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This is to certify that the
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HEMODYNAMIC MONITORING BY SYSTEM
IDENTIFICATION

presented by

ZHENWEI LU

has been accepted towards fulfillment
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HEMODYNAMIC MONITORING BY SYSTEM IDENTIFICATION
By

Zhenwei Lu

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Electrical and Computer Engineering

2006

ABSTACT
HEMODYNAMIC MONITORING BY SYSTEM IDENTIFICATION
By

Zhenwei Lu

The hemodynamic variables, cardiac output (CO), left atrial pressure (LAP), and
left ventricular contractility in terms of the maximum elastance (BI:lax ), may be utilized

either individually or collectively to guide therapy in patients with cardiovascular disease.
However, the conventional methods for monitoring each of these variables are highly
invasive and/or operator dependent, thereby limiting their clinical application. In this
dissertation, we introduce three signal processing techniques for monitoring the
aforementioned hemodynamic variables. The unifying theme of the three techniques is
the analysis of subtle beat-to-beat variations in cardiovascular signals that may be
routinely measured in clinical practice using the system identification method in
conjunction with prior physiologic knowledge. The three techniques specifically aim to
monitor 1) CO changes from a single peripheral arterial blood pressure (ABP) waveform,

2) CO changes and absolute LAP from either a pulmonary artery pressure waveform or a
right ventricular pressure waveform, and 3) Ban" changes from random-interval,

respiratory-induced ABP variations. In this dissertation, we also initially validate each of
these techniques with respect to hemodynamic data obtained from realistic computer
simulations, animal subjects, human volunteers, and patients. With further successful

testing, the techniques may ultimately be employed to expand the monitoring of CO,

LAP, and 13:33" in clinical applications such as critical care, home health care, and even

combat casualty care.

T 0 my wife, Ling Mei,
my parents, F ujiang Lu and Xian Zhang,

and my sister, T ian Lu.

iv

ACKNOWLEGDEMENTS

I want to thank these people who make this thesis work become possible. First of
all, I am deeply indebted to my advisor Dr. Ramakrishna Mukkamala for introducing me
to the cardiovascular signal processing research area and guiding me through all the
thesis work. He has set a role model of a serious and hardworking young scientist. He
was always there to help and encourage me. His unique approach of physiological
monitoring by system identification is the basis of this thesis. Moreover, the first
technique in the thesis is the continuous research of his work in MIT.

I would like to thank my thesis committee, Dr. Bari Olivier, Dr. Robert Scheluter
and Dr. Lalita Udpa. Their invaluable guidance is very important for the completion of
this thesis. Especially, Dr. Bari Olivier and his laboratory helped us collect the dog data
for the preliminary evaluation of the second and third techniques presented in the thesis.
And he gave good suggestions about the experiment design and the thesis writing.

I am grateful to my colleagues for their generous help: Mr. Jacob Kuiper, who
helped me download and evaluate the two sets of ICU data; Mr. Rafat Elahi, who
generated the simulation data; and Dr. Ahmed Tfirkman, who gave me valuable
suggestions in algorithm development. I enjoyed working with them. I also want to thank
those scientists who provided the ICU patients data and the non-invasive data for
technique evaluations.

Finally, I thank my wife Ling Mei. I believe that without her love, understanding,
and encouragement during the past four years, I could not have completed the thesis

work. I thank my parents for their selfless love even they are on the other side of the

planet. I also thank my teachers from the elementary school to graduate school and my
former advisors in China.
This work is supported by Michigan State University, National Heart and Lung

Institute Grant HL-O8OS68, and American Heart Association Grant SDG 05355232.

vi

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. ix
LIST OF FIGURES ............................................................................................................ x
CHAPTER 1
INTRODUCTION .............................................................................................................. 1
1 .1 Hemodynamics ................................................................................................... 1
1.2 Conventional Hemodynamic Monitoring ........................................................... l
1.3 Hemodynamic Monitoring by System Identification ......................................... 3
1.4 Thesis Organization and Contributions .............................................................. 3
CHAPTER 2
BACKGROUND ................................................................................................................ 6
2.1 Cardiovascular System ........................................................................................ 6
2. 1 . 1 Circulations ................................................................................................. 6
2.1.2 Cardiovascular Regulation .......................................................................... 9
2.1.3 Hemodynamic Waveforms ......................................................................... 9
2.2 System Identification Analysis in Hemodynamics ........................................... 17
2.2.1 Nonparametric Identification .................................................................... 17
2.2.2 Parametric Identification ........................................................................... 18
CHAPTER 3
CONTINUOUS MONITORING OF CARDIAC OUTPUT FROM A PERIPHERAL
ARTERIAL BLOOD PRESSURE WAVEFORM ........................................................... 24
3.1 Background ....................................................................................................... 24
3.2 The Technique .................................................................................................. 31
3.3 Technique Evaluation ....................................................................................... 41
3.3.1 Invasive ICU Patient Data ........................................................................ 41
3.3.2 Non-Invasive Human Experimental Data ................................................. 42
3.3.3 Data Analysis ............................................................................................ 44
3.4 Evaluation Results ............................................................................................ 45
3.5 Discussion ......................................................................................................... 49
3.5.1 Potential Sources of CO Error .................................................................. 50
3.5.2 Comparison to Intra-Beat Pulse Contour Analysis Techniques ............... 54
3.5.3 Limitations of the Long Time Interval Analysis Techniques ................... 55
3.5.4 Limitations of the Human Evaluation Study ............................................ 56
3.5.5 Potential Applications of the Mathematical Analysis Technique ............. 58
CHAPTER 4

CONTINUOUS MONITORING OF CARDIAC OUTPUT AND LEFT ATRIAL

PRESSURE FROM A PULMONARY ARTERY PRESSURE OR RIGHT

VENTRICULAR PRESSURE WAVEFORM ................................................................. 60
4.1 Background ....................................................................................................... 6O

vii

4.2 Monitoring of CO and LAP from PAP ............................................................. 63

4.2.1 The Technique .......................................................................................... 63
4.2.2 Technique Evaluation ............................................................................... 69
4.2.3 Evaluation Results .................................................................................... 72
4.2.4 Discussion ................................................................................................. 75
4.3 Monitoring of CO and LAP from RVP ............................................................. 78
4.3.1 The Technique .......................................................................................... 78
4.3.2 Pilot Evaluation of the Technique ............................................................. 80
4.3.3 Results ....................................................................................................... 81
CHAPTER 5
MONITORING LEFT VENTRICULAR CONTRACTILITY FROM RESPIRATORY-
INDUCED BLOOD PRESSURE VARIABILITY .......................................................... 84
5.1 Background ....................................................................................................... 84
5.2 Physiologic Basis .............................................................................................. 90
5.2.1 Respiratory-Induced Pa Variability Mechanisms ...................................... 90
5.2.2 Direct Capacitive Effects .......................................................................... 93
5.2.3 Ventilatory Mechanism ............................................................................. 97
5.2.4 Three Indices Derived From BIT” ........................................................... 99
5.3 Signal Processing Algorithm .......................................................................... 100
5.4 Evaluation ....................................................................................................... 106
5.4.1 Theoretical Evaluation ............................................................................ 106
5.4.2 Pilot Experimental Evaluation ................................................................ 110
5.5 Evaluation Results .......................................................................................... 111
5.5.1 Theoretical Evaluation Results ............................................................... 111
5.5.2 Pilot Experimental Evaluation Results ................................................... 1 15
5.6 Discussion ....................................................................................................... 1 18
CHAPTER 6
CONCLUSIONS ............................................................................................................. 122
6.1 Summary ......................................................................................................... 122
6.2 Future Work .................................................................................................... 123
BIBLIOGRAPHY ........................................................................................................... 126

viii

LIST OF TABLES

Table 3.1: Advantages and disadvantages of some conventional cardiac output (CO)
measurement techniques ................................................................................................... 27

Table 3.2: Summary of the intensive care unit patient records and CO estimation results
of the invasive human hemodynamic data set .................................................................. 46

Table 3.3: Summary of the healthy young adult records and CO estimation results of the
non-invasive human hemodynamic data set ..................................................................... 48

Table 4.1: Summary of the intensive care unit patient records and cardiac output (CO)
and left atrial pressure (LAP) estimation results of the human hemodynamic data set.... 73

Table 6.1 Summary of three hemodynamic monitoring techniques. ............................. 123

ix

LIST OF FIGURES

Figure 1.1 A simple diagnostic algorithm based on the monitoring of cardiac output
(CO), left atrial pressure (LAP) and left ventricular maximum elastance (Eflm) .............. 5

Figure 2.1 Two-element Windkessel model of systemic circulation in terms of its
electrical circuit analog ....................................................................................................... 7

Figure 2.2 Two-element Windkessel model of pulmonary circulation in terms of its

electrical circuit analog ....................................................................................................... 8
Figure 2.3 Interaction between heart rate (HR) and ABP .................................................. 8
Figure 2.4 Hemodynamic signals and electrocardiogram (ECG) waveforms in one

cardiac cycle ...................................................................................................................... 12
Figure 2.5 Left ventricular pressure-volume loop ........................................................... 13
Figure 2.6 Respiratory waves on ABP waveform ........................................................... 15
Figure 2.7 Illustration of respiratory sinus arrhythmia .................................................... 15
Figure 2.8 Power spectrum of HR fluctuation ................................................................. 16

Figure 3.1 Comparison of the changes in blood pressure (BP) and cardiac output (CO)
during venesection and resulting faint .............................................................................. 25

Figure 3.2 Illustration of thermodilution CO and pulmonary capillary wedge pressure
(PCWP) measurements using pulmonary artery catheter (PAC) ...................................... 28

Figure 3.3 The technique of Bourgeois et al for monitoring CO from ABP waveform .. 32

Figure 3.4 Comparison of central ABP measured in aorta and peripheral ABP waveforms
, measured in radial artery ................................................................................................... 33

Figure 3.5 Two swine ABP waveforms measured at the same time but at different sites
in the arterial tree .............................................................................................................. 36

Figure 3.6 ABP waveform (top panel) can be viewed as a sum of a group of blood
pressure responses (lower panels) to cardiac contractions ............................................... 36

Figure 3.7 Illustration of identifying the time constant 1: from a peripheral ABP
waveform .......................................................................................................................... 4O

Figure 3.8 Visual examples of CO estimation results in three intensive care unit (ICU)
patients .............................................................................................................................. 47

Figure 3.9 Visual examples of CO estimation in three healthy subjects ......................... 49
Figure 4.1 Illustration of pulmonary capillary wedge pressure (PCWP) measurement .. 62

Figure 4.2 Illustration of construction of pulmonary artery pressure (PAP) from right

ventricular pressure (RVP) during ejection phase ............................................................ 62
Figure 4.3 PAP waveform and pulmonary circulation Windkessel model ...................... 65
Figure 4.4 Illustration of identifying the time constant T and LAP from a PAP waveforrg5
Figure 4.5 Illustration of the “knee” order selection algorithm ....................................... 68
Figure 4.6 PCWP measurement evaluation procedure .................................................... 71
Figure 4.7 Visual examples of CO and LAP estimation from three intensive care unit

(ICU) patients .................................................................................................................... 75
Figure 4.8 Illustration of identifying the time constant T and LAP from RVP ................ 82

Figure 4.9 Estimation results of CO and LAP from long time-interval PAP waveform and
RVP waveform in a dog .................................................................................................... 83

Figure 5.1 Illustration of left ventricular elastance (Ely) and the left ventricular maximum

elastance ( E {3“ ) .............................................................................................................. 86
Figure 5.2 Illustration of conventional Ear/lax measurement method .............................. 88
Figure 5.3 Respiratory waves on ABP waveform. .......................................................... 92
Figure 5.4 Illustration of respiratory sinus arrhythmia (RSA) ......................................... 92
Figure 5.5 Two-compartment model of the lefl ventricle and systemic arteries in terms

of the electrical circuit analog ........................................................................................... 94
Figure 5.6 Model of ventilatory mechanics in terms of its electrical circuit analog ....... 98
Figure 5.7 Illustration of enhanced venous return phenomenon .................................... 101

Figure 5.8 Random interval breathing power spectrum is much wider than spontaneous
breathing power spectrum. .............................................................................................. 102

xi

Figure 5.9 Illustration of system identification of index hi ........................................... 104
Figure 5.10 Block diagram summarizing the human cardiovascular simulator ............ 108

Figure 5.11 Summary of theoretical evaluation results against the corresponding actual

simulator Big“ value ..................................................................................................... 114

Figure 5.12 Pressure signals in canine experiment of monitoring left ventricular
contractility ..................................................................................................................... 1 16

Figure 5.13 Comparison of our technique with a highly invasive measurement of canine
experiment ....................................................................................................................... 117

xii

CHAPTER 1

INTRODUCTION

1.1 Hemodynamics

Cardiovascular disease is the number one cause of mortality in the United States. A
properly functioning, well-regulated cardiovascular system is essential to meet the
metabolic and mechanical demands of the various physiologic and pathophysiologic
situations. Hemodynamics is a branch of cardiovascular physiology studying the dynamic
properties of blood: flow (velocity), pressure, volume, and their relationships. It is very
important for the body to maintain the hemodynamic parameters in a narrow range
despite a wide variety of physiological perturbations. Otherwise, the person may be in
serious status. For example, a very low arterial blood pressure (ABP) may cause the death
of the brain in a few seconds, and low cardiac contractility may cause heart failure.
Therefore, hemodynamic monitoring is extremely important for directing therapy in

patients with cardiovascular disease.

1.2 Conventional Hemodynamic Monitoring

Most current hemodynamic monitoring systems provide continuous, automatic
measurements of blood pressures. Invasive fluid-filled catheters are broadly utilized in
critically ill patients to monitor the pressures in the radial artery and pulmonary artery.

Peripheral ABP may be measured non-invasively via tonometry and finger-cuff

photoplethysmography. Right ventricular pressure (RVP) could be measured by
implanted devices (e.g., two-lead pacemaker).

To a large extent, conventional patient monitoring systems simply measure and
display physiologic signals without attempting to interpret them. As a result, these
systems are limited in that they require a high level of invasiveness, necessitate an
operator, and/or provide nonspecific clinical information. For instance, the continuous
monitoring of ABP is commonly utilized to help physicians to assess the patients’
cardiovascular status. However, the main limitation of this monitoring is that the
measured ABP are multi-factorial and therefore not sufficiently specific to guide therapy.
For example, hypotension or low pressure may be caused by the inability of the heart to
fill or contract or the inability of the circulation to return blood to heart. To assess the
hemodynamic status, the measurement of other clinical parameters such as cardiac output
(CO) is desirable (Fig. 1.1). The thermodilution method is currently employed in most
intensive care units (ICU) and operating rooms to measure CO. This method involves
inserting a pulmonary artery catheter (PAC), injecting cold saline in the right atrium,
measuring temperature change downstream in the pulmonary artery, and then computing
CO using conservation ofmass laws. This method is very invasive and only warrants use
in a subset of critically ill patients. In addition, because an operator is required, the CO
cannot be monitored continuously. Finally, it is not very accurate due to the many
assumptions upon which it is based.

Other important specific hemodynamic parameters include left atrial pressure
(LAP) and cardiac contractility. Left atrial pressure (LAP), also known as left heart

filling pressure, can be utilized together with CO to distinguish between circulatory and

cardiac diseases. The standard LAP monitoring method is the pulmonary capillary wedge

pressure (PCWP) method. This method also requires an operator and is therefore discrete.

Left ventricular maxim elastance ( E13“) is a specific index heart contractility. The
monitoring of BS“ can help detect left ventricular systolic failure. The conventional

measurement method of ER?“ involves catheterizing the left ventricle through the aorta

to measure the left ventricular pressure and volume, altering the loading conditions by,
for example, inferior vena cava balloon occlusion, and then computing the slope of the
line that best fits the end-systolic pressure-volume points. This method is clearly too

invasive for routine use.

1.3 Hemodynamic Monitoring by System Identification

In this thesis, we seek to overcome limitations of conventional hemodynamic
monitoring systems. Our general approach to advancing the state—of-the-art of patient
monitoring systems is to reveal the significant, “hidden” information in routinely
measured blood pressure waveforms by employing system identification with physiologic
knowledge. In this way, the patient monitoring systems are possibly less invasive,
provide automated physiologic assessment, and/or indicate specific clinical parameters

that significantly contribute to therapeutic decision-making.

1.4 Thesis Organization and Contributions

The main contributions of this thesis is in the development and evaluation of three

techniques for monitoring CO, LAP and/or left ventricular contractility in terms of

Big“. Common to the three techniques is the analysis of continuous long time intervals

of blood pressure waveforms.

In Chapter 2, we discuss the background for this thesis, namely, cardiovascular
physiology, hemodynamic models, and basic system identification algorithms. In chapter
3, we describe a previously developed technique for continuously monitoring CO from
peripheral ABP. We then describe the refinement of the technique and its validation, for
the first time, in humans. In chapter 4, we extend the algorithm of Chapter 3 to a PAP or
RVP waveform for continuously monitoring LAP and CO and describe its preliminary

evaluation in ICU patients and a canine experiment. In Chapter 5, we introduce a
technique to monitor changes in E133" from the ABP waveform variations induced by

respiratory activity during a random interval breathing protocol. We then describe its
evaluation with respect to beat-to-beat variability generated from a realistic human
cardiovascular simulator and a canine experiment. Finally, in chapter 6, we summarize

the thesis work and outline fiiture directions.

CO Decrease

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hemodynamic
Problem
|
LAP
\
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/ \
Clrculatory Cardiac
Problem Problem
|
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Dysfunction Systollc Heart Fallure

 

 

 

 

Figure 1.1 A simple diagnostic algorithm based on the monitoring of cardiac output

(C0), left atrial pressure (LAP) and left ventricular maximum elastance (Ewax)

(Modified from Pinsky and Vincent, 2005).

 

CHAPTER 2

BACKGROUND

2.1 Cardiovascular System

The cardiovascular system serves to transport and distribute essential substances to
the tissues and to remove by—products of metabolism as well as regulate body
temperature, adjust oxygen and nutrient supply and etc. [Berne and Levy, 1998]. The

cardiovascular system includes the circulatory system and the nervous control system.

2.1.1 Circulations

The circulatory system consists of a pump (the heart), a series of distributing and
collecting tubes (blood vessels), and thin vessels for exchange between the tissues and the
vascular channels (capillaries). The vascular system is composed of two major
subdivisions in series with one another: the pulmonary circulation and systemic
circulation. Each subdivision consists of several types of vessels (e.g., arteries,
capillaries, veins) aligned in series with one another. In the pulmonary circulation, the
right ventricle propels oxygenated blood through the lungs for exchange of oxygen and
carbon dioxide. In the systemic circulation, the left ventricle propels blood to all other
tissues of the body.

There have been numerous models of the circulation. For example, Fig. 2.1 shows a
simple electrical analog model of the systemic circulation. Here, the left heart is
represented by a current source supplying the CO. The systemic arterial tree is

represented by a two-element Windkessel model accounting for the lumped compliance

of the large arteries (arterial compliance, AC) and the total peripheral resistance (TPR) of
the small arteries. The veins are not considered in the model, because due to the high
value of TPR, the venous pressure is usually negligible with respect to ABP.

Similarly, the pulmonary circulation could also be modeled as an electrical circuit
as shown in Fig. 2.2. The right heart is represented by a current source supplying the CO;
puhnonary vessels (including arteries, capillaries and veins) are represented by a
Windkesssel model accounting for pulmonary vessel compliance (PVC) and pulmonary
vessel resistance (PVR). LAP must be considered in the model, because the pulmonary

circulation is a low pressure system.

ABP

 

co CD :: AC TPR

 

 

 

Figure 2.1 Two-element Windkessel model of systemic circulation in terms of its
electrical circuit analog. Left ventricle is represented by a current source with a value of
cardiac output (CO) and arterial tree is represented by total peripheral resistance (TPR)

and arterial compliance (AC). ABP, arterial blood pressure.

