater than mean PAP (approximated as

Psys/3+2ePAD/3) or a negative h(t) results, then the parameter values providing the

75

next lowest mean square of n(t) over the ejection intervals are selected as the
estimates.

Fourth, a single exponential is fitted to the tail end of the h(t) once the faster
wave reflections and inertial effects have vanished in order to determine the
Windkessel time constant (I) of the pulmonary arterial tree, which is equal to the
product of its total resistance (PAR) and compliance (PAC) (see Eq. 3.3). In principle,
reliable determination of ‘L' as well as average LAP is achieved by virtue of faithfully
coupling x(t) to the inter-beat variations in the ejection intervals of y(t).

' Fifth, the complete PAP waveform segment including its diastolic intervals (z(t))
is constructed by adding average LAP to the convolution between x(t) and h(t). In
theory, z(t) will lack the high frequency detail in the actual PAP waveform segment
due to the lower order of h(t) but will permit reliable estimation of mean PAP.

Finally, assuming constant PAC, proportional CO is determined by applying

Ohm’s law as follows:

0C z(t) — LAP
1'

co (5.2)

Note that, while PAC has been shown to be relatively constant over a wide
hemodynamic range (see (156) and references therein), the relative CO change here is
not expected to be valid over the course of years and an indefinite hemodynamic
range. To account for significant PAC changes, the proportional CO could be
calibrated every so often (e. g., annually and whenever mean PAP changes greatly)

with absolute CO measurements (via, e.g., ultrasound).

76

 

5.3 Methods

5.3.1 Experimental procedures

Experiments were performed in four normal adult dogs (IO-26 kg). The
experiments were approved by the MSU All-University Committee on Animal Use
and Care and are described in detail in Chapter 4. Briefly, each dog was studied on
two separate days under general anesthesia. On the first day, chronic instrumentation
was installed in the dog. An ultrasonic flow probe was placed around the ascending
aorta for reference CO, and a fluid-filled catheter was inserted through the left atrial
appendage for reference LAP. The dog was then allowed up to two weeks to recover
from the open-chest surgery. On the second day, additional instrumentation was first
placed in the dog. Micromanometer—tipped catheters were positioned for the RVP
waveform for analysis, the reference PAP waveform, as well as the aortic pressure
waveform (in two of the dogs). Surface electrodes were placed for standard ECGs.
The measurements were then recorded at a sampling rate of 500-1000 Hz over the
course of 100-230 minutes during a baseline period and three or four of the following
interventions: various infusions of dobutamine, esmolol, phenylephrine, nitroglycerin,
and volume. Generally speaking, dobutamine and volume increased CO and mean
PAP with the latter intervention also enhancing LAP; esmolol and phenylephrine
increased LAP and mean PAP; and nitroglycerin did not elicit a significant
hemodynamic response. Overall, CO ranged fi'om 0.9 to 6.5 L/min; LAP, from 4.5 to
31.5 mmHg; and mean PAP, from 10.2 to 36.3 mmHg. See Table 4.1 (dogs 1-4) for

additional intervention details.

77

5.3.2 Data analysis

The technique was applied to 6-min disjoint segments of the RVP waveforms
resampled to 90 Hz to estimate proportional CO and absolute LAP trends for each
dog. Each estimated proportional CO trend was then normalized by its mean value so
as to produce a trend in relative CO change expressed in percent (e.g., values of 60%
and 140% would respectively indicate a 40% decrease and increase in CO from the
mean value). (Note that the mean value was utilized here, because normalization with
any single estimated proportional CO value would bias the subsequent evaluation
results.) The estimated relative CO change and LAP trends were then evaluated
against their corresponding reference trends derived from the aortic flow probe CO
and LAP catheter measurements through 1) classic regression plots to illustrate the
estimated values versus the reference values; 2) Bland-Altman plots to show the
estimation errors versus the accurate reference values and indicate the constant bias u
and precision o of the estimation errors; 3) the root-mean-square of the estimation
errors (RMSE = \/(u2+o“2)) to quantitatively indicate the overall error size; and 4) the
slope and (y—)intercept of the Bland-Altman plots, including the statistical
significance of the linear model, to quantitatively reveal any relationship between the
estimation errors and reference values. Percent errors in the estimated relative CO
change and absolute errors in the estimated LAP were specifically assessed to allow
comparisons with many related studies in the past including our own (e.g., the
calculation of the former errors here is identical to the computation of the percent

errors in the estimated and once calibrated CO in Chapter 3 and Chapter 4). In

78

addition, the trends in mean PAP also estimated by the technique were evaluated
against their corresponding reference trends derived from the measured PAP
waveforms through the quantitative metrics only for the sake of brevity.

The previous, related techniques were also applied to the RVP waveforms. These
techniques included the ePAD technique and the aforementioned technique for
estimating proportional CO through a portion of the systolic RVP area of each beat
(“PCCO”) as well as a technique for estimating mean PAP fi'om intra-beat RVP
features and an ECG (“meAP”). These three intra-beat analysis techniques are
described in detail elsewhere (28, 69-71, 107, 110, 124) and firlly specified in Fig. 5.2.
To have a fair comparison, the resulting estimates of proportional CO, LAP, and mean
PAP for each beat were averaged over the same 6-min segments analyzed by the LTIA
technique. The estimated trends were then likewise evaluated through the

quantitative metrics.

5.4 Results

Table 5.1 lists the RMSEs of the relative CO change, absolute LAP, and mean
PAP estimated by the LTIA technique for each dog. Table 5.2 shows the RMSEs, the
slopes, and the intercepts of Bland-Altman plots of the relative CO change, LAP, and
mean PAP estimated by the new technique as well as the previous intra-beat analysis
techniques over all four dogs, while Fig. 5.3 illustrates regression and Bland-Altman
plots of the relative CO change and LAP estimated by the LTIA technique pooled

over all the dogs.

