CARDIAC OUTPUT MONITORING TECHNIQUES BY PHYSIOLOGIC SIGNAL
PROCESSING
By
Guanqun Zhang

A DISSERTATION
Submitted
to Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Electrical Engineering
2012

ABSTRACT
CARDIAC OUTPUT MONITORING TECHNIQUES BY PHYSIOLOGIC SIGNAL
PROCESSING
By
Guanqun Zhang
Continuous cardiac output monitoring is urgently required because of the growth of elderly population and shortage of clinical staff. However, the reliable, less-invasive solution of monitoring
cardiac output has not been determined. On the other hand, the measurement of peripheral arterial blood pressure waveform can be conveniently collected. In the dissertation, we proposed
novel physiologic waveform analysis techniques which can estimate cardiac output from a peripheral arterial blood pressure waveform. The techniques can overcome the confounding reflection
by estimating the cardiac output over multiple cardiac cycles. Validation results have indicated
that our method was comparative with other traditional methods at the baseline level and became
increasingly superior to others with more challenging cardiac output changes.
We also introduced pulse transit time to overcome the estimation error due to varying arterial compliance. As a direct function of arterial compliance, pulse transit time can reduce the
estimation variation and thus improve the accuracy. Two conventional approaches for measuring
pulse transit time were compared, and both methods were sensitive to artifact. Therefore, a novel
method was developed which can robustly estimate the pulse transit time, with which the accuracy
of estimating cardiac output was significantly improved.
A tube-load model with an adaptive transfer function was further proposed. The model can
reconstruct the central blood pressure of flow waveforms from the peripheral measurements beat
by beat. In this study, the reconstructed central blood pressure waveform is an earlier marker of
hypovolemia than the peripheral blood pressure waveform in a simulated hemorrhage experiment.
Cardiac output can also be derived from the reconstructed central blood pressure waveform.
In addition, an extended model was proposed for estimating cardiac output from a pulmonary

artery pressure. This extension allows to simultaneously estimate cardiac output and left atrial
pressure, which are two important determinants of pulmonary artery pressure. Validation in a large
critical/medical population database demonstrated the proof of concept.
The techniques will ultimately be employed for continuous and non-invasive cardiac output
monitoring for clinical settings. One potential future direction would be end-diastolic volume and
ejection fraction estimation from a peripheral arterial blood pressure waveform.

Copyright by
GUANQUN ZHANG
2012

To my parents, Yaming Zhang and Li Shan

v

ACKNOWLEDGEMENTS

Though only my name appears on the cover of this dissertation, a great many people have contributed to its production. I owe my gratitude to all those people who have made this dissertation
possible and because of whom my graduate experience has been one that I will cherish forever.
I would like to gratefully and sincerely thank Dr. Ramakrishna Mukkamala for his guidance,
understanding, patience, and most importantly, his friendship during my graduate studies at Michigan State University. His mentorship was paramount in providing a well rounded experience consistent my long-term career goals. I am highly impressed with his in-depth understanding of research areas, his diligent and enthusiastic working style, his ability to control the multi-disciplinary
knowledge and his sincere and friendly attitude with people.
I am also grateful to my dissertation committee members, Dr. Selin Aviyente, Dr. N. Bari Olivier and Dr. Lalita Udpa, for the valuable experience of their courses, experiments and comments
on my research. It is my great honor to cooperate with these three outstanding teachers. I would
also like to thank many faculty members of MSU who were the instructors for the courses I took.
The course works have greatly enriched my knowledge.
I would like to express my special thanks to the colleagues at our PSPML lab, Gokul Swamy,
Federico Aletti, Xiaoxiao Chen, Sorour Soltani, Da Xu, Mohsen Moslehpour, Mingwu Gao and
Jiankun Liu. Thank you for the collaboration over the last five years.
I also want to thank my friends at Fudan University and Michigan State University. Especially,
I would like to thank Jiemei Wang and Dashun Wang. The conversation with them can always
provide me insights and inspirations of my research.
Finally, none of this would have been possible without the love and support of my parents, to
whom this dissertation is dedicated. I would like to express my heart-felt gratitude to my family.

vi

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . .
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Circulation and cardiac output . . . . . . . . . . . . . . . .
1.1.2 Pulse wave velocity, pulse transit time and pulse arrival time
1.2 Arterial system modeling . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Windkessel model . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Tube-load model . . . . . . . . . . . . . . . . . . . . . . .
1.2.2.1 Model description . . . . . . . . . . . . . . . . .
1.2.2.2 Assumptions and validity . . . . . . . . . . . . .
1.2.2.3 Parameter estimation . . . . . . . . . . . . . . . .
1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CARDIAC OUTPUT MONITORING FROM PERIPHERAL ARTERIAL BLOOD PRESSURE BY LONG TIME INTERVAL ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experiment 1: validation in the MIMIC II database . . . . . . . . . . . . . . . .
2.3.1 Materials and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experiment 2: validation in a lower body negative pressure study . . . . . . . . .
2.4.1 Materials and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CHAPTER 2

2.1
2.2
2.3

2.4

CHAPTER 3
3.1
3.2
3.3

PULSE TRANSIT TIME FOR CORRECTING ARTERIAL COMPLIANCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pulse arrival time is not an adequate surrogate for pulse transit time as a marker
of blood pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Improved pulse transit time estimation by system identification analysis of proximal and distal arterial waveforms . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2.1 Physiological data . . . . . . . . . . . . . . . . . . . . . . .
3.3.2.2 PTT estimation . . . . . . . . . . . . . . . . . . . . . . . . .
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3.3.2.3 Conventional foot-to-foot detection techniques . . . .
3.3.2.4 Parametric system identification technique . . . . . .
3.3.2.5 PTT assessment and comparison . . . . . . . . . . . .
3.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4.1 System identification approach for PTT estimation . .
3.3.4.2 Evaluation approach and limitations . . . . . . . . . .
3.3.4.3 Tracking DP . . . . . . . . . . . . . . . . . . . . . .
3.3.4.4 Tracking other ABP parameters . . . . . . . . . . . .
3.3.4.5 Reproducibility . . . . . . . . . . . . . . . . . . . . .
3.3.4.6 Future directions and potential clinical applications . .
Cardiac output monitoring techniques with pulse transit time correction
3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 The technique . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 Technique evaluation in an animal study . . . . . . . . . . . . .
3.4.3.1 Results . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3.2 Discussion . . . . . . . . . . . . . . . . . . . . . . .
3.4.4 Technique evaluation in a human lbnp study . . . . . . . . . . .
3.4.4.1 Results . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CHAPTER 4

4.1
4.2

4.3

4.4
4.5

CARDIAC OUTPUT MONITORING FROM PERIPHERAL ARTERIAL BLOOD PRESSURE BY SHORT TIME INTERVAL ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Central blood and flow waveform reconstruction from a peripheral arterial blood pressure waveform . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Stroke volume estimation from a central blood pressure waveform . . . .
Materials and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CHAPTER 5
5.1
5.2
5.3

5.4
5.5

CARDIAC OUTPUT MONITORING FROM PULMONARY ARTERIAL PRESSURE BY LONG TIME INTERVAL ANALYSIS . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Materials and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Pulmonary artery catheterization data . . . . . . . . . . . . . . . . . .
5.3.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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viii

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CHAPTER 6 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

ix

LIST OF TABLES

Table 1.1

Limitations of conventional methods. . . . . . . . . . . . . . . . . . . . . . . .

5

Table 2.1

Average characteristics of patients and data.

Table 2.2

Overall cardiac output estimation accuracy of the investigational techniques.

Table 3.1

Subject-by-subject results and interventions.

Table 3.2

Subject average results.

Table 3.3

Results of each pulse transit time estimation technique per subject.

Table 3.4

Characteristics of ABP and RMSNE values of original and corrected techniques for every individual subject. . . . . . . . . . . . . . . . . . . . . . . . . 71

Table 3.5

RMSNE values of original and corrected techniques for segments at two extremes in every individual subject. . . . . . . . . . . . . . . . . . . . . . . . . . 71

Table 5.1

Overall cardiac output estimation accuracy of the investigational techniques.

Table 5.2

Overall left atrial pressure estimation accuracy of the investigational techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

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LIST OF FIGURES

Figure 1.1

The cardiovascular system. For interpretation of the references to color in
this and all other figures, the reader is referred to the electronic version of
this dissertation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

Figure 1.2

Physiologic response in a hemorrhage study. . . . . . . . . . . . . . . . . . . .

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Figure 1.3

Schematic diagram of thermodilution. . . . . . . . . . . . . . . . . . . . . . .

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Figure 1.4

Pulse pressure and heart rate. . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Figure 1.5

Windkessel model for estimating CO from central ABP. . . . . . . . . . . . . .

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Figure 1.6

Wave reflection and amplification. . . . . . . . . . . . . . . . . . . . . . . . .

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Figure 1.7

Two pressure waveforms simultaneously measured at two different positions. . . 10

Figure 1.8

Measurement of PTT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Figure 1.9

Measurement of PAT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Figure 1.10 The Windkessel model which characterizes the arterial tree. . . . . . . . . . . . 15
Figure 1.11 (A) The tube-load model with arbitrary load. (B) Three types of commonly
used loads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Figure 1.12 Experimental arterial pressure with increasing distance from the heart. . . . . . 21
Figure 2.1

Continuous and minimally invasive technique for estimating relative cardiac
output (CO) change by unique long time interval analysis (LTIA) of an arterial blood pressure (ABP) waveform obtained with an existing radial artery
line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 2.2

CO estimation accuracy of the investigational techniques (on log scale) as a
function of the magnitude of the reference CO change. . . . . . . . . . . . . . . 31

Figure 2.3

One subject in the LBNP experiment.

Figure 2.4

Comparison of the candidate techniques for estimating CO. . . . . . . . . . . . 38

Figure 3.1

Procedure for evaluating pulse arrival time (PAT) and pulse transit time (PTT)
in terms of their ability to predict arterial blood pressure (ABP) parameters
within a subject. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

xi

. . . . . . . . . . . . . . . . . . . . . . 36

Figure 3.2

Plots of beat-to-beat DBP versus beat-to-beat 1/PTT (black, closed circles)
and 1/PAT (gray, open circles) in each subject. . . . . . . . . . . . . . . . . . . 45

Figure 3.3

Sample trends in DBP, PTT, and the pre-ejection period (PEP) from subject
1 during phenylephrine infusion. . . . . . . . . . . . . . . . . . . . . . . . . . 46

Figure 3.4

Sample trends in DBP, 1/PTT, and 1/PAT from subject 6

Figure 3.5

Optimized conventional foot-to-foot detection techniques for estimating pulse
transit time (PTT) from either an ECG or impedance cardiography (ICG)
waveform (a proximal waveform) and a simultaneous noninvasive peripheral
arterial blood pressure (ABP) waveform (a distal waveform) [the time delays
between each R wave and subsequent DP (Td1 ) and between each B point
and ensuing DP (Td2 )]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 3.6

Parametric system identification technique for estimating PTT from simultaneous ICG and noninvasive peripheral ABP waveforms. . . . . . . . . . . . . . 56

Figure 3.7

Plots of measured DP vs. the proportional PWV estimated by each technique
from subjects 15 and 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Figure 3.8

Plots of the DP predicted from the proportional PWV estimates of each technique vs. measured DP from all 15 subjects. . . . . . . . . . . . . . . . . . . . 61

Figure 3.9

Conventional techniques employing empirical curves for correcting AC. . . . . 66

. . . . . . . . . . . . 47

Figure 3.10 LTIA with PTT correction for estimating CO. . . . . . . . . . . . . . . . . . . 69
Figure 3.11 CO trends of the measured reference (solid), uncorrected estimation (dashed)
and fPTT corrected estimation (dot dashed). . . . . . . . . . . . . . . . . . . . 72
Figure 3.12 Comparison of the candidate techniques for estimating CO. LTIA was corrected with PTT for the changing AC. . . . . . . . . . . . . . . . . . . . . . . 74
Figure 4.1

Structure of the tube-load model and the model transfer functions. . . . . . . . 77

Figure 4.2

Sample plot of measured arterial blood pressure (solid) and computed forward (short dash) and backward (dash dot) waves in the central aorta and a
peripheral artery. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Figure 4.3

Group average results of reconstructed central pulse pressure vs. measured
peripheral pulse pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Figure 5.1

(a) Windkessel model of the pulmonary artery pressure (PAP) waveform. (b)
Experimental PAP waveform and diastolic decay fitting. . . . . . . . . . . . . . 86

xii

Figure 5.2

Illustration of how the mathematical analysis technique determines the time
constant τ of the Windkessel model in Figure 5.1, average left atrial pressure (LAP), and proportional cardiac output (CO) from a pulmonary artery
pressure (PAP) waveform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Figure 5.3

Illustration of how the mathematical analysis technique determines the time
constant τ of the Windkessel model in Figure 5.1, average left atrial pressure (LAP), and proportional cardiac output (CO) from a pulmonary artery
pressure (PAP) waveform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Figure 6.1

New technique for monitoring EDV by analysis of the central ABP waveform, which may be derived from a peripheral ABP waveform. (a) Lumped
parameter model of the left ventricle and arterial tree upon which the technique is based. (b) The unknown model parameters (in gray) are estimated
by fitting the model to the ejection and diastolic intervals of each beat of the
ABP waveform so as to compute relative change in beat-to-beat EDV. . . . . . . 94

xiii

Chapter 1
INTRODUCTION

The increasing number of occurrence of cardiovascular diseases requires novel techniques which
can effectively and conveniently monitor hemodynamics for patients and clinicians. Nowadays, the
continuous measurement of peripheral arterial blood pressure (ABP) has drawn intense attention.
Although the invasive catheters are being broadly utilized in clinical practice, the requirement of
less-invasive or even non-invasive monitoring techniques is on the rise. Comparing with the routine measurement of ABP, the cardiac output (CO) can introduce more comprehensive information
for the diagnose in the therapy and more predictive of patient outcome. However, conventional methods for measuring CO require an experienced operator or an unacceptably high level of
invasiveness. Therefore, the application of the CO measurement is limited by the disadvantage.
In our opinion, CO may be continuously and less invasively monitored by physiologic-based
mathematical model, which can extract relevant information for the routinely measured ABP waveforms. In this report, several techniques deriving CO from ABP waveforms will be discussed.
Those techniques yielded more accurate results and more robust to noises, wave reflection and
measurement artifacts. Some techniques have been validated in a series of previous studies, and
they are further evaluated for the proof-of-concept. The development of the techniques may ultimately be used in critical care monitoring with invasive ABP catheters and emergency and home
monitoring with non-invasive ABP transducers. Successful achievement of these specific aims
will lead to an improved understanding of the clinical information embedded in various, routinely
measured ABP waveforms.