PAP

co CD :E PVC

 

PVR

LAP

 

 

 

Figure 2.2 Two-element Windkessel model of pulmonary circulation in terms of its
electrical circuit analog. Right ventricle is represented by a current source with a value of
CO and pulmonary vessels are represented by pulmonary vessel resistance (PVR) and

pulmonary vessel compliance (PVC). LAP, left atrial pressure.

 

 

_ CIRCULATORY
T MECHANICS 69
HR <— —-> ABP

€9<—— HR BAROREFLEX .—

 

 

 

 

 

 

 

 

 

Figure 2.3 Interaction between heart rate (HR) and ABP. NHR, NABp, noise disturbance of

HR and ABP.

2.1.2 Cardiovascular Regulation

A principle objective of the cardiovascular system is to maintain ABP within a
narrow range in order to drive blood through the tissues and provide oxygen and other
essential substances. This goal is realized by not only the mechanical system
(circulation), but also the cardiovascular regulatory system. In the short term (seconds to
minutes, which is the focus of this thesis), the arterial and cardiopulmonary baroreflex
feedback systems are normally responsible for extrinsic regulation over short time scales
of seconds to minutes. For example, ABP is sensed via baroreceptors that lie in the
carotid sinus and aortic arch and this pressure is transfered to the brainstem via afferent

nerve fibers. The brain then try to keep ABP near its desired value by adjusting heart rate
(HR), left ventricular contractility (i.e., E133" ), TPR, and systemic venous unstressed

volume (SVUV). If ABP decreases, then HR, ventricular contractility and TPR would

increase, while SVUV would decrease. Then, ABP would be increased back towards its
desired value via the mechanical system. Thus, the system is closed-loop. For example,
HR affects ABP through circulatory mechanics, while ABP also affects HR through the

baroreflex feedback control system (Fig. 2.3) [Mullen et al., 1997].

2.1.3 Hemodynamic Waveforms

Knowledge of the variability of hemodynamic signals (blood pressures, flows and
volumes) and the electrocardiogram (ECG) is very important in this thesis. In this
section, we will discuss the waveform variability and the mechanisms underlying this

phenomenon.

Intra-Beat Variability

The cardiac cycle refers to the sequence of electrical and mechanical events
occurring in the heart during a single beat. These events result in the changes of blood
pressures, volumes and flows, and the body surface potential that is usually monitored
with the ECG. The waveforms of aortic pressure (AOP, central ABP), left ventricular
pressure (LVP), LAP, left ventricular volume, and ECG during one cardiac cycle are
shown in Fig. 2.4. Ventricular systole (contraction) and diastole (relaxation) can be
defined in terms of both mechanical and electrical events. In mechanical terms, systole is
defined as the period between the closure of the mitral valve and the closure of the aortic
valve. In electrical terms, it is the period between the QRS complex and the end of the
“T” wave in the ECG signal. Ventricular diastole is remaining time of the cardiac cycle.
Systole is composed of the isovolumetric contraction phase and the ejection phase.
During the ejection phase, the aortic valve is opened and blood flows out from the
ventricle, thus the ventricular volume decreases and the waveforms of AOP and LVP are
overlapped. In the remaining of the cardiac cycle, the aortic valve closes, thus the AOP
waveform is always above the LVP waveform due to the blood conservation effect of the
AC. Note that the “R” wave in the ECG waveform corresponds to the beginning of
isovolumetric contraction, when the LVP begins to increase rapidly and the mitral valve
closes. Two waves appear in LAP waveform during one beat: the “a” wave after the “P”
wave of the ECG and the “v” wave after the “T” wave of the ECG (Fig. 2.4). The “v”
wave corresponds to the end of the isovolumetric relaxation when the mitral valve opens.

PAP and right ventricular pressure (RVP) waveforms are very similar with AOP and

10

LVP respectively except that their values are much lower. As implied above, a left

ventricular pressure-volume loop of the cardiac cycle in Fig. 2.4 is shown in Fig. 2.5.

11

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Figure 2.4 Hemodynamic signals and electrocardiogram (ECG) waveforms in one
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ECG are shown from top to bottom. Ejection happens when the aortic valve is open. “a ”

andv “ ” waves are apparent in LAP waveform. “R” wave in ECG corresponds to the

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systole.

13

Beat-to-Beat Variability

Hemodynamic waveforms also vary from beat-to-beat due to various naturally
occurring physiological perturbations and the response of the short-term cardiovascular
regulation to these perturbations. For example, the beat-to-beat fluctuations in ABP due
to respiration are clearly seen in Fi g. 2.6. These fluctuations are caused by both the
mechanical effects and the autonomic nervous system. The variation of intrathoracic
pressure caused by chest expansion (inspiration) or chest contraction (expiration)
mechanically perturbs the venous return, ventricular pressure, and the arterial pressure.
Autonomic mechanisms are responsible for the respiratory sinus arrhythmia phenomenon
in which HR and respiratory variations are in synchrony (Fig. 2.7) [Eckberg et al., 1984;
Saul and Cohen, 1994]. The HR changes will then cause ABP changes through
circulation. These mechanisms are mediated by the fast parasympathetic nervous system
and the slower sympathetic nervous system [Akselrod et al., 1981]. Another example of
an ongoing perturbation is fluctuations in the TPR as vascular beds regulate their own
resistance in order to match blood flow demand. These fluctuations in turn can perturb
arterial pressure and affect HR.

With the conventional power spectral analysis, we can study the frequency content
of the fluctuations in HR (Fig. 2.8). The short-tenn fluctuations are normally
concentrated in three principal spectral peaks: low-frequency peak (0.02-0.09 Hz), mid-
frequency peak (0.09-0.15Hz), and high-frequency peak (respiratory frequency). The two
lower frequency peaks in the power spectrum proves that other perturbations (e. g.,

autoregulation of local vascular beds) aside from respiration exist.

14

 

 

 

 

o s 140 15 20 25
Time [sec]

Figure 2.6 Respiratory waves on ABP waveform.

 

 

ECG
Pa
Qlu
0 2 4 6 8 10
Time (see)

Figure 2.7 Illustration of respiratory sinus arrhythmia. The heart rate (ECG) is in

synchrony with the respiratory activity (Qlu, instantaneous lung volume).

15

Low-freq ue ncy pea k

r-‘fi
0.02 -

 

Mid-frequency peak

0.01 *- High-frequency peak

r—-~

     
 

 

Power spectrum of HR fluctuations

 

 

I

0.1 0.3 0.5
Frequency (Hz)

 

Figure 2.8 Power spectrum of HR fluctuation featuring 3 main peaks: low-frequency
peak (0.02-0.09 Hz), mid-frequency peak (0.09—0.15Hz), and high-fiequency peak

(around respiratory frequency) [Akslrod et al., 1981].

16

2.2 System Identification Analysis in Hemodynamics

The construction of the cardiovascular models described in Fi g. 2.1 and Fig. 2.2 is
called forward modeling, which could be utilized in hemodynamic computation. For
example, the blood flow can be computed fiom ABP by solving differential equations
based on the systemic circulation model shown in Fig. 2.1. The inverse modeling
problem is to identify dynamic models from observed data. This approach is called
system identification and is the basis of signal processing methods used in this thesis.

System identification could be categorized into nonparametric and parametric methods.

2.2.1 Nonparametric Identification

Multivariable statistical methods such as cross-correlation functions, cross-spectra,
and nonparametric transfer functions have been used to analyze the relationships between
fluctuations in different cardiovascular signals [Mullen et al., 1997]. Consider an LTI
(linear time invariant) system whose input-output relationship can be expressed as
follows:

00
y(t) = Z h(k)u(t — k) + e(t), (2.1)
k=—oo

where t is discrete time; u(t), input; y(t), output; h(t), impulse response; and e(t),
unobserved, stochastic process that is uncorrelated to u(t). Thus, the output signal can be
computed by convolving the impulse response and the input signal plus an unobserved
noise signal. The impulse response is defined to be the system response to an arbitrarily

narrow, unit-area input and completely characterizes the LTI system. The Fourier

l7

transform of the impulse response, transfer function, may be estimated from input-output

data in closed-form as follows:

(2.2)

where Suy (ejznf) is the cross-spectrum from u(t) to y(t); Suu (ejan) , auto-spectrum of

u(t); and H(ej27If ) , optimal transfer function in the least squares sense [ijg, 1999],

which is also known as the Wiener filter. Since the cross-spectrum is generally complex,

H(ej2”f) provides both magnitude and phase characteristics of the system. The

nonparametric transfer function has been used to analyze the arterial heart rate baroreflex
system [Berger et al., 1989b] and respiratory sinus arrhythmia.

Nonparametric identification methods have proven to be powerful analytic tools
because they are easy to use and capable of giving unique results without assuming any
model structure. However, the major limitation is that they only can be utilized in
identifying systems operating in open-loop. For example, in Fig. 2.3, the nonparametric
transfer function analysis of HR and ABP fluctuations would provide a single transfer
function relating the two variables and include the properties of both circulatory
mechanics and HR baroreflex. These two totally distinct physiological mechanisms
would thus be intertwined together. Therefore, neither circulatory mechanics cannot be
characterized due to the existence of the baroreflex system. Similarly, the HR baroreflex

characteristics cannot be obtained either.

2.2.2 Parametric Identification

18

On the other hand, the parametric identification may be even more illuminating.
The advantage of this approach is that it provides a quantitative characterization of the
open-loop hemodynamic mechanisms responsible for coupling the variability between
hemodynamic signals despite the pressure of the feedback. Beginning from the middle to
late 19808, parametric identification has become an increasingly popular approach for
quantitatively probing cardiovascular mechanisms. Next, we will introduce three

mathematical models popularly utilized for parametric identification.

ARX Model and MA model

Amongst different existing models, the autoregressive exogenous input (ARX)
model is perhaps the most widely employed parametric model in system identification.
For example, in Fig. 2.3, since each pathway of the closed-loop coupling is causal,
parametric identification has been utilized to estimate the circulatory mechanics and HR
baroreflex separately [Mullen et al., 1997]. Each channel can be represented by an ARX
model and quantitated with a limited number of parameters. The details of the ARX
modeling approach are described below.

Given an LTI causal system, where u(t) is the input, y(t) is the output, and e(t) is an
unobserved white noise disturbance that is uncorrelated with the input, the ARX model

can be conveniently represented as follows:
y(t):Za,y(t-i)+2b,u(t—i)+e(t). (2.3)
i=1 i=0

The unknown coefficients {(1,} and {b,-} are respectively referred to as the autoregressive
(AR) and exogeneous parameters. The AR part refers to the effect of the past values of

y(t) on the current value of y(t); the exogeneous part refers to the effect of the past and

19

current values of u(t) on the current value of y(t). The constants m and n are model orders
limiting the number of these parameters. The coefficients may be estimated from
measured input-output data by minimizing the variance of e(t) via the closed form linear
least squares solution. The Z transform of the ARX model may be expressed with the
following equation:

_ B(Z) E(Z)
Y(z) _ ——1 __ A(z) U(z) + 1 _ A(z) , (2.4)

 

where A(z) = alz’l +azz‘2 +---+an , B(z) = b0 +blz'l + bzz’2 +~~+ bm, and E(z) is the
Z transform of the unobserved noise e(t). This equation illustrates that the influence of
the unobserved, white disturbance on the system output is colored by the AR coefficients.
Thus, the ARX model is able to represent LTI systems in the presence of colored noise.
The impulse response h(t) can be obtained by substituting u(t)=6(t) into Eq. 2.3. The
transfer firnction H(z) is the Z transform of the impulse response h(t) and may be
computed with the following equation:

I)
Zka—k

H(z) = “=0 . (2.5)

m
1— Zakfk
k=l

 

If the AR part is removed from Eq. 2.3, we obtain a finite impulse response (FIR)

model as follows:

y(t) = ibiuu — i) + e(t). (2.6)

i=0
Here, the output only depends on the input. For an LTI causal system represented by Eq.

2.6, the impulse response h(t) is actually the coefficients {b.-}. The coefficients {bi} could

20

be estimated by the linear least squares solution from measured input-output data. The Z
transform of the FIR model is as follows:
Y(z) = B(z)X(z) + B(z) . (2.7)
OE Model
The relationship between x(t) and y(t) may also be represented by an output error
(OE) model given in Z transform as follows:

3(2)
———1 _ A(z) X(z) + E(z). (2.8)

Y(z) =

Comparison of Models

Comparing Eq. 2.4, Eq. 2.7 and Eq. 2.8, we can see that the three models are
different based on the noise portion. The unobserved noise e(t) is “colored” by AR
coefficients in the ARX model, whereas e(t) is not limited by this assumptions in FIR and
DE model. One big advantage of the ARX and FIR models is that they can be
conveniently estimated by solving the linear equations 2.3 and 2.6 using the linear least
squares solution. In contrast, the parameters of the OE model have to be estimated
numerically by, for example, Newton’s iteration method. Another advantage of the FIR
model is that it does not make any assumptions about the model structure (no poles in Eq.
2.7) and therefore its impulse response has no restriction. However, accurate system
identification using an MA FIR model requires a large number of parameters. Thus, the

FIR model can only characterize the system whose true impulse response is very short.

Model Order Selection

21

In order to identify the coefficients of the models, the model orders m and it must be
determined. Because the ARX model is perhaps the most widely used, we describe model
order selection method based on the ARX model.

Assuming the true model orders in Eq. 2.3 are no and mo, and no=m0, if the selected
model order n<no, then the estimated model will not include all of the true parameters
and therefore lacks the degrees of freedom necessary to represent the system. On the
other hand, if the selected model order n>n0, then there would be extra parameters in the
estimated model that do not exist in the true model. These extra parameters serve only to
make the estimated model more sensitive to the noise during the particular time period
[Perrott and Cohen, 1996]. Thus, order selection is a tradeoff between completeness and
robustness.

To obtain the true model order, first, a set of candidate model orders are chosen
based on the physical properties of system. Next, the best model order is sought from the
candidate orders. We cannot choose the order corresponding to the minimum mean
square error (MSE) of e(t), because the MSE is a monotonically decreasing function of
model order. The most popular strategy is to minimize a theoretically derived formula or
criterion, which consists of a goodness-of-fit index such as MSE and a penalty factor for
model complexity. The Minimum Description Length (MDL) and Final Prediction Error
(FPE) [Ljung, 1999; Perrott and Cohen, 1996] are amongst the most widely used model

order selection criteria. The MDL value is computed via the following formula:

 

= log(N) llekllz
MDL(k)_(1+k N j N , (2.9)

where k is defined to be the number of parameters contained within the model, N is the

number of samples contains in the input and output data sets, and ||ek| [2 is the MSE.

22

Model order selection using the MDL criterion amounts to finding the model amongst the
candidate set with the minimum MDL value. The FPE value is computed via the
following formula:

N+k IIerII2

FPE(k) _=_
N —k N

(2.10)

Similarly, model order selection using the FPE criterion aims to find the model order

with the minimum FPE value.

23

CHAPTER 3
CONTINUOUS MONITORING OF CARDIAC OUTPUT FROM A

PERIPHERAL ARTERIAL BLOOD PRESSURE WAVEFORM

3.1 Background

Since cardiac output (CO) represents the total flow of blood supplying all the tissue
beds of the body, it is perhaps the most valuable indicator of overall cardiovascular
health. For example, circulatory status is typically monitored through ABP, which is easy
to measure. However, in the early stages of a bleed, ABP is maintained while CO is
falling due to the body’s multiple feedback and control systems (Fig. 3.1) [Barcroft et al.,
1944]. Thus, continuous CO monitoring would provide an early indication of deleterious
changes in circulatory status and thereby provide sufficient time for successful therapy.

Due to the importance of CO, it is currently monitored in most ICUs and surgical
suites in order to guide therapy for critically ill patients. These patients include, for
example, those in shock (e.g., cardiogenic, septic, and hemorrhagic) or heart failure and
those during and after surgery (e.g., coronary artery bypass grafting or heart valve
replacement). An ideal method for CO measurement should be continuous (autonomous
operation), minimally invasive, accurate, and inexpensive. Although numerous
techniques have been developed for the measurement of CO, none of the conventional
techniques possesses all these characteristics (Table 3.1) [Ehlers et al., 1986]. Consider,
for example, the standard thermodilution technique, which is currently employed in most
ICUs and surgical suites. This technique involves introducing a pulmonary artery catheter

(PAC) [Swan et al., 1970] in the right heart, injecting cold saline in right atrium, and

24

 

 

 

    

 

«N’ 50
m‘ t
m
E's
ss
Em took:
3% 3&3
«.3 ' §
80
E9 E 8
ES fie
- 30§
l20
. too - VENESECTION _ '00
%“ '080 ccm.
Q £3 ‘. ’ x
a E. " -- “,.- a, .' ”so. .. 80
E5. 12 m
to . r a
'0 -\
E's
3
S a 3‘
3 a a gs
x 3 '6
$3 4 '«2
3'5

 

 

O 4 8 l2 36
MINUTES

Figure 3.1 Comparison of the changes in blood pressure (BP) and cardiac output (CO)
during venesection and resulting faint. Until to the end of venesection, BP is maintained
by peripheral vasoconstriction (increased total peripheral resistance) in spite of falling
CO. During the faint, the cardiac output increases slightly and the fall in BP is therefore

due to the decrease in total peripheral resistance (TPR) [Barcroft et al., 1944].

25

measuring the temperature downstream in the pulmonary artery (Fig. 3.2). The average
CO over the measurement period may then be computed based on conservation of mass
laws. Although the technique is relatively inexpensive, it is very invasive and does not
operate autonomously. Moreover, the measurement is not very accurate due to the many
assumptions upon which it is based (e. g., no saline recirculation and thorough blood
mixing) [Ehlers et al., 1986]. As a result, it is used in only a minority (e. g., 10-20%) of
all critically ill patients [Rapoport et al., 2000]. In fact, although PAC can be utilized to
measure pressures (right atrial, right ventricle, pulmonary capillary wedge pressure, and
pulmonary artery pressures) as well as other important hemodynamic parameters (e. g.,
CO, LAP, mixed venous oxygen saturation), the apparent failure to demonstrate
improvements in patient outcome and risks associated with the PAC use have long been
criticized and therefore the applications of PAC are falling in this decade [Pinsky and
Vincent, 2005]. Another conventional technique for monitoring CO is transthoracic
impedance. Thoracic bioimpedance involves the placement of voltage sensing and
current transmitting electrodes on the chest, which may be regarded as a conductor whose
impedance is altered by changes in blood volume and velocity with each heartbeat.
Stroke volume is calculated from an equation involving baseline and maximum rate of
change in impedance, ventricular ejection time, and thoracic segment length. This
measurement technique is non-invasive and operates autonomously; however, it is
generally considered to be very inaccurate, especially in critically ill patients who often
have excessive lung fluids [Critchley et al., 1998]. Doppler ultrasound methods, which
measure the Doppler shift in the frequency of an ultrasound beam reflected from the

flowing aortic blood, require an expert operator to stabilize an external ultrasound

26

transducer as well as expensive equipment. The most accurate, conventional technique

for measuring CO involves surgically implanting a flow probe, either electromagnetic or

ultrasonic, directly on the aorta. Although this technique operates autonomously, it does

require the drastic procedure of opening the chest. A practical, continuous, minimally

invasive or non-invasive CO monitoring method would benefit not only ICU and surgical

suite care but also potentially home health care, primary care, and even combat casualty

care.