79

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1ooo ‘ STI on
‘ I! h

£
U) I W
3E: I, \ N [dP/dtlmax
E / \ dpldt

0 A ....-..m.§_\ 7"“?

fiP/dtlmin :

 

PCCO: CO 0C PP1-EDIRR
ePAD: LAP = ePAD
meAP: Mean PAP = (DTIIRR)-ePAD + (STIIRR)-Psys

Figure 5.2 The three previous techniques for monitoring relative CO change, LAP,
and mean PAP by intra-beat analysis of the RVP waveform (28, 69-71, 107, 110, 124).

Plst indicates the value of RVP at the time of the first zero crossing (from positive to

negative) of the third derivative of the waveform following the time of its maximal
positive first derivative. (Adapted from (71).)

Visually, the relative CO change and LAP estimates from the new technique

showed a good overall correspondence with their accurate reference values.

80

 

Quantitatively, the RMSE of the relative CO change estimates was 16.0% over all the
dogs (ranging from 11.7% to 24.2% for each dog), whereas the RMSE of the LAP
estimates was 2.0 mmHg over all the dogs (spanning from 1.7 mmHg to 2.5 mmHg
for each dog).

Table 5.1 RMSEs of the hemodynamic variables estimated by the LTIA technique of
Fig. 5.1 for each dog.

 

 

 

Dog co RMSE [%] LAP RMSE [mmHg] Mean PAP RMSE [mmHg]
1 16.4 2.3 2.6
2 24.2 1.9 4.6
3 12.2 2.5 3.5
4 11.7 1.7 1.9
TOTAL 16.0 2.0 3.1

 

Table 5.2 RMSEs, slopes, and intercepts of Bland-Altman plots of the hemodynamic
variables estimated by the LTIA technique of Fig. 5.1 and the previous techniques of
Fig. 5.2 over all the dogs.

 

 

CO LAP Mean PAP

Technique RMSE Slope Intercept RMSE Slope Intercept RMSE Slope Intercept
[%] [unitless] [%] [mmHg] [unitless] [mmHg] [mmHg] [unitless] [mmHg]

 

New 16.0 NS 2.0 -033 2.2 3.1 023 5.0
PCCO 19.4 -029 30.1 — — _ _ _ _
ePAD - - — 5.2 NS — — —

meAP - - - - — — 3.7 -027 7.1

 

NS indicates that the linear model is not statistically significant (i.e., p > 0.05).

However, for unclear reasons, the LAP estimation errors did possess an inverse
relationship with the reference LAP values (not quantitatively indicated in Fig. 5.3).
These errors also have a small constant bias of -0.8 mmHg presumably due to a
similar bias in the estimated end-diastolic PAP (results not shown). The RMSE of the

mean PAP estimates from the new technique was 3.1 mmHg over all the dogs (with a

81

 

low of 1.9 mmHg and a high of 4.6 mmHg for each dog). The mean PAP estimates
were also inversely related to their reference values, which likely stemmed from the

similar relationship for the LAP estimates.

(a)

 

 

 

 

 

 

 

 

 

 

O 220 a 21
O I
o E 18
.2 '7,- E .
5 E. 160 » z 15» ,
o o - .
°‘ 2’ - ... 5 12» . ' - ’f
'0 a ‘9 . 0 e 0 e ,
8 I: ‘ . e .8 .
I! o 100 ' .’ :: g 95 o
g 00 e. e E “’1' “‘3'.
E ' 7' . E 6’ °'" ' 0':
4o 1 1 1 3 1 1 1 1 1 1
40 100 160 220 3 6 9 12 15 18 21
Relative CO Change via Aortic Direct Catheterization LAP [mmHg]
Flow Probe [%]
(b)
g _ 80 . 5.
out \2 F"
a 9.. ‘3’ .
E o e - I 4 '
= 61 ° 5 ’
O c 40 ’ '- E 21 '0‘ ’
I" 0 ° -- 12 +
“-11: . ta ...-....o-T-Jd ————————— "a
00 _—-._Lé-_‘°_—T ------ "+0 m 0’ 0:... ..e e
30 ‘ 32"" - .1 85 "tin“ ' . 1'
to 0 ”..-. 1" ' 2'5-2 aw"? ' °
3:: ---*::*-*=+--.-' ----- "-0 3% ---°*:"----:‘-'-----"*’
Ea " 35*
2 3 '40“ iii
3 n: In '5‘ °
40 100 160 3 6 9 12 15 18 21
Relative CO Change via Aortic Direct Catheterization LAP [mmHg]
Flow Probe [%]

Figure 5.3 (a) Regression plots and (b) Bland-Altman plots of the relative CO
change and LAP estimated by the new technique of Fig. 5.1 over all four dogs. 11 and
0' respectively indicate the constant bias and precision error.

For comparison, the corresponding overall RMSEs of the relative CO change,
LAP, and mean PAP estimates from the previous intra-beat techniques were 21%,

160%, and 19% higher, respectively. Further, these relative CO change and mean

PAP estimates have inverse relationships with their reference values. Note that the

82

 

above results exclude one RVP waveform segment (i.e., one data point) for which all

techniques revealed gross estimation errors (see Discussion).