1

1.1 Background
1.1.1

Circulation and cardiac output

The cardiovascular system serves to pass and distribute nutrients to the tissues and to remove
metabolism substances as well as help stabilize body temperature (Figure 1.1)[77]. In the mammal
cardiovascular system, the cardiovascular system consists of a pump (the heart) and a series of
connecting and distributing tubes (blood vessels). The cardiovascular system has two division:
the systemic circulation, whose blood is pumped from the left ventricle and circulates oxygenated
blood to the body tissues; and the pulmonary circulation, whose blood is pumped from the right
ventricle and circulates deoxygenated blood to the lungs. Cardiac output (CO), is the volume of
blood being pumped from the heart, in the unit of liter per minute. Therefore, CO is equal to the
stroke volume (SV, i.e. the volume per beat) multiplied by heart rate (HR).
Arterial blood pressure (ABP), is the pressure of blood exerted on the vessel wall. During each
cardiac cycle, the maximum and minimum of ABP are defined as systolic and diastolic pressure,
respectively. The driving force of ABP in the circulation is due to the pumping action of the heart.
During the circulation, ABP is significantly decreased in arterioles, where accounts for the most
resistance in the arterial tree. Therefore, the ABP returning to the heart is negligible comparing
with the ABP in major arteries. This hemodynamic phenomenon in the systemic circulation can be
mathematically described as the mean of ABP is equal to the produce of CO and total peripheral
resistance (TPR).
Today, hemodynamic monitoring techniques enable the measurement and display of blood
pressure waveforms. For example, in each year, millions of invasive catheters are inserted in
surgery and intensive care patients to monitor the peripheral ABP. Moreover, FDA approved systems have recently been commercialized to non-invasively measure blood pressure in peripheral
arteries. With the availability of these systems, the monitoring of ABP condition becomes so simple that patients can utilized them at home. While these systems are continuous and safe enough for
clinical use, they are ineffective in the sense that the measured blood pressure levels are imprecise

2

Figure 1.1: The cardiovascular system. For interpretation of the references to color in this and all
other figures, the reader is referred to the electronic version of this dissertation.

3

indicators of circulatory status.
One reason of the ineffectiveness is that ABP levels do not provide an early indicator of a
hemodynamic event. For example, at the early stage of hemorrhage, ABP is maintained even while
CO is falling due to compensatory physiologic mechanisms (Figure 1.2). While frank hypotension
or low blood pressure will eventually occur, it is often too late to intervene at this point. So, it is
the CO, which represents the total blood flow rate in the circulation, that would actually give an
early enough indication of the need for a life saving intervention.
Another reason is that ABP levels are dependent on multiple physiologic factors and therefore
do not permit diagnosis. For example, when the compensatory physiologic mechanisms eventually fail so as to result in hypotension, the root cause could be bacterial blood poisoning, more
commonly called sepsis, the inability of the heart to fill or contract, or an internal bleed. With
the information of CO, however, the sepsis can be distinguished from cardiac dysfunction and
hemorrhage.
The standard CO measurement is the thermodilution (Figure 1.3). This technique involves
introducing a catheter into the right atrium, injecting cold saline into the heart, measuring temperature downstream in the pulmonary artery and computing the time-averaged CO based on conservation laws. Although this approach is relatively easy and inexpensive, it is very invasive and it
requires an operator to intermittently inject saline. Therefore, this method doesn’t permit continuous CO monitoring.
Some other traditional techniques also suffer significant limitations (Table 1.1). For example,
the most accurate method is to place a flow probe across the aorta. However, this method is too
invasive to be practical.
Therefore, it is relative difficult to directly measure cardiac output. On the other hand, peripheral arterial blood pressure can be reliably obtained by mature techniques. So the problem
naturally arises that if CO can be estimated by some mathematical analysis of peripheral arterial blood pressure. This approach is named as pulse contour analysis. A number of investigators
have sought techniques to estimate CO from peripheral ABP signals. The earliest technique was

4

80
HR
60
120

ABP
SYSTOLIC BP
[mmHg]

HEART RATE
[per min]

TOTAL PERIPHERAL
RESISTANCE CHANGE [%]

100

TPR

100

RAP

12

CARDIAC
OUTPUT
[litres per min]

10
CO
CO
8
6
4

RT AURICULAR PRESSURE
[cm. SALINE]

80

MINUTES
Figure 1.2: Physiologic response in a hemorrhage study.

Table 1.1: Limitations of conventional methods.
Method
aortic flow probe
doppler ultrasound
oxygen fick

Advantages
most accurate, continuous
non-invasive
accurate, inexpensive

thermodilution

inexpensive

thoracic bioimpedance

non-invasive, continuous

5

Disadvantages
thoracotomy
expert operator, expensive
two catheterizations, operator
pulmonary artery catheterization,
inaccurate, operator
inaccurate

Temperature

Thermistor
Output

Time

Left Atrium

Pulmonary Artery
Right Atrium

Left Ventricle

Right Ventricle

Figure 1.3: Schematic diagram of thermodilution.

based on the observation that central pulse pressure, that is, the systolic minus diastolic pressure
in the central aorta, is dependent on SV (Figure 1.4). This technique therefore involves detecting
the pulse pressure and multiplying it by the HR to determine CO to within a proportionality constant. In this way, the technique could be utilized to monitor relative changes in cardiac output
or absolute cardiac output after a single calibration. However, this simple technique assumes that
cardiac ejection occurs instantaneously. In actuality, cardiac ejection occurs in finite time in which
a portion of the ejected blood passes through the aorta and into the periphery.
Many years later, an improved technique was proposed that made no assumptions about the
cardiac ejection time. This technique models the arterial tree with an RC circuit. It accounts for
the compliance of the large arteries and the total peripheral resistance of the small arteries. If CO
is considered as the input excitation of the circuit, arterial blood pressure should decay like a pure
exponential during each diastolic interval. Further, the time constant of this pressure decay should

6

140

PP

120

[mmHg]

100
80
60

HR

40
20
0
1

1.5

2

2.5

3

Time [sec]
Figure 1.4: Pulse pressure and heart rate.

equal to the product of the total peripheral resistance and the arterial compliance. By assuming
constant arterial compliance, the technique fits the exponential, estimates the RC time constant tau
and then divides the time-averaged arterial blood pressure to compute proportional cardiac output.
This RC circuit technique showed excellent correspondence to the aortic flow probe, as illustrated
in figure 1.10.
However, central ABP is not measured for regular patient monitoring. On the other hand,
peripheral ABP can be easily collected but its shape is much different from the central pressure,
which is due to wave reflection. That is, when the heart ejects blood, a pressure wave is initiated
that travels through the arteries. When this wave reaches the level of the arterioles , a significant
part of the wave is reflected back towards the heart. As a result, the actual blood pressure waveform
at a given arterial site arises as the sum of the forward and backward traveling waves at that site.

7

CO

20

ABP

[ml/s]

CO

10
0
1

2

2.5

3

Central ABP

TPR
[mmHg]

AC

1.5

140
120
100
80

W

1

1.5

2
2.5
Time [sec]

3

Figure 1.5: Windkessel model for estimating CO from central ABP.

Since wave reflection occurs mainly at the arterioles, there is little time delay between the forward
and backward waves in the periphery (Figure 1.6). So the backward wave adds to the forward wave
and it increases the peripheral pulse pressure. On the other hand, the forward and backward waves
in the central aorta are shifted away from each other. For this reason, pulse pressure becomes much
amplified with increasing distance from the heart. And the exponential becomes less apparent.
Further, the magnitude of the backward wave relative to the forward wave increases with total
peripheral resistance. As a result, peripheral pulse pressure increases with vasoconstriction and
decreases with vasodilation.
We found that the wave reflection ceases to be a major factor over long time scales. Figure 1.7
shows two blood pressure signals measured at the same time but at different sites in the arterial
tree. Note that the signal variations are different within a beat, since the wave reflections differs
between the two measurement sites. However, if we zoom out to see the signal envelopes, they are
more similar. These beat-to-beat variations are always present and due to, for example, breathing
and compensatory physiologic mechanisms. Therefore, we proposed several techniques which can
estimate CO from peripheral ABP over long time scales.

8

(A)

(B)

Figure 1.6: Wave reflection and amplification.

9

Central BP
[mmHg]

mmHg

100
90
80
70
60
50
6486.2

100
90
80
70

6487.2

sec

60
50
6490

6495

6510

6515

6510

6515

Peripheral BP
[mmHg]

mmHg

100
90
80
70
60
50
6486.2

6500
6505
Time [sec]

100
90
80
70

sec

6487.2

60
50
6490

6495

6500
6505
Time [sec]

Figure 1.7: Two pressure waveforms simultaneously measured at two different positions.

10

[http://home.lu.lv/]

PTT
Figure 1.8: Measurement of PTT.

1.1.2

Pulse wave velocity, pulse transit time and pulse arrival time

Pulse wave velocity (PWV) is the speed of energy wave transmission in the arteries. According
to the Bramwell-Hill equation, PWV varies inversely with the square root of arterial compliance
(AC) [11]. Indeed, PWV increases as the arteries stiffen with aging and disease [43, 56]. PWV is
now the most important index of arterial stiffness for two reasons [60]. Firstly, it is an independent
predictor of all-cause mortality and cardiovascular events in hypertensive and other patients [60,
109]. Secondly, while direct measurement of AC involves nontrivial tracking of changes in vessel
area and ABP, PWV is easier to measure [10, 60].
PWV is most easily determined as the ratio of the distance and pulse transit time (PTT) between
central and peripheral arterial sites. PTT is estimated by measuring typically ABP waveforms at the
two sites with non-invasive, handheld tonometers or Doppler ultrasound probes and then detecting
the foot-to-foot time delay between the waveforms (Figure 1.8). This regional PWV measurement
technique is used by most clinicians [60] and commercial systems [96].
A simpler method measures the time delay between the R-wave of an ECG waveform and

11

PEP

PTT

PAT

Figure 1.9: Measurement of PAT.

the distal arterial waveform foot has captured great interest [1, 37, 48, 62, 70, 113]. This time
delay is called pulse arrival time (PAT) and it has captured great interest recently. PAT is equal
to the sum of PTT and the pre-ejection period (PEP), where PEP is determined by the ventricular
electro-mechanical delay and isovolumic contraction phase (Figure 1.9).

12

1.2 Arterial system modeling
Mathematical modeling of arterial hemodynamics has been longstanding. Two basic modeling
approaches have been employed: forward modeling and inverse modeling. Forward modeling
concerns building a model based on physical principles to predict data (i.e., estimating data from
physical models with known parameters). This approach is useful for testing our understanding of
the physiology underlying arterial hemodynamics. On the other hand, inverse modeling concerns
building a model from observed data (e.g., estimating model parameters by fitting measured waveforms). Although less developed than its forward modeling counterpart, this approach is becoming
more and more important by virtue of its ability to permit individualized monitoring of arterial
hemodynamics.
The available models may be divided into two classes: lumped-parameter models and distributedparameter models. The most popular lumped-parameter model is the "Windkessel" model proposed by Frank [91]. It analogizes the arterial system as a capacitor connected in parallel with
a resistor. The capacitor represents the large artery compliance, whereas the resistor represents
the total peripheral resistance. This 2-parameter Windkessel model can be extended to include
additional circuit elements in order to improve accuracy [98]. Because Windkessel models are so
simple, they are highly suitable for parameter estimation purposes. That is, Windkessel models
are characterized by only a few parameters, which can be readily estimated from the limited arterial waveforms typically available in practice. However, lumped-parameter models assume infinite
pulse wave velocity and therefore cannot reproduce wave propagation and reflection phenomena
that are essential in shaping these waveforms.
By contrast, distributed-parameter models can reproduce wave propagation and reflection phenomena through finite pulse wave velocity. Most often, distributed-parameter models represent the
arterial system using a one-dimensional simplification of the Navier-Stokes equation. These models usually account for both geometrical and mechanical properties of the arteries explicitly as model parameters. Detailed distributed-parameter models have been built that account for multi-level
branching, elastic and geometric tapering, and arterial terminations [3, 4, 44, 86, 95, 110, 117].
13

These comprehensive models can provide great accuracy. However, the models cannot be readily
applied for parameter estimation purposes, because they are characterized by an excessive number
of model parameters that makes it virtually impossible to obtain unique parameter estimates from
limited arterial waveforms.
Less accurate, yet mathematically tractable, distributed-parameter models have also been developed. These models usually consist of multiple tubes with terminal loads in parallel. Often
times, the model comprises two such tubes and loads ("T-tube" model). The tube represents the
wave propagation path in the large conduit arteries, whereas the load signifies the wave reflection
site (e.g., arterial bed distal to a peripheral artery). The tube can be elastically and/or geometrically tapered or uniform as well as lossy (i.e., exhibits energy dissipation) or lossless, while the load
can be non-parametric (i.e., characterized without a model structure through a generic frequency
response) or parametric. It turns out that the simplest of these models, the uniform, lossless tube
with parametric load, is almost as accurate as the most complicated of the models. Indeed, this
model, which will henceforth be referred to simply as the tube-load model, is often able to fit
arterial pressure and flow waveforms remarkably well despite being characterized by only a few
parameters. Consequently, the tube-load model carries advantages of both Windkessel and comprehensive distributed-parameter models and therefore permits an attractive platform for improved
monitoring of arterial hemodynamics.

1.2.1

Windkessel model

Over a century ago, Frank first suggested that SV could be measured from ABP waveforms [91].
Shortly thereafter, Erlanger et al. introduced the first analysis technique for doing so [34]. They
observed that pulse pressure (PP, i.e., systolic pressure minus diastolic pressure) in the aorta was
positively correlated to SV. Thus, their technique simply involved detecting PP from the central
ABP waveform to monitor relative change in SV for each beat or CO via PP·HR. However, a
major assumption of this PP technique is that cardiac ejection occurs instantly when, in actuality,
it occurs over finite time in which a portion of the ejected blood passes through the aorta and into

14

CO

ABP

AC

TPR

Figure 1.10: The Windkessel model which characterizes the arterial tree.

the periphery. Amongst the many ensuing studies, Bourgeois et al. performed perhaps the most
compelling [9]. These investigators developed a more intricate central ABP waveform analysis
technique that made no assumptions about the cardiac ejection time. They specifically represented
the arterial tree with a Windkessel model accounting for the lumped compliance of the large arteries
(AC) and the TPR of the small arteries (Figure 1.10). According to this model, central ABP should
decay like a pure exponential during each diastolic interval with a time constant (τ ) equal to the
product of TPR and AC.