Table 3.1: Advantages and disadvantages of some conventional cardiac output (CO)

measurement techniques [Ehlers et al., 1986]

 

 

 

 

 

CONVENTIONAL ADVANTAGES DISADVANTAGES
TECHNIQUES
Aortic Flow Probe most accurate; continuous thoracotomy; expensive
Doppler Ultrasound accurate; non-invasive expert operator; expensive
Oxygen Fick inexpensive two catheterizations;
inaccurate; discrete
Thermodilution inexpensive heart catheterization;

inaccurate; discrete

 

 

Transthoracic Impedance

 

non-invasive; inexpensive;
continuous

 

inaccurate

 

27

 

Right Pulmonary Pulmonary

 

 

 

Atrium Artery Capillary
Cold saline RA Lumen
4' PA
I v—l Lumen
Therrnistor
Balloon
0 l
g
L“
a
E
(D
.—

 

 

Time

Figure 3.2 Illustration of thermodilution CO and pulmonary capillary wedge pressure
(PCWP) measurements using pulmonary artery catheter (PAC). PAC is a flow-directed
balloon-tipped catheter. Thermodilution measurement steps: insert PAC into pulmonary
artery through right heart, inject cold saline from syringe to right atrium, measure the
temperature changes downstream in pulmonary artery and compute CO by the mass
conservation law. The curve on the bottom is the temperature measured in pulmonary
artery by a thermistor. CO measurement value is proportional to the reciprocal of the area
below the curve. PCWP measurement: after inserting PAC into puhnonary artery,
position the tip in a small branch of pulmonary artery, and inflate the balloon to occlude

blood flow. The pressure measured is PCWP.

28

While the measurement of CO has proven to be difficult, peripheral arterial blood
pressure (ABP), which is related to CO through arterial tree, may be measured reliably
and continuously via minimally invasive radial artery catheterization. Indeed, this
relatively safe procedure is performed in a majority (e.g., 50-80%) of all critically ill
patients [Rhodes and Sunderland, 2005]. Moreover, totally non-invasive methods have
been developed to continuously measure peripheral ABP based on finger-cuff
photoplethymography [Imholz et al., 1998] and arterial tonometry. These non-invasive
methods are available as commercial systems at present, for example, Finapres Medical
System. Indeed, since at least 1904 [Erlanger and Hooker, 1904], numerous investigators
have therefore sought analysis techniques to monitor CO from ABP waveforms.
Techniques based on an adaptive aorta model, which require ABP waveforms measured
at two peripheral sites, have been proposed [Redling and Akay,1997; Welkovitz et al.,
1991]. Learning techniques, which require large training data sets consisting of
simultaneous measurements of CO and ABP waveforms obtained over the entire
physiologic range, have also been suggested [Cerutti et al., 2001; Gratz et al., 1992;
Martin et al., 1994]. Finally, Wesseling et a1 [1993], Linton et al [2001], and other
investigators have proposed techniques requiring only the analysis of a single radial ABP
waveform. However, Linton et a1 only showed that their heuristic technique was accurate
over a narrow physiologic range, and several studies have demonstrated limitations of the
technique of Wesseling et a1 [Gerhardt et al., 2001; Houtman et al., 1999].

Although a wide variety of techniques have been proposed, they are all
conceptually the same to the extent the waveform analysis is performed only over time

scales within a cardiac cycle. However, over such short time scales, peripheral ABP

29

waveforms are heavily corrupted by complex waves propagating back and forth in the
distributed arterial tree. Thus, the previous analysis techniques have generally proven to
be too inaccurate for clinical use. To date, no non-invasive method has been clinically
accepted as a replacement for thermodilution [Levett et al., 1979; Redling et al., 1997].

Our ongoing hypothesis is that CO may be accurately monitored from ABP
variations occurring over time scales greater than a cardiac cycle. This hypothesis
originates from transmission line theory, which predicts that the confounding effects of
wave reflection will diminish with increasing time scale [Noordergraaf, 1978]. Based on
the hypothesis, we previously developed a technique to monitor changes in CO by
analyzing a single peripheral ABP waveform over long time scales [Mukkamala et al.,
2003a, 2004, 2006]. In this study, we refined the technique and evaluated it, for the first
time, in humans based on previously published invasive and non-invasive hemodynamic
data sets [Elstad etal., 2001; Moody et al., 1996, 2001; Mukkamala et al., 2003b]. With
these data, we were specifically able to compare the application of the technique to 1)
invasive peripheral ABP waveforms obtained via radial artery catheterization with
reference thermodilution measurements in 15 intensive care unit (ICU) patients in which
CO was changing due to disease progression and therapy and 2) non-invasive peripheral
ABP waveforms obtained via a commercial finger-cuff photoplethysmography system
with reference Doppler ultrasound measurements made by an expert in ten healthy

subjects in which CO was altered through pharmacological and postural interventions.

3O

3.2 The Technique

Our technique builds upon the previous pulse contour analysis work of Bourgeois et
a1. [1976]. In the systemic circulation, arterioles and small arteries contribute 75% of the
total resistance, and the large arteries act as a capacitive reservoir [Beme and Levy,
1998]. Therefore, these investigators assumed that the arterial tree could be well
represents by a two-element Windkessel model accounting for the lumped compliance of
the large arteries (arterial compliance, AC) and the resistance of small arteries and
arterioles (total peripheral resistance, TPR) as shown in Fig. 3.3a. They further assumed
that TPR does not change within a diastolic interval since the autonomic nervous
mechanisms responsible for modulating TPR are relatively slow [Berger et al., 1989b]. In
addition, AC may be approximately constant over a wide pressure range and on the time
scale of days to months [Hallock, 1937; Bourgeois et al., 1976]. Based on these
assumptions, these investigators predicted that ABP may decay like a pure exponential
during each diastolic interval with a time constant (1) equal to the product of the TPR and
AC (Fig. 3.2b). Thus, their pulse contour technique involved fitting a mono—exponential

function to each ABP diastolic interval to measure I and then dividing the time-averaged

ABP with 1: to compute the proportional CO scaled by a constant factor of l/AC (Fig.
3.3b).

Bourgeois et al were able to successfully validate their technique with respect to
central ABP waveforms measured near the heart, because the diastolic interval of these
waveforms resembles an exponential decay (Fig. 3.4a). However, central ABP is rarely
measured clinically because of the risk of blood clot formation and embolization. In

contrast, in readily available peripheral ABP waveforms, an exponential diastolic decay

31

is not apparent (Fig. 3.4b). The reason is that the arterial tree is not simply a lumped
system like the two-element Windkessel model suggests but rather a complicated
distributed system with impedance mismatches, throughout due to vessel tapering,
bifurcations, and caliber changes. The diastolic (and systolic) intervals of peripheral ABP
waveforms are therefore corrupted by the complex wave propagation and reflections
occurring at every site of impedance mismatch. Thus, the technique of Bourgeois et al

cannot be applied to peripheral ABP waveforms.

 

ABP E, 500.
8

co d5 :: AC TPR g”:
E r

 

L

24.5 25 25.5 26 26.57 27 27.5
tD= TPR'IAC

 

 

 

 

 

 

24.5 25 25.5 26 26.5 27 27.5
Time [s]

(a) (b)

Figure 3.3 The technique of Bourgeois et al for monitoring CO from ABP waveform. (a),

 

two-element Windkessel model of artery including total peripheral resistance (TPR) and
arterial compliance (AC); (b), CO and ABP waveform. ABP decays like an exponential
during diastole with a time constant (1) equal to the product of TPR and the nearly
constant AC. The proportional CO is calculated by dividing the mean ABP with ‘l.’

[Bourgeois et al., 1976].

32

 

 

 

 

 

 

 

 

 

 

130' 90“
120- --
2 a
_. 70
too 0-
% 2
< 90‘ Eco
E 2
C 80* g.
8 050.
70 “-
6°" as" ' " *1‘ 1‘s 2 ' $5“'“5515:5“"3329"”"3527‘5 " " ‘
Time iseci Time lsecl
(a) (b)

Figure 3.4 Comparison of central ABP measured in aorta (a) and peripheral ABP
waveforms measured in radial artery (b). The diastolic intervals of the central ABP
waveform resemble exponential decays; however, central ABP is rarely measured
clinically. In contrast, exponential diastolic decays are not visible in the peripheral ABP

waveforms, which are corrupted by complex wave reflections.

However, the two-element Windkessel model is a more valid representation of the
long time scale dynamics of the systemic arterial tree. That is, according to transmission
line theory, the confounding effects of complex waves in the arterial tree will diminish
with increasing time scale [Noordergraaf, 1978]. That is, the wave effects significantly
corrupt the peripheral ABP waveforms within a cardiac cycle (high frequencies) without
complicating the waveforms over long time scales (low frequencies). This important
concept is demonstrated in Fig. 3.5, which illustrates two ABP waveforms measured at

the same time but at different sites in the arterial tree. The short time scale (within a beat)

33

variations are different in the two waveforms, as the characteristics of the complex wave
effects differ at the two measurement sites. In contrast, the long time scale (beat-to-beat)
variations are more similar, since the confounding effects of wave phenomena are less
significant. (Note, the beat-to-beat variations are due to ongoing perturbations to the
cardiovascular system (e. g., breathing), and the dynamic, compensatory response of the
regulatory system (e. g., baroreflex)). Thus, the two-element Windkessel model is a more
valid representation of the long time scale behavior of the arterial tree. This implies that if
the pulsatile activity suddenly ceased, then a peripheral ABP waveform may eventually
decay like a pure exponential as soon as the faster wave reflections vanish. Similarly, the
peripheral ABP response to a single cardiac contraction would be corrupted in short time
and would appear like a pure exponential decay in long time. In Fig. 3.6, the peripheral
ABP waveform of an ICU patient is shown in the top panel, and the ABP responses to
cardiac contractions, which are located at the beginning of each beat, are shown in the
lower panels. The peripheral ABP waveform is actually the sum of ABP response to each

cardiac contraction.

34

Central ABP [mmHg]

Peripheral ABP [mmHg]

 

 

01
I
E 70
E
50
486.2 487.2
sec
90 ,
7o
50
1 l I l l J
490 495 500 505 510 515
Time [sec]
(8)
90
O)
:1:
E 70
E
50
405.2 487.2
/ sec
90
70‘
50

l l 1 I

 

1 I
490 495 .500 505 510 515
Time [sec]

0))

35

Figure 3.5 Two swine ABP waveforms measured at the same time but at different sites
in the arterial tree. (a), ABP waveform measured centrally in the aorta; (b), ABP
waveform measured peripherally in the radial artery. While the short time scale variations
(top panels) differ due to highly complex wave motion, the long time scale variations
(bottom panels) are more similar as the wave phenomena are only a high frequency

effect.

Figure 3.6 ABP waveform (top panel) can be viewed as a sum of a group of blood
pressure responses (lower panels) to cardiac contractions. y(t), arterial blood
pressure; Rj, onset time of upstroke of No. j ABP wavelet; yj-(t), blood pressure
response located at Rj. In the short time (high frequency), y,-(t) oscillates vigorously;
while in the long time scale (low frequency), for example, longer than 2 sec, it

decays like a pure exponential.

36

 

 

 

 

m w m m
m
1H. .............................................................................................
R m m m .m.
m m m m
m w w u
0 O O O
m m .m ..m.
O O O O
m m .m .m
m m .m .m
2 1 1 4| I
.H. Q
R; _ ..1
1 0 0 OF
.+J m m W . 1 4 2 -m
......................... 1 ..1:: ..H; 1
R w m 0R EIEEH
R1..- R1 m EE «are»
. . . .m. m _ z _ .m. : m

 

120 -

100 —

w m w m

32.55 a;

 

HmIEEH
32+;

1
07 Rj+12108

O.

.1—
106

 

[see]

Time

37

Therefore, our technique analyzes a peripheral ABP waveform over time scales
greater than a cardiac cycle in order to determine the pure exponential decay in a
peripheral ABP response (h(t)) to a single cardiac contraction after the wave reflection
vanishes. In Fig. 3.6, in order to clearly illustrate the technique on a beat to beat basis, we
only show an eight-second segment of the peripheral ABP waveform. In the analysis, we
selected a time interval of about six-minute in order to provide enough beat to beat
variability for system identification. One may think h(t) could be estimated by computing
the nonparametric transfer function derived from power spectral of input and cross power
spectral of input and output using Eq. 2.2. However, as we explained in Chapter 2, the
circulatory mechanics cannot be obtained independently due to the existence of
baroreflex feedback mechanism (Fig. 2.3). Therefore, we must use system identification
to solely estimate the circulatory mechanics.

Fig. 3.7 illustrates the technique and indicates that the single contraction ABP
response h(t) is determined in two steps. First, a signal representing the cardiac
contractions (x(t)) is constructed from the ABP waveform based on a slightly modified
impulse ejection model. That is, x(t) is formed as an impulse train in which each impulse
is located at the onset of upstroke of an ABP pulse and has an area equal to the pulse
pressure determined after lowpass filtering the waveform (with a cutoff frequency of 2
Hz) to attenuate the wave effects (FPP, filtered pulse pressure). Then, the impulse
response function h(t) which when convolved with x(t) best fits the (unfiltered) ABP
waveform (y(t)) in the least squares sense is estimated according to the following

autoregressive exogenous (ARX) input equation:

y(t)=Zaky(t—k)+Zbkx(t—k)+e(t), (3.1)
k=l k=l

38

where e(t) is the unobserved residual error, the parameters {al., bk} completely specify
h(t), and m and n limit the number of these parameters (model order) [Ljung, 1999]. For a
fixed model order, the parameters are closed form solution. The model order is
determined by minimizing the Minimum Description Length (MDL) criterion introduced
in Chapter 2. By definition, the estimated h(t) represents the (scaled) ABP response to a
single, solitary cardiac contraction.

Next, ris determined over the interval of h(t) ranging from two to four seconds

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

h(t) = Ae'Vr + w(t). (3.2)

(This time interval was established empirically by almost always observing a pure
exponential decay in h(t) over this period in the hemodynamic data sets studied herein.)
The parameters A and rare estimated through the least squares minimization of the
unmeasured residual error w(t). This optimization problem is solved in closed-form by
log transformation of h(t) [Ljung, 1999]. In theory, accurate determination of the
Windkessel time constant ris achieved by virtue of h(t) coupling the long time scale or
beat-to-beat variations in x(t) to y(t). That is, the technique is not just trivially
extrapolating the ABP waveform at the end of diastole.

Finally, CO is computed to within a constant scale factor equal to 1/AC by
dividing the time-averaged ABP with 2'. Note that the above mathematical steps can
easily be implemented in near real time with only a delay on order of a few seconds with

a standard home PC.

39

30 [ x(t) [mmHg] 150_ Y“) [mmHg]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

h(t)
PP
PP . 2 1+1
FP FPP] H1 PPH PF:
20 PH 1-5 100
_, 1 T ——> RH Rl R144
10r 0-5 i 50 r
00 2 4 6
o . 1R)" I?J [RM Time [3”] o . . . .
28 29 30 31 _ 28 29 30 31
Time [sec] C 0 0c Y(t) Time [sec]
1:

Figure 3.7 Illustration of identifying the time constant I from a peripheral ABP
waveform. FPP is pulse pressure of the filtered ABP (lowpass filter with cutting
frequency of 2Hz); R, onset time of upstroke of each ABP wavelet; j, beat number; x(t), a
constructed cardiac contractions signal; y(t), an ABP waveform; and h(t), an estimated

impulse response coupling x(t) to y(t). Then proportional CO is ratio of mean y(t) to r.

40

3.3 Technique Evaluation

To validate the technique, we applied it to invasive and non-invasive human data

and compared the results with corresponding reference CO measurements.

3.3.1 Invasive ICU Patient Data

The hemodynamic data utilized to evaluate the mathematical analysis technique
with respect to human invasive peripheral ABP waveforms were obtained from the
MIMIC (Multi-parameter Intelligent Monitoring for Intensive Care) database, which is
freely available from the PhysioNet website (www.physionet.org) and described in detail
elsewhere [Moody et al., 1996, 2001]. Briefly, this database includes 72 ICU patient
records, typically ranging from 24 to 48 hours in duration, which were archived from
patient monitors in the medical, surgical, and cardiac ICUs of the hospital formerly
known as the Beth Israel Hospital, Boston, MA. Each of these records consists of
continuous waveforms sampled at 125 Hz such as invasive peripheral ABP via radial
artery catheterization and surface ECG leads as well as one-minute trends such as
thermodilution CO, mean ABP (MAP), and heart rate (HR). 16 of the 72 patient records
were applicable to the present evaluation study, as they included radial ABP waveforms
and multiple, reference thermodilution CO measurements. Within each of these records,
CO was changing due to disease progression and therapy.

Based on these 16 MIMIC patient records, we created a data set for technique
evaluation as follows. First, we downloaded from these records all of the distinct, one-
rninute thermodilution CO measurements and six-minute contiguous segments of the

corresponding radial ABP waveforms (from 2.5 minutes preceding the one-minute CO

41

measurements to 2.5 minutes following these measurements). Then, we visually
examined each of the radial ABP waveforms and extracted the longest contiguous,
artifact-freed segment from each of these waveforms (see Discussion section). Finally,
we excluded from the study all radial ABP waveforms that were less than 5 minutes in
duration, had a significant linear trend (2 20 mmHg change), or represented the only
waveform segment within a patient record (as the technique estimates changes in CO). A
total of 101 pairs of simultaneous measurements of invasive radial ABP waveforms and
reference thermodilution CO from 15 ICU patients [ten men and five women; age: 67 i
12 yr (meaniSD)] remained for technique evaluation. Table 3.2 summarizes the clinical

class and hemodynamic data for each of these patients.

3.3.2 Non-Invasive Human Experimental Data

The hemodynamic data utilized to evaluate the technique with respect to human
non-invasive peripheral ABP waveforms were obtained from previous experiments
designed to address different specific aims and are described in detail elsewhere [Elstad
et al., 2001]. Here, we briefly present those aspects of the experiments that are relevant
to the present study.

Ten healthy human volunteers [five men and five women, age: 25 i 4 year
(meaniSD)] participated in the experiments. Each subject was instrumented for non-
invasive measurement of peripheral ABP, instantaneous CO, and other cardio-respiratory
signals. The peripheral ABP waveform was measured with a finger-cuff PPG system
(2300 F inapres Continuous Blood Pressure Monitor, Ohmeda; Englewood, CO), while

instantaneous CO was measured according to a previously described Doppler ultrasound

42

technique [Eriksen et al., 1990] implemented by an expert. Specifically, aortic blood
velocity was measured with a bi-directional ultrasound Doppler velocimeter (CF M-750,
GE Vingmed; Horten, Norway), which was operated in pulsed mode at 2MHz with the
hand-held transducer placed on the suprastemal notch. The area of the rigid aortic ring
was determined in a separate session by parastemal sector-scanner imaging (CFM-750,
GE Vingmed). Instantaneous CO was then calculated via the product of the measured
instantaneous maximum blood velocity and the area of the aortic valve orifice.

Each instrumented subject was studied on two separate days before and after the
administration of atropine (0.04 mg/kg) and/or propranolol (14.6 mg) under different
postures to vary the experimental conditions. For each experimental condition,
approximately six-minute intervals of the non-invasive measurements were continuously
recorded at a sampling frequency of 50 Hz. In the present study, we specifically
analyzed the digitized recordings from the following six experimental conditions: 1)
supine, baseline, 2) supine, propranolol, 3) supine, propranolol+atropine, 4) 30° upright
tilt, baseline, 5) 30° upright tilt, atropine, and 6) 30° upright tilt, atropine+propranolol.
Based on these non-invasive recordings, we created a data set for technique evaluation
following a similar procedure as the invasive study. First, we visually examined each
non-invasive finger ABP waveform and instantaneous CO waveform and extracted the
longest contiguous, artifact free segment from each waveform. Then, we excluded from
the study the four instantaneous CO waveforms that were less than one minute in
duration and the three finger ABP waveforms that were less than five minutes in duration
or had unreasonably hi gh-pressure values (see discussion). Finally, the reference CO

value corresponding to each of the remaining instantaneous CO waveforms was

43

determined by computing its time-average. A total of 57 pairs of simultaneous
measurements of artifact-free, non-invasive finger ABP waveforms and reference
Doppler ultrasound CO values from the ten healthy subjects remained for technique

evaluation. Table 3.3 summarizes the hemodynamic data for each of the subjects.

3.3.3 Data Analysis

Before applying the technique to the invasive radial ABP waveforms, we resampled
ABP from 125Hz to 90Hz. In Eq. 3.1, we empirically chose the maxim orders m and n as
15. For the non-invasive finger ABP waveforms, we chose the maxim orders m and n as
10 due to the lower sampling frequency (50Hz).