5.5 Discussion

We previously developed two impulse response based techniques to continuously
monitor relative CO change from a minimally invasive or non-invasive peripheral
ABP waveform (90, 106) and LAP in addition to absolute CO (after a single
calibration) from the PAP waveform (156) (see Chapter 3 and Chapter 4). The major
steps are to estimate an impulse response and, in the case of the latter technique, an
additive constant term (representing LAP) that optimally coup1e(s) a cardiac
contractions input to the BP waveform output and then determine the Windkessel time
constant for computing proportional CO from the tail end of the impulse response
once the faster wave reflections and inertial effects vanish. Here, we adapted these
steps for application to the RVP waveform by invoking the fact that RVP is, in general,
nearly equal to PAP during the ejection intervals. In particular, the ejection intervals
of the RVP waveform are detected (see below), and then an impulse response and
constant term are estimated that optimally couple the cardiac contractions input to
effectively the ejection intervals of the PAP waveform output (see Fig. 5.1a).
Significantly, the entire PAP waveform may be constructed thereafter to monitor
mean PAP as well (see Fig. 5.1b). The impetus for the latest technique is to permit
long-term monitoring of vital hemodynamic variables with an established implantable
RVP measurement device. Such monitoring could also be achieved by way of passing

the pressure sensor lead of the device from the right ventricle to the pulmonary artery

83

 

and then applying our PAP waveform analysis technique. However, lead instability
and increased risk (e.g., arrhythmias) in the latter site render this alternative less
practical (124).

We tested the new RVP waveform analysis technique against aortic flow probe
CO and LAP and PAP catheter measurements from four dogs during common
hemodynamic interventions. The estimated relative CO change, LAP, and mean PAP
generally showed good agreement to the accurate reference measurements (see Table
5.1 and Fig. 5.3), with overall RMSEs of 16.0%, 2.0 mmHg, and 3.1 mmHg,
respectively. For comparison, the corresponding RMSEs of the previous intra-beat
analysis techniques (see Fig. 5.2) were all higher, especially for LAP (see Table 5.2).
Thus, analysis of the subtle, inter-beat variations in the RVP waveform can indeed
improve the estimation of average hemodynamic variables. (Of course, the trade-off
of this type of analysis is that very rapid changes cannot be detected (see Discussion
in Chapter 4).) For further comparison, the overall RMSEs of the relative CO change
and LAP estimated from the same four dogs by our previous PAP waveform analysis
technique were 15.6% and 1.6 mmHg (156). Thus, aside from one outlier (see below),
the new technique was largely able to overcome the missing PAP information.

A key step of our technique is the identification of the ejection intervals of the
RVP waveform. Specifically, reliable detection of the onset of each ejection interval
(or, equivalently, pulmonary artery end-diastolic pressure) is considerably more
important than the end of each ejection interval, as a faithful estimate of PP is most
crucial (see, e. g., x(t) in Fig. 5.1a). The non-trivial detection of each ejection interval

onset was accomplished here with the well-tested ePAD technique (28, 110, 124).

84

 

However, for one of the analyzed RVP waveform segments, this technique provided
an estimate of pulmonary artery end-diastolic pressure that was much smaller than the
reference LAP value. As a result, the new technique, the ePAD technique, and the
PCCO and meAP techniques, which are also based on ePAD (see Fig. 5.2), all
showed marked estimation errors for this segment. This single outlier was excluded
to avoid misleading results. While the ePAD technique was otherwise able to provide
satisfactory estimates of pulmonary artery end-diastolic pressure (but not LAP),
future efforts to improve the detection are certainly warranted.

In summary, we have developed a new technique to monitor relative CO change
and LAP by RVP waveform analysis and have demonstrated its feasibility based on
four chronic canine experiments. With future successful testing, the technique may be
employed for chronic hemodynamic monitoring of congestive heart failure patients
with an implanted RVP measurement device. For example, after transferring the RVP
waveform recorded from the established device to a personal computer using an
external telemeter (112), the technique could be readily executed in near real-time on
the personal computer. In addition, the technique may potentially be utilized for
continuous hemodynamic monitoring of critically ill patients via a right ventricular

catheterization rather than the more risky pulmonary artery catheterization.

85

 

CHAPTER 6

ROBUST PULSE WAVE VELOCITY ESTIMATION BY SYSTEM

IDENTIFICATION

6.1 Introduction

Aortic stiffness has been shown to be an independent predictor of mortality in
hypertensive patients. PWV is a marker of aortic stiffness and is convenient to
measure compared to other indices of aortic stiffness (93). Moreover, PWV may
permit continuous, non-invasive, and cuff-less monitoring of BP as they show strong,
positive correlation (119). In the context of this dissertation, since AC is inversely

related to arterial stiffness, PWV can be used to track the changes of AC

1
PWV2

 

{AC oc

‘\ J and hence eliminate the assumption of constant AC in the LTIA
technique described in Chapter 3. Furthermore, the cuff-less BP estimated fiom PWV
can be utilized for calibration in the LTIA technique based on PPG waveform (see
Section 3.6).

PWV is conventionally determined through the foot-to-foot time delay between
the onsets of upstroke of proximal and distal arterial waveforms (27, 48). Typically,
the waveforms are obtained non-invasively using a handheld transducer that measures

pressure via applanation tonometry from carotid and femoral artery. However, such

measurements are particularly susceptible to motion artifact that may restrict the

86

‘L

 

 

value of the PWV marker of aortic stiffness. In the case of BP monitoring via PWV,
BP variations induce relatively small changes in PWV (119). Thus, even seemingly
small inaccuracies in PWV measurements can lead to large BP errors. Indeed, as
exemplified in Fig. 6.1, plots of PWV versus BP often show a great deal of scatter

about the line of best fit (97, 119). Such scatter obviously limits the utility of PWV in

tracking BP changes.