1.2.2 Tube-load model
1.2.2.1 Model description
Figure 1.11(A) illustrates the tube-load model. This model represents the arterial system as a
parallel connection of m uniform, lossless tubes with parametric loads. The meaning of the tubes
and loads depend on perspective. From the perspective of the central (ascending) aorta, a tube
represents the wave propagation path through a segment of the aorta, whereas the load represents an
effective reflection site due to the entire arterial network distal to the segment. For example, for the

15

T-tube model in which m is equal to two, the two effective reflection sites correspond to the headend and body-end arterial beds. The flow through the body-end tube represents the descending
aortic flow, whereas the flow through the head-end tube represents the difference between central
and descending aortic flows. From the perspective of a peripheral artery, on the other hand, a
tube represents the wave propagation path from the central aorta to the peripheral artery, whereas
the load represents the reflection site due to the arterial bed distal to the peripheral artery. In this
case, m is equal to the number of peripheral arteries. The flow at the proximal end of a tube is
not measurable. It represents the component of central aortic flow that reaches a peripheral artery.
However, the sum of the flows at the proximal end of all tubes corresponds to the total central
aortic flow.

√
The ith tube is of length di and has constant characteristic impedance Zci = li /ci , where

li and ci are the large artery inertance and compliance, respectively. Pressure and flow waves
√
propagate with constant time delay Ti = li · ci from one end of the tube to the other. Note that
this time delay corresponds to pulse transit time and that its governing equation arises from the
Bramwell-Hill equation [11]. The mean value of the waves is constant throughout the tube.
The ith load has frequency-dependent impedance ZLi ( jω ), where j is the imaginary number
and ω is the frequency, that is characterized by a pole-zero structure. Figure 1.11(B) shows three
types of commonly used loads along with the specific form of their ZLi ( jω ). The Type I and
Type II loads are 3-parameter Windkessel models. These models account for the resistance R
and compliance C of the effective load or peripheral resistance and compliance (depending on
perspective) while matching the tube impedance at infinite frequency per arterial input impedance
studies [72, 73]. The Type III load is a generic pole-zero model. A principal advantage of this
type of model is that it allows a flexible system order rather than being fixed to first-order as with
its Type I and Type II counterparts. The disadvantage is that it has no physiologic meaning. As
a result, its coefficients are neither dependent on each other nor constrained as they are with the
Type I and Type II loads. For any load, the wave reflection coefficient at the ith load is given by
the following relationship involving tube and load impedances:

16

(A)
Central Aorta

Distal Arterial Beds
T1

P1(d1, jZ)

Zc1

Q1(d1, jZ)

P1(0, jZ)
Q1(0, jZ)

ZL1(jZ)

Pfi(x, jZ)
Qfi(x, jZ)
P(jZ)
Q(jZ)

Ti

Pi(di, jZ)
Qi(di, jZ)

Pi(0, jZ)
Zci
Qi(0, jZ)
x
Pbi(x, jZ)
Qbi(x, jZ)

Tm

Pm(dm, jZ)
Qm(dm, jZ)

Zcm

Pm(0, jZ)
Qm(0, jZ)

ZLi(jZ)

ZLm(jZ)

(B)

Type I

Type II

Zc
C

Type III

Generic Pole-Zero
Model

Zc
R
C

R

Figure 1.11: (A) The tube-load model with arbitrary load. (B) Three types of commonly used
loads.

17

Z ( jω ) − Zci
Γi ( jω ) = Li
.
ZLi ( jω ) + Zci

(1.1)

Qualitatively, pressure and flow waves propagate in the forward direction (proximal to distal
tube ends) along a tube without distortion and are proportional to each other. These waves are
reflected in the opposite direction at the load due to the impedance mismatch (Zci ̸= ZLi ( jω )). The
resulting backward pressure and flow waves likewise propagate along the tube without distortion
and are proportional to each other but have opposite sign. The actual arterial pressure and flow
waveforms at any point on the tube then arise as the sum of the forward and backward propagating
waves shifted in time to account for their wave propagation time to the point of interest.
Quantitatively, pressure and flow waves on a tube are related through its characteristic impedance
as follows:

Q f i (x, jω ) =

Pf i (x, jω )
P (x, jω )
, Qbi (x, jω ) = bi
.
Zci
Zci

(1.2)

Here, Pf i (x, jω ) and Pbi (x, jω ) are forward and backward propagating pressure waves in the
frequency-domain at a point x on the ith tube, and Q f i (x, jω ) and Qbi (x, jω ) are the corresponding
flow waves at the same point. Note that the forward waves actually represent the sum of all waves
propagating from the proximal to distal tube ends (i.e., the incident wave from the heart and the
backward waves re-reflected at the heart), while the backward waves may be interpreted analogously. Also, note that x = 0 and x = di correspond to the distal and proximal ends of the tube,
respectively.
The forward and backward waves at a distal tube end are related to each other through the wave
reflection coefficient as follows:

Pbi (0, jω ) = Γi ( jω ) · Pf i (0, jω ).

(1.3)

The forward and backward waves at any point on a tube may be expressed in terms of the
corresponding waves at the distal tube end as follows:

18

Pf i (x, jω ) = Pf i (0, jω )e jω Ti ·x/di
Pbi (x, jω ) = Pbi (0, jω )e− jω Ti ·x/di ,

(1.4)

where the exponential term is the frequency-domain time-shifting operator.
By combining equations (1.1) to (1.3), the actual arterial pressure and flow waveforms at any
point on a tube may then be expressed in terms of the forward and backward waves as follows:

Pi (x, jω ) = Pf i (x, jω ) + Pbi (x, jω )
= Pf i (0, jω ) · [e jω Ti ·x/di + Γi ( jω )e− jω Ti ·x/di ]
Qi (x, jω ) = Q f i (x, jω ) + Qbi (x, jω )
=

Pf i (0, jω ) jω T ·x/d
· [e i i − Γi ( jω )e− jω Ti ·x/di ],
Zci

(1.5)

where Pi (x, jω ) and Qi (x, jω ) are the arterial pressure and flow waveforms in the frequencydomain at point x on the ith tube.
Due to the parallel connection of the model, the central aortic pressure waveform is identical to the arterial pressure waveforms at each proximal tube end, whereas the central aortic flow
waveform is the sum of all flow waveforms at the proximal tube ends as follows:

P( jω ) = Pi (di , jω ) = Pf i (0, jω ) · [e jω Ti + Γi ( jω )e− jω Ti ]
Q( jω ) =

m

∑ Q(di, jω ) =

i=1

m P (0, jω )
fi

∑

i=1

Zci

· [e jω Ti − Γi ( jω )e− jω Ti ],

(1.6)

where P( jω ) and Q( jω ) are the central aortic pressure and flow waveforms in the frequencydomain.
Finally, equations (1.5) and (1.6) may be given explicitly in terms of the tube-load model
parameters by substituting a Γ( jω ) from figure 1.11(B) into these equations.

19

1.2.2.2

Assumptions and validity

Assumptions of the tube-load model include: (a) wave propagation without energy loss in large
conduit arteries, (b) a load characterized by a few parameters, and (c) non-interacting reflections
occurring at distal sites only by virtue of neglecting elastic and geometric tapering and multi-level
branching. Assumption (a) is quite valid. Friction in the large conduit arteries is indeed negligible,
because resistance is inversely proportional to the fourth power of the vessel radius. Pressure
loss in the descending aorta, for example, has been shown to be trivial [15]. Assumption (b) is
justifiable based on empirical data. That is, while the actual load is certainly complicated with
many parameters needed for its representation, the arterial input impedance computed with the
tube-load model has been shown to match that determined with standard non-parametric Fourier
analysis [13, 14]. Note, however, that an even simpler purely real load may not be supported by
empirical data [15]. Assumption (c) is the least tenable but can be defended to some extent. The
arterial terminations do often constitute the dominant reflection sites for two reasons. First, they
pose the greatest impedance mismatch, as the radius of the arterioles is much smaller than that of
proximal arteries [77]. Second, vessel tapering tends to be offset by vessel branching in the forward
direction so as to achieve relative impedance matching [73]. In addition, the tube-load model has
been shown to fit experimental waveforms almost as well as an exponentially tapered version of
the model [36]. On the other hand, backward waves should experience strong re-reflections as they
return to the heart due to necessarily significant impedance mismatches in the backward direction
[73]. Further, the multiple reflected waves that return from distal sites actually interact in the aorta
due to multi-level branching.
In short, the tube-load model has a physiologic foundation but does ignore aspects of actual
arterial hemodynamics. Despite its simplicity, it is able to fit experimental arterial pressure and
flow waveforms remarkably well. Figure 1.12 illustrates major waveform phenomena that the
model can predict. This ability to fit experimental data provides further validation of the tube-load
model and suggests that it may be phenomenological in addition to physiological.

20

BP [mmHg]

100
80
60
Central

Peripheral

Figure 1.12: Experimental arterial pressure with increasing distance from the heart.

1.2.2.3

Parameter estimation

Most often, estimating the tube-load model parameters is accomplished by casting the governing
equations into a transfer function. The transfer function relating a pair of arterial pressure and/or
flow waveforms at any points on a tube may be obtained based on equation (1.5). For example,
using the T-tube model with Type II load, the transfer function relating the central aortic pressure
waveform to the central aortic flow waveform is given as follows:
1 e jω Ti − Γi ( jω )e− jω Ti
· P( jω ) i = 1, 2.
Zci e jω Ti + Γi ( jω )e− jω Ti

Qi (di , jω ) = Hi ( jω ) · P( jω ) =

(1.7)

As another example, using the Type I load, the transfer function relating the central aortic
pressure waveform to a peripheral arterial pressure waveform is given as follows:

1 + Γi ( jω )
Pi (0, jω ) = jω T
· P( jω )
e i + Γi ( jω )e− jω Ti
jω +
=
( jω +

RiCi

RiCi

1

1
+

1

1

2ZciCi

+

ZciCi

)e jω Ti +

· P( jω ).
1

2ZciCi

(1.8)

e− jω Ti

The former transfer function is defined by the eight unknown parameters of the T-tube model.
However, while the latter transfer function includes all four unknown model parameters of a single
tube and load, only three aggregate parameters are actually observable (Ti , RiCi and ZciCi ). Thus,

21

all four parameters cannot be estimated, but identification of the transfer function is simplified to a
three-parameter problem.
Estimation of the observable model parameters is accomplished in two steps. First, arterial pressure and flow waveforms corresponding to the input and output of the transfer function
of interest are measured. Then, the parameters are estimated by finding the transfer function,
which when applied to the measured input, optimally fits the measured output. Alternatively, in
some instances, the parameters of the transfer function may be optimally estimated using a priori
physiologic knowledge. The advantage of this alternative is to reduce the burden on the required
waveform measurements. In either case, parameter estimation is usually performed in the timedomain by converting the transfer function into a recursive difference equation, and the optimality
is typically established in the least squares sense.
The step of estimating the tube-load model parameters is actually quite challenging. First, the
transfer functions are not simply linear in distinct parameters. For example, as can be ascertained
from equations (1.7) and (1.8), the transfer functions are nonlinear in the Ti (pulse transit time) parameter. Second, the parameter values have numerical constraints. For instance, the characteristic
impedance should be smaller than the peripheral resistance, and all parameters must be positive and
not exceed physiologic bounds. For these two reasons, straightforward parameter estimation techniques with analytical solutions are generally not applicable. The parameters are instead typically
estimated via numerical search in which the needed global optimum cannot be guaranteed. Use
of brute force methods that search over a discretized grid in multi-dimensional parameter space
increases the likelihood of identifying the global optimum at the expense of substantial computational time. On the other hand, use of available local search methods such as the steepest descent
method, conjugate gradient method, Newton’s method and its Levenberg-Marquardt modification,
and simplex method (possibly with penalty factors for keeping the parameters within physiologic
bounds) [58] require little computational time, but the global optimum is seldom found without an
initial guess that resides near the global optimum. This problem is often mitigated by employing
multiple, initial guesses and then choosing the solution that represents the optimum amongst the

22

multiple solutions of the local search method. However, the computational time will obviously
increase with the number of initial guesses. Another practical issue is that the upper physiologic
bounds on the parameters are often unclear. However, the challenge of parameter estimation can
be alleviated to some degree by direct measurement of one or more parameters, especially pulse
transit time and load resistance [14, 17, 40, 105]. Despite these challenges, asymptotic variance
analysis has shown that the confidence intervals on the parameters estimates can be tight [40].

1.3 Organization
In this report, we will review the contribution of novel techniques for CO monitoring from a peripheral arterial blood pressure waveform. Chapter 2 discusses the proposed long time interval
analysis (LTIA) and applies the technique to a large, ICU human dataset (MIMIC II) and a human
lower body negative pressure (LBNP) experiment. Our technique was superior to other conventional methods when the change in CO became challenging. In the study, we found that the varying
AC introduced estimation errors. Therefore, we introduced the pulse transit time to eliminate the
influence of arterial compliance, as discussed in Chapter 3. Comparing with pulse transit time,
pulse arrival time gains popularity since it is even easier to measure. However, it is not adequate
to be a surrogate in replacing with pulse transit time. Therefore, we can only recommend pulse
transit time for monitoring arterial compliance changes. Conventional detection of pulse transit
time is sensitive to artifact, so we applied a black-box model which can robustly estimate pulse
transit time from blood pressure waveforms. Pulse transit time estimated in this approach was
employed to correct AC, which was validated both in an animal study and the LBNP experiment.
In Chapter 4, a novel technique of short time interval analysis was proposed to monitor the cardiac
output variation which permits beat-by-beat monitoring. The accuracy was also improved by the
pulse transit time correction. Further, we added an additional term to the LTIA method, which can
estimate CO from a pulmonary artery pressure. In the end, future direction is discussed in Chapter
6.

23

Chapter 2
CARDIAC OUTPUT MONITORING FROM PERIPHERAL ARTERIAL BLOOD
PRESSURE BY LONG TIME INTERVAL ANALYSIS

2.1 Introduction
The acute shortage of clinical personnel [35], declining pulmonary artery catheter usage [112],
and recent success of goal-directed therapy [64, 81] collectively indicate the urgent need for an
accurate, continuous (i.e., automated), and minimally invasive cardiac output (CO) monitoring
technique. A potential practical approach for intensive care unit (ICU) patients is to track CO
by mathematical analysis of an arterial blood pressure (ABP) waveform obtained with an existing
radial artery line. Indeed, various "pulse contour analysis" techniques have been suggested in the
literature ([69] and references therein), and a few such techniques are now commercially offered
[26, 31]. The assessment of these techniques in patients has been the subject of a number of recent
articles published in this journal [6, 7, 19, 33, 76] and others. However, the relative accuracy of the
techniques has yet to be conclusively established [79].