After applying the mathematical analysis technique to all of the invasive and non-
invasive peripheral ABP waveforms in the two human data sets, we quantitatively
compared the resulting, proportional CO estimates with their reference, absolute CO
values in each data set as follows. First, we scaled the proportional CO estimates to have
the same mean value as the corresponding reference CO in each patient/subj ect. Then, we
pooled the data together from all the patients/subj ects in each data set and computed the
root-mean-squared-normalized error (RMSNE) of the calibrated CO estimates
(normalized by their reference CO values and given in percent) as a metric for
comparison. (This metric indicates the ability of the technique to measure changes in CO
from its mean value within an individual.) We also computed the correlation coefficient
(p) between the pooled CO error and the corresponding CO, MAP, TPR, and HR values
in each data set to determine the extent to which the hemodynamic conditions affected

the performance of the technique.

3.4 Evaluation Results

Tables 3.2 and 3.3 respectively summarize the results of evaluating the
mathematical analysis technique based on the invasive and non-invasive human
hemodynamic data sets. These results indicate that the technique as applied to invasive
radial ABP waveforms was in strong agreement with thermodilution measurements with
an overall CO RMSNE of 15.3% in 15 ICU patients, while the technique as applied to
non-invasive finger ABP waveforms was in equally strong agreement with Doppler
ultrasound measurements made by an expert with an overall CO RMSNE of 15.1% in ten
healthy subjects. Figs. 3.8 and 3.9 provide visual examples of the correspondence
between the once calibrated CO estimates and their reference CO values in three
individuals from each data set. Moreover, as indicated in the table captions, the CO error

was only mildly correlated with MAP and even less correlated with CO, HR, and TPR.

45

Table 3.2: Summary of the intensive care unit patient records and CO estimation results

of the invasive human hemodynamic data set. The technique was applied to 101 invasive

radial ABP waveform segments from 15 patients achieved an overall CO root-mean-

squared-norrnalized error (RMSNE) of 15.3% with respect to reference thermodilution

measurements. Moreover, the CO error here was essentially uncorrelated with CO (p=-

0.14) and heart rate (HR; p=0.04) and only mildly correlated with mean ABP (MAP;

p=0.4l) and TPR (p=0.38).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NUMBER
PATIENT CLINICAL OF CO MAP TPR HR CO
RECORD CLASS COMPA- RANGE RANGE RANGE RANGE RMSNE

RISONS [UMIN] [MMHG] [PRU] [13PM] {/o]

041 Bleed 2 8.5-9.5 74-81 0.5-0.6 78-104 0.5
055 Resp. failure 7 3.9-5.2 78-106 0.9-1.4 88-106 6.9
281 NA 4 3.7-4.9 94-99 1.2-1.6 100-114 6.8
410 Sepsis 7 4.3-9.4 74-97 0.6-1 .1 60-94 22.3
411 Resp. failure 6 3.2-4.6 84-94 1.2-1.7 50-61 14.4
451 CHF 5 4.1-5.8 51-58 0.5-0.9 74-84 15.0
453 Post-op valve 12 3.4-4.8 60-79 0.9-1.3 50-89 10.7
454 Post-op valve 5 3.7-4.8 67-74 0.9-1 .1 49-70 5.4
456 Post-op CABG 8 3.8-8.5 57-100 0.6-1 .0 67-108 22.5
474 NA 5 3.8-4.4 72-79 1.1-1.2 86-94 15.6
476 Post-op CABG 6 4.2-4.6 58-71 0.8-0.9 90-105 1 1.2
477 Post-op CABG 6 4.5-6 54-75 06-08 79-11 1 10.6
480 Post-op CABG 6 5-6.7 63-75 06-08 85-112 1 1.1
484 NA 9 5.1-7.5 62-78 06-08 79-96 12.4
485 NA 13 2.9-4.7 69-87 1.0-1.8 94-126 23.0
TOTAL 101 2.9-9.5 51-106 0.5-1.8 49-126 15.3

 

 

 

 

 

 

 

 

46

 

Patient Record 055 Patient Record 453 Patient Record 484

 

 

 

 

 

 

6r 5.5. 10-
§5.5» 5 9
5. o
O 8» o
O o
o 5— 4.5» o
E O 7 0°
£45 4 0
fi . O O a O 0 0°
0 0 6
°5 0
:8; 4» 3.5- o 5
a .
.§
‘5
was» 3 4_
3 - . - 2.5 1 4 . 3 . .
3 4 5 6 3 4 5 5 1o

Thermodilution CO [lein]

Figure 3.8 Visual examples of CO estimation results in three intensive care unit (ICU)
patients. For each patient, the estimated and calibrated CO is plotted against

corresponding thermodilution measurement.

47

Table 3.3: Summary of the healthy young adult records and CO estimation results of the

non-invasive human hemodynamic data set. The technique was applied to 5 7 non-

invasive finger ABP waveform segments from ten healthy young adults achieved an

overall CO root-mean-squared-norrnalized error (RMSNE) of 15. 1% with respect to

reference Doppler ultrasound measurements made by an expert. Moreover, the CO error

here was essentially uncorrelated with CO (p=-0.17), TPR (p=0.10) and heart rate (HR;

p=0.19) and only mildly correlated with mean ABP (MAP; p=0.37).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CO MAP TPR HR CO
SUBJECT NUMBER OF
RANGE RANGE RANGE RANGE RMSNE
RECORD COMPARISONS
[L/MIN] [MMHG] [PRU] [BPM] [%]
LD 5 3.6-6.8 82-128 1.0-1.9 43-108 13.0
WP 6 4.3-63 68-93 0.7-1.1 60-113 16.9
CG 6 4.5-7.7 75-118 09-13 48-98 20.2
JE 6 4.5-8.2 85-125 09-14 51-135 14.6
AB 6 3.5-5.3 79-124 1.2-1.5 32-72 18.3
DL 4 3.5-4.7 92-104 1.2-1.9 60-88 14.8
GB 6 4.6-7.2 65-83 0.6-1.0 56-126 13.3
LB 6 4.3-7.1 70-95 0.8-1.1 47-100 9.0
MR 6 4.4-6.8 75-102 08-12 50-115 12.1
NB 6 3.7-8.4 72-116 0.8-1.5 48-99 15.3
TOTAL 57 3.5-8.4 65-128 (1.6-1.9 32-135 15.1

 

48

 

Subject GB Subject LB Subject MR

 

 

 

 

 

 

9 9- 8
3 0
E8» 0 7-
E o
.3. 7-
07- 6
o o
6.
E o
86 5
.9
8 o 5*
'85 O 4.
o
E
4- 3r 3
3 . r 3 2 . I . 2 r . .
4 6 8 2 4 6 8. 2 4 6 8

Doppler Ultrasound CO [lein]

Figure 3.9 Visual examples of CO estimation in three healthy subjects. For each patient,
the estimated and calibrated CO is plotted against corresponding DOppler ultrasound

measurement.

3.5 Discussion

In summary, we improved and further evaluated a previously developed CO
monitoring technique from a peripheral ABP waveform. The uniqueness of the technique
lies in the analysis of the peripheral ABP waveform over long time scales in which the
confounding effects of wave phenomena are attenuated. Here, to better reduce the short-

terrn reflection effect on the system identification, the pulse train representing the cardiac

49

contractions (input of the system identification) was weighted by the pulse pressure of the
filtered ABP waveform; while in our previous technique, the pulse train was weighted
simply by the pulse pressure of the original ABP waveform. We evaluated the technique
in humans based on previously published invasive and non-invasive hemodynamic data
sets. With the former data set, we compared the application of the technique to invasive
radial ABP waveforms with reference thermodilution measurements in 15 ICU patients in
which CO was changing due to disease progression and therapy. With the latter data set,
we compared the application of the technique to non-invasive finger ABP waveforms
with reference Doppler ultrasound measurements made by an expert in 10 healthy
subjects during pharmacological and postural interventions. We report an overall CO
estimation error of about 15% with respect to each of these human data sets (see Tables
3.2 and 3.3 and Figs. 3.8 and 3.9). Although the evaluations described herein were
retrospective, it is noteworthy that neither of these data sets was designed for the

evaluation of our technique or any other pulse contour analysis technique.

3.5.1 Potential Sources of CO Error

The CO errors reported here could be partly explained by inadequacies in the
quality and accuracy of the hemodynamic measurements within the studied invasive and
non-invasive data sets. However, as described below, we excluded from the study all
data segments of poor quality (e. g., corrupted by significant noise artifact) so as to
benchmark technique performance. On the other hand, nothing could be done in this
retrospective study to improve upon the accuracy of the measurements, which is largely

intrinsic to the employed transducers.

50

The radial ABP waveforms in the invasive data set were measured with generally
accurate, intra-arterial catheters. However, in the MIMIC database upon which this data
set was based, ABP waveform artifact was sometimes present. The artifact may have
been due to, for example, patient movement, arterial line flushing, catheter obstruction,
loss of signal, and proximal ABP cuff inflation. We excluded from the study all radial
ABP waveforms that were significantly corrupted by such artifact (~11% of the available,
simultaneous pairs of radial ABP waveforms and thermodilution measurements). While
we identified ABP artifact here by visual means, it may be possible to automatically and
reliably detect ABP artifact in real time (e. g., with a simultaneous surface ECG
measurement based on an algorithm recently introduced by long et al. [2004]) so as to
warn the clinician that the CO estimate derived from the ABP analysis may not be valid
or preclude the output of such a CO estimate. Note that, for reasons described above, we
also excluded from the study all radial ABP waveforms with linear trends of 220 mmHg
(~13% of the available, simultaneous pairs of radial ABP waveforms and thermodilution
measurements).

In contrast to the radial ABP waveforms in the invasive data set, it was not
possible to assess the quality of the corresponding thermodilution measurements.
However, the error in clinical thermodilution measurements is known to be in the 15-20%
range [Levett et al., 1979; Stetz et al., 1982]. Assuming such an error, Critchley et a1.
argued that a new CO measurement method should be accepted as an alternative to
thermodilution provided that their limits of agreements are within i30% [1999]. We note
that the level of agreement between our technique and thermodilution measurements

from 15 ICU patients is essentially in this range (see Table 3.2 and Fig. 3.8).

51

The non-invasive hemodynamic data utilized in this study were Obtained from
controlled experiments, and none of the non-invasive finger ABP waveforms were
excluded from the study due to noise artifact. However, two non-invasive finger ABP
waveforms were excluded from the study because of unreasonably high-pressure levels.
This artifact may have been due to an upward drift in finger ABP caused by prolonged
application of cuff pressure [Ristuccia et al., 1997]. Note that this finger-cuff
photoplethysmography artifact may be attenuated or eliminated by intermittent finger
exercise [Ristuccia et al., 1997] or with the currently available Portrapres system, which
alternates the application of cuff pressure between different fingers.

Although artifact in the non-invasive finger ABP waveforms was not a significant
factor here, the intrinsic level of accuracy of the employed F inapres system may have
affected our results. In a review of F inapres technology, Irnholz et a1. gathered 43
previous studies comparing the F inapres system with intra-arterial or non-invasive,
discrete ABP measurements and reported that the systolic and mean pressure levels of the
Finapres system were not within the limits of accuracy suggested by the American
Association for the Advancement of Medical Instruments [Imholz et al., 1998]. On the
other hand, Omboni et al. showed that the F inapres system and radial artery
catheterization produce similar beat-to-beat (mean) ABP fluctuations [Omboni et al.,
1993]. That is, while the Finapres system distorts the peripheral ABP waveform over
short time scales, it may have little effect on the waveform over longer time scales. Thus,
since the technique analyzes the ABP waveform over long time intervals, the inherent

inaccuracies of the F inapres system may not have been a major contributor to the CO

52

error reported herein. However, we cannot confirm this possibility, because simultaneous
intra-arterial ABP recordings were not available.

The reference Doppler ultrasound measurements in the non-invasive data set were
made by an expert, and only four of these CO measurements were excluded from the
study due to poor signal quality. Despite the generally excellent signal quality, the
assumptions underlying the Doppler ultrasound technique could have been partially
violated thereby affecting our results. These assumptions include the following: 1) the
velocity profile in the aortic valve orifice is rectangular and this velocity is conserved as
the central maximum velocity of a jet 3-4 cm downstream; 2) the insonication angle is
20°; and 3) the aortic valve is circular [Eriksen and Walloe, 1990]. However, these
assumptions are likely to have little effect on the accuracy of the measured relative
changes in CO. Since our technique is designed to measure relative changes in CO and
we evaluated it here as such (see Statistical Analysis section), we believe that the Doppler
ultrasound measurements serve as a reasonably accurate reference here (i.e., at least as
accurate as standard thermodilution measurements).

Other potential sources of the CO errors reported here are any violations to the
assumptions upon which the technique is based. These assumptions include the
following: 1) AC is constant within each individual; 2) peripheral venous pressure is
negligible with respect to ABP; 3) ABP exceeds the critical closing pressure; and 4) the
time constant governing arterial viscoelastic effects is negligible with respect to the
Windkessel time constant [Mukkamala et al., 2006]. The first of these assrunptions is
perhaps the most controversial, since there is currently no generally accepted, gold

standard method for measuring in vivo AC. Nevertheless, we believe that in vivo AC

53

must be nearly constant over a wide hemodynamic range in at least some animals based
on the success of the pulse contour analysis of Bourgeois et al. and Osborn et a1. with
respect to canine central ABP waveforms [Bourgeois et al., 1974; Osborn et al., 1968]
and the present mathematical analysis technique with respect to swine peripheral ABP
waveforms [Mukkamala et al., 2006]. We are unaware of any existing in vivo data
likewise demonstrating constancy of the human AC. However, Hallock and Benson did
show that, although the compliance of excised human aortas of various ages at autopsy
(ranging from young adults to the elderly) decreased with increasing pressure, in vitro
aortic compliance could be approximated as constant over a wide pressure range [Hallock
and Benson, 193 7]. If in vivo AC sharply changed in the opposite direction of MAP
within each individual record of our study, then our technique would have grossly
overestimated CO at high MAP levels and underestimated CO at low MAP levels (i.e., a
strong, positive correlation between CO error and MAP). Although the correlation
between CO error and MAP is positive, the degree of correlation is mild (see above),
suggesting that in vivo AC within each of thel 5 ICU patient and ten healthy young adult

records may have been approximately constant.

3.5.2 Comparison to Intra-Beat Pulse Contour Analysis Techniques

In a previous paper introducing our mathematical analysis technique [Mukkamala et
al., 2006], we used signal-to-noise theory to argue that estimating the average Windkessel
time constant I (and thus average, proportional CO via Ohm’s law) by analyzing a
peripheral ABP waveform over time intervals greater than a cardiac cycle should be more

accurate than analyzing the ABP waveform over individual cardiac cycles and then

54

averaging the beat-to-beat results. To support this theoretical argument, we fitted
complex exponentials function(s) to individual diastolic decay intervals of swine
peripheral ABP waveforms to estimate r on a beat-to-beat basis, averaged the resulting
individual I estimates, and then computed average, proportional CO via Ohm’s law. The
best result we were able to achieve with this intra-beat analysis was an overall CO
RMSNE that was 52% larger than that obtained by our technique. We repeated this intra-
beat analysis with respect to the human invasive and non-invasive hemodynamic data sets
here and obtained overall CO RMSNEs that were respectively 23% and 81% higher than
those obtained by our technique. (Note that one possible reason that this intra-beat
analysis is much less effective with respect to the non-invasive hemodynamic data set is
that, as described above, the non-invasive ABP waveforms may suffer from high
frequency distortion due to the employed Finapres system). We believe that these
comparative studies confirm the theory that important information is indeed present in
beat-to-beat ABP variations and that analysis of these subtle variations leads to improved
average, proportional CO estimation in practice. However, we note that future studies
should also be conducted to compare our technique with the recent intra-beat techniques
of [Wesseling et al., 1993] and [Linton et al., 2001], which also require a single

peripheral ABP waveform for analysis.

3.5.3 Limitations of the Long Time Interval Analysis Techniques
Two limitations of the current form of the long time interval analysis technique are:
1) beat-to-beat CO monitoring is not feasible and 2) artifact is a more significant problem

(as compared to beat-to-beat pulse contour analysis techniques such as the

55

aforementioned). With respect to the former limitation, we feel that attempts to improve
the accuracy of average, proportional CO estimation, even at the cost of temporal .
resolution, are worthwhile from a clinical point of view. For example, although many
previous pulse contour analysis techniques can offer beat-to-beat proportional CO
monitoring, they have still not been widely adopted in clinical practice presumably due to
accuracy concerns. Moreover, automatic estimation of proportional CO at intervals on
the order of seconds but representing the last six-minutes (i.e., boxcar moving average)
would represent a significant improvement upon discrete, operator-required
determinations of CO by the clinical thermodilution method (assuming similar accuracy).
With respect to the second limitation, the requirement of approximately six-minute
intervals of relatively artifact-free ABP waveforms does not substantially limit the
practical applicability of the technique. For example, only ~11% of the invasive radial
ABP waveforms from the real world MIMIC database were discarded in our study due to
artifact. Moreover, the six-minute intervals of analysis may be reduced to smaller
intervals (e. g., one minute) without materially affecting the accuracy of the estimates

(e. g., CO RMSNE of 15.1% in the invasive hemodynamic data set and 15.7% in the non-
invasive hemodynamic data set). Future formal studies are needed to determine the
minimum interval for analysis that does not significantly compromise the accuracy of the

technique.
3.5.4 Limitations of the Human Evaluation Study

In the invasive hemodynamic data set, CO was naturally changing within each ICU

patient record due to disease progression and therapy. Typical ICU therapy is known to

56

include medications such as dobutanrine, dopamine, intravenous fluids, and nitroprusside
(i.e., both cardiac and vascular interventions) [Marino, 1998]. However, since time-
stamped annotations were not available here, we were not able to evaluate the technique
in the ICU patients with respect to each of these common therapeutic interventions. In
contrast, in the non-invasive hemodynamic data set, CO was changing in each healthy
subject due to precisely known interventions of atropine, propranolol, and/or a 30°
upright shift in posture. As described above, the CO RMSNEs were largest during the
double blockade conditions, presumably because beat-to-beat HR variability was totally
abolished. While vascular changes (TPR and fluid shifts) occurred reflexively upon
administration of atropine and propranolol as well as via the postural shift (see Table 2),
we were not able to test the technique with respect to non-invasive ABP waveforms
during interventions that directly act on the vasculature (e. g., phenylephrine,
nitroprusside). Finally, since the reference thermodilution CO in the invasive
hemodynamic data set could not be assumed to be valid during unsteady conditions (e. g.,
ABP waveform segments with significant trends) and the non-invasive ABP waveforms
were only recorded during steady conditions (see above), we were not able to evaluate
the technique in humans during unsteady conditions (i.e., rapid changes in CO).
However, we have previously shown that the technique performs quite accurately during
unsteady conditions in swine instrumented with aortic flow probes measuring
instantaneous flow [Mukkamala et al., 2006]. Moreover, in the present human study, we
were at least able to show that the technique performed approximately the same
regardless of the size or direction of the CO change, as the correlations between the CO

error and ACO and |ACO| were only mild (see above).

57

3.5.5 Potential Applications of the Mathematical Analysis Technique

Our technique mathematically analyzes a single peripheral ABP waveform over
long time intervals in order to continuously (i.e., automatically and without the need for
an operator) measure CO to within a constant scale factor. The technique may therefore
be utilized to quantitatively monitor relative changes in CO. The proportional CO may
be calibrated, if desired, with a single, absolute CO measurement (e. g., thermodilution).
For normal individuals, it may be possible to determine the proportionality constant from
a nomogram. However, we believe determination of the proportionality constant is
unnecessary in the context of continuous monitoring in the acute setting in which only
CO changes are clinically relevant.