120

 

100

DP [mmHg]

6)
O

 

4o— —

 

 

l l l l I l l
12 14 16 18 20

cc PWV [sec‘1]

 

Figure 6.1 Typical plot of diastolic pressure (DP) versus proportional pulse wave
velocity (PWV). (Adapted from (97).)

87

Previous investigators have sought to reduce the error in PWV measurements
through signal processing. Sola et a1. more accurately detected the foot of an arterial
waveform via parametric modeling (135). Pruett et al. determined the time delay
through measurement of multiple time delays taken from the early systolic portions
(i.e., before return of the reflected wave) of two arterial pressure waveforms (119).
This particular method is notable in that it seeks to extract the time delay from more
than one pair of samples of the waveforms (i.e., additional waveform information).
However, the drawback is that is may only be applicable to arterial pressure
waveforms and not other, more readily available arterial waveforms such as those
indicating pulsatile volume.

In this chapter, robust estimation of PWV was sought using the general approach
of system identification through two types of modeling: physiologic-based (i.e., gray-
box) model and black-box model.

In the first study, PWV is estimated based on the well-known tube model of
arterial wave reflection (139, 151). First, the transfer function relating a measured
central arterial pressure waveform to a peripheral arterial pressure waveform
measured from the lower body is defined in terms of the parameters of the model,
which include the time delay for wave travel between the two measurement sites.
Then, all parameters are estimated by finding the transfer function that optimally
couples the two waveforms. Finally, PWV is computed from the reciprocal of the
time delay estimate. Thus, this arterial tube model-based technique effectively
computes PWV from all pairs of samples of the waveforms after mathematically

eliminating the reflected wave. The technique was applied to high fidelity canine

88

 

arterial pressure waveforms obtained over a wide pressure range before and after
contamination with known amounts of noise.

In the second study, an arbitrary proximal arterial waveform is regarded as an
input to a dynamic black-box system, while any distal arterial waveform is considered
to be the resulting output. Then, the system, which optimally couples the input to
output, is identified. Finally, the time delay of the identified system is used to
calculate PWV. Similar to the first technique, PWV is effectively determined from all
waveform information. The technique was applied to arterial waveforms collected
fiom humans subjected to a LBNP protocol described in Chapter 3.

We quantitatively evaluated the resulting PWV estimates of both techniques in
terms of their correspondence to arterial pressure, the principal acute determinant of
aortic stiffness. For comparison, the conventional foot-to—foot detection techniques

were likewise assessed.

6.2 The Techniques

6.2.1 Arterial tube model-based technique
The technique estimates PWV by tube model-based analysis of measured central
and peripheral (lower body) arterial pressure waveforms (pc(t) and pp(t)). The

technique is shown in Fig. 6.2 and is implemented as follows.

First, the transfer function relating pc(t) to pp(t) is specified through a uniform

tube terminated by a lumped parameter load (see Fig. 6.2a). More specifically, the

tube represents the path for wave travel between the two measurement sites.

89

Consistent with Poiseuille’s law, this tube is frictionless and therefore has constant
characteristic impedance (Zc = \/(I/AC), where I and AC are the arterial inertance and

compliance) and allows waves to travel with constant delay time from one end of the

tube to the other (Td = \f(I-AC)).

 

 

 

 

pom 0 TE 9 ppm

 

 

 

 

 

Figure 6.2 Technique for robust estimation of PWV from central and peripheral
(lower limb) arterial pressure waveforms (pc(t) and pp(t)) based on an arterial tube

model.

The terminal load represents the arterial bed distal to the peripheral artery
measurement site. This load is characterized by a three-element Windkessel
accounting for peripheral resistance and compliance (R and C) while matching the

tube impedance at infinite frequency. Waves traveling along the tube in the forward

90

 

 

(lefi-to-right) direction are reflected backwards at the terminal load in a frequency-
dependent manner. By summing the forward and backward waves at each tube end

(after appropriate time shifting to account for the wave travel time delay), the transfer

function relating pc(t) to pp(t) is defined in terms of three unknown parameters,

namely Td, RC, and ZCC (see Fig. 6.2b).

The three parameters are then estimated by finding the tube model-based transfer
function, which when applied to pc(t), best fits pp(t) in the least squares sense. This
nonlinear optimization is specifically achieved through a numerical search over a
physiologic range of the parameters. Finally, proportional PWV is computed through
the reciprocal of the estimated Td. (Note that the proportionality constant, which may
be determined by the physical distance between the proximal and distal waveform
measurement sites, is irrelevant for both stiffness and BP monitoring.)

The conventional foot-to-foot detection technique is implemented by identifying
each waveform foot through the maximal second derivative between the minimum
(i.e., DP) and maximal first derivative of the beat. PWV is then computed from the

average of the foot-to-foot time delay over the same data segment analyzed by the

new technique.
6.2.2 Black-box system identification technique

Based on waveforms collected in this study, a differentiated ICG waveform,
which is related to the central aortic flow rate, is regarded as the input (x(t)) to the

black-box system. A peripheral ABP waveform is considered to be the corresponding

91

output (y(t)). Fig. 6.3 illustrates the technique implemented as follows.

Zero-mean

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Differentiated ICG h (t) peripheral ABP
2 1.2 80
.— 1 i "' 4o
3 0.6 :‘E
3 Ta E
E --> ' --> E.
8 0 l g o
x 0 l A A >5
0V 0.25 0.5
_1 A A Time [sec] A A
0 1 2 Tm: time of maximal ° 1 2
Time [sec] 2nd derivative Time [sec]
1
PWV 0C —
Td1

Figure 6.3 Black-box system identification technique for robust estimation of PWV
from impedance cardiography (ICG) and peripheral ABP waveforms.