2.2 The technique
We too have previously proposed a mathematical analysis technique to estimates relative CO
changes from an ABP waveform measured at any arterial site including the radial artery (Figure 2.1)[69]. Unlike all other techniques, the technique analyzes the slow, beat-to-beat changes in
the waveform wherein confounding arterial wave reflections cease to be a major factor in an attempt to maximize accuracy. More specifically, first, the ABP response to a single heart beat (h(t))
is estimated by analyzing the waveform over many beats. Then, the Windkessel time constant
(τ ), which is equal to the product of the total peripheral resistance (TPR) and the approximately
constant arterial compliance (AC), is determined by fitting an exponential to the tail end of this

24

Peripheral BP
60

120

h(t)

PP
j-1

40

PPj-1

PPj PPj+1
0.5

20

0

y(t) [mmHg]

x(t) [mmHg]

1

R j-1 R j Rj+1
0
1
2
Time [sec]

00

W

3
Time [sec]

6

PPj PPj+1

80
Rj-1

Rj

Rj+1

40

0

0

1
Time [sec]

2

MAP
CO v W
Figure 2.1: Continuous and minimally invasive technique for estimating relative cardiac output
(CO) change by unique long time interval analysis (LTIA) of an arterial blood pressure (ABP)
waveform obtained with an existing radial artery line.

response once the faster wave reflections vanish. Finally, CO is computed to within a 1/AC scale
factor by dividing mean ABP (MAP) with τ . (Figure reffig:MIMIC-LTIA caption for further details.) We have verified this "long time interval analysis" (LTIA) technique against reference CO
measurements from animals and humans during various physiologic conditions [69, 59, 87]. However, as recommended in a recent editorial in this journal [19], the technique has yet to be assessed
in a significant ICU patient population.
Recently, Sun et al. used their "MIMIC II" database, which includes radial ABP waveforms
and thermodilution CO measurements from a substantial number of ICU patients, to compare eight
published pulse contour analysis techniques [103]. These investigators found that pulse pressure
times heart rate normalized by the sum of systolic and diastolic pressures (PP · HR/(SP+DP)),
as proposed by Liljestrand et al. [57], was most accurate in tracking changes in the reference
thermodilution CO measurements. They concluded that their electronic database could represent
a useful standard for testing pulse contour analysis techniques, with the PP · HR/(SP+DP) technique serving as a benchmark for comparison, and invited others to assess their own techniques by

25

making the database readily and freely available.
We assessed the LTIA technique using the MIMIC II database. In this way, we were able
to demonstrate the relative accuracy of the technique while testing it in a significant ICU patient
population. We describe the retrospective data analysis below.

2.3 Experiment 1: validation in the MIMIC II database
2.3.1

Materials and analysis

We studied all pairs of radial ABP waveforms and reference thermodilution CO measurements
in the MIMIC II database that did not meet any pre-defined exclusion criteria. We applied the
LTIA, PP·HR/(SP+DP), and other previous techniques to the ABP waveforms. Since all of these
techniques estimate CO to within a patient specific scale factor (i.e., K·CO or "proportional CO"),
we calibrated each technique (i.e., determined K for each technique) by scaling its proportional CO
estimates to a single value yielded by thermodilution per patient. We then assessed the accuracy
of each technique based on the magnitude of the differences between its calibrated CO estimates
and the thermodilution CO measurements ("CO errors"). Finally, we compared the accuracy of the
techniques via statistical tests of their CO error magnitudes.
The MIMIC (Multiparameter Intelligent Monitoring in Intensive Care) II database is described
in detail elsewhere[103, 90]. Briefly, the database includes anonymised, physiologic and clinical
data from patients of various ICUs of a university hospital. The public database is growing. At
the time of our downloading of the database, data from 2,769 patients were available. The physiologic data consist of continuous measurements such as invasive radial ABP and ECG waveforms
sampled at 125 Hz and time aligned, discrete measurements including thermodilution CO. Each
of the available thermodilution measurements was obtained via the pulmonary artery catheter and
a single bolus injection (rather than multiple bolus injections). The clinical data constitute wide
ranging information including patient characteristics. Our analysis of the database was approved
by the Michigan State University IRB (# X05-597). We extracted all 1-min segments of the ra-

26

dial ABP waveforms that coincided with each reference thermodilution CO measurement in the
database and included all of these data pairs in the study. A total of 1,915 pairs of ABP (and ECG)
waveform segments and thermodilution CO measurements from 197 patients were available. We
then excluded those pairs (a) from patients with only one thermodilution measurement (as relative
CO changes within a subject is effectively estimated); (b) from patients on intra-aortic balloon
pumps as indicated by the presence of diastolic augmentation in the ABP waveforms (a standard
contraindication of pulse contour analysis); and (c) with obvious artifact in the ABP waveform segments as ascertained by visual examination (to evaluate the ability to track CO rather than to detect
and suppress artifact). A total of 1,482 data pairs from 169 patients remained for analysis. We applied the LTIA technique to the 1-min radial ABP waveform segments to estimate proportional CO
in each patient. Since our data for analysis were not identical to those of Sun et al. (who actually
analyzed 1,164 data pairs from 120 patients [103]), we also likewise estimated proportional CO
with the benchmark PP·HR/(SP+DP) technique and two other previous techniques of particular
relevance, namely PP·HR and MAP. The PP·HR technique, which tracks CO via the product of
pulse pressure and heart rate, is perhaps the most widely used pulse contour analysis (e.g., two
commercial devices are based on this technique [88]). The MAP technique, which tracks CO via mean ABP, is the most basic pulse contour analysis and therefore serves as a useful reference
for comparison [103]. In addition, we similarly explored our technique after the normalization of
Liljestrand et al. [57] (LTIA/(SP+DP)). We calibrated each of the five investigational techniques
using a single value yielded by thermodilution per patient. We specifically scaled the proportional
CO (i.e., K · CO) estimates of each technique to have the same mean value as the thermodilution
measurements in each patient. Thus, for each patient, K was effectively set to the ratio of the mean
value of the K ·CO estimates of the technique to the mean value of the thermodilution CO measurements. We assessed the accuracy of each technique through the differences between its calibrated
CO estimates and the thermodilution CO measurements. We quantified the magnitude of these
CO errors in terms of two metrics drawn from Bland-Altman analysis. One metric is the limitsof-agreement of the absolute errors (µ − 1.96 · σ /µ + 1.96 · σ , where µ and σ are respectively the

27

bias error (i.e., average of all errors) and precision error (i.e., standard deviation of all errors)).
Use of this metric allowed comparisons to the investigation of Sun et al. [103]. The other met√
ric is the root-mean-square of the relative errors (RMSE= µ 2 + σ 2 ). Use of this metric, which
combines the bias and precision errors into a single number reflecting the total error, permitted
comparisons to our previous studies [69, 59]. Further, use of relative errors allowed comparisons
to the recommendations of Critchley et al. [28]. We statistically compared the techniques based
on the square of their relative errors, which similarly reflect the total error. Since these squarederrors were not normally distributed, we used the Wilcoxon signed-rank test to determine whether
the median of the differences between the squared-errors of the published LTIA technique and the
squared-errors of another investigational technique was statistically significant. It should be noted that these squared-error differences (i.e., the squared-errors of the LTIA technique minus the
corresponding squared-errors of another technique) actually constituted repeated measures rather
than truly independent samples with zero correlation.
However, we did not make adjustments for the repeated measures for two reasons. Firstly, the
adjustment required would be very complicated and therefore difficult to follow (unlike the basic
Wilcoxon signed-rank test). Secondly, and most importantly, we tested these data in terms of the
extent of the dependence of samples and found that the samples correlated only little (0.08 to 0.22).
Thus, adjustment for repeated measures would not have materially altered the results.

2.3.2

Results

The average characteristics of the 1,482 pairs of 1-min radial ABP waveform segments and reference thermodilution CO measurements from 169 patients for study are as follows. The patients
were mostly old (Table 2.1), with two-thirds being male. Three-quarters of the patients had ischemic or other forms of heart disease, whereas the remaining patients had various other conditions. The patients stayed mainly in the cardiac surgery recovery unit (70%) but also in the
coronary care unit (19%) and medical or surgical ICUs (11%). Their average SAPS (Simplified
Acute Physiology Score) I was 15.5 (4.4 SD) (Table 2.1). On average, 8.8 (6.3) thermodilution CO

28

Table 2.1: Average characteristics of patients and data.
Characteristic
Age
SAPS I
Number of CO measurements per patient
Duration of CO measurements per patient day
CO
MAP
HR
CO change magnitude (relative to mean CO in patient)

Units
year

Mean(SD)
N
67.7(13.0) 169
15.5(4.4)
169
8.8(6.3)
169
1.1(1.1)
169
L/min
5.3(1.7)
1,482
mmHg 73.6(10.8) 1,482
bpm
86.2(12.6) 1,482
%
12.3(9.9) 1,482

Table 2.2: Overall cardiac output estimation accuracy of the investigational techniques.
Technique

RMSE (%)

Limits-of-Agreement (L/min)

LTIA
MAP
PP·HR
PP·HR/(SP+DP)
LTIA/(SP+DP)

18.8
19.8
18.4
14.8
15.0

-1.96/+1.96
-1.90/+1.90
-1.92/+1.92
-1.51/+1.51
-1.56/+1.56

Wilcoxon Signed-Rank
Test (p)
0.85
0.02
<0.0005
<0.0005

measurements made over the course of 1.1 (1.1) days were available from each patient (Table 2.1).
The average thermodilution CO was similar to that of a healthy adult population, whereas the average MAP and heart rate (HR) were not (Table 2.1). The average magnitude of the thermodilution
CO change relative to the mean thermodilution CO in the patient was 12.3 (9.9) percent (Table 2.1).
Over all the data pairs and patients, the LTIA technique achieved a RMSE of 18.8% and a
limits-of-agreement of -1.96/+1.96 L/min (Table 2.2). The MAP and PP·HR techniques attained
very similar overall error magnitudes, though the median squared-error difference between the
LTIA technique and the latter technique did reach statistical significance (Table 2.2). The normalization of Liljestrand et al. [57] somewhat improved the overall accuracy of both the PP·HR
and LTIA techniques. That is, the PP·HR/(SP+DP) and LTIA/(SP+DP) techniques both showed
reductions in RMSE by ∼3.7% and in the lower and upper limits-of-agreement by ∼0.4 L/min
(Table 2.2). Further, the median squared-error difference between the original LTIA technique and
each of these techniques was statistically significant (Table 2.2).
The CO estimation accuracy of the investigational techniques is indicated as a function of
29

minimum thermodilution CO change magnitude (Figure 2.2). That is, the data points at Z on the
x-axis denote the squared-errors (median ± quartiles) of each technique only over those data pairs
for which the magnitude of the thermodilution CO change relative to the mean thermodilution CO
in the patient exceeded Z%. So, for example, 0 on the x-axis would correspond to the results
over all the data pairs (which are shown in Table 2.2). The p-values reveal the levels of statistical
significance of the median squared-error difference between the pair of techniques with the lowest
median squared-errors. (These p-values represent upper bounds on the significance level of the
median squared-error difference between the technique with the lowest median squared-error and
the remaining techniques in the figure.)
The median squared-error of the LTIA technique increased with the minimum thermodilution
CO change magnitude (Figure 2.2). However, the median squared-errors of the PP·HR technique
and especially the MAP technique rose at a greater rate (Figure 2.2). As a result, the median
squared-error difference between the LTIA technique and each of these basic techniques became
greater with minimum thermodilution CO change magnitude and reached statistical significance
when the minimum change magnitude was ≥30% (Figure˜effig:MIMIC-Result). In particular, the
r
median squared-error differences between the LTIA technique and the PP·HR technique were 45 (-322:69 quartiles), -128 (-704:23), and -862 (-2871:306)%2 for thermodilution CO change
magnitudes exceeding 30, 50, and 70%, respectively. The normalization of Liljestrand et al. [57]
was able to yield modest, statistically significant reductions in the median squared-error for both
the PP·HR and LTIA techniques when the minimum thermodilution CO change magnitude was
10%, but not any higher (Figure 2.2). In fact, the median squared-errors of these techniques often
increased relative to the un-normalized techniques as the minimum thermodilution CO change
magnitude grew (Figure 2.2 wherein the results of the normalized LTIA technique are not shown
to simplify the figure.)

30

789(152)

9(5)

MAP
PP·HR
PP·HR/(SP+DP)
LTIA

2

CO Squared-Error [% ]

104

Number of CO Measurements (and Patients)
142(72)
31(23)

3

10

2

10

p<0.005
10

p=0.007

p=0.006

30
50
Minimum CO Change Magnitude [%]

p=0.055
70

Figure 2.2: CO estimation accuracy of the investigational techniques (on log scale) as a function
of the magnitude of the reference CO change.