The results of this retrospective human evaluation study indicate that the technique
may be sufficiently accurate in terms of estimating relative changes in CO with respect to
invasive radial ABP waveforms from critically ill patients and non-invasive finger ABP
waveforms from healthy subjects. With further mathematical analysis deve10pment
(including the incorporation of an automated artifact detector) and successful prospective
testing, the technique may potentially be applied to continuously monitor CO in the acute
setting. The most prominent such application is in critically ill patients in the ICU and
Operating and recovery rooms. In critically ill patients instrumented with both puhnonary
and radial artery catheters, the technique could be calibrated with a single thermodilution
measurement to permit subsequent continuous monitoring of absolute CO. In the
numerous critically ill patients with only radial artery catheters installed (see above), the
technique could provide continuous, quantitative monitoring of relative changes in CO.

Other such applications in which non-invasive peripheral ABP transducers would be

58

most appropriate include patients in the emergency room and the hospital ward, trauma
patients in transport, as well as soldiers in combat. The human evaluation study

described herein represents an initial step towards the realization of such applications.

59

CHAPTER 4
CONTINUOUS MONITORING OF CARDIAC OUTPUT AND LEFT
ATRIAL PRESSURE FROM A PULMONARY ARTERY PRESSURE

OR RIGHT VENTRICULAR PRESSURE WAVEFORM

4.1 Background

Left atrial pressure (LAP) generally indicates the blood pressure attained in the left
ventricle during the cardiac filling phase. LAP can be utilized together with CO to
distinguish the two types of cardiovascular diseases. When both CO and LAP decrease
over time period, the disease should be circulatory problem such as hemorrhage; while
when CO decreases and LAP increases, the disease should be a cardiac problem due to,
for example, a heart attack. In the ICU, LAP is approximated with the pulmonary
capillary wedge pressure (PCWP), which is also known as the puhnonary artery wedge
pressure (PAWP) or the pulmonary artery occlusion pressure (PAOP). In order to
measure PCWP, a puhnonary artery catheter (PAC, see Chapter 3) is wedged in a branch
of the pulmonary artery and then a balloon is inflated at the tip of the catheter [Swan et
al., 1970]. The resulting non-pulsatile pressure tracing is the PCWP (Fig. 4.1). Under the
proper circumstances that a static column is created between the PAC tip and the left
atrium, this pressure approximately reflects the mean LAP. This approximation is correct
only if the PAC tip is in the proper lung zone and no vascular obstruction, such as
pulmonary vein stenosis, occurs downstream. In fact, the measurement of PCWP is

associated with a high incidence of technical problems due to partial wedging, over

60

inflation of the balloon, lack of fluid column continuity between the transducer and the
vascular lumen, and etc [Morris et al., 1984]. Moreover, recent researches has indicated
that the inadequate knowledge of physicians (and nurses) in using this technique might
lead to incorrect interpretation of PCWP [Marik etal., 1998]. Even if the PCWP
measurement is proper, it can only be obtained every few hours, as it requires an operator
to inflate the balloon. Therefore, PCWP has ‘been criticized due to the apparent failure to
demonstrate improvements in patient outcome and risks associated with its use for a long
time [Pinsky and Vincent, 2005].

As a result, physicians may resort to, for example, crude estimates of LAP through
puhnonary artery diastolic pressure (PADP) in order to obtain immediate feedback about
patient status. Although LAP may be measured continuously by direct catheterization of
the left heart, this procedure is too invasive and risky for clinical use. A few non-invasive
methods have been suggested for estimating LAP through physical signs, cardiac
imaging, and the Valsalva maneuver [McIntyre et al., 1992]. However, these methods are
evidently insensitive and inaccurate [Chakko et al., 1991; Diamond et al., 1993;
Stevenson et al., 1989]. Moreover, each of these methods can only provide discrete
estimates of LAP. Although the empirical techniques have been developed to monitor
LAP using Doppler ultrasound [Nishimura and Tajik, 1997; Dokainish et al., 2004], they
are proved to be not accuracy. A clinically usable technique for continuous LAP
monitoring is therefore needed to permit more optimal therapy.

In fact, with the PAC, pulmonary artery pressure (PAP), right atrial pressure and
right ventricular pressure (RVP) can be measured reliably and continuously (i.e.,

autonomous operation) via fluid-filled systems attached to external pressure transducers.

61

Balloon Balloon
inflated deflated

45

35
30

 

 

 

 

25 ii 17

 

 

 

 

2° ‘ PCWP
15 -

10-

PAP [mmHg]

 

 

420 425 430 435 440 445
Time [see]
Figure 4.1 Illustration of pulmonary capillary wedge pressure (PCWP) measurement.

PCWP is obtained by inserting pulmonary artery catheter into puhnonary artery, and

inflating its balloon at a branch of artery to occlude blood flow.

 

 

26 -
zo- l \’“"":.21'.‘{.?.""’ \ I
l \ \ l
.3 l l \ \ l
:r: j l \ ' l l
E 15 l / I \ I‘ ; | f‘ l
o \ \ \ l
5 \ I \ \ '
re 10 - \ \
8
i
5 .
Right Ventricular
o L Precaurq .
193 193.6 194 194.6
Time [see]

Figure 4.2 Illustration of construction of puhnonary artery pressure (PAP) from right
ventricular pressure (RVP) during ejection phase. Thin line, RVP; dash line, actual PAP;

thick line, RVP during ejection phase, which is used as a surrogate of PAP.

62

If PAP or other pressure measurements could be utilized to monitor LAP as well as CO,
this continuous monitoring technique could help doctors to, for example, assess the
effects of fluid and pharmaceutical interventions and be quickly altered to possible
complications. A few intra-beat techniques to monitor CO from PAP waveform (e. g.,
[Tajimi et al., 1983]). But these techniques faced the similar difficulty as technique
monitoring CO from peripheral ABP: distortion caused by the complex vascular structure
and mechanical character. Moreover, to our knowledge, no technique has yet been
developed to continuously monitor both CO and LAP from a PAP waveform. In Chapter
3, we have introduced a minimally invasive or non-invasive technique for continuously
monitoring CO changes from a single peripheral ABP waveform. Here, we extend the
technique in order to monitor CO and LAP simultaneously from a single PAP waveform.
We can firrther extend the technique to RVP. The implanted devices, such as two-
lead pacemaker, can measure both LAP and RVP. Similarly to LVP and ABP (Fig. 2.4),
during the ejection period of the right ventricle, RVP and PAP waveforms are ahnost
overlapped as shown in Fig. 4.2 provided there is no stenosis of the pulmonary valve.
Thus, the PAP waveform during the ejection period may be approximated by the RVP
waveform and therefore the technique for estimating CO and LAP from PAP may be

extended to RVP.

4.2 Monitoring of CO and LAP from PAP

4.2.1 The Technique
Unlike the systemic arterial tree, pulmonary circulation is a low resistance system

with high bifurcation. In a person breathing normally, the alveolar wall capillaries

63

contribute up to 40% of the total resistance, the arteries about 50%, and the veins about
10% [Beme and Levy, 1998]. Pulmonary capillaries also contribute a large fraction of the
total pulmonary vessel compliance. These properties result in more serious wave
reflections (Fig. 4.3a). In addition, unlike right atrial pressure, LAP is a significant
fraction of PAP due to the low resistance of the puhnonary microcirculation. Despite
these complications, we assume the simple two-element Windkessel model (Fig. 4.3b) is
a valid representation of the behavior of pulmonary circulation over long time scales
greater than one cardiac cycle. Here, pulmonary vessel compliance (PVC) consists of the
compliances of all vessels (arteries, capillaries and veins), and pulmonary vessel
resistance (PVR) consists of the resistances of all vessels. We also assume that PVC is a
constant.

Thus, we have extended the technique in Chapter 3 to also account for the
contribution of LAP to PAP. The technique analyzes a PAP waveform over long time
intervals in order to determine the pure exponential decay to LAP that would eventually
result once pulsatile activity abruptly ceased. More specifically, the extension is to
estimate both the average LAP and the response of PAP-LAP to a single cardiac
contraction. Fig. 4.4 illustrates the technique, which is applied to a PAP waveform of
duration of approximately 6 minutes. This technique is employed analogously to the
technique in Chapter 3, except that the contributions of both a cardiac contractions signal

(x(t)) and average LAP to the PAP waveform (y(t)) are incorporated.

64

25:

PAP
20i i
; PVR
co we
11 LAP

115511555 115611565 1157
Time lsecl

 

PAP [mmHg]
5.

.5
CL

 

 

 

 

(a) (b)
Figure 4.3 PAP waveform (a) and pulmonary circulation Windkessel model (b). PVC,

pulmonary vessel compliance; PVR, pulmonary vessel resistance; CO, cardiac output;

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LAP, left atrial pressure.
x(t) [mmHg] y(t) [mmHg]
h(t) PP1+1
PP 1.1 PP]
20 . 1 20 .
PP“ ”’1 ”1+1
1° ’ 0'5’ 1' 10 \j Rj+1
R R]
1
0 RH - R] - R1211 °o 1\‘&=2 LAP 0
o 0.5 1 1.5 Time (sec) 0 0.5 1 1.5
Time (see) Time (sec)
co 0. my;

Figure 4.4 Illustration of identifying the time constant rand LAP from a puhnonary PAP
waveform. PP is pulse pressure; R, onset time of upstroke of each PAP wavelet; j, beat
number; x(t), a constructed cardiac contractions signal; y(t), an PAP waveform; and h(t),

an estimated impulse response coupling x(t) to y(t). Then proportional CO is ratio of

mean PAP (MPAP)-LAP to r.

65

First, a cardiac contractions signal is constructed by formation of an impulse train.
Each impulse is located at the R-wave of a simultaneous surface electrocardiogram
(ECG) measurement and has unity area.

Second, the PAP waveform segment (y(t)) is fitted according to the sum of an
unknown constant term and the convolution between an unknown impulse response (h(t))
and the constructed cardiac contractions signal (x(t)). That is, the constant term and h(t)
are estimated so as to permit the best fit or prediction ofy(t) in the least squares sense.
The estimated constant term represents the average LAP, while the estimated h(t) is
defined to represent the PAP-LAP response to a single cardiac contraction. The impulse
response h(t) and average LAP are specifically estimated with the following

autoregressive exogenous (ARX) input equation with constant term c:
y(t)=c+2aky(t—k)+Zbkx(t—k)+e(t), (4.1)
k=1 k=l

where e(t) is the unmeasured residual error, {al., 6;.) are unknown parameters, and m and
n limit the number of these parameters (model order) [Ljung, 1999]. For a fixed model
order, the parameters including c are estimated fi'om x(t) and y(t) through the least-
squares minimization of e(t), which has a closed-form solution [Ljung, 1999]. With the

estimated parameters, average LAP is computed as follows:

LAP=——
1..

, (4.2)

Ma ..

at

r
ll

where " indicates estimates.

66

Next, r is computed similarly as in Chapter 3. Finally, proportional CO may be
computed by dividing the time-averaged PAP-LAP with r and calibrated with
thermodilution measurements.

We developed a new model order selection algorithm. Basically, we search the best
model order from a set of candidate orders within a pre-defined range by analyzing the
relationship between the mean square error (MSE) of the estimation and the model order.
The estimation MSE is equal to ||e||2/N, where e is the residual error in Eq. 4.1, N is the
length of the signals. As described in Chapter 2, the estimation MSE is a monotonically
decreasing function of model order, while the decreasing speed of MSE becomes slower
as the model order increases. Irnportantly, at a certain model order (knee), the decreasing
speed dramatically becomes very slower. We regard this model order as the true model
order. This model order selection criterion is based on the fact that initially the MSE
decrease is caused by minimizing the estimation error due to the incompleteness of the
estimation model; while after the model order is greater than the true model order, the
MSE decrease is caused by minimizing the estimation error due to the noise.

Specifically, the best order is obtained as follows (Fig. 4.5). First we plotted the
estimation MSE=||e||2/N against the model order (r). Next, for each order r, we fit the
curve with two straight lines intercepted at the point (r,P,). The slopes of the two lines
and the value of P, are chosen optimally to fit the curve best using the minimal square
error criterion. The mean square error of this fitting is f,.. Finally, among the candidate
model orders, the model order m with the minimum fitting error, fm, is selected as the true

model order. In addition to the knee selection criterion, we also constrained that the

67

estimated h(t) must be positive and finite after its peak value, and the estimated LAP

must be greater than zero as well as smaller than PADP.

   
   
  

Best Fitting Lines
( r = m )

Fitting Lines
( r = i )

(m, Pm)

 

P (MSE of Estimation) [mmng]

 

 

 

 

r ( Model Order )

Figure 4.5 Illustration of the “knee” order selection algorithm. The solid line is the
estimation mean square error (MSE) of Eq. 4.1 plotted against the MA model order (r).
The two dash lines are two fitting lines at r=i and r=m respectively. (i, Pi) and (m, Pm) are
interceptions of the fitting lines. Because the fitting error at r=m is minimum (could be

seen from the plot), the true model order is m.

68

4.2.2 Technique Evaluation

We evaluated this technique with respect to puhnonary artery catheterization data
from the MIMIC database (see Chapter 3). We created a sub-database based on 8 patient
records including both PAP waveforms and multiple CO measurements and 5 patient
records including both PAP waveforms and PCWP measurements as follows.

Step 1, we downloaded all of the one-minute thermodilution CO values as well as
twelve-minute contiguous segments of the corresponding PAP waveforms (from 6
minutes preceding the beginning of the CO measurements to 6 minutes after the
beginning of the CO measurements). We downloaded the PCWP and PAP measurement
pairs in the same way.

Step 2, we visually examined each PAP waveform and extracted the longest
continuous segment of relatively artifact free data from each waveform. We discarded
those segments that were less than 5 minutes in duration. To this end, a total of 52 pairs
of simultaneous measurements of PAP waveforms and thermodilution CO from 8 patient
records, and 33 pairs of simultaneous measurements of PAP waveforms and PCWP from
7 patient records remain. For LAP estimation, we further evaluated the gold standard
PCWP measurements according to the next three steps.

Step 3, we looked through all of the PAP waveforms corresponding to the PCWP
measurements and eliminated those that apparently did not contain PCWP measurements
and those invalid measurements.

Step 4, we eliminated those PAP waveforms with misinterpreted PCWP
measurements. The timing of PCWP measurement is critical because intrathoracic

pressures can vary widely with inspiration and expiration and are transmitted to the

69

pulmonary vasculature. During spontaneous inspiration, the intrathoracic pressures
decrease (more negative); during expiration, intrathoracic pressures increase (more
positive). The situation is reversed by the positive pressure ventilation. In order to
minimize the effect of the respiratory cycle on intrathoracic pressure, measurements are
usually obtained at end-expiration, when intrathoracic pressure is closest to zero. To
simplify the measurement, the mean pressure during wedge measurement period could be
utilized as a rough approximation of end-expiratory pressure. Therefore, we used the
mean pressure during the wedging measurement period as a gold standard to evaluate the
PCWP measurement value in the database.

Step 5, we evaluated the PCWP measurements following the selection criteria
shown in Fig. 4.6. The physiologic principles behind the criteria are: a) mean PAP must
be higher than LAP to maintain uni-direction blood flow from right ventricle to left
atrium; b) under certain conditions, “a” and “v” waves on LAP must be visible on the
wedge pressure waveform while PAP pulses are not visible [ Morris et al., 1984;
Leatherman et al., 2003]. The possible reason of mean PAP<=PCWP may be the balloon
over-inflation. Pulmonary hypertension is defined as the condition that pulmonary artery
pressure higher than 25mmHg [Weir et al., 1998].

Finally, 26 pairs of simultaneous measurements of PAP waveforms and PCWP
from 5 patient records, as well as 52 pairs of simultaneous measurements of PAP
waveforms and thermodilution CO fiom 8 patient records, remained for the subsequent

evaluation of our mathematical analysis technique.

70

/\

 

Mean PAP < PCWP Mean PAP > PCWP
NOT Pulmonary Hypertension Pulmonary Hypertenelon
(lean PAP<25) (Mean PAP>251
PADP-PCWP>0 PADP-PCWP<0 PADP-PCWP>5 PADP-PCWP<5
Wedglng Preeeure Weaning Preeeure Wedglng Preeeure Wedglng Preeeure
Waveform NOT ~ PAP Waveform ~ PAP Wevet‘onn NOT ~ PAP Wavetonn - PAP
V / § *
Bad Good Bad Good Bad

Figure 4.6 PCWP measurement evaluation procedure. Pulmonary hypertension is
defined as the condition that puhnonary artery pressure higher than 25mmHg [Weir et al.,

1998].

We observed that, for the same patient record in the MIMIC database, the PAP
waveforms were generally much more corrupted than radial ABP waveforms, mainly
because the pulmonary circulation is a low pressure and low resistance system. In
addition, the phenomena of bifurcation and tapering are much more serious than the
arterial tree. Moreover, the periodic respiration waves on the PAP waveforms were more
significant, because the whole pulmonary circulation is in the thorax and as a result, the
intrathoracic pressure (negative pressure in thorax) has bigger effect on the PAP than
ABP. The movement of the catheter due to respiration also causes big artifact. This
corruption introduced a problem was that sometimes the beginning of the upstroke of
PAP was difficult to determine. In contrast, the “R” wave in ECG signal (measured in
most ICU patients) was easy to identify and therefore used as a surrogate for the

beginning of the upstroke of PAP. Then, the input (x(t)) in Eq. 4.1 was constructed as a

71

train of unit-area impulses located at the “R” waves. In fact, “R” wave represents the
beginning of the ventricular systole, which is a more valid representation of cardiac
contraction theoretically. For Eq. 4.1, we empirically set the AR order m to equal half of
the MA order n and searched the optimal MA order from 15 to 70.

We were then able to compare the technique as applied to each PAP waveform
segment with the corresponding thermodilution measurement or corresponding PCWP
measurement. After scaling the resulting proportional CO estimates to have the same
mean value as thermodilution in each patient record, we computed the CO RMSNE
(normalized by thermodilution measurement value and given in percent) as well as the
LAP RMSNE (normalized by PCWP and given in percent) as scalar metrics for

comparison.

4.2.3 Evaluation Results

Table 4.1 summarizes the study and shows that the technique achieved an overall
CO RMSNE of 14.6% and overall LAP RMSNE of 15.2%, which would be acceptable
levels of error according to Critchley [1998]. For comparison, LAP estimation via median
puhnonary artery diastolic pressure (PADP) resulted in an overall LAP RMSNE of
34.6%. Our estimated LAP values distribute evenly above and below the PCWP
measurements. Fig. 4.7a gives visual examples of the CO estimation results from 3
patients, in which the estimated and calibrated CO values are plotted against the
corresponding thermodilution measurements. Fig. 4.7b gives visual examples of the LAP

estimation results fi'om 3 patients, in which the estimated LAP values are plotted against

72

the corresponding PCWP values. We believe that these estimation results demonstrate the

feasibility of the technique.

Table 4.1: Summary of the intensive care unit patient records and CO and LAP

estimation results of the human hemodynamic data set. The technique was applied to

PAP waveforms from 9 patient records and achieved an overall CO root-mean-squared-

normalized error (RMSNE) of 14.6% with respect to 52 thermodilution measurements

and an overall LAP error of 15.2% with respect to 26 PCWP measurements. MPAP is

 

 

 

 

 

 

 

 

 

 

 

 

mean PAP.
PATIENT CO MPAP PCWP HR CO LAP
RECORD RANGE RANGE RANGE RANGE RMSNE RMSNE
[L/MIN] [MMHG] [MMHG] [BPM] [%] [%]
253 --- 23-41 13-26 54-72 --- 13.2
410 4.3-6.8 19-23 --- 60-90 7.6 ---
411 3.2-4.6 30-37 --- 58-60 13.8 ---
456 4.4-8.5 22-33 13-22 78-108 14.8 11.4
474 3.8-4.9 21-26 9-14 84-108 15.7 12.7
476 3.8-4.8 15-20 --- 102-108 13.8 ---
482 4-4.3 25-28 13 84 5 25.4
484 5.1-6.8 28-31 --- 84-96 7.4 ---
485 3.0-4.1 23-44 19-30 102-114 21.9 16.3
TOTAL 3.0-10.5 15-44 9-30 50-116 14.6 15.2

 

 

 

 

 

 

 

73

 

Patlent Record 410
7.5 -

Estimated 8: Calibrated CO [Umln]
- .. a: - a? .-

9’
or

 

 

Patlent Record 253

N (a)
U! 0

Estimated LAP [mmHg]
N
O

15.