First, the system impulse response (h(t)) is identified, which when convolved
with x(t), best fits y(t) in the least squares sense. More specifically, h(t) is estimated

according to the following ARX equation:

y(t) = Zak y(t — k) + zbkxa — k) + e(t) (6.1)
k=1 k=l

where e(t) is an unobserved residual error, {ak, bk} are unknown parameters fully

defining h(t), and m and 11 represent the model order (89). The term m is set to five,

while 11 is set to the time delay estimated by the conventional foot-to-foot detection

technique (i.e., sz (see below)). (Note that the results that follow were not very

sensitive to the choice of m.) The parameters are estimated from x(t) and y(t) through

92

 

linear least squares minimization of e(t).

Next, the time delay of the impulse response h(t) (le) is detected as the time at
the maximum of the second derivative between the first zero-crossover with positive
derivative and the peak value. The le estimate may be viewed as the time delay
between the entire differentiated ICG and peripheral ABP waveform segments after

equalizing their shapes. Finally, the reciprocal of le is taken to arrive at the

proportional PWV estimate.
Fig. 6.4 illustrates the conventional foot-to-foot detection method for PWV

estimation from the two waveforms.

  

Differentiated
ICG [fl/sec]

 
  

1----

d
N
O
V
...
a.
N

minimum
\
o 6.5 i
Time [sec]

 
 

Peripheral ABP
[mmHg]
'2‘

 

 

 

Figure 6.4 Conventional detection method for estimation of PWV from ICG and
peripheral ABP waveforms.

93

 

 

 

First, the standard B points of the differentiated ICG waveform (41, 154) and the
minima (i.e., DP) of the peripheral ABP waveform are detected to indicate their foots
for each beat. (Note that other commonly used detection methods actually yielded

inferior correspondence to BP here.) Then, the time delay between each B point and

ensuing DP (sz) is determined. Finally, this time delay is averaged over the same

data segment analyzed by the system identification technique, and the reciprocal is

taken for the PWV estimate.

6.3 Methods

6.3.1 Arterial tube model-based technique

Experiments were performed in six healthy adult beagles (10-12 kg) under an
experimental protocol approved by the MSU All-University Committee on Animal
Use and Care. For each dog, general anesthesia was induced by an intravenous
injection of propofol (2.2-6.6 mg/kg) and maintained with an inhaled mixture of
oxygen and isoflurane (1.5-2.5%). A micromanometer-tipped catheter (Millar
Instruments, Houston, TX) was placed in a femoral artery for the peripheral ABP
waveform. A similar catheter was inserted in the opposite femoral artery or a carotid
artery and positioned in the ascending aorta for the aortic pressure waveform. A
catheter was also placed in a cephalic vein for drug and isotonic fluid administration,
and electrodes were positioned for standard ECG measurements. In the fifth dog, a
bipolar electrode catheter (EP Technologies, Boston Scientific, Sunnyvale, CA) was

inserted into a jugular vein and advanced to the right atrium for high rate pacing with

94

 

 

an external pulse generator (Medtronic, Minneapolis, MN). In the sixth dog, a
quadrapolar ablation catheter (EP Technologies) was inserted into a femoral vein and
positioned to ablate the AV node and to then apply bipolar electrical stimulation to the
His bundle as previously described (128) for low rate pacing with the external pulse
generator. Placement of all central catheters was accomplished by guidance with a
single-plane lateral projection fluoroscopic imaging unit (GE, Milwaukee, WI). The
analog transducer outputs were interfaced to a personal computer via an A/D
conversion system (DataQ Instruments, Akron, OH). The arterial pressure waveforms
and ECG measurements were recorded at a sampling rate of 1000 Hz during a
baseline period and following infusions of phenylephrine and nitroglycerin in the first
dog; dobutamine and esmolol in the second dog; norepinephrine and xylazine in the
third dog; saline and progressive hemorrhage in the fourth dog; verapamil and high
rate pacing in the fifth dog; and vasopressin (prior to AV node ablation) and low rate
pacing in the sixth dog. Several infusion and pacing rates were employed followed
by recovery periods.

In absence of a noise model for handheld tonometer measurements, the model of
Li et a1. (84) of arterial pressure waveform artifact arising from patient movement was
utilized. That is, different realizations of zero-mean brown noise between 1.5 and 18
Hz was added to each of the arterial pressure waveforms to attain signal-to-noise
ratios (SNRs) of 10, 5, and 0 dB. The technique was then applied to estimate PWV
fiom each 15 sec segment of the clean and noisy pairs of waveforms resampled at 500
Hz.

The conventional foot-to-foot detection technique was also applied to estimate

95

 

PWV from the same pairs of waveform segments. At the low SNRs, each beat could
only be properly delineated from the R-wave of the ECG waveform. Thus, the
conventional technique here assumes that the R—wave can be accurately detected
despite the noise. (Note that identifying the waveform foot via DP or prefiltering the
waveforms did not improve the results.)

Finally, the PWV estimates of each technique at each SNR were assessed in
terms of their ability to predict DP and MAP of the noiseless waveforms. In particular,
the arterial pressure was predicted by mapping the PWV estimates through the best-fit
line between these estimates and the arterial pressure measurements for each animal.

The RMSE of the predicted arterial pressure was then calculated over all the animals.
6.3.2 Black-box system identification technique

Previously collected physiologic data from humans subjected to a LBNP protocol
to simulate hemorrhage and retransfusion were studied. The experimental procedures
were approved by the Institutional Review Board of the Brooke Army Medical Center
and are described in detail in Chapter 3.