31

2.3.3

Discussion

In this study, we assessed our previously developed LTIA technique for uniquely estimating proportional CO from an ABP waveform (Figure 2.1) using the readily and freely available MIMIC
II database18. For comparison, we also investigated previous pulse contour analysis techniques of
particular relevance. Our results not only provide a first-time indication of the efficacy of the LTIA
technique in a significant ICU patient population but also permit future comparisons of it to other
techniques.
We specifically studied 1,482 pairs of 1-min radial ABP waveform segments without obvious artifact and reference CO measurements via single bolus injection thermodilution from 169
patients (Table 2.1). The LTIA technique achieved an overall CO error of 18.8% after a single
calibration with thermodilution in each patient (Table 2.2). Note that since the precision error of
the reference measurements here is known to be ∼17% [99, 46, 100], a clinically acceptable level
of agreement would be within 19.7% according to the recommendations of Critchley et al. [28].
The overall calibrated CO errors of the PP·HR technique, which has perhaps been the most
widely used pulse contour analysis, and the MAP technique, which represents the most basic
analysis, were equivalent to that of the LTIA technique (Table 2.1). Further, these much simpler,
previous techniques may offer some practical advantages. Importantly, however, the magnitude of
the reference CO change was often small in the database. In fact, approximately three-quarters of
the thermodilution CO change magnitudes (relative to the mean thermodilution CO in the patient)
were less than the precision error of the reference measurements. Without significant changes, any
reproducible pulse contour analysis technique, when calibrated, will be able to achieve a reasonable
level of CO estimation accuracy.
The MIMIC II database did allow for reasonable comparisons of the techniques only during
the appreciable reference CO changes. Indeed, as the magnitude of the thermodilution CO change
increased, the accuracy of the LTIA technique became increasingly and statistically superior to the
PP·HR and MAP techniques (Figure 2.2).
The normalization with SP+DP suggested by Liljestrand et al. to correct for any ABP-dependent

32

AC changes [57] did afford some improvement in the overall accuracy of the PP·HR technique as
well as the LTIA technique. In particular, the PP·HR /(SP+DP) technique, which was shown to
perform best amongst the eight pulse contour analysis techniques studied by Sun et al. using the
same database [103], and the LTIA/(SP+DP) technique both achieved overall calibrated CO errors
of ∼15% (Table 2.2). However, when the magnitude of the thermodilution CO change increased,
the normalization was not helpful and even had a tendency to degrade the accuracy of the PP·HR
and LTIA techniques (Figure 2.2). Thus, the effectiveness of the normalization here may merely
be due to blunting the estimated CO change so as to yield better correspondence to the largely
unvarying thermodilution CO measurements rather than actually correcting for changes in AC.
Consequently, this normalization may not be generally advisable. However, other types of AC
correction factors should not be discounted.
Like the pulse contour analysis study with the MIMIC II database by Sun et al. [103], we
assessed all of the investigational techniques using 1-min radial ABP waveform segments for analysis. However, we initially verified the LTIA technique with 6-min ABP waveform segments
[69, 59]. We therefore also applied the LTIA technique to ABP waveform segments of 6-min durations here, and its performance did not materially improve (e.g., the overall calibrated CO error was
17.8%). This comparative result indicates that the LTIA technique may be applied to a waveform
duration that is comparable to those employed by conventional techniques without any significant
sacrifice in accuracy.
In addition to the assessment of the LTIA technique, there were other differences in methodology and materials between this study and that of Sun et al. [103]. Firstly, we had more data
for analysis, because the MIMIC II database had grown since their study. Secondly, we excluded
∼22% of the available data (1% for only one reference CO measurement from the patient; 15%
for patients on intra-aortic balloon pumps; and 6% for obvious waveform artifact), whereas Sun
et al. discarded only ∼15% mainly due to a greater tolerance of artifact in the ABP waveforms.
(Note that, like these investigators, we did not exclude data due to unsteady conditions wherein
the thermodilution measurements may be less useful as a CO reference, arterial line damping, or

33

aortic valve regurgitation, all of which may represent sources of error here.) Thirdly, we calibrated
the proportional CO estimates with the mean thermodilution CO in a patient, while Sun et al. employed an optimal calibration likewise involving all thermodilution CO measurements in a patient
and a calibration with one thermodilution measurement per patient. Fourthly, we studied the CO
estimation accuracy as a function of relative CO change magnitude instead of directional (sign)
agreement with the largest reference CO change in each patient as they did. Despite these differences, our results were quite similar to the analogous ones of Sun et al. In particular, the average
patient and data characteristics contrasted little. Also, our mean calibration turned out to yield
only slightly higher CO errors than their optimal calibration (results not shown). Finally, although
the limits-of-agreement here are a bit tighter than those of Sun et al. due to our more stringent
requirements on waveform quality, the relative standing of the previous techniques based on this
accuracy metric as well as the RMSE metric was maintained over all the data.
The main limitation of this study is the non-trivial error in the reference CO measurements
available in the MIMIC II database. (Note that, to somewhat compensate for this error, we performed the calibration using the mean, rather than a single, thermodilution CO in each patient.)
Even with this limitation, we felt that it was sensible to test the LTIA technique using the readily
and freely available database for two reasons. Firstly, the study would be efficient and without
any risk to human subjects. Secondly, and most importantly, the accuracy of the technique relative
to other techniques could be fairly revealed, because all technique developers, including vendors
offering proprietary techniques, have access to the same data.
In conclusion, we have assessed a continuous and minimally invasive technique for estimating relative CO change by unique LTIA of a radial ABP waveform in a significant ICU patient
population using a database that may ultimately develop into a standard for testing pulse contour
analysis techniques. The technique achieved a CO estimation error that was overall within recommended clinical limits and became increasingly and significantly smaller than previous techniques
as the reference CO change became more meaningful. While the ability to continuously monitor
relative CO change would be useful for detecting a hemodynamic event or directing therapy in

34

ICU patients, future extensions of the LTIA technique to provide absolute CO via a non-invasive
calibration and to effectively correct for any AC change are worthwhile.

2.4 Experiment 2: validation in a lower body negative pressure study
2.4.1

Materials and analysis

The ACEMMR Team has developed a safe and reproducible human LBNP protocol that is approved by the Institutional Review Board of the Brooke Army Medical Center (BAMC; Fort
Sam Houston, TX). The protocol is documented in detail in several recent publications (e.g.,
[22, 25, 24]). Briefly, 129 volunteers are recruited from military personnel at the USAISR and
BAMC as well as nearby civilian communities. Men and women between 18 and 55 years of age
that are nonsmokers and not pregnant, have no cardiovascular abnormalities (e.g., hypotension,
neural dysfunction), and meet military fitness and health standards are included in the study after
obtaining informed, written consent. Prior to experimentation, the subjects are instructed to abstain
from stimulants (e.g., caffeine) and are familiarized with the protocol.
The subject is placed in the supine posture and secured in an LBNP chamber using a neoprene
skirt designed to form an airtight seal between the subject and the chamber (Figure 2.3). Instruments for measuring hemodynamic, neural, and metabolic variables are positioned. The physiologic variables are recorded during a five-minute baseline period and following sequential exposure to
15, 30, 45, 60, 70, 90, and 100 mmHg of LBNP for five minutes each. Early termination of LBNP
occurs (i.e., return of chamber pressure to 0 mmHg) upon the appearance of cardiovascular collapse defined as follows: (1) precipitous fall in systolic ABP > 15 mmHg and/or precipitous fall in
HR > 15 bpm; (2) systolic ABP < 80 mmHg; and/or (3) subject request due to symptoms such as
nausea, dizziness, or lightheadedness. After cessation of LBNP and a five-minute transition period
to allow the return of fluid sequestered in the lower body, the physiologic variables are recorded for
an additional five-minute recovery period. Note that subjects usually reach cardiovascular stability
within one to two minutes after termination of the final level of LBNP.

35

Figure 2.3: One subject in the LBNP experiment.

A non-invasive peripheral ABP waveform is measured with finger-cuff PPG (Finometer, TNOTPD Biomedical Instrumentation, Amsterdam, The Netherlands). ECG waveforms are measured
with a standard four-lead system. CO and beat-to-beat SV are measured non-invasively with EBI (BioZ Impedance Cardiograph, Cardiodynamics, San Diego, CA). EBI correlates SV changes
with the electrical impedance changes in the thorax over each heart beat that are elicited by a lowintensity, high frequency alternating current [27]. Other physiologic variables not directly pertinent
to the project are also measured including arterial oxygen saturation via pulse oximetry and, sometimes, tissue (muscle) oxygen saturation and pH via near-infrared spectroscopy. All transducers
are interfaced to a personal computer with commercial hardware and software (WINDAQ, Dataq
Instruments, Akron, OH). The physiologic variables are recorded at a sampling rate of 500 Hz.

36

We compared three techniques for the estimation of CO: MAP, PP·HR and LTIA. We again
evaluated the accuracy of the individual techniques in terms of the RMSNE.

2.4.2 Results
Figure 2.4 shows the result of LTIA comparing with the reference measurement. As expected,
mean ABP was maintained around the baseline level due to compensatory physiologic mechanisms. The PP·HR did not follow the decreasing trend during the LBNP process. Comparing
the reference, the Modelflow method overestimated the CO during the LBNP process. The LTIA
technique is similar with the Modelflow technique during the LBNP stages. At the recovery stage,
however, the LTIA returned to baseline level but Modelflow failed to indicate the return.

2.4.3

Discussion

The human LBNP experiment is considered as a safe simulation of central hypovolemia. In this
study, we evaluated the accuracy of five techniques in terms of the capabilities in indicating hemorrhage and recovery. MAP and PP·HR did not indicate the decreasing trend in the LBNP stage.
Modelflow and LTIA showed falling during the experiment but the former method failed to return
to baseline at the recovery stage. Among all candidate methods, CO estimated by ICG is the most
sensitive marker of hypovolemia.
In this study, we assume the AC should be constant. However, AC may be adjusted by varying
ABP and vasomotor tone. In the next chapter, we introduced a technique which utilizing PTT to
correct the influence of AC.

37

Group Average Results
110

CO Estimation [%]

100

90

80
MAP
PP HR
LTIA

70

Modelflow
ICG
60
Baseline

-15

-30
-45
LBNP Level [mmHg]

-60

Figure 2.4: Comparison of the candidate techniques for estimating CO.

38

Recovery

Chapter 3
PULSE TRANSIT TIME FOR CORRECTING ARTERIAL COMPLIANCE

3.1 Introduction
In the previous chapter, we investigated a technique for estimating CO from peripheral ABP waveform. The technique can overcome the problem of wave contour distortion introduced by wave
reflection. The accuracy has been validated in a ICU patient study and a human LBNP study.
However, we also found that the varying AC could be a confounding factor in the estimation.
Previous techniques employ empirical curves, in which AC is a averaged function of pressure. This
approach ignores the patient-to-patient variation and vasomotor tone. Another potentially feasible
approach for correcting AC is the introduction of PTT, which is a direct function of AC. In this
study, we will investigate the efficacy of PTT in correcting AC. We first compared the most precise
indicator between two transit times in terms of their capabilities in tracking with ABP. Next, we
proposed a technique which can robustly estimate PTT. Further, we improved the accuracy of the
LTIA in monitoring CO in an animal study and the LBNP study via PTT.

3.2 Pulse arrival time is not an adequate surrogate for pulse transit time as
a marker of blood pressure
The tight relationship between pulse transit time (PTT) and arterial blood pressure (ABP) has long
been known [5, 12]. The physiologic mechanisms responsible for this relationship are well understood. PTT decreases as the arterial elastic modulus increases according to the Moens-Korteweg
equation [73, 83]. The arterial elastic modulus, in turn, increases as ABP increases, because collagen fibers are slack and do not apply tension until the arterial wall is stretched. While changes in
vasomotor tone can also modulate the arterial elastic modulus, this effect is less of a factor in the
aorta wherein smooth muscle is relatively sparse [16].

39

PTT can be estimated simply as the foot-to-foot time delay between proximal and distal arterial
waveforms. Thus, PTT could conceivably permit continuous, non-invasive, and cuff-less ABP
monitoring in the acute setting (after an initial calibration). Indeed, many researchers have pursued
PTT as a marker of ABP [83].
Thomas proposed to make the measurement process even simpler by instead using the time
delay between the R-wave of an ECG waveform and the distal arterial waveform foot [108]. This
pulse arrival time (PAT) has captured great interest recently [1, 37, 70, 113]. PAT is equal to
the sum of PTT and the pre-ejection period (PEP). However, PEP, which is determined by the
ventricular electro-mechanical delay and isovolumic contraction phase, can vary with contractility
and afterload while often constituting a nontrivial fraction of PTT [41, 71, 80, 89]. Thus, PAT, on
the contrary, may not be an adequate surrogate for PTT as a marker of ABP.
To our knowledge, only a few researchers have compared PAT to PTT in terms of their ability
to predict ABP. Steptoe et al. studied humans and concluded that PAT could be used in lieu of PTT
[97]; however, for ethical reasons, the elicited ABP range was too narrow to provide a significant
challenge. Ochiai et al. examined animals during several different hemodynamic interventions and
drew a similar conclusion [75]; however, the comparisons were made over just a single intervention
at a time and were therefore likewise less challenging. Geddes et al. investigated animals over a
wide ABP range and concluded that PAT could not be used in place of PTT [39]; however, only
a qualitative result from one subject was provided to justify this conclusion. Payne et al. recently
performed a complex study in humans and concluded that PAT was an unreliable marker of ABP
[78]; however, PTT was similarly ineffective perhaps due to artifact in the non-invasive arterial
waveforms that were measured. Thus, continued efforts are needed to determine whether PAT may
be used as a surrogate for PTT as a marker of ABP or not.
In this study, we compared PAT and PTT in terms of their ability to predict ABP in animals.
Notable aspects of the study include: (a) estimating PAT and PTT through the aorta from high
fidelity, invasive arterial waveforms; (b) inducing a wide ABP range via a broad array of hemodynamic interventions; (c) evaluating PAT and PTT across multiple interventions at a time; and (d)

40

Table 3.1: Subject-by-subject results and interventions.
DBP Range [mmHg]
MIN
MAX
32
138

RMSE [mmHg]
1/PTT
1/PAT
5.8
12.4

Subject

Interventions

1

Phenylephrine
Nitroglycerin

2

Dobutamine
Esmolol

51

77

6.1

6.3

3

Norepinephrine
Xylazine

42

117

5.2

6.6

4

Hemorrhage
Saline

42

78

3.1

3.8

40

144

5.1

11.4

5

Phenylephrine
Nitroglycerin
Verapamil
High Rate Cardiac Pacing

29

106

6.5

18.0

6

Dobutamine
Esmolol
Vasopressin
Low Rate Cardiac Pacing

Mean±SD

-

39±8

110±29

5.3±1.2 9.8±5.2

providing quantitative results from all subjects.
We studied experimental data collected from six anesthetized dogs under a protocol approved
by the MSU All-University Committee on Animal Use and Care. The materials and methods for
data collection are described in detail elsewhere [104]. Briefly, the data included ABP waveforms
from the ascending aorta and femoral artery via micromanometer-tipped catheters and ECG waveforms, all at sampling rates of 500 Hz. For each subject, the data were obtained during a baseline
period and two to four hemodynamic interventions out of a set of 12 different interventions (Table 3.1).
We estimated PAT and PTT using the standard methods [72, 75, 83]. These methods approximate the time delays from the feet of the ABP waveforms wherein wave reflection interference is

41

minimal. More specifically, first, we automatically detected each foot of the ABP waveforms as the
intersection of a line tangent to the initial systolic rise and a horizontal line through the minimum
point [20]. This automatic foot detection method was most effective amongst a set of conventional
methods (e.g., peak of the derivative) [20]. Then, we visually examined many of the resulting foot
detections and, in effect, manually corrected most, if not all, of the misdetections. Finally, we estimated PAT for each beat as the time delay between the ECG R-wave and the subsequent femoral
artery ABP foot and PTT for each beat as the time delay between the ascending aortic ABP foot
and the ensuing femoral artery ABP foot.
We evaluated the beat-to-beat PAT and PTT estimates in terms of their ability to track beatto-beat ABP changes. (Note that averaging these quantities over multiple beats did not materially
improve the results.) Figure 3.1 illustrates our evaluation procedure per subject. First, we determined diastolic ABP (DBP), mean ABP (MBP), and systolic ABP (SBP) for each beat of the
femoral artery ABP waveforms.
Second, we calibrated each of the time delays to each of the ABP parameters using all of the
time delay estimates and ABP parameter measurements of the subject. That is, we found the line
that best fits these data and then mapped each time delay through the best fit line so as to predict
√
the ABP parameter. Third, we computed the root-mean-squared-error (RMSE = µ 2 + σ 2 , where

µ and σ are the mean (bias) and standard deviation (precision) of the errors) between the predicted
and measured ABP parameters. Then, because velocity often shows better linear correlation to
ABP than time delay [39, 96], we repeated this procedure for 1/PAT and 1/PTT. Finally, while we
focused on linear correlations, we also explored the effects of fitting curves instead of lines.
We statistically compared the ABP tracking ability of the time delays and their reciprocals.
We employed straightforward one-way repeated measures ANOVA to compare the subject average
RMSE values after log transformation (for more normally distributed data). When this test yielded
p < 0.05, we performed multiple pairwise comparisons using the Student-Newman-Keuls post hoc
test.
Table 3.2 summarizes the subject average results. The range of each ABP parameter was

42

Subject i

DBP or MBP or SBP [mmHg]

Line of best fit

eN

ek

e1

Measured
Predicted

-1

PTT or 1/PTT or PAT or 1/PAT [s or s ]

RMSE =

¦

N
k 1

2
ek

N
Figure 3.1: Procedure for evaluating pulse arrival time (PAT) and pulse transit time (PTT) in
terms of their ability to predict arterial blood pressure (ABP) parameters within a subject.