 

 

io 30

12-

11-

10»

Patlent Record 456

 

 

2.....
24681012

Thermodilution CO [Umin]

 

 

(a)
Patient Record 456
25.
20- o
o
15-
10 . - .
10 15 20 25

PCWP [mmHg]

0?)

74

 

 

 

 

Patient Record 485
8r
5.5 -
5 .
O
4.5 -
4 ~ ‘8
3.5 -
3 » o
o
2.5 ~ 00
2 .
1.5 »
2 4 6
Patient Record 485
40 F
35 » o
30 - °
0 o
25 »
o
o
20 . 0 °
0
0
o
15 -
10 1 - J
10 20 30 40

Figure 4.7 Visual examples of CO and LAP estimation from three intensive care unit
(ICU) patients. (a), for each patient, the estimated and calibrated CO is plotted against
corresponding thermodilution measurement; (b), for each patient, the estimated LAP is
plotted against corresponding puhnonary capillary wedge pressure (PCWP)

measurement.

4.2.4 Discussion

We have developed a technique to continuously monitor CO and LAP by analyzing
a PAP waveform measured with a PAC over time intervals of about 6 minutes. This
technique is an extension of the technique in Chapter 3: continuous monitoring of CO
from a peripheral ABP waveform. We evaluated the technique in humans based on the
MIMIC database. With this database, we were able to compare the application of the
technique to PAP waveforms obtained from the PAC with reference thermodilution and
PCWP measurements in a total of a total of 9 ICU patients in which CO and LAP were
changing due to disease progression and therapy. We report an overall CO estimation
error of 14.6% and an overall LAP estimation error of 15.2% (see Table 4.1 and Fig. 4.7).

The technique is based on the assumption that the simple Windkessel model (Fig.

4.3b) is a valid representation of the long time scale behavior of the pulmonary

75

 

circulation. The model has two important assumptions. The model ignores ITP which
contributes more to PAP than ABP because PAP is much lower than ABP. The model
also assumes that the PVC is constant over time scales of hours to days. Any violation to
these assumptions may introduce CO and LAP estimation error. However, the
preliminary evaluation result implies that this assumption is valid at least to this data set.

The main advantage of this technique with respect to previous techniques for
monitoring CO from PAP is the additional capability of estimating the absolute value of
LAP. If the technique could estimate LAP accurately, then theoretically the CO
estimation would also be accurate. Thus, LAP estimation should actually help improve
the CO estimation.

Bourgeois et al may be utilized to compute the time constant I if the diastolic
pressure waveform of one specific cardiac cycle resembles an exponential decay. It
works well especially when part of the waveform is very clean while the overall quality is
corrupted. However, it is hard to evaluate the waveform quality and extract the good part
automatically.

As discussed in the introduction, the clinical measurement methods, thermodilution
and PCWP, have questionable accuracy due to their assumptions, potentially poor
operation, and misinterpretation. In the MIMIC data, many PCWP waveforms have large
periodic artifact caused by respiration (e.g., movement of catheter). We also found that
there were significant differences in the quality of PCWP measurements between
different patients. That is, the PCWP measurement quality was highly dependent upon
the experience of the operator, which is consistent with the findings of Morris et a1. For

example, for patient record 456, all of the wedging pressure waveforms were clean and

76

all of the PCWP values were measured at the end-expiration. However, for patient record
485, most of the wedging pressure waveforms were affected by the respiration and the
PCWP values were computed by simply taking the averages of the pressure during the
wedging period. Because the PCWP waveform can be observed on the PAP waveform,
we can at least to some degree assess its quality. This is an advantage of PCWP over
thermodilution.

The CO may be easily calibrated with thermodilution because a PAC has already
been used to measure PAP. However, the measurement of absolute CO value may be
unnecessary in the context of continuous monitoring in the acute setting in which only
CO changes are clinically relevant.

Comparison of the CO estimation results of this technique and the technique of
Chapter 3 is very interesting. As shown in Table 3.2 and Table 4.1, seven patients had
both radial ABP and PAP measurements and consisted of more than one thermodilution
measurement. In four patient records, 411, 474, 476, and 485 the estimation results from
the two techniques have equivalent accuracy. While in the other three patient records,
410, 456, and 484, the estimation of CO from PAP is much better than from ABP. This
comparison is surprising, because the ABP signals are much “cleaner” than the PAP
signals (e. g., patient record 456). However, we note that the comparison is based on a few
data points.

The result of this ICU patient evaluation study indicates that our mathematical
analysis technique for continuously monitoring CO and LAP may be sufficiently accurate

with respect to PAP waveforms measured from critically ill patients. With further

77

successful human testing, the technique may potentially be applied in ICU patients

instrumented with the PAC.

4.3 Monitoring of CO and LAP from RVP

4.3.1 The Technique

First, we rewrite the ARX model of Eq. 4.1 as follows:

m n
y(t) = c + Zakya — k) + Zbkxa — k) + w(t), (4.3)
k=l k=l

where, y(t) is the partially constructed the PAP waveform from RVP waveform (Fig. 4.2),
x(t) is a pulse train representing heart contractions, and c is reflective of the contribution
of LAP to PAP. The solution of this ARX model equation requires continuous
measurement of the PAP waveform. However, by constructing the PAP waveform from
RVP waveform, we can only obtain the PAP waveform during each ejection phase. Thus,
the {ak} and {bk} parameters cannot be identified, and the response of PAP to a single
ventricular contraction and the average LAP cannot be obtained.

Instead of the ARX model in Eq. 4.3, the relationship between x(t) and y(t) may be

represented by an output error (OE) model in Z transform as follows:

Y(z) = E5)— X(z) + c + W(z) , (4.4)
A(z)
where A(z) =1 — Z akz'l is the Z transform of the coefficients {ak} , B(z) = Z bkz'l is
k=l k=l

the Z transform of the coefficients {bk} , and W(z) is the Z transform of the unobserved
noise [Ljung, 1999]. Note that the coefficients {ak}, {bk}, and c are different from those

parameters in Eq. 4.3.

78

In order to solve the coefficients {0],}, {bk}, and c, we convert Eq. 4.4 to a linear
equation. Assuming for the moment that {a} is known, we establish a time series u(t)

with the Z transform as follows:

1 .

Then, by substituting Eq. 4.5 into Eq. 4.4, we obtain
Y(z) = B(z)U(z) + c + W(z) . (4.6)
The {bk} and c can then be estimated using the linear least square method.

To estimate the {ark} parameters, for the sake of simplicity, we assume that the poles
are composed of two components: a pure exponential decay (with time constant ti) and a
cosine (frequency f) attenuated exponentially (with time constant Q). The first component
is due to the long time scale behavior of the pulmonary vessels, which are represented by
the pulmonary vessel resistance (PVR) and compliance (PVC) as shown in Fig. 4.3b. The
second component represents faster wave reflection and inertial effects. Thus, in Eq. 4.4,
the order of A(z) is n=3, and Z transform of {a} is specifically:

A(z) = (1 — e_T/le—1)(l— 2e_T/12 cos(21th)z—l + €2th 2‘2 ) , (4.7)
where T is sampling period.

Therefore, in our estimation algorithm, we compute coefficients the {ca}, {bk} and c
as follows. First, we choose the values of r1, r; and fin Eq. 4.7 within a physiologically
reasonable range to compute A(z). Then, we compute u(t) using Eq. 4.5. Next, we
estimate {bk} and c in Eq. 4.6 using the linear least squares method by minimizing
||w(t)||2. LAP is given by c, and the time constant of the pulmonary artery is given by

r=m. We repeat these steps for a range of different time constants r; and r; and frequency

79

f. The true {ak}, {bk} and c are those parameters that result in the minimal least square

error in Eq. 4.6. The proportional CO is then computed as the convolution of h(t) and u(t)
divided by r.

Fig. 4.8 illustrates the technique, which is an extension of the estimation technique
of CO and LAP from a single PAP waveform. The difference here is that the PAP
waveform (y(t)) is known only during the ejection phase (thick solid line) while unknown
during the remaining time (thin dash line). The technique is basically to minimize the
estimation error of the PAP waveform constructed from the RVP waveform during the

ejection phase.

4.3.2 Pilot Evaluation of the Technique

To evaluate this technique, we conducted a pilot experiment in a female adult
anaesthetized dog on a ventilator. ECG, CO, aortic pressure, RVP, PAP and LAP were
measured and sampled at 1000Hz. The dog’s chest was open for measurements of CO
with an aortic flow probe and LAP with a catheter in the lefi atrium. These signals were
recorded during the following four interventions: baseline, high dose dobutamine, low
dose dobutamine, and volume depletion. Each intervention was ten minutes long. The
experiment was done carefully and the measured waveforms were artifact-free (F ig.4.2).

We applied the technique in Section 4.2 to the measured PAP waveform and the
extended technique in this section. For the RVP waveform, we performed the estimation
as follows. First, the RVP signal was decimated down to 100Hz. The beginning of
ejection period was determined by finding the maximum slope of the RVP waveform for

beat, which conflicts with the assumption based on. Finally we obtained the best

80

parameters {ak}, {bk} and c by minimizing the mean square error in Eq. 4.6.each beat
[Adamson et al., 2003]. We assumed that the ejection period ended at a time 0.02 seconds
after RVP reaches its peak value. The pulse train representing right ventricular
contractions is located at the beginning of ventricular systole with an area equal to the
ensuing pulse pressure of the constructed PAP.
The n, r; and f in Eq. 4.7 were selected within a physically valid range and

constrained with the criteria rl>r2 and f> I/n. A total of 20000 different sets of r1, 1') and
f were evaluated. We then removed those parameters whose resulting impulse response

was physiologically unreasonable, for example, the impulse response became after one

4.3.3 Results

The estimation results of monitoring CO and LAP from the PAP and RVP
waveforms in the dog experiment are shown in Fig.4.9. For each technique, the CO
estimation error is very small, and the LAP estimation is fairly accurate except one data
point. The results demonstrate the potential of the techniques to be utilized in either ICU
patients instrumented with PAC or patients with implanted devices for monitoring RVP.

However, much more future animal testing is needed.

81

x(t) [mmHg]

PPj-1 PP]

10’

 

Rl-1.Rl

 

ppl+1

R1”.

 

o o 0.5 1
Time (sec)

1.5

 

 

 

 

 

 

 

 

 

h(t)
1 .
0.5 . a:
0 IL \\
o 1 2
Time (sec)
CO at x(t)* h(t)
t

LAP

Y(t) [mmHg]

Haj-1”,} PPM
20» r‘.

\
II

|

l' l‘
l

II

t
I \ th

10 ii “i Rj+1

 

 

 

 

 

o 0.5 1 115
Time (see)

Figure 4.8 Illustration of identifying the time constant rand LAP from RVP. The h(t)

and LAP are obtained by minimizing the mean square estimation error of RVP of the

ejection phase. x(t), a cardiac contractions signal constructed from RVP; y(t), a systolic

PAP waveform (thick solid line) constructed from ejection phase of RVP; and h(t), an

estimated impulse response coupling x(t) to y(t).

82

16'

..L
O

 

 

 

 

 

 

 

 

f3 o
E E 14 .
E E
:1 3 ’ ""
“' x A 12 »
8 5
O.
. 10 ’
B 6 5 °
.9 '8 8
:9 .. o 0
To 4 ’ g x
05 a) x
3: Lu
1: _ x
Q) A ,
T0, 2 r O 4 "
..E. I
173 D 2 '
“J <
O.
o A A A 1 I 0 A 1 4| 1 J
o 2 4 6 8 1o 2 o 2 4 6 8 1o
Aortic Flow Probe CO [Umin] LAP via Direct Catheterization [mmHg]
(a)
10 . ._ 16 '
35:” o
E E 14 r
E E
a 8 ’ e—a
A 12 r
8 35.
O.
1 .
E, 6 ‘ x S 0 o
to
:2 E 8 o o
E 4 g x
O ’ '3: 5 .
°° (fl
'0 -
2 ,k A 4 .
co 2 _ o
E V x
a: a_ 2
(D O r
“J <
0 r . . . . g 0 r . . . .
0 2 4 6 8 1O 0 2 4 6 8 10
Aortic Flow Probe CO [Umin] LAP via Direct Catheterization [mmHg]
(13)

Figure 4.9 Estimation results of CO and LAP from long time-interval PAP waveform and
RVP waveform in a dog. (a), CO estimated from PAP waveform plotted against CO
measured by aortic flow probe, and LAP estimated from PAP waveform plotted against
LAP measured by direct catheterization; (b), CO estimated from RVP waveform plotted
against CO measured by aortic flow probe, and LAP estimated from RVP waveform

plotted against LAP measured by direct catheterization.

83

CHAPTER 5
MONITORING LEFT VENTRICULAR CONTRACTILITY FROM

RESPIRATORY-INDUCED BLOOD PRESSURE VARIABILITY

5.1 Background

The fastest growing cardiac disease is heart failure (the progressive weakening of
the heart), which can lead to exhaustion and disability. It currently affects nearly five
million Americans. Heart failure can be a life threatening condition; but if it is detected
early enough, it can be treated with life style changes, relatively inexpensive drugs such
as ACE inhibitors and beta-blockers, bypass surgery or angioplasty, and implantable
devices. Thus, it is becoming increasingly important to be able to measure a specific
index of left ventricular contractility so as to guide therapy.

The clinical approach for monitoring cardiac function usually involves employing
imaging techniques such as echocardiography and radionuclide ventriculography to
measure the ejection fraction (the ratio of the stroke volume to the ventricular end-
diastolic volume). Although the ejection fraction is relatively easy to estimate, it is
heavily dependent on the pressure in the ventricle prior to ejection (preload) and the
pressure against which the ventricle pumps blood (afterload). That is, ejection fraction is
not a specific or pure index of ventricular contractility. While other indices have been
introduced (e.g., maximum rate of change of left ventricular pressure [Katz et al., 1992]),
they all generally suffer from substantial load dependence as well.

Suga and Sagawa were able to identify a relatively specific index of left ventricular

contractility [Suga and Sagawa, 1974; Sagawa et al., 1977]. In their pioneering work,

84

they demonstrated that the pressure-volume relationship of the isolated canine left
ventricle can be represented by a line whose slope (elastance) varies from its minimum
value at the end of diastole to its maximum value at the end of systole (Fig. 5.1). That is,
the left ventricle behaves analogously to a time-varying electrical capacitor whose
capacitance is simply the reciprocal of elastance. More importantly, the maximum
elastance is highly sensitive to the changes in ventricular contractility, but relatively
insensitive to the alterations of the loading conditions [Sagawa et al., 1977; Suga et al.,

1973b; Suga and Sagawa, 1974]. They referred to this specific index of left ventricular
contractility as Bf?“ (Fig. 5.1). While subsequent investigators corroborated this result
in intact dogs [Kass et al., 1986] and humans [Kass et al., 1989], others complicated the
ER?“ concept by reporting afterload dependence [Suga et al., 1973a; van der Velde et

al., 1991] and contractility-dependent curvilinearity of the ventricular end-systolic
pressure-volume relationship [Burkhoff et al., 1987; Kass et al., 1989; van der Velde et
al., 1991]. However, the most significant load-dependence and nonlinearity occurred over

a wide range of ventricular volumes and/or in vivo in which the accuracy of the
measurement technique is reduced (see below). Therefore, BE“ as determined over a

limited range of ventricular volumes, is generally considered to be a valuable index of
left ventricular contractility [Burkhoff et al., 1986; Chen et al., 2001; Kass et al., 1989;

Takeuchi et al., 1991].

85

 

Control

mmHg
8

V!
O

150

VENTRICULAR PRESSURE

50

 

VENTRICULAR VOLUME ml

Figure 5.1 Illustration of left ventricular elastance (Elv) and the left ventricular maximum
elastance (Efillax ). The left ventricular pressure is plotted against the left ventricular
volume. Left ventricle can be represented by a time-varying capacitor, which is reciprocal

of Eh, (slope of lines). E3“ is a specific index of left ventricular contractility. [Suga and

Sagawa, 1974].

86

 

Although the significance of BK,“ is well appreciated, it is rarely employed

because of the difficulties involved in its measurement. The conventional technique
involves measuring the multiple left ventricular pressure-volume loops during the
interventions that ideally alter the loading conditions without affecting the contractility
(Fig. 5.2a). Left ventricular pressure can be measured with high fidelity, but very
invasive methods are required to do so. Moreover, although left ventricular volume can
be estimated with non-invasive methods such as echocardiography, even highly invasive
methods are not reliable [Burkhoff, 1990]. An example of experimental left ventricular
pressure-volume loops is shown in Fig. 5.2b [Kass et al., 1988]. Finally, the adjustment

of loading conditions is not only invasive but also may change the contractile state.
Perhaps, as a consequence, Freeman et al reported that E1?“ was dependent on the

method utilized to adjust the loading conditions [Freeman et al., 1986].

87

120 -

 

 

 

 

 

 

 

 

 

 

 

15
I

E

E.

a) max

5 8° '1 Iv

w -

GD :

9 i

a

a

a

E 40 " r

C ,r'

a: .-

> .- ’ ed

. .....-----
f 'n bd WW”
I! Em. M ”I“
0 ”‘" .............. r r l
50 100 150
Ventricular Volume [ml]
(3)
180-

1204

 

Pressure
£3

 

 

 

s'o
Volume

0))

Figure 5.2 Illustration of conventional Elf?“ measurement method. (a), ideal left
ventricular loop changed by preload, and the slope of the line fitting the end systolic
pressure-volume points is ER)“; (b), an experimental result, where left ventricular

pressure-volume loop with loading condition were altered by drug administration and

inferior vena cava balloon occlusion [Kass et al., 1988].

88

Previous investigators tried to pursue less invasive methods to measure Eff".

Most of these methods aimed to estimate E {33" without adjusting the loading conditions

from only one single beat. These techniques must be based on strict assumptions, as they
are essentially attempting to measure a slope from only one single data point.
Investigators have specifically assumed the time evolution of left ventricular elastance
normalized in both amplitude and time is identical or very similar for all individuals
regardless of cardiac state [Chen et al., 2001; Senzaki et al., 1996; Shishido et al., 2000].
Researchers have also assumed that the maximal isovolumic pressure at a given end—
diastolic volume can be extrapolated from isovolumic phase pressure with an empirical
formula [Chang et al., 1997; Shih et al., 1997; Sunagawa et al., 1980; Takeuchi et al.,
1991]. Perhaps, as a result, it is not surprising subsequent investigators have found poor
agreement between the conventional multiple beat method and single beat methods
[Iwase et al., 1992; Kjorstad et al., 2002]. Moreover, only a few of the single beat
methods did not require the measurement of left ventricular volume [Chang et al., 1997;
Shishido et al., 2000], however, these methods do require aortic flow, which is not easy

to measure as well [Ehlers et al., 1986].
In this Chapter, we present a practical technique for monitoring Bi?“ which may

ultimately be employed to guide the clinical management of heart failure patients. In

contrast to the previous multiple beat method and single beat methods, the novel
technique specifically estimate the changes in Big“ by mathematically analyzing the

beat-to-beat fluctuation of arterial blood pressure (Pa) and respiratory activities in terms

of instantaneous lung volume (qu) or intrathoracic pressure (Pm) during random-interval

89

breathing protocol [Berger et al., 1989a] in approximately six minutes. The key idea of
this technique is based on the phenomenon named direct capacitive effect, which means

that the magnitude of the immediate drop of Pa mechanically induced by inspiration is
mainly due to changes in E133". Irnportantly, minimally invasive or non-invasive

methods exist to continuously measure Pa (e. g., radial artery catheterization, arterial

tonomatry), Qlu (chest-abdomen inductance plethysmography) and Pa, (esophageal
balloon). Moreover, the technique monitors Eli/m while the ventricular loading
conditions are varied via a random-interval breathing protocol. Thus, multiple data points
are effectively utilized to measure the Eigax slope. We then describe the performance of

the technique with respect to realistic beat-to-beat variability generated by a human
cardiovascular simulator [Mukkamala and Cohen, 2001]. We also conducted a pilot

vealuation of the technique with respect to an anesthetized closed-chest canine model.