Briefly, healthy human volunteers in the supine posture were secured in an LBNP
chamber. Instruments were positioned for measurement of hemodynamic, neural, and
metabolic variables. These measurements included a non-invasive ICG waveform for
calculation of beat-to-beat stroke volume (BIC-2000 Bio-Electric Impedance
Cardiograph, Bio-impedance Technology, Chapel Hill, NC) and a non-invasive finger
ABP waveform (Finometer, Finapres Medical Systems, Amsterdam, The Netherlands).

The physiologic variables were recorded during a 5-min baseline period and

96

 

 

 

following sequential exposure to -15, -30, -45, -60, -70, -80, -90, and -100 mmHg of
LBNP for 5 minutes each. LBNP was terminated early, if signs and symptoms of
hemodynamic decompensation appeared. Hemodynamic decompensation was
identified in real time by the attending investigator as a precipitous fall in systolic
pressure greater than 15 mmHg concurrent with the onset of pre-syncopal symptoms
such as bradycardia, grey—out (loss of color vision), tunnel vision, sweating, nausea,
or dizziness. After cessation of LBNP and a 5-min equilibration period, the
physiologic variables were recorded for an additional 5-min recovery period.

Steady segments of the physiologic data during the baseline period, each
available LBNP level, and the recovery period were analyzed. To obtain a reasonable
evaluation of the ability of PWV estimates to track changes in the BP of a subject,
physiologic data were included in this study only from those subjects whose DP
varied by >20 mmHg. 15 subjects from a total of 66 available subjects met this
inclusion criterion.

The conventional detection method was first employed to estimate PWV from
the contemporaneous pairs of lS-sec segments of ICG and peripheral ABP waveforms.
PWV was then estimated by applying the black-box system identification technique to
the same pairs of waveform segments.

Each of the PWV estimates was evaluated in terms of its correspondence to DP
through two quantitative metrics. First, the correlation coefficient (p) between the
PWV estimates and corresponding DP measurements was calculated per subject. The

p-values were then averaged over all the subjects. Second, DP was estimated by

97

 

mapping the' PWV estimates from a subject through the line of best fit determined via
the aforesaid correlation analysis for that subject. The RMSE of the estimated DP

was then calculated over all the subjects.

6.4 Results

6.4.1 Arterial tube model-based technique

Arterial pressure varied widely over analyzed waveform segments. In particular,
DP ranged from 30 to 142 mmHg, while MAP changed from 45 to 172 mmHg.

Fig. 6.5 illustrates sample segments of the arterial pressure waveforms before
and after contamination with noise of varying amounts. Although the artifact in the
waveforms particularly at the lowest SNR may appear excessive, this level of noise
permitted assessment of the full capabilities and limitations of our arterial tube model-
based technique. Fig. 6.6 shows the arterial pressure RMSEs of our technique and the
conventional foot-to-foot detection technique versus SNR. Without noise, the DP and
MAP RMSEs of our technique were 5 .1 and 5.4 mmHg, respectively, whereas the
corresponding RMSEs of the conventional technique were 6.2 and 6.0 mmHg. Thus,
even when applied. to high fidelity waveforms, our technique can yield some
improvement in accuracy. But more significantly, as the SNR decreased, the DP and
MAP RMSEs of our technique became progressively smaller relative to their
conventional technique counterparts. In fact, our technique was roughly twice as
accurate as the conventional technique at the lowest SNR and only mildly affected by

artifact at higher SNRs.

98

 

 

 

 

Ascending Aortic Pressure Femoral Artery Pressure

 

 

 

 

 

 

 

 

 

 

 

 

 

120-
40 I . . . .
12m ’
3’ 40
E120" t
40 . . . . . .
120' '
4o 1 . . ‘ . . .
0 0.5 1 1.5 0 0.5 1 1.5
Time [see]

Figure 6.5 Sample segments of measured arterial pressure waveforms before and
after contamination with noise of varying amounts. SNR is signal-to-noise ratio.

   
  
 

DP

Anni
A“

 

 

  

RMSE [mmHg]
‘1 (D

 

 

 

 

5 ‘ ‘ a
Noiseiess 10 5 0 Noiseiess
SNR [dB]
-9- Arterial tube model-based technique
-B— Conventional foot-to-foot detection technique

 

Figure 6.6 RMSE of the predicted DP and mean arterial pressure (MAP) as a
function of SNR.

99

 

 

6.4.2 Black-box system identification technique

The average p-value (meaniSD) between the PWV estimates of the system

identification technique and the DP measurements was 0.811016, whereas the

corresponding p-value for the conventional detection method was 0.59:0.37. Fig. 6.7

illustrates plots of the DP estimated via each of the PWV estimates versus reference

DP over all of the subjects.

The RMSE of the PWV estimates of the system

identification technique was 4.5 mmHg. For comparison, the corresponding error of

the conventional detection method was 6.5 mmHg.

1401
is
I
E
E.
D.
‘3 90
1,
3
1'5
3%
+-
v:
1.1.1
40

System Identification

 

(1de1)
RMSE = 4.5 mmHg

0

 

40

90

140

140

90’

40

Conventional Detection

 

 

(1de2)
RMSE = 6.5 mmHg
t
O
O O
g 0
O o
06’ 5x>
O
0
° <9
40 96 110

Measured DP [mmHg]

Figure 6.7 DP estimated via proportional PWV estimate versus measured DP over all
the subjects.