43

Table 3.2: Subject average results.
Range [mmHg]

PTT
1/PTT
PAT
1/PAT

DBP
MBP
MIN
MAX
MIN
MAX
39±8 110±29 52±6 138±32
RMSE [mmHg]
6.5±2.1
6.0±2.3
5.3±1.2
4.8±1.0
10.5±5.4*
1.2±5.7**
9.8±5.2*
10.4±5.6**

SBP
MIN
MAX
70±9 192±38
8.2±2.4++
7.5±2.2+
13.1±6.1*
11.9±6.1*

wide, with SBP varying the most and DBP changing the least. For each ABP parameter, 1/PTT
and 1/PAT yielded a lower RMSE value than their non-reciprocal counterparts. However, none
of these differences was significant. For PTT and 1/PTT, the DBP and MBP RMSE values were
significantly lower than the SBP RMSE value by 1.7 to 2.7 mmHg. For PAT and 1/PAT, the three
RMSE values were not significantly different. For each ABP parameter, the RMSE values for PAT
and 1/PAT were significantly higher than those for PTT and 1/PTT. The hike in RMSE obtained
via PAT over PTT and via 1/PAT over 1/PTT ranged from 4.0 to 5.6 mmHg. The DBP RMSE value
for 1/PAT, which was the lowest RMSE value attained via PAT, was 9.8±5.2 mmHg, whereas the
corresponding value for 1/PTT was 5.3±1.2 mmHg.
Table 3.1 shows the DBP RMSE values for 1/PTT and 1/PAT as well as the interventions
employed for each subject, while Figure 3.7 visually illustrates the correlation between DBP and
the reciprocal of the time delays per subject. For each subject, 1/PAT was less effective in tracking
DBP changes than 1/PTT. However, the extent of the difference was quite variable because of the
intervention disparities. For subject 1, phenylephrine and nitroglycerin were infused. Figure 3.3
illustrates that the vasoconstrictor caused PTT to decrease due to the ABP increase and PEP to
increase due to the afterload increase. These opposite direction variations blunted the change in
PAT. Thus, the RMSE value for 1/PAT was over twice as large as for 1/PTT. For subjects 5 and 6,
twice as many interventions were used compared to the other subjects. PEP was therefore more
variable, and, as a result, the RMSE values for 1/PAT were again over twice as large as for 1/PTT.
By contrast, for subjects 2 and 4, the DBP ranges were much narrower and thus constituted less of

44

Subject 1

Subject 2

160

160

120

120

80

80

40

40

DBP [mmHg]

5
160

10
15
Subject 3

20

6

8

6

8

160

120

80

40

14

120

80

10
12
Subject 4

40
5

10

15

20

Subject 5

160

160

120

14

Subject 6

80

40

12

120

80

10

40
5

10

15

20
5
7
-1
1/PTT or 1/PAT [s ]

9

11

13

15

Figure 3.2: Plots of beat-to-beat DBP versus beat-to-beat 1/PTT (black, closed circles) and 1/PAT
(gray, open circles) in each subject.

a challenge. Consequently, the RMSE values for 1/PAT were not that much higher than for 1/PTT.
For subject 3, norepinephrine and xylazine were infused. These interventions caused PEP and PTT
to change in the same direction. For example, norepinephrine caused PTT to decrease because of
the increase in ABP and PEP to decrease as the enhancement in cardiac contractility evidently
dominated the increase in afterload. Thus, the RMSE value for 1/PAT was again not considerably
greater than for 1/PTT.
Figure 3.4 illustrates the trends in DBP, 1/PAT, and 1/PTT from subject 6. In this subject,
1/PAT was far less effective than 1/PTT in tracking the direction of changes in DBP. However, note
45

100
DBP [mmHg]

90
80
70
60
50

55

PTT [ms]

50
45
40
35
30

20

PEP [ms]

18
16
14
12

54

55

56

Time [min]
Figure 3.3: Sample trends in DBP, PTT, and the pre-ejection period (PEP) from subject 1 during
phenylephrine infusion.

46

DBP [mmHg]

120

Low Rate Cardiac Pacing

100
80
60
40

1/PTT [s-1]

20
≈
12
11
10
9
8
≈
14
1/PAT [s-1]

12
10
8
6
4
0

12.5

25

37.5

50

62.5

75

87.5

100

Time [min]

Figure 3.4: Sample trends in DBP, 1/PTT, and 1/PAT from subject 6

47

112.5

that even 1/PTT was ineffective during low rate cardiac pacing. During this intervention, 1/PTT
predicted an increase in DBP, but DBP actually fell. In the remaining five subjects, 1/PAT and
1/PTT performed similarly in terms of following directional DBP changes.
In this study, we estimated PAT and PTT through the aorta using high fidelity, invasive arterial waveforms obtained during multiple hemodynamic interventions in each of six animals that
induced wide ABP changes on average. We compared these time delays and their reciprocals in
terms of their linear correlation with DBP, MBP, and SBP per animal. In contrast to similar studies
in the past, our results quantitatively indicate that PAT is not an adequate surrogate for PTT in
terms of detecting challenging ABP changes.
Taking the reciprocals of the time delays tended to improve their ability to track ABP. This
result is consistent with previous studies that have shown that velocity, rather than time delay,
exhibits an excellent linear relationship with ABP over a wide range [39, 96]. To confirm, we
employed quadratic and cubic polynomials instead of lines to fit the data [38, 68]. We indeed
found that the polynomial fitting tended to reduce the RMSE values much more for the time delays
than for their reciprocals. For example, for cubic polynomial fitting, the DBP RMSE values for
PTT and 1/PTT were both 4.7 mmHg on average. So, the reciprocals of the time delays were
essentially linearly related to the ABP parameters. The use of reciprocals may therefore offer
greater simplicity for ABP calibration.
PTT and its reciprocal predicted DBP and MBP significantly better than SBP. These results are
consistent with previous experimental studies [74, 114] and theory. That is, PTT should be able
predict DBP the best, because it is estimated from the waveform feet. Further, PTT should also
be able to predict MBP but not SBP, as only the former generally shows strong correlation with
DBP. The difference in the DBP/MBP and SBP RMSE values was 2.2 mmHg on average. This
difference can actually be more substantial. For example, we recently showed that the difference in
the DBP and SBP RMSE values for 1/PTT was about 4.5 mmHg in conscious humans subjected to
lower body negative pressure [114]. On the other hand, PAT and its reciprocal did not predict any
of the ABP parameters significantly better than the others. These results are in contrast to theory,

48

which predicts that PAT should be able to predict DBP and MBP better than SBP for the same
reasons as PTT, and previous experimental studies, which have paradoxically shown that PAT is
most effective in predicting SBP [73, 96]. Thus, PEP is a confounding factor.
PAT and its reciprocal were significantly inferior to PTT and its reciprocal in tracking all ABP
parameters. The RMSE values for PAT and 1/PAT ranged from 9.8 to 13.1 mmHg on average,
whereas the corresponding values for PTT and 1/PTT varied from 4.8 to 8.2 mmHg. Further, the
RMSE values for PAT and 1/PAT were, on average, 78±23% higher than their PTT counterparts.
Thus, tracking ABP via PAT was not only markedly worse than via PTT but also unable to meet
the FDA bias and precision error limits of 5 and 8 mmHg. These results are congruent with the
conclusion of Geddes et al. that PAT cannot be used in place of PTT [39].
For each subject, 1/PAT always tracked DBP less effectively than 1/PTT. However, the extent
of the RMSE difference was quite variable and depended on the nature of the ABP changes elicited
in the subject. For example, consistent with the results of Steptoe et al. [97], this difference was
modest when the ABP range was narrow. In general, the difference increased with the magnitude
of ABP change, degree of vasoconstriction, and number of interventions. Thus, in essence, the
adequacy of PAT as a surrogate for PTT diminished as the ABP changes became more challenging.
In one subject, 1/PAT was also strikingly less effective than 1/PTT in tracking the direction
of the ABP changes. However, in the same subject, even 1/PTT was not useful in this capacity
during low rate cardiac pacing. As heart rate fell, 1/PTT increased even though ABP declined.
Indeed, the foot-to-foot detection technique can increasingly underestimate PTT with decreasing
heart rate, because the extent of constructive interference of the reflected wave with the forward
wave increases [73]. Although the FDA only considers the error of ABP measurement devices, the
omission of a rigorous assessment of the time delays and their reciprocals in terms of their ability
to track dynamic ABP changes does constitute a study limitation.
We were able to accurately locate the waveform feet for PAT and PTT estimation by manual
detection of invasive arterial waveforms with little artifact. However, in practice, the time delays
would be estimated by automatic detection of the feet of non-invasive arterial waveforms with

49

nontrivial artifact. Thus, waveform foot misdetections are actually inevitable. Since accurate,
automatic detection of the R-wave is feasible even when the ECG waveform is buried in artifact,
PAT is less susceptible to misdetections. Thus, as indicated by the results of Payne et al. [78], the
difference in tracking ABP via PAT and PTT may be closer in practice. However, ABP tracking
via both time delays would obviously become worse with misdetections.
We tested the ABP predicted via PAT and PTT against the same measured ABP that was utilized to calibrate these time delays to ABP. In practice, a ABP calibration curve would first be
constructed from simultaneous measurements of the time delays and peripheral ABP during a
hemodynamic perturbation and then future peripheral ABP values would be predicted from only
measurements of the time delay using the ABP calibration curve. Thus, we effectively employed
the optimal ABP calibration curves for both PAT and PTT to reveal (and fairly compare) their best
case results. A realistic, sub-optimal ABP calibration curve would certainly further degrade the
ABP tracking ability of either time delay in practice.
In this study, PAT yielded ABP errors that were about 80% larger than those of PTT. Further, in
contrast to PTT, the ABP errors of PAT exceeded the FDA ABP bias and precision error limits of
5 and 8 mmHg. Thus, PAT was not an adequate surrogate for PTT as a marker of ABP despite the
ideal circumstances of this study. Since significant, additional error will result in practice, further
pursuit of PAT for continuous, non-invasive, and cuff-less ABP monitoring may not be fruitful.
However, further studies comparing PAT to PTT are still needed to draw an irrefutable conclusion.
Other useful future research directions include the development of simpler sensors for measuring
proximal arterial waveforms, convenient, patient-specific ABP calibration curves, techniques for
artifact-robust estimation of the true PTT in the absence of wave reflection, and techniques for
more accurately tracking SBP via PTT.

50

3.3 Improved pulse transit time estimation by system identification analysis
of proximal and distal arterial waveforms
3.3.1

Introduction

According to the Moens-Korteweg equation, pulse wave velocity (PWV) increases as the arteries
stiffen. Indeed, PWV is the most popular index of arterial stiffness because of the ease of its
measurement and its proven independent value in predicting cardiovascular events and mortality
in hypertensive patients [8, 53, 60]. In addition, because arterial stiffness increases with arterial
blood pressure (ABP), PWV and ABP often show positive correlation, suggesting that PWV could
provide a means to achieve continuous, noninvasive, and cuffless ABP monitoring [83].
Conventionally, PWV is determined from the distance and pulse transit time (PTT) between
proximal and distal arterial sites [10]. PTT is, in turn, estimated by acquiring arterial waveforms
from the two sites and then detecting the foot-to-foot time delay between the waveforms. The
premise is that the foot of the proximal waveform represents a time before the return of the reflected wave to its measurement site. However, wave reflection may not always be negligible at the
proximal waveform foot. Just as important, it is often difficult to detect the waveform feet reliably
because of motion and other artifact [65]. Thus, the foot-to-foot detection technique can yield
inaccurate PTT estimates. Compounding matters, ABP changes perturb PWV relatively little [83].
Thus, typical plots of ABP vs. PWV show significant vertical scatter about the line of best fit [83].
This scatter limits the ability of PWV to track ABP.
Several investigators have aimed to improve PTT estimation by more sophisticated analysis of
proximal and distal arterial waveforms. Sola et al. [96] applied parametric modeling to the systolic
upstrokes of the waveforms to identify their feet more reliably. Pruett et al. [83] computed an
average of multiple time delays taken from the early systolic samples of two ABP waveforms to
establish PTT estimates that were able to reduce the scatter in ABP vs. PWV plots. While their idea
of mitigating PTT error by using more than one pair of samples of the waveforms is interesting,
wave reflection becomes a greater factor as the cardiac cycle progresses. This technique is also

51

restricted to ABP and flow waveforms. Latson et al. applied nonparametric system identification
to estimate the impulse response (time domain version of the transfer function) relating a proximal
ABP waveform (input) to a distal ABP waveform (output) and then estimated PTT as its time
delay [52]. Their intriguing idea was that, since the impulse response represents the distal ABP
response to a very narrow pulse applied to proximal ABP at time 0, this PTT estimate should not be
corrupted by wave reflection. However, neither Latson et al. nor an ensuing group who reproduced
their technique [66] showed that it actually improved PTT estimation. Furthermore, this approach
is applicable to arbitrary arterial waveforms (rather than being limited to ABP waveforms) and
should afford great robustness to artifact, since PTT is determined from all pairs of waveform
samples. However, these latter ideas may have not been noted until now.
We investigated the system identification approach for PTT estimation. We specifically applied
a robust parametric system identification technique to an impedance cardiography (ICG) waveform
(the proximal input) and a noninvasive peripheral ABP waveform (the distal output) recorded from
humans subjected to progressive reductions in central blood volume using a lower-body negative
pressure (LBNP) protocol. Because it is difficult to independently measure the true PTT in the
absence of wave reflection, we assessed the technique in terms of the ability of its (proportional)
PWV estimates to track ABP changes. Our results show that the technique greatly reduced the
scatter in ABP vs. PWV plots compared with conventional foot-to-foot detection techniques. A
preliminary version of this study has been reported in abbreviated form [115].