Both experiments show the promise of the technique in monitoring changes in Big“.

5.2 Physiologic Basis

5.2.1 Respiratory-Induced P. Variability Mechanisms

Beat-to-beat fluctuations due to respiration are readily apparent in Pa waveforms
(Fig. 5.3). These fluctuations are usually slower than the heart rate (HR) and are caused
by multiple, distinct physiologic mechanisms operating over different time courses.
These mechanisms may be categorized into those mediated by the autonomic nervous

system and those governed by mechanical phenomena.

9O

Autonomic mechanisms are responsible for the well-known respiratory sinus
arrhythmia phenomenon in which HR and respiratory variations are in synchrony (Fig.
5.4) [Eckberg et al., 1984; Saul and Cohen, 1994]. It has been shown that HR variations,
which may initiate Pa variations through changes in cardiac output, actually precede the
respiratory variations [Mukkamala et al., 1999; Mullen et al., 1997]. Specific mechanisms
responsible for respiratory sinus arrhythmia may include direct neural coupling of HR
and respiratory control centers in the brain (accounting for the non-causal effect) as well
as the baroreflex system, which is stimulated by the changes in Pa [Saul and Cohen,
1994]. These mechanisms are mediated by the fast parasympathetic nervous system and
the slower sympathetic nervous system [Akselrod etal., 1985]. Baroreflex excitation also
causes variations in ventricular contractility, systemic arterial resistance, and systemic
venous unstressed volume, which are solely mediated by the slow sympathetic nervous

system [Guyton and Hall, 1996].

91

 

 

 

 

 

0 5 10 15 20 25
Time [sec]

Figure 5.3 Respiratory waves on ABP waveform.

 

 

ECG
Pa
Q In
0 2 4 6 8 10
Time (see)

Figure 5.4 Illustration of respiratory sinus arrhythmia (RSA). The heart rate (ECG) is in

synchrony with respiratory activity (Qlu, instantaneous lung volume).

92

The mechanical phenomena are initiated by changes in Pa, caused by chest
expansion (inspiration) or chest contraction (expiration) [Guyton and Hall, 1996]. For
example, the act of inspiration causes Pm to drop. This drop is immediately transmitted to
left ventricular pressure and Pa, which we refer to direct capacitive effects. Then after a
couple of beats Pa increases due to the enhanced venous return to the right heart [Saul
and Cohen, 1994]. For a given Pm drop, the extent to which the enhanced venous return
affects Pa is dependent on the properties of the right heart, puhnonary circulation, left
heart, and systemic circulation. Thus, it would not be possible to distinguish between, for
example, left and right ventricular failure or systolic and diastolic failure even if the
extent of increase in Pa due solely to the enhanced venous return to the right heart could
be quantified. In contrast, the direct capacitive effects essentially reflect only left

ventricular contractility. We will discuss the direct capacitive effects in the next section.

5.2.2 Direct Capacitive Effects

The two-compartment electrical analog model in Fig. 5.5a represents the left
ventricle and systemic arteries system. Each compartment consists of a conduit for
viscous blood flow, which is characterized by a resistance (R), and a volume storage
element, which is characterized by a capacitance (C). The external pressure (P) is Pa, for
left ventricle and X Pm for the systemic arteries, where X is the fraction of the total
arterial compliance (Ca) subject to Pm. (X is caused by only parts of arteries is inside the
chest and affected by Pm. X is typically about 1/3 in humans [Lawson, 1962]). The
capacitance of the left ventricle oscillates over time (t) and is responsible for driving the

flow of blood. Finally, the ideal diode represents the aortic valve and ensures uni-

93

Pull)

 

 

(a)

1/EE“"+ Ca AP (t)
a

ll

XC EL?“ +1 _ .
——-‘————-AP t ‘ R *
CaEr'cax +1 th( ) <_P a XAPth (t) <_> Ra

—_ ——
— — — —
- _ — -

 

 

(b) (C)
Figure 5.5 Two-compartment model of the left ventricle and systemic arteries in terms
of the electrical circuit analog. (a), Model during one beat. R, resistance; C, compliance;
P, pressure; diode, aortic valve; A, changes; 1v, left ventricle; a, artery; th, intrathoracic; t,
time. (b), Model during systole (diode representing aortic valve is shorted) in which
Rlv=0 and CIv (t) z 1 / Eff" (as justified in the text). (c), Model during diastole (diode is

opened). The technique herein aims to estimate quantities derived from this model that

can reflect changes in left ventricular contractility in terms of Elf/13x.

94

directional blood flow. (Note that fast inertial and distributed effects are not considered
here.) According to this model, when P“, increases suddenly, the arterial blood pressure
Pa would increase immediately because the capacitors C|v(t) and Ca always tend to
maintain blood volume, which is the reason why the phenomena are called Direct
Capacitive Effects. Increasing Pa, in a very short time requires very fast breathing, which
is difficult to realize practically. We will describe the direct capacitive effects during
normal breathing and then quantitate direct capacitive effects below.

First, we study the two-compartment model shown in Fig. 5.5a. We assume that 1)
R|v=0 (i.e. no stenosis of the aortic valve) and 2) ClV (t) z NEE” during systole. Note
that any discrepancy in the second assumption is small and likely to be within the
estimation error of the technique (see below), as the systolic ejection time and time
derivative of left ventricular elastance (Ely) at the end of systole are both very small,
especially for failing hearts [Senzaki et al., 1996; Suga and Sagawa, 1974]. The nonlinear
model of Fig. 5.5c may be viewed as two distinct first-order linear systems with the input
z(t)APth(t) and the output APa(t), one during systole (Fi g. 5.5b) and the other during

diastole (Fig. 5.5c). The input z(t)APm(t) of this model is

XCa‘Ef'v“1x +1

 

APth (t) during systole, and

XAPth (t) during diastole.
The transfer function is

jmkaa/Ef‘v‘a" +Ca)
1+ij,(1/E;{}a" +c,)

 

during systole, and

95

ijaCa
l+ijaCa

 

during diastole.

According to the above transfer function, this system works like a high pass filter with
the approximate cutting off frequency of mcut=(RaCa)".

Next we will prove that because the frequency components of input are much
higher than the cutting off frequency, the input signals will all transfer to output.
Assuming the fluctuations APth (t) = Ccos(2rrt / Tr + 4)) , where Tr is the respiratory
period, to compute the lowest frequency in input, we utilize the exponential Fourier series

to expand z(t) as follows:

.2nn

 

oo J—t
z(t): ZDne T .
n=—w
where
-J———— XC E +1
Dn=—J— l—e T - a 1" forn¢0,and
27m caEfv‘a" +1

 

 

C Emax+1

3 IV

nmx
DozT-Tsx.1s.[xca-Elv +1].

co j2n[ 1 +n]t+j¢ j21r[n 1 Jr j¢
_ _ co ____ _
Then, the inputz(t)APth(t) = Z C—Dfi e T, T + Z Cfi e T T’ .
n=—oo n=-oo
According to the equation, for Tr 2 2T, the smallest frequency of an exponential term in
S(t) is 2n/T r. Thus, since 21t/Tr(~1.6 rad/sec) is usually larger than (RaCa)'I (~0.5

rad/sec [Sato et al., 1974]), we arrive at the approximations

AP, (t) z z(t)APth (t). (5.1)

96

Therefore, the response of Pa to a known change in Pm during systole as a result of

only the direct capacitive effects is approximately given as follows:

Apam ~ xcaEflvlax +1
APmU) Caeffla" +1

 

(5.2)

whereas the response of Pa to a known change in Pa, during diastole due to only direct

capacitive effects is approximately given as follows:

w z X (5.3)
APth (0
Since Ca (and X) is relatively constant on the time scale of days to months and over a

wide pressure range [Bourgeois et al., 1976; Hallock and Benson, 1937; Mukkamala et

al., 2003b; Remington et al., 1945], any changes in the direct capacitive coupling

between Pm and Pa must be specifically due to changes in E3“.

5.2.3 Ventilatory Mechanism

The measurement of Pa, is somewhat invasive. The instantaneous lung volume (Qlu)
may be measured non-invasively by placing belt around the chest and abdomen, as a
surrogate of Pm. We utilized the electrical analog model of ventilatory mechanics
depicted in Fig. 5.6. This model includes a resistor (Rafi) representing the viscous airways
and a capacitor (C1,) indicating the volume capability of the lungs. Based on this model,

changes in Pm are related to changes in Qlu as follows:

CluAPtha) =—Td—AE12—thl‘("t')’—AQlu(t)a (5.4)

97

where T=RairC|u represents the time constant governing ventilatory mechanics. If 1: were
known, the proportional Pa. changes could be obtained via Eq. 5.4 and act as a surrogate

of Pm in Eqs. 5.2 and 5.3 to compute the direct capacitive effects.

 

 

dQ w(t)
dt :
F,alva)
Patmfl) O——l\/\/\l _|_
Rair

T
Pm“) c

Figure 5.6 Model of ventilatory mechanics in terms of its electrical circuit analog. air,
airway; lu, lung; atrn, atmosphere; alv, alveolar pressure. See Fig. 5.5 caption for
remaining variable definitions. This model is utilized to formulate a quantitative

mapping from Qlu to proportional Pm in order to develop a.totally non-invasive technique

for monitoring index h3 derived from BE“.

98

5.2.4 Three Indices Derived From E3“

Since this technique does not require measuring volume (or blood flow), the
absolute value of E1?“ cannot be measured. However, from the concept of ER:ax we

derived three indices of left ventricular contractility, which are sufficient to monitor the
changes in left ventricular contractility under different circumstances.

The first index analyzes beat-to-beat Pa and Pa, fluctuations without regard to the
phase of the cardiac cycle (i.e., systole and diastole) in order to estimate a single lumped

index reflecting both Eqs. 5.2 and 5.3 (hr). The actual value of h. is determined by Ca,

E3” , X and the ratio of systolic period to diastolic period. This index is expected to
increase with decreasing E3“.

The second index is h2= C 3E3” , which can be computed from Eqs. 5.2 and 5.3.

Since'Ca is a constant as stated above, this index is proportional to E13“. The direct

capacitive effects in systole and diastole are identified by analyzing beat-to-beat Pa and

Pth fluctuations separately.
In order to monitor E133" non-invasively, we utilize the Pa and Qlu to identify a

specific index h3. With the proportional Pm (Eq. 5.4) and Pa, the technique could then
estimate the two quantities in Eqs. 5.2 and 5.3, which would each be scaled by C]... By

computing the ratio of the two estimated quantities, the scale factor Ch, would be

canceled and then the ratio, the third index h3, only reflects the changes in BE“ :

~ XCaEflfa" +1

113.. max .
XCaElv +X

 

(5.5)

99

This index would increase with decreasing E13“ .

5.3 Signal Processing Algorithm

The direct capacitive effects cannot be measured from beat-to-beat variability by
simply computing ratios of Pa fluctuations to P01 fluctuations (as indicated in Eqs. 5.2 and
5.3). The reason is that the Pa fluctuations are also due to the past histories of Pm
fluctuations (e. g., enhanced venous return to the right heart) and Pa fluctuations (e. g.,
baroreflex control of Ra and stroke volume) (Fig. 5.7). Moreover, unlike the other
baroreflex controllable parameters, the Pa fluctuations caused by HR variability may not
be as adequately reflected in the past histories of Pa (and Pa.) because of non-causal,
parasympathetically mediated respiratory sinus arrhythmia.

Thus, to measure the direct capacitive effects, our general approach is to employ a
system identification analysis to six-minute intervals of the beat-to-beat measurements
[Ljung, 1999]. This analysis is able to determine the effect of present fluctuation in Pm on
present fluctuation in Pa) independent of all confounding input variables (past
fluctuations in Pa, and Pa and present and past HR fluctuations). Since system
identification is most effective when the input is rich in spectral content, we employ a
previous broadband excitation protocol in which the subject breathes according to a
sequence of randomly spaced auditory tones (with a mean of five seconds and a range of
one to fifteen seconds) [Berger et al., 1989a]. Fig. 5.8 shows that the Pm power spectrum

of random-interval breathing is much wider than that of spontaneous breathing. Since

BE“ may vary (to a small degree) over the six-minute analysis interval due to the

100

baroreflex [Sagawa et al., 1977], the estimation result reflects the average BE“ value

over this interval.

 

 

 

 

 

 

 

 

 

1 20 — :
110~ l f
§?100
E
3;
m 90 .
a
80
7g . . . . . »
05 206 x 207 208 209 210
enhancedf' direct
venous .i' elastic
return ,~' effects
-3 F' !

 

 

 

 

 

 

 

'205 206 207 208 209 210
Time [see]

Figure 5.7 Illustration of enhanced venous return phenomenon. In the expiration, Pm
drops due to the expansion of chest, as a result the venous blood flow back to right atrium
increases. Then after a couple of beats, Pa increases. Therefore, Pa changes are not only
caused by direct elastic effects, but also by the past history of Pm. The phenomenon is

dependent on properties of the whole circulation.

lOl

 

 

 

 

 

N H

E 6 i 6

”or "or

E 3 E 3

E E

5 o 4.- 5 o ‘ _ _

“- 0 0.2 0.4 “- 0 0.2 0.4
r [Hz] f [H2]
(3) (b)

Figure 5.8 Random interval breathing power spectrum (b) is much wider than

 

spontaneous breathing power spectrum (a).

max
lv

Based on this general approach, we now identify three indices for monitoring E
changes. The detailed signal processing steps are outlined below. The signals Pa and
respiratory activity in terms of either Pm or Q“ are continuously recorded for six minutes
during random-interval breathing protocol and digitized at a sampling frequency of 90Hz.
Then the pulsatile components (i.e., HR variability) are removed from the Pa signal
according to the following steps [Mullen et al., 1997]. First, a pulsatile heart rate (F p)
signal is defined to be a train of unit-area impulses located at the times of ventricular

contraction. Then the coupling between Pa and pulsatile Fp is identified based on the

following dual-input autoregressive exogenous input (ARX) equation [Perrott et al.,

l996l

102

o P q
P, (t) = za,P,(t — i) + Zbina — i) + ZciRG - i) + w,(t) (5.6)
' i=1 i=0

i=1
where R(t) = P,h (t) or Qlu (t) ; 0, p, and q limit the number of terms in the model (model

order); and wa(t) is an unobserved noise term. This equation includes three sets of
unknown parameters {a,-, b,, c,-} whose values are determined by minimizing the variance
of the unobserved noise term (linear least squares estimation). The model order is chosen

by minimizing the Final Prediction Error (FPE, see Chapter 2). Next, with the newly
estimated parameters {ai , b, }, the blood pressure component due only to pulsatile heart

rate is calculated as follows:
F ° F p ..
P,p(t)=ZéiP,p(t—i)+Zbina—i). (5.7)
i=1 i=0

This portion is finally subtracted from the original blood pressure signal to arrive at the

blood pressure component not explained by pulsatile heart rate. That is,

F— F
Papa) =Pa(t)—Pap(t). (5.8)
To simplify the description, from now on we use Pa to represent the blood pressure

signal after removing the pulsatile components.

1) Index 111
We decimate Pa (without the pulsatile component) and Pth into 1.5Hz signals,
because the respiratory activity frequencies are much lower than pulsatile activity. Then

h] (similarly to the above) is estimated based on the following ARX equation:

AP, (t) = imp, (t — i) + ibiAPtha — i) + w(t). (5.9)
i=1 i=0

103

 

The resulting estimate of the parameter b0 specifically represents the effects of APm(t) on

APa(t) independent of HR and all the other regressor variables in the above equation.

Thus, the estimated index h1 (in) is be. The process to identify h] is shown in Fig. 5.9.

The impulse response from Pu, to Pa (without pulsatile component) is fully defined by the
parameters {ai,b,-} and reflect the mechanical effects (i.e., direct capacitive effects and

enhance venous return) and sympathetic baroreflex. The direct capacitive effect ho is the

estimated index h].

.20 .5, ABP ,

[ill]

30

i” [it’ll]

 

 

 

 

 

 

 

 
     
 

 

 

 

 

 

 

 

 

    

 

”250 from ABP identify ITP->ABPII!
Eta]; Impulse Response

'--- ~~ ' 05’ Sympatheticj

220 $321 w / Baroreflex l

, ITP 4 .

 

 

 

 

 

 

 

 

 

a V) [\ /\
l ./V
H V . . 0.6.
$331 240 Direct Elastic Effect 2”
(Random Breathing) (b0) .1 2 Return
110 "0 10 20 30""70

 

Figure 5.9 Illustration of system identification of index h]. First, pulsatility components
are removed from Pa; then P3, and the blood pressure after removing pulsatile
components are decimated to 1.5Hz. the impulse response fi'om Pa, to the blood pressure
after removing pulsatile components is identified. The estimated h] is the value of

impulse response at time zero be.

104

2) Index hz

We establish four 90Hz signals, P: , P: , Pfh and P31 , to identify the direct

capacitive effects of systole and diastole. For example, the 90Hz P: signal is formed as

follows. First, compute the average value of Pa during systole in each beat. Then assign

this value as the P: signal in this beat. That is, during one specific beat, P: signal is a

constant value. Pg , P:h and P31 signals are established similarly. Finally, we decimate

these four signals into 1.5Hz. To obtain an estimate of the quantity in Eq. 5.2, we identify

the following three input ARX equation:

m n q l'
APSU):ZaiAPasU—iHZbiAPgU-iHZCiAPf},(t-i)+2diAPg,(t-i)+ws(t). (5.10)

i=1 i=1 i=0 i=1

The resulting estimate of the parameter co specifically represents the effects of AP:h (t)

on AP: (t) independent of HR and all the other regressor variables in the above equation.

Thus, co represents an estimate of the quantity in Eq. 5.2. Similarly, we identify the

following equation:

5 u V Y
Apg‘a) = ZeiAP§(t—i)+2fiAP§(t—i)+ ZgiAP3,(t-i)+ ZpiAPfh(t-i)+wd(t).(5.ll)
1:] 1:0 i=0 i=0

Here, the go parameter analogously represents an estimate of quantity in Eq. 5.3. Finally,

based on Eqs. 5.2 and 5.3, we obtain an estimate of h; (CaEEax) from co and go as

follows:

 

. (5.12)
C0 '80

105

3) Index h;

We select an initial, physiologic value for I to obtain an estimate of pr0portional Pm
(at 90Hz) from the observed Qlu signal according to Eq. 5.4. Then, we implement the
above steps outlined to identify h; using the candidate proportional Pu, signal to estimate
co and go. In this case, co and g0 respectively represent the estimates of the quantities in
Eqs. 5.2 and 5.3, each scaled by C1“. We determine an optimal estimate of r (i) and the
ARX parameters by repeating the above steps over physiologic range of T (e. g. 0.2-1.2
sec) and selecting the resulting parameters that minimizes the joint FPE of Eqs. 5.10 and

5.11. This optimization problem may also be solved efficiently with the Golden Section

Search [Wilde et al., 1964]. Finally, we obtain an estimate of h3 via {13 = c0 / go.

5.4 Evaluation

5.4.1 Theoretical Evaluation

We theoretically evaluated the three techniques based on realistic short-term beat-
to-beat variability from a human cardiovascular simulator [Mukkamala and Cohen,
2001]. This simulator basically includes three parts: heart and circulation, short-term
regulation and resting physiologic perturbations (Fig. 5.10) [Mukkamala et al., 2003b].

The specific aims of our simulation experiments were to determine if 1) the technique as

applied to Pa and Pm signals could detect changes in BE“ via h]; 2) the technique as
applied to Pa and Pa, signals could determine the value of h; (C 313:3“ ) and detect

changes in ER?“ via hz; and 3) the third technique as applied to Pa and Qlu signals could

106

 

determine the value of h; and detect changes in ER)“ via h3 as well as determine

ventilatory constant I.