100

 

 

 

6.5 Discussion

System identification techniques via both physiologic-based and black-box
model were proposed to estimate PWV by analysis of proximal and distal arterial
waveforms. Preliminary results showed that both techniques were superior to the
conventional foot-to-foot detection technique in terms of predicting arterial pressure.
However, in absence of reference aortic stiffness measurements and data recorded
from clinical patients, to what extent the techniques can track the changes of arterial
stiffness and improve the prediction of patient outcomes remains to be determined.

The arterial tube model-based technique is actually more general than what has
been described above. Firstly, the technique as shown in Fig. 6.2 may be directly
applied to any pair of proximal and distal arterial pressure waveforms to obtain the
PWV between the two measurement sites. Secondly, this technique is also applicable
to proximal and/or distal arterial waveforms that reflect flow rate after differencing
(rather than summing) the forward and backward waves to define an appropriate
transfer function in terms of the model parameters (see, e. g., (142)).

One disadvantage of the arterial tube model-based technique is that it can not be
applied to arbitrary arterial waveforms other than pressure and flow rate waveforms.
Another drawback of this technique as described above is that it is intended for
application to simultaneously measured arterial waveforms. In practice, however,
proximal and distal arterial waveform measurements for aortic stiffiress monitoring
are often made one at a time with a handheld transducer while an ECG waveform is

being continuously recorded. One potential way for the technique to accommodate

101

 

this practice is as follows. First, the impulse response relating the ECG waveform to

the proximal arterial waveform (h¢(t)) is estimated using standard black-box system

identification (89). Then, the impulse response relating the ECG waveform to the

distal arterial waveform (hp(t)) is likewise estimated. Finally, the arterial tube model-

based technique is applied to the impulse response estimates (i.e., for arterial pressure
waveforms, pc(t) = hc(t) and pp(t) = hp(t) in Fig. 6.2).

The black-box system identification technique also improves PWV estimation
accuracy. In addition, another advantage of the technique is that it is applicable to
arbitrary pulsatile arterial waveforms including those indicating pressure, volume,
flow rate, and even body weight measured with contact sensors (e.g., PPG, impedance
pneumography without filtering out the “heart bump”, and BCG) or non-contact
systems (e. g., laser Doppler vibrometry, infrared thermal imaging). An ECG
waveform may even be used as the proximal waveform. Therefore, the black-box
system identification technique may be more applicable in practice than the arterial
tube model-based technique. The disadvantage of the black—box system identification
approach is that it may not be able to monitor beat-to-beat BP.

In conclusion, the two system identification techniques may be directly used to
potentially improve the monitoring of arterial stiffness. Such capability could
conceivably allow for meaningful aortic stiffness monitoring even by a less
experienced operator of applanation tonometry or Doppler ultrasound. However,
further evaluation should be performed on clinical data with reference arterial

stiffness measurements to assess the ability of improving the prediction of patient

102

 

 

outcomes. For cuff-less BP monitoring, more challenges need to be resolved before it
could be employed in practice. For example, a PWV-BP calibration curve must be
constructed. Moreover, PWV estimated by regular methods (including the
conventional foot-to-foot detection technique and the two system identification
techniques) generally corresponds better to DP and MAP than SP. Thus, determining
SP accurately is another large issue in cuff-less BP monitoring through PWV estimate.
One potential improvement for the system identification techniques to resolve this
problem is to set the system parameters to be pressure-dependent and obtain three

PWV estimates corresponding to DP, MAP, and SP respectively.

103

 

CHAPTER 7

SUMMARY AND FUTURE WORK

7.1 Accomplishments and Summary

We have developed several techniques to monitor vital hemodynamic variables
(i.e., CO, LAP, and PWV) by mathematical analysis of readily available physiologic
measurements (e.g., BP, PPG, and ICG waveforms) in an attempt to achieve
continuous and effective hemodynamic monitoring. The key step in all the techniques
is to first identify an impulse response from available measurements and then estimate
the hemodynamic variables based on the impulse response (i.e., impulse response
estimation).

More specifically, a LTIA technique and two extensions of it were proposed to
monitor CO and LAP (in the latter two techniques) by analyzing peripheral ABP, PAP,
and RVP waveforms respectively. These three techniques were evaluated by
experimental data from animal/human subjects and generally showed good
agreements with reference measurements and superiorities to other competing
techniques.

In addition, pilot studies were conducted to demonstrate the feasibility of
extending the LTIA technique to the calibrated PPG waveform for CO monitoring and
estimating PWV robustly to monitor arterial stiffness and cuff-less BP from proximal

and distal arterial waveforms. Preliminary results derived from experimental

104

 

animal/human data have shown application potentiality of these techniques in clinical
practices.

With further successful testing on clinical data over wide hemodynamic ranges,
these impulse response estimation techniques may ultimately be applied in various
clinical settings (e.g., ICU, combat casualty care, outpatient settings, and home

healthcare) for continuous and effective hemodynamic monitoring.

7.2 Future Work

Although we have shown feasibilities of the impulse response estimation
techniques for clinical application, further investigation and method improvement are
required, which are summarized as follows.