3.3.2
3.3.2.1

Materials and methods
Physiological data

Existing, de-identified physiological data from humans subjected to a LBNP protocol were analyzed. The data collection procedures were approved by the Institutional Review Board of the
Brooke Army Medical Center (Fort Sam Houston, TX) and are described in detail in several recent
publications [23, 87]. Briefly, fit and typically young subjects that showed no signs of cardiovascu-

52

lar abnormalities (e.g., hypertension, hypotension, autonomic nervous dysfunction) and were not
pregnant or taking any medications known to alter autonomic nervous function were studied.
The subjects were instrumented for measurement of various physiological data, including noninvasive stroke volume estimates via ICG, a noninvasive peripheral ABP waveform via finger-cuff
photoplethysmography, and an ECG waveform. Subjects were positioned supine in a LBNP chamber. The data were then recorded at a sampling rate of 500 Hz during 1) a 5-min baseline period;
2) 5-min chamber decompression at -15, -30, -45, and -60 mmHg each; 3) additional increments
of -10 mmHg for 5 min until the onset of hemodynamic decompensation [as indicated by presyncopal symptoms, sudden fall in ABP or heart rate (HR), systolic pressure (SP) < 80 mmHg, or at
the subject’s request]; and 4) a 10-min recovery period.
For this study, 15-s steady segments of data during the baseline period, each distinct LBNP period, and the recovery period were extracted. Because PWV estimates would be assessed in terms
of their ability to track ABP changes, appreciable changes in ABP within a subject were needed for
the assessment to be challenging and useful. Thus, data from subjects with more modest diastolic
pressure (DP) changes (maximum average DP over the periods minus the minimum average DP
over the periods < 20 mmHg) were excluded. Data from 15 of 66 available subjects (nine males
and six females; age 31 ± 8 yr; height 173 ± 12 cm; weight 76 ± 15 kg) remained for analysis.

3.3.2.2

PTT estimation

PTT was estimated by applying conventional foot-to-foot detection techniques to the simultaneous
pairs of the 15-s segments of the differentiated ICG waveform (a proximal arterial waveform that
is specifically related to thoracic flow) or the ECG waveform (a commonly proposed surrogate for
the proximal arterial waveform) and the peripheral ABP waveform (a distal arterial waveform).
PTT was then estimated by applying a parametric system identification technique to the same pairs
of ICG and peripheral ABP waveform segments.

53

3.3.2.3

Conventional foot-to-foot detection techniques

Figure 3.5 shows the conventional foot-to-foot detection techniques. First, the waveform feet were
detected as the R waves for the ECG waveform, the standard B points for the ICG waveform (i.e.,
the time of zero derivative before the peak), and the minima for the peripheral ABP waveform
(i.e., DP). These foot detection techniques yielded the best results among a set of conventional
techniques [20] and are thus referred to as optimized henceforth. Next, the time delays between
each R wave and subsequent DP (Td1 ) and between each B point and ensuing DP (Td2 ) were
determined. Finally, the time delays were averaged over the 15-s waveform segments to reduce
noise in the PTT estimates.

3.3.2.4

Parametric system identification technique

Figure 3.6 shows the parametric system identification technique. The differentiated ICG waveform
was considered to be the input x(t) to a system while the peripheral ABP waveform y(t) was
regarded as the resulting output. The system was identified by finding its impulse response h(t),
which when convolved with x(t), optimally fitted y(t). The time delay of h(t) (Td3 ) was then
detected as the estimate of PTT. This estimate may be viewed as the time delay for a very narrow
pulse of thoracic flow to reach the peripheral ABP measurement site or the time delay between the
entire ICG and peripheral ABP waveforms after equalizing their shapes. Mathematical details are
provided immediately below.
The impulse response h(t) was estimated as per the following autoregressive exogenous input
structure:
n

y(t) =

∑

ak y(t − k) +

k=1

m

∑ bk x(t − k) + e(t).

(3.1)

k=0

where ak and bk are sets of unknown parameters that define h(t), n and m denote the number
of parameters in the sets, and e(t) is the unmeasured residual error [58]. The term n had little
effect on the results and was arbitrarily fixed to five, whereas the term m should scale with PTT

54

R

ECG
[mV]

200

100
S

Differentiated ICG
[ /sec]

0
≈
2

Td1

PWV v

1
Td1

1
B point
0
Td2
≈
170

Peripheral ABP
[mmHg]

Q

PWV v

1
Td2

130
minimum
90
0

0.5

1

Time [sec]
Figure 3.5: Optimized conventional foot-to-foot detection techniques for estimating pulse transit
time (PTT) from either an ECG or impedance cardiography (ICG) waveform (a proximal
waveform) and a simultaneous noninvasive peripheral arterial blood pressure (ABP) waveform (a
distal waveform) [the time delays between each R wave and subsequent DP (Td1 ) and between
each B point and ensuing DP (Td2 )].

55

Zero-mean
Peripheral ABP

Differentiated ICG
80

h(t)

2
1.2
1

y(t) [mmHg]

x(t) [ /sec]

Td2
0.6
0
0
0
-1

0

1
Time [sec]

2

0.25

40

0

0.5

Time [sec]
nd
Td2: time of maximal 2
derivative
1
PWV v
Td2

-40
0

1

2

Time [sec]

Figure 3.6: Parametric system identification technique for estimating PTT from simultaneous
ICG and noninvasive peripheral ABP waveforms.

and was simply set to Td2 times the sampling rate. The parameters were then estimated from the
15-s segments of x(t) and zero-mean y(t) by linear least-squares minimization of e(t) [58]. The
time delay Td3 was thereafter determined as the time of the maximal second derivative of h(t)
between its first zero-crossover with positive derivative and its peak. This time, which denotes
when the slope of h(t) is changing most during its rise to the peak, provided a good marker of the
foot location of h(t) [20]. [Determining Td3 as the first zero-crossover with positive derivative,
which indicates when h(t) first becomes positive as it rises to the peak, yielded similar results.]

3.3.2.5 PTT assessment and comparison
The PTT estimates of each technique were assessed based on their ability to track the average DP
of the analyzed peripheral ABP waveform segments in each subject. Figure 3.1 shows the PTT
assessment procedure. First, since PWV generally shows better linear correlation to DP than PTT,
the reciprocals of the PTT estimates were first taken to arrive at proportional PWV estimates per
56

subject. (Note that the proportionality constant, which represents the distance between the proximal and distal arterial sites, was not needed here.) Next, two quantitative metrics were computed.
One metric was the standard correlation coefficient (r) between the proportional PWV estimates
and measured DP. The other metric was the root mean squared error (RMSE) between the DP predicted by mapping the proportional PWV estimates through the line of best fit established from the
correlation analysis and the measured DP.
The PTT estimates of the techniques were then statistically compared. Straightforward oneway repeated-measures ANOVA was specifically employed to compare the subject average r values
and log-transformed RMSE values of the three techniques. Because both of these tests revealed
P < 0.05, multiple pairwise comparisons between all techniques were then performed using the
Student-Newman-Keuls post hoc test.

3.3.3

Results

Figure 3.7 shows sample plots of measured DP vs. the proportional PWV estimated by each
technique from subjects 15 and 12. In subject 15, the parametric system identification technique
noticeably reduced the scatter about the line of best fit compared with the conventional foot-tofoot detection techniques, especially with the ECG waveform substituted for the ICG waveform.
In subject 12, the conventional techniques produced proportional PWV estimates that showed nonphysiological, negative correlation with DP, whereas the system identification technique yielded
estimates that revealed the expected positive correlation.
Figure 3.8 shows plots of the DP predicted by each technique vs. measured DP from all 15
subjects and the corresponding overall RMSE values (i.e., the root mean square of the errors pooled
together from all of the subjects). The system identification technique showed better predictions
than both of the conventional techniques. Table 3.3 shows the DP range and r and RMSE values of
each technique per subject. The average r and RMSE values of the system identification technique
were 0.81 ± 0.16 and 4.3 ± 1.3 mmHg. For comparison, the corresponding values were 0.59 ±
0.37 (P < 0.05) and 5.9 ± 2.5 (P < 0.01) mmHg for the conventional technique applied to the same

57

Foot-to-Foot
Detection (ECG for
Central Signal)
90

Foot-to-Foot
Detection

System
Identification

DP [mmHg]

Subject 15 75

60
5.2

5.8

6.4

8

13

18

9

8

9.5

11 10

13

17

11.5

13

90

Subject 1277.5

65
5.3

5.65

6

1/PTT [sec-1]
Figure 3.7: Plots of measured DP vs. the proportional PWV estimated by each technique from
subjects 15 and 12.
waveforms and 0.28 ± 0.40 (P < 0.001) and 7.2 ± 1.8 (P < 0.001) mmHg for the conventional
technique with the ECG waveform substituted for the ICG waveform. [Although not indicated in
Table 1, the r and RMSE values of the two conventional techniques were also statistically different
(P < 0.05).] Furthermore, of the 15 r values corresponding to each subject, only 3 were < 0.80 for
the system identification technique compared with 8 and 15 for the conventional techniques.

3.3.4

Discussion

In summary, PWV is a useful marker of arterial stiffness and may permit continuous, noninvasive,
and cuffless ABP monitoring. Conventionally, PWV is determined as the ratio of the distance and
PTT between proximal and distal arterial sites. PTT is, in turn, estimated by detecting the footto-foot time delay between waveforms measured at the two arterial sites of interest. However, this
58

Table 3.3: Results of each pulse transit time estimation technique per subject.

Subject

DP Range

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

75-101
97-121
71-99
95-116
88-130
64-86
69-100
54-75
64-85
65-91
72-95
65-86
50-71
62-83
62-89

Average

70-95

System
Identification
(PTT = Td3 )
r
RMSE
0.55
6.8
0.96
2.7
0.85
4.2
0.85
4.0
0.95
4.8
0.92
2.4
0.84
5.9
0.83
3.6
0.38
6.5
0.85
4.5
0.91
3.3
0.63
5.0
0.82
3.9
0.91
3.4
0.92
3.7
0.81 ± 4.3 ±
0.16
1.3

Conventional
Detection (PTT =
Td2 )
r
RMSE
0.39
7.5
0.91
3.8
0.86
4.2
0.88
3.6
0.66
11.8
0.86
3.1
0.18
10.8
0.81
3.8
0.61
5.6
0.85
4.5
0.71
5.4
-0.15
6.4
-0.23
6.6
0.69
5.9
0.81
5.5
0.59 ± 5.9 ±
0.37
2.5

Conventional
Detection (PTT =
Td1 )
r
RMSE
0.33
7.7
0.53
7.8
0.63
6.3
0.46
6.8
0.76
10.1
0.47
5.3
0.20
10.7
0.36
6.1
-0.89
3.2
0.29
8.2
0.35
7.2
-0.13
6.4
-0.12
6.8
0.49
7.1
0.39
8.6
0.28 ± 7.2 ±
0.40
1.8

technique can provide inaccurate PTT estimates because of wave reflection interference and waveFig. 2. Parametric system identification technique for estimating PTT from simultaneous ICG and
noninvasive peripheral ABP waveforms. First, the former waveform is regarded as an input x(t) to
a system while the latter waveform is considered to be the resulting output y(t). Next, the system
is identified by finding a parametric impulse response h(t) (see equation in MATERIALS AND
METHODS) that, when convolved with x(t), optimally fits y(t). Finally, the time delay (Td3 ) of h(t)
is detected as the time of its maximal second derivative so as to yield as an estimate of PTT. Fig.
3. Procedure for evaluating the PTT estimates of the techniques in terms of their ability to track
diastolic pressure (DP) within a subject. Note that 1/PTT here is simply proportional to pulse wave
velocity (PWV). RMSE is the root mean squared error. form artifact. The system identification
approach for estimating PTT potentially provides a means to overcome both of these limitations
while being applicable to arbitrary types of arterial waveforms. We applied a parametric system

59

identification technique to noninvasive ICG and peripheral (finger) ABP waveforms measured from
healthy humans during progressive LBNP. The resulting PTT estimates correlated with ABP much
better than those of optimized conventional techniques. To our knowledge, these results are the
first to demonstrate that the system identification approach can indeed improve PTT estimation.

3.3.4.1

System identification approach for PTT estimation

The system identification approach for PTT estimation is employed as follows. First, proximal and
distal arterial waveforms are measured and respectively regarded as the input and output of a system. Next, the system impulse response is identified from the measured input and output. Finally,
the time delay of the impulse response is detected as an estimate of PTT. This approach is similar
in concept to previous techniques for estimating PTT that have experimentally eliminated the reflected wave by applying a transient perturbation to a proximal arterial site and then measuring the
time delay for the response to occur at a distal arterial site [2, 50]. However, the obvious advantage
of the system identification approach is that no experimental perturbation is needed. The system
identification approach should also afford significant advantages over conventional foot-to-foot detection techniques and other previous techniques for estimating PTT without a perturbation. First,
this approach effectively determines PTT from all pairs of samples of the waveforms, rather than
just one pair or a few pairs, by mathematically eliminating the reflected wave or, more generally,
equalizing the waveform shapes. In this way, the approach should be robust to waveform artifact
while revealing the true PTT in the absence of wave reflection. The approach is therefore intended
to improve the accuracy of PTT estimation rather than to make the PTT measurement process more
convenient as others have proposed via an ECG or otherwise [85]. Second, the system identification approach is applicable to arbitrary types of arterial waveforms, including those indicative of
ABP, flow, and volume, instead of being restricted to certain types of waveforms [83]. For example, the waveforms could be acquired with tonometry, ultrasound, ballistocardiography (proximal
only), electrical impedance, pulse oximetry, and even noncontact laser Doppler vibrometry [29].
The disadvantage of the approach is that it may not be able to estimate PTT on a beat-to-beat basis,

60

Predicted DP [mmHg]

140

System Identification
(ICG-Peripheral ABP)
[PTT = Td3]
RMSE = 4.5 mmHg

Conventional Detection
(ICG-Peripheral ABP)
[PTT = Td2]
RMSE = 6.5 mmHg

Conventional Detection
(ECG-Peripheral ABP)
[PTT = Td1]
RMSE = 7.5 mmHg

90

40
40

90

140 40

90

140 40

90

140

Measured DP [mmHg]
Figure 3.8: Plots of the DP predicted from the proportional PWV estimates of each technique vs.
measured DP from all 15 subjects.

since longer waveform segments are typically needed to reliably identify the impulse response.