To address these specific aims, we conducted over 1000 simulation experiments
under different sets of parameter values. For each set of investigated parameter values,
we specifically performed the following steps. First, we executed the simulator to obtain
six-minute intervals of 9OHz Pa, Pm, and Q1u signals during simulated random-interval
breathing. Second, we modeled measurement noise by adding zero-mean Gaussian white
noise band—limited within 0.75Hz to each of these signals with a standard deviation (SD)

equal to 3% of the SD of the corresponding band-limited signals. Although this SD level

 

was chosen arbitrarily, our results were not significantly altered by at least a doubling of
this SD level). Third, we applied these three techniques to the noise corrupted signals.

Fourth, we repeated the above three steps 50 times to determine the mean and 95%

confidence intervals of each of the estimates (h1,h2 , h3 and i) according to a Gaussian
distribution-based method [Announdas et al., 2003]. In Eq. 5.6, the orders 0:15, p=35,
and q=lO; in Eq. 5.9, the orders m=n=10; in Eq. 5.10, the orders m=n=q$7; in Eq. 5.11,
the orders s=u=v=y=2. Once the above steps were completed for all of the investigated

parameter value sets, we finally compared the estimated results with corresponding actual

BE“ and r values that we knew exactly.

 

107

Figure 5.10 Block diagram summarizing the human cardiovascular simulator (redrawn
from Mukkamala, et al., 2003b). It is utilized here as the basis for theoretically evaluating
the three techniques. The simulator, which generates realistic beat—to-beat hemodynamic
variability, includes a pulsatile heart and circulation, a negative feedback, setpoint (sp)
representation of a short—term regulatory system, and resting physiologic perturbations.
The blocks in the diagram are mathematically characterized as follows: pulsatile heart
and systemic and puhnonary circulations with a lumped parameter system accounting for
viscous and volume storage effects; sinoatrial (SA) node with an integrate and fire
device; each neural coupling and baroreflex block with impulse responses of varying
static gains and system dynamics; baroreflex saturation with arctan functions; and

airways and lungs with a lumped parameter system accounting for airway resistance and
lung compliance. HR, heart rate; Q: , systemic venous unstressed volume; HCT, HR

contraction times; Pra, right atrial pressure. See Figs. 5.5 and 5.6 captions for remaining
variable definitions. WHR is l/f noise (where f is frequency), and NHR is assumed to be an
unmeasured, physiologic disturbance to HR. NR3 is band-limited white noise that is

assumed to be an unmeasured, physiologic disturbance to Ra.

108

 

 

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109

5.4.2 Pilot Experimental Evaluation

We conducted a pilot experiment in an anesthetized intact canine model. A single
adult purpose-bred hound cross dog (25kg) was instrumented as follows. Afier induction
of anesthesia, the animal was intubated but allowed to maintain its own respiratory rate
and depth except during certain experimental interventions. The electrocardiogram
(ECG), instantaneous lung volume (integral of the airflow), intrathoracic pressure
(esophageal pressure), arterial blood pressure (thoracic aortic pressure), and left
ventricular pressure were measured. A syringe pump catheter was positioned in the
femoral vein for drug administration. The cardio-respiratory measurements were recorded
(at a sampling rate of lOOHz and 12-bit resolution) during the following three
interventions: 1) baseline; 2) high dose dobutamine (3 ug/kg/min i.v.); and 3) lower dose
dobutamine (1.5ug/kg/min i.v.). Dobutamine was utilized to increase the left ventricular
contractility. Each intervention included a spontaneous breathing period of six minutes
followed by a random-interval breathing (with a manual resuscitation bag and a sequence
of randomly spaced auditory tones with a mean of five seconds and a range of one to
fifteen seconds) period of six minutes. A five to ten minute period of hemodynamic
equilibration was allowed between each intervention.

We applied the first technique to the continuous measurements of arterial blood
pressure and intrathoracic pressure at 100Hz obtained during the six-minute random-
interval breathing period of each intervention. We resampled the signals to 3.3Hz in the
second system identification step. In Eq. 5.6, the orders were set as follows: o=15, p=40,

and q=10; in Eq. 5.9, the orders were set as m=n=5. Since we were not able to

independently determine Eff)“ , we computed the maximum rate of change of left

110

ventricular pressure (ldP.v(t)/dt|max) as an independent measure of left ventricular
contractility for each intervention. We then compared the 13:33" changes predicted by

index h] during the pharmacological interventions with the corresponding reference

measure of contractility determined from left ventricular pressure. Note only h was

predicted because other indices were less sensitive to the changes in BE“.

5.5 Evaluation Results

5.5.1 Theoretical Evaluation Results

Fig. 5.11 summarizes the theoretical evaluation results of the technique as applied
to realistic simulated signals. All of the estimated quantities are shown in terms of their
mean (x) and 95% confidence intervals (bar).

Fig. 5.11a shows the estimation results of the index h] as the technique is applied on

the Pa and P3, signals during random-interval breathing. This figure specifically illustrates
the estimated index h1 (h1) plotted against the corresponding actual simulator value of
Big“. These results indicated that this technique was able to detect changes in BE” as

small as 10%.
Fig. 5.11b shows the h; estimation results of the technique applied on the Pa and Pm
signals during random-interval breathing but with a more sophisticated analysis so as to

provide more precise quantitative information. This figure specifically illustrated the

estimated index hz i.e., C Emax) lotted a ainst the corres ondin actual simulator
3 IV p g p g

value of BS“. The circles in the figure indicate the actual h; simulator value. These

111

results demonstrate that our technique was able to determine C aEEax with little
estimation bias (close correspondence between crosses and circles). However, its
sensitivity in detecting changes in Eff" is reduced with respect to the estimation of h]

due to the increased mathematical complexity.
Fig. 5.11c and 5.11d show the h3 estimation results of the technique applied on the
Pa and Q1u signals during random-interval breathing. In contrast to the first two estimation

methods, this method could be employed in practice with totally non-invasive

measurements. These two figures specifically illustrate the resulting h, and i: (an
estimate of t=Rai,C.u) respectively against the corresponding actual BE” and Ram values.

The circles in the figures indicate the actual simulator values for the h3 and r respectively.

These results demonstrate that the technique was able to estimate each of these quantities

with small bias and detect actual changes in both Eff/m and Rair. However, its sensitivity

in detecting ER?” changes is the least amongst the three techniques, as it is the most

complex.

112

0.7

h1 (unitless)

9
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0.3

2.5

ha (unitless)

A

1.5

 

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0.1

0.2 0.3 0.5 0.7 1
E R)” (ml/mmHg)

(a)

0.2 0.3 0.5 0.7 1
E [38" (ml/mmHg)

(C)

p.....

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113

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A
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1.5 ~

0.5

(a)

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0.1 0.2 0.3 0.5 0.7- 1 2 3 A
E W” (ml/mmHg)

(b)

 

1.5 2 2.5 3 3.5
RaMmmHa-sec/ml)

i i

x10‘3

((0

 

Figure 5.11 Summary of theoretical evaluation results. The results are obtained by
applying the technique to realistic beat-to-beat variability generated by the human
cardiovascular simulator in Fig. 5.10. All of the estimated quantities are shown in terms
of their mean (x) and 95% confidence intervals (bar), whereas the corresponding actual

simulator values are indicated with circles. See Figs. 5.5 and 5.6 captions for variable

definitions. (a), h] (an estimate of a lumped index reflecting Eqs. 5.2 and 5.3) is plotted

against the corresponding actual simulator E133" value. (b), hz (an estimate of Ca BIT“)
is plotted against the corresponding actual simulator BE“ value. (c), It, (an estimate of

h3 in Eq. 5.5) is plotted against the corresponding actual Big“ simulator value. ((1), “i

(an estimate of T=Rairclu) is plotted against Rair-

114

 

 

5.5.2 Pilot Experimental Evaluation Results

Fig. 5.12a shows example segments of the measured left ventricular and arterial
blood pressure waveforms obtained during baseline and high dose dobutamine
conditions. Fig. 5.12b shows example segments of changes in the measured intrathoracic
pressure waveform during spontaneous (negative-pressure) breathing and random-
interval (positive-pressure) breathing. This figure demonstrates that the canine respiratory
pattern can indeed be randomized manually with a resuscitation bag.

Fig. 5.13 shows the contractility changes predicted by the two methods. The cross
represents the value of the predicted h1 (h1 ), and the circle represents the value of dPlv/dt,

and the bars represent the standard deviation. The extent of hl increase from high dose to

low dose dobutamine is more significant than the decrease of the value of |dP|v(t)/dt|max.
These pilot results demonstrate that our technique may predict more precisely left

ventricular contractility changes than the more invasive method.

115

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Baseline Conditions High Dose Dobutamine Conditions
140. 140
120% 120 L
100 'k 100» \ '
1 , r t i
" fl \\ m\ '5 \ \t
80 - ' 80‘»
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of 60? 60:‘
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0- : l
40i 40‘)
i l
; a
20; U 20f-
. MUUU
o.’s‘"“"""i 175"""“"2 0.5 "'1 F‘ 2
Time [see] Time [sec]
(a)
Spontaneous Breathing Random-interval Breathing
5f 5 "
°fl
3 :
I E
E l
g. l
6 i
0- I
4 l
-5; -5.
11m [see] Time [8°C]
0))

Figure 5.12 Pressure signals in canine experiment of monitoring left ventricular

contractility. (a), comparison of left ventricular pressure (P1,) and aorta pressure (Pa) in

control and high dobutamine conditions. Ply: solid line, Pa: dash line. (b), comparison of

APth during spontaneous

negative breathing and random-interval positive breathing.

116

 

 

0.6 . . . a 5000
0.55 ~ -- - ****** - 4500
"o"
d)
0.5 - ‘ 4000 1’.’
O)
I
0.45 , ~ 3500 E
.: ’ "'
0.4 1 3000 g
_.§
0.35 ~ ”‘- 2500 §
3 z
; n.
0.25 . l 1500

 

 

0 1:5 3
Dobutamine dose [mglkglmin ]

Figure 5.13 Comparison of our technique with a highly invasive measurement of canine

experiment. Estimated index h, and |dP1,,(t)/dt|max plotted against dobutamine dose. The

estimated quantities h, are shown in terms of their mean (x) and standard deviation (bar).

The measured quantities |dP1V(t)/dt|max are shown in terms of their mean (0) and standard

deviation (bar). When more dobutamine is injected, contractility increases, thus hl should

decrease and IdPh,(t)/dt|max should increase. However, hl is more sensitive than

ldP]V(t)/dtlmax .

117

5.6 Discussion

To formulate the technique, we restricted its applicability to patients without aortic
stenosis and did not model both inertial and distribution effects in arterial tree. While
inertial effects contribute to the detailed structure of Pa waveforms within a beat, they are
relatively insignificant in accounting for the slow beat-to-beat variations that are
considered here. For example, even if cardiac output increased by 50% from one beat to
the next, the Pa waveform in Fig. 5.5a would be in error by 0.5mmHg (inductance of
blood is typically ~0.015mmHg.52/ml [Gurarini et al., 1998]). It is likewise known that
distributed effects (e. g., wave reflections in peripheral Pa waveforms) do‘not confound
slow beat-to-beat variations [Noordergraaf, 1978]. This may be understood by
considering the limiting case in which the time scales are sufficiently long (i.e., slow
changes) such that the wavelengths of the propagating waves are much longer than the
dimension of the arterial tree. Under these circumstances, the arterial tree may be well
represented by the lumped model in Fig. 5.5a. Importantly, this implies that beat-to-beat
variability in Pa waveform is not significantly dependent on the site of its measurement in
the arterial tree. We also did not model these fast effects in the ventilatory system (Fig.
5.6), as similar arguments may likewise hold [Staub, 1991].

However, in considering the identification of the second and third indices, the
inertial and distribution effects in real experimental data does introduce difficulties. The
dicrotic notch which denotes aortic valve closure is apparent in central arterial blood
pressure waveform and could be utilized to identify the systolic and diastolic intervals.
While in the readily available peripheral Pa waveform the dicrotic notch is not apparent

due to distributed and viscous effects. It may be possible to determine the systolic and

118

 

diastolic intervals based on the cardiac cycle length using, for example, the well-known
Bazett formula [Bazett, 1920]. Alternatively, it may only be necessary to identify a single
systolic Pa and diastolic Pa sample for each beat. Studies with the human cardiovascular

simulator have shown that this approach does not materially affect our results.

Index hz (C aBalm) can be utilized to estimate the ventriculo-arterial energy

coupling. hz is closely related to BE“ / Biff , where Biff is the effective arterial
elastance characterizing both the viscous and capacitive properties of the arteries
[Sunagawa et al., 1983], not the reciprocal of Ca. The quantity E13“ /E§ff is a useful

index of ventriculo-arterial coupling [Chang et al., 1997; Sunagawa et al., 1983], and may

be essential for optimizing chronic heart failure therapy [Binkley et al., 1990]. h; may be
utilized to measure the value of Eff" if Ca is calibrated by the technique described in

Chapter 3.
In order to improve the efficiency of the system identification algorithm, a random-
interval breathing protocol is employed. However it is difficult for those severe patients.

The random-interval breathing then could be realized by a programmed ventilator.
Therefore the monitoring of BE” could be performed continuously. In the left ventricle

and artery model in Fig. 5.5a, we assumed X is equal to 1/3. Actually, we simulated with
X varying from 0.25 to 0.4 and applied the technique on the data. The results suggest that
the value of X only affects the estimation results a little.

The results of this theoretical study indicate that the sensitivity in detecting changes

in Big“ is best when Pa and the somewhat invasive Pm signals are available for analysis.

119

 

However, if only Pa and the non-invasive Q1u are available, an estimate of the ventilatory
system time constant I = R3,, C1u may also be obtained. Both Raj, and Ch, can vary in heart
failure patients as a result of puhnonary edema. Thus, the I estimate may possibly be
utilized as a quantitative index of puhnonary edema. However, in puhnonary edema, we
note that Raj]- may increase while Clu decreases. The estimate of I may therefore be more
useful in which only one of these parameters is altered (e. g., asthma). This is significant
to the extent that 1: here may potentially be measured non-invasively.

The precise theoretical evaluation could not be achieved in an experimental model
in which all of the actual parameter values would be difficult to ascertain. The theoretical

validation here indeed justifies and promotes experimental testing of the technique
against the traditional method for measuring Bf?“ during different levels of ventricular

contractile state.

In the pilot animal experiment, the hi estimates were obtained with an invasive
aortic blood pressure waveform. However, we contend that the estimates would not be
significantly altered, if a less invasive peripheral blood pressure waveform were
measured, because these two waveforms are similar on slow, beat-to-beat time scales.
One difference from the theoretical evaluation is that we only were able to increase the
contractility, while our technique works better when the contractility is small.

In summary, we present a novel technique to monitor the changes in lefi ventricular
contractility in terms of Eff)“ from only respiratory-induced Pa variations obtained

during a random-interval breathing protocol. The validation based on the simulated data

and the pilot animal study shows the promise of the technique. With experiments on

120

animals and even humans in which the absolute values of Bf?“ are measured, this

technique may be potentially utilized in clinical practice to help guide therapy in heart

failure patients.

121

 

CHAPTER 6

CONCLUSIONS

6.1 Summary

In this thesis, we introduced three novel techniques to monitor three hemodynamic
parameters, CO, LAP and left ventricular contractility in terms of Biz/m" by mathematical

analysis of long time intervals of blood pressure waveforms. First, we refined a
previously developed technique for continuously monitoring CO from a peripheral ABP
waveform and validated it, for the first time, in humans. Second, we extended the first
technique to a PAP or RVP waveform to continuously monitor both LAP and CO and

evaluated it in ICU patients and a canine experiment. Third, we introduced a technique
for monitoring changes in BE“ from peripheral ABP waveform variability induced by

random-interval respiratory activity and evaluated it with respect to data sets generated
from a realistic human cardiovascular simulator and a canine experiment. Each of these
techniques estimate the hemodynamic parameters using system identification method
combined with physiologic knowledge. The advantages of these techniques over
conventional methods are that they may be realized in a less invasive, continuous, and/or
safer manner. The preliminary evaluations with respect to hemodynamic data obtained
from realistic computer simulations, animal subjects, human volunteers, and patients

demonstrate that these techniques may indeed be capable of accurately estimating CO,
LAP and E3“ with an acceptable accuracy in clinic. Table 6.1 summarizes the

developed techniques.

122

 

Table 6.1 Summary of three hemodynamic monitoring techniques. These techniques

analyze long time intervals of blood pressure waveforms using system identification

combined with physiologic knowledge and are validated with different sets of

experimental data.

 

 

 

 

 

 

 

 

 

 

Objectives Measurements Physiologic Knowledge Advantage Validation
CO Peripheral Windkessel model can Less invasive, Healthy
ABP represent arterial tree in a continuous volunteers, ICU
long time scale patients
CO, LAP PAP or RVP Windkessel model can Continuous, ICU patients,
represent pulmonary artery safer dog experiment
in a long time scale
Emax ABP, Pth or Direct elastic effects Less invasive Simulated data,
1" Qlu dog experiment
6.2 Future Work

This thesis does not signify an end but only a beginning. I have come to realize that

there are several areas of future investigation that would be worthwhile. First, a universal

model order selection criterion for both the first and second techniques is needed.

Learning methods may be one possible option. We can also try to use the OE model

instead of ARX model to optimize full prediction. Second, it is very important to develop

an algorithm to identify the artifact-free segments from ABP and PAP waveforms in

order to have a truly automatic technique. Of course, a large number of high quality

experimental measurements (both pressure waveforms and gold standard reference

measurements) from animals and humans under different physiologic conditions are

required to further evaluate and improve the techniques.

123

 

 

By the end of my thesis work, I also formulated a new technique to compute
Ca Emax and therefore quantitatively monitor changes in BE“. The advantage of this

technique is that it does not require random-interval breathings, but it does need an
invasive measurement of aortic pressure. More specifically, according the two-
compartment left ventricle and arterial tree model (Fig. 5.5), blood flow Qa to aorta is
given by:

_ dPa(t) Pa(t)
Qa-Ca dt + Ra . (6.1)

 

 

Since the volume of left ventricle is C1v(t)P1V(t), the blood flow le from left ventricle is

 

 

 

given by:
le (t)_ _ d(Clv (t)Plv (t))_ dClv (t) Ply (0+ Clv (t) dPlv (t) (62)
dt dt dt
During the ejection phase, assuming R1V=O (no aortic stenosis), P.v(t)= Pa (t), and
le (t) = -Qa (t) . Thus,
dClv (t) Pa dtz(t) _ dPa (0 Pa (0
dt ——Pa (t)+ C1v(t)——— [Ca dt + Ra ]. (6.3)

At the time tm when Elv reaches its maximum value BE“ , Ch, reaches its minimum

 

dC t . .
value. Then Clv (tm) = “1m , 1:1: m) = 0. Substituting these two values into Eq.
1v

6. 3, we finally arrive at a simple equation for proportional Emax .

-l
Emax = . 4
Ca 1V 1+ Pa(tm) (6 )
dPa(tm)

dt

 

 

Race

124

Because tm is not genenally at the time of end-ejection [Sagawa, 1981], we would need to

find a method to determine it. Once tm is determined, CaEfl,lax could be computed at tm

using Eq. 6.4 without measuring left ventricular pressure and volume. As described in

Chapter 5, Ca is nearly a constant over a long time period, thus Eq. 6.4 could be utilized

max
Iv

to monitor changes in E . Here, RaCa could be computed using the method of Chapter

3 or direct exponential fitting. Note that Ca can be obtained with an additional

measurement of stroke volume or blood flow (e. g., flow probe, thermodilution, Doppler
ultrasound) and therefore the absolute value of Elf,“ could be computed.

It is our hope that this thesis sparks these future investigations and ultimately leads
to new hemodynamic monitoring systems in hospitals, at home, and with implanted

devices.

125

 

10.

11.

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