1) Only pilot studies have been performed to assess the system identification
techniques for estimating PWV and further the arterial stiffness and BP. The
evaluations in the studies are based on the correspondence between the PWV
estimates and BP measurements rather than the reference arterial stiffness. Therefore,
the abilities of these techniques to accurately monitor the stiffness changes need to be
validated with clinical data including reference arterial stiffness measurements. For
cuff-less BP monitoring, as discussed in Chapter 6, challenges such as the PWV-BP
calibration curve and the determination of SP via PWV estimate need to be settled as
well. (Note that the PWV-BP calibration curve and separate estimation of DP, MAP,
and SP via PWV are also necessary for the PPG calibration in the extended LTIA
technique (see Section 3.6).) In terms of technical improvement, the arterial tube

model-based technique can potentially be enhanced in several ways. For example, the

105

 

transfer function parameters may be estimated using total least squares to better
account for measurement artifact in both arterial waveforms (17). As another
example, a tapered tube and/or a higher order or even optimal order terminal load
may be employed to more accurately represent the arterial system. However, these
refinements come at the cost of substantially increased mathematical complexity. In
the black-box system identification technique, while ARX linear least squares
identification using implicit time delay estimation was applied (see Chapter 6), any of
the available system identification techniques (e. g., OE equation, Laguerre basis
functions, total least squares parameter estimation, explicit time delay estimation,
nonlinear system representation) may be employed (1 8, 148).

2) The LTIA technique for peripheral ABP waveform analysis assumes constant
AC through the period of analysis, which represents a source of error in CO estimates.
To improve the technique, AC changes must be monitored as well. As mentioned in
Chapter 6, PWV could be used for AC monitoring because AC is inversely related to
PWV. In this case, to estimate PWV using system identification techniques, the
peripheral ABP waveform is available as the distal arterial waveform. While a central
pressure waveform is needed for the arterial tube model-based technique, the black-
box system identification technique shows greater flexibility in practice and any
pulsatile central arterial measurement can be used as the proximal arterial waveform.
For example, the proximal waveform can be recorded by the BCG technique, which is
a simple non-invasive measurement of the recoil of the body weight to cardiac
ejection forces and only requires a weighing scale (64, 137). Of course, the PWV

estimation by black-box system identification technique from BCG and peripheral

106

 

ABP waveform and the LTIA technique with AC compensation must be further
investigated.

Mth aforesaid technique improvements and evaluations, a continuous and non-
invasive system for CO and arterial stiffness monitoring, as illustrated in Fig. 7.1,
may be employed in home healthcare, various inpatient and outpatient settings, and
even combat casualty care with proper design of the scale for BCG measurement.
Specifically, PWV is first estimated by the black-box system identification technique
from BCG and peripheral ABP waveforms. Then, the LT IA technique accounting for
the AC variations tracked by PWV estimate is applied to the peripheral ABP
waveform for CO monitoring. Meanwhile, the PWV also provides a marker of the

arterial stiffness.

Pwv:) AC

 
  

 

 

 

 

140

a CO
:> E 100 ::) :> Arterial

E. Stiffness

601 2 3

Time [sec]
BCG

'fi'
2
’5'
.2.

 

Time [see]

Figure 7.1 Continuous and non-invasive monitoring system for CO and arterial
stiffness by mathematical analysis of ballistocardiography (BCG) and peripheral ABP
waveforms. (Reproduced in part from (1).)

107

 

3) Demonstrated only by two canine experiments with undesired anesthesia
procedures, the PPG-based LTIA technique (see Section 3.6) needs much more
validation studies with difierent data sets. In addition, the AC compensation
described above may likewise be used in this technique as well. Furthermore, the
PPG waveform has to be calibrated to BP levels before applying the technique. The
calibration can be achieved provided the two problems in cuff-less BP monitoring via
PWV (i.e., the PWV-BP calibration curve and separate estimation of DP, MAP, and
SP) are solved. Likewise, Fig. 7.2 shows a potential hemodynamic system upon the
completion of the above work, which is similar to the one shown in Fig. 7.1 except
that the peripheral ABP waveform is replaced by a PPG waveform. Therefore, this

system is more economical and may have wider applications.

Calibration

 
  

 

[unitless]

 

Time [sec]

 

 

 

 

BCG
'3‘
n
2
'E
.2.
'21 ' ”i‘T‘B
Time [see]

Figure 7.2 Continuous, non-invasive, and low-cost monitoring system for CO and
arterial stiffness by mathematical analysis of BCG and PPG waveforms. (Reproduced
in part from (9).)

108

 

 

In Fig. 7 .2, to calibrate the PPG waveform, three PWV values are estimated and
mapped to DP, MAP, and SP respectively through the PWV-BP curve. The resulting
DP, MAP, and SP values are then used to calibrate the PPG waveform. The PPG can
also be measured from lower limb (e.g. the toe) so that the PWV estimate would in
principle have better correspondence to arterial compliance/stiffness.

4) The LTIA techniques based on PAP and RVP waveforms (see Chapter 4 and
Chapter 5) need to be further validated by data collected from critically ill patients or
congestive heart failure patients with implanted devices measuring RVP waveforms.
In principle, the assumption of constant PAC could likewise be removed by estimate
the PWV in the pulmonary circulation. However, puhnonary arterial waveforms are
relatively difficult to measure, especially for non-invasive measurements. Thus, the
PAC compensation is not considered here. Fig. 7.3 shows continuous CO and LAP
monitoring systems based on the two LTIA techniques, which may be applied to ICU
patients with pulmonary artery or right ventricular catheterization and patients with

implanted RVP measurement devices for long-term hemodynamic monitoring.

109

Catheter Entrance

‘ l - PAP
. - ‘ ‘ 25
3 ,. 2°

  

 

5 i

 

 

 

 

1 2 ‘ 3
. Time [sec]
'~ u. 1
Pulmonary Artery Catheter CO
LAP
Programable
Memory Device RVP
_ 30;
g 20
E
E. 1o
01 2 ‘ :3.
Time [sec]

Chronicle (Medtronlc)

Figure 7 .3 Continuous CO and LAP monitoring systems by mathematical analysis of
PAP and RVP waveforms. (Reproduced in part from (7, 10).)

110

10.

ll.

12.

13.

14.

15.

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