3.3.4.2

Evaluation approach and limitations

Ideally, we would have evaluated the parametric system identification technique against reference
measurements of PTT. However, these measurements are not simple to make. We therefore evaluated the technique in terms of the ability of its proportional PWV estimates to track changes in
ABP induced by progressive LBNP. Note that the approach of evaluating PWV estimates in terms
of their ability to track ABP changes is not new and originates from many studies that have shown
a tight, acute relationship between PWV and ABP [39, 83].
However, we acknowledge that ABP was likely not the only significant determinant of the true
PWV in this study. Indeed, vasomotor tone changes (e.g., vasoconstriction occurred during LBNP
as a compensatory response), which may have altered PWV without appreciably influencing ABP,
constitute the major study limitation. If PWV were estimated through the aorta, which is relatively

61

sparse in smooth muscle [63], rather than to a finger, such changes may have been less of a factor.
On the other hand, HR and cardiac output were probably not significant determinants of PWV
in this study for the following reasons. First, PWV in large arteries is essentially constant across
frequencies because of negligible viscous effects [65]. Thus, since we investigated PWV through
largely nonviscous arteries, PWV here should have been mostly independent of HR. Second, PWV
characterizes the properties of the arteries only. Therefore, cardiac output could have only impacted
PWV via alterations in ABP.
Although the relationship between ABP and PWV generally follows an exponential [83], it
could be well approximated here as linear because of the relatively narrow ABP range elicited by
the LBNP. Thus, we quantitatively evaluated the ability of the technique to track ABP changes in
terms of the linear correlation between its PWV estimates and ABP.

3.3.4.3

Tracking DP

In 15 subjects, DP was perturbed appreciably (20 mmHg) by the LBNP. In these subjects, the parametric system identification technique achieved an average r value between its proportional PWV
estimates and measured DP of 0.81 ± 0.16 and an average RMSE value between the DP predicted
from these estimates and measured DP of 4.3 ± 1.3 mmHg. These averages were ∼30% better
than those of an optimized version of the conventional foot-to-foot detection technique applied
to the same waveforms. Furthermore, in two subjects, the system identification technique was
able to profoundly "correct" the PWV estimates of the conventional technique to show appropriate
positive, rather than negative, correlation with DP.
We also assessed the conventional foot-to-foot detection technique with the ECG waveform
substituted for the ICG waveform. This commonly proposed technique actually estimates the sum
of PTT and the preejection period (PEP). Because PEP generally changed in the opposite direction
of PTT with progressive LBNP (results not shown), the technique performed poorly in tracking DP.
Note that the RMSE values of this technique should be interpreted with caution. For example, in
subject 9, the technique showed a strong, nonphysiological negative correlation between its PWV

62

estimates and DP and consequently a small RMSE value.

3.3.4.4

Tracking other ABP parameters

The proportional PWV estimates of the parametric system identification technique may correlate
best with mean ABP, as they arise from all waveform samples. However, because LBNP perturbed
DP much more than mean ABP, we focused on DP tracking. Note that the PWV estimates of the
conventional techniques are designed to track DP by virtue of being derived from the waveform
feet. Nevertheless, the PWV estimates of the system identification technique were able to follow
DP better than those of the conventional techniques. The likely reason is that DP correlated well
with mean ABP here, which is generally the case. On the other hand, SP can show less correlation
to DP and mean ABP. Indeed, for those subjects whose SP changed by >20 mmHg (n = 12), none
of techniques yielded proportional PWV estimates that were able to track SP (average r and RMSE
values ranged from 0.11 ± 0.50 to 0.29 ± 0.45 and from 8.6 ± 3.6 to 9.0 ± 4.3 mmHg; P =
not significant). These results are not an indictment against the system identification technique or
the conventional technique applied to the same waveforms, since their PWV estimates correlated
significantly better with DP. However, because the PWV estimates of the conventional technique
applied to the ECG waveforms showed poor tracking of all ABP parameters, we conclude that it is
not suitable during progressive central hypovolemia.

3.3.4.5

Reproducibility

In addition to accuracy, reproducibility across time in the same subjects would be another necessary attribute for the parametric system identification technique. In subjects 1 and 4, repeated
measurements were available on a second day. We therefore conducted preliminary reproducibility
testing of the technique. The overall RMSE of the PTT estimates on the second day relative to the
first day was just 4.9%. Thus, the technique was highly reproducible. Furthermore, the first and
second day r values between the proportional PWV estimates and measured DP were 0.55 and
0.51 in one of the subjects and 0.85 and 0.80 in the other subject. Thus, the evaluation results of
63

the technique were also reproducible. For the conventional techniques, the corresponding reproducibility results were generally not as strong. For example, the overall RMSE values of their PTT
estimates between the two days were ∼13% each.

3.3.4.6 Future directions and potential clinical applications
Further investigation of the system identification approach for PTT estimation is warranted. First
and foremost, testing of the approach in patients recommended for PWV monitoring (e.g., elderly,
hypertensives) is a must. Thorough reproducibility testing also remains to be performed. In addition, refinements to the specific technique described herein via other system identification and
time-delay estimation techniques are also needed to reduce or even eliminate instances of poor
performance (i.e., subject 9).
With successful future efforts, the system identification approach for PTT estimation may be
employed for improved arterial stiffness monitoring in hypertension patients. For example, consistent with common practice [60], this approach could be applied to noninvasive carotid and femoral
ABP waveforms obtained with tonometry in these patients for more accurate PWV estimation
and thus potentially superior prognostic information (although nontrivial PWV error may still be
present because of transit distance measurement inaccuracy). The approach could also be applied
to arterial waveforms acquired with simple sensors (e.g., carotid artery and toe pulse oximeters)
for potentially accurate, continuous, noninvasive, and cuffless ABP monitoring. However, other
problems, including convenient construction of patient-specific calibration curves relating DP and
mean ABP to PWV as well as SP estimation, must be solved before it could be used for such
convenient ABP monitoring.

64

3.4 Cardiac output monitoring techniques with pulse transit time correction
3.4.1

Introduction

Cardiac output (CO) is perhaps the most important hemodynamic variable to be able to monitor
in critically ill patients. It can provide timely indication of a hemodynamic event, aid in diagnosis
[82], and direct therapy so as to improve patient outcomes [64, 81]. Even so, the pulmonary artery
catheter, which has been the standard CO monitoring device, is declining in use due to the frequent
complications that result from its invasiveness [112].
A potential approach for minimally invasive CO monitoring is to mathematically analyze the
radial arterial blood pressure (ABP) waveform that is already being measured in many patients.
Indeed, various "pulse contour analysis" techniques have been proposed [69]. For example, the
most popular technique assumes that the pulse pressure (PP) is proportional to stroke volume in
order to estimate relative CO changes via the product of PP and heart rate (HR) [34]. However,
these techniques have generally been unable to track CO during hemodynamic instability, when
monitoring is of greatest need (see, e.g., [18, 55, 84] and references therein). As a result, they have
not been widely adopted in clinical practice.
Pulse contour analysis has proven challenging, because the shape of the radial ABP waveform
not only changes with CO but also with wave reflection and total arterial compliance (AC). More
specifically, this waveform arises as the sum of forward and backward traveling waves that are
in-phase, and the magnitude of the backward wave relative to the forward wave (i.e., the reflection
index) increases with peripheral resistance and may likewise be sensitive to other arterial parameters [102, 104]. So, for example, increases in the reflection index induced by vasoconstriction can
cause PP to rise despite no change, or even a decrease, in stroke volume. Yet, most techniques
assume that each beat of the radial ABP waveform can be represented with a simple lumped model
such as a Windkessel and thus ignore this phenomenon [69]. AC decreases with increasing ABP
due to slack collagen fibers and may be modulated by vasomotor tone. While such changes in AC,
which is mainly determined by the aorta, may often be small compared to CO changes due in part

65

2

A(P) (cm )
Am

-3

C(P)
100

2

-1

Cm
Cm

r=0.999

(10 cm

mmHg )

2
10

Am
2
10
0

P0

20
100

kPa
200

1
P (mmHg)

10
0

P0

20
100

kPa
200

Figure 3.9: Conventional techniques employing empirical curves for correcting AC.

to relatively sparse aortic smooth muscle [16], they likely become significant near the limits of the
ABP range. So, for example, decreases in AC induced by severe hypertension can cause PP to escalate independent of stroke volume. Many techniques do incorporate corrections for AC changes.
Most notably, current techniques employ nomograms derived from in vitro experiments that allow
AC to be estimated from ABP such as the one shown in figure 3.9 [51, 88, 111]. However, the AC
to ABP relationship surely varies amongst subjects and in vivo, and vasomotor tone-induced AC
changes may become appreciable.
In sum, a pulse contour analysis technique is needed that can overcome the challenges posed
by both confounding wave reflection and AC changes. In this way, CO may be tracked accurately
and minimally invasively during the crucial periods of hemodynamic instability.
We previously proposed a technique for estimating relative CO changes by long time interval
analysis of a radial ABP waveform [69]. The idea is to circumvent the confounding wave reflection
by analyzing the slow, beat-to-beat variations in the waveform wherein such phenomenon is no
longer a major factor. We showed that this technique can track CO fairly well during several
physiologic conditions [69, 87]. However, the technique assumes constant AC.

66

In this study, we aimed to (1) correct the CO estimates of the long time interval analysis technique for any AC changes using pulse transit time (PTT), a well-known marker of AC that can be
non-invasively measured, and (2) demonstrate proof of concept via comparison of the corrected
and original techniques using invasive hemodynamic waveforms.

3.4.2

The technique

The original technique is shown in Figure 3.10 and is described in detail elsewhere [69, 59]. Briefly,
first, a cardiac contractions signal x(t) is formed through an impulse train in which each impulse
is located at the foot of the radial ABP waveform y(t) and is scaled by the ensuing PP. Then, an
impulse response h(t) is identified, which when convolved with x(t), optimally fits y(t). By definition, h(t) represents the ABP response to a single cardiac contraction. Next, the slow Windkessel
time constant τ , which is equal to the product of the total peripheral resistance (TPR) and AC, is
determined by fitting an exponential to the tail end of h(t) once the faster wave reflections have
vanished. In principle, τ is reliably determined by virtue of accurate coupling of the slow, beat-tobeat variations in x(t) to y(t). Finally, mean ABP (MAP) is divided by τ to determine CO to within
a scale factor equal to 1/AC. This scale factor is assumed to be constant so as to permit estimation
of relative CO changes in a subject over a monitoring period.
The assumption of constant AC is not satisfactory in situations like major blood pressure
changes. To correct this technique for any AC changes, PTT is introduced through simultaneous
measurements from central and peripheral sites in the aorta, where dominantly determines AC.
According to the Bramwell-Hill equation, the PTT and AC are approximately related as follows:
√
PT T =

ρl
AC
A

(3.2)

where ρ is the blood density, d is distance between the two measurement sites, and A is the average
arterial cross-sectional area [11]. Thus, the original technique can be corrected for AC changes
precisely as follows:

67

CO ∝ PT T 2

MAP
τ

(3.3)

The scale factor is now ρ d/A. While ρ and d are constant per subject, A could change with ABP.
However, A is controlled by the product of AC and ABP, which are two inversely related terms.
So, as shown in figure 3.9, A should change significantly smaller comparing with AC [51]. In this
way, the PTT correction may support improved estimation of relative CO changes.
To robustly estimate PTT, a system identification technique is applied to the central and peripheral arterial waveforms. This technique is described in detail in the previous section. Briefly,
a rational system is built which convolves the central arterial waveform to optimally fit the peripheral arterial waveform. Second, the impulse response of the system is excited. Third, PTT
is determined as the time delay of the impulse response. Thus, PTT is effectively determined
from both of the entire waveforms, rather than just their feet, after mathematically eliminating the
reflected wave by virtue of equalizing their shapes. In this way, the technique will be robust to
artifact while revealing the true PTT in the absence of wave reflection.
The corrected technique is summarized in figure 3.10. First, τ is estimated by long time interval
radial ABP waveform analysis. Then, PTT is estimated by system identification analysis of central
and peripheral arterial waveforms. Finally, proportional CO is computed from τ and PTT so as to
monitor relative CO changes in a subject.

3.4.3 Technique evaluation in an animal study
Our technique was first validated in an animal study. Our experimental data were collected from
five anesthetized Yorkshire swine under a protocol approved by the MIT Committee on Animal
Care. Details of the materials and methods for data collection are described elsewhere [69]. Specifically, blood pressure waveforms from the thoracic aorta and femoral artery were collected via
micromanometer-tipped catheters. An additional radial ABP was obtained via a 23- or 25-gauge
angiocatheter which was placed as distal as possible to the brachial artery. The reference CO was
measured via an ultrasonic flow probe around the aortic root. All data were recorded at a sampling
68

1) Estimate τ = TPR · AC
60

120

h(t)

40

PPj PPj+1
0.5

20

0

y(t) [mmHg]

x(t) [mmHg]

1
PPj-1

Rj+1
Rj
0
1
2
Time [sec]
Rj-1

2) Estimate PTT

00

τ

3
Time [sec]

6

Radial ABP
PPj-1
PPj PPj+1

80
Rj-1
40

0

0

1
2
Time [sec]

ρl
AC
A

x(t)
(Central Signal)

h(t  Td )
PTT

y(t)
(Peripheral Signal)

Td

3) Compute proportional CO

CO v PTT 2

ABP
τ

Figure 3.10: LTIA with PTT correction for estimating CO.

69

Rj Rj+1

frequency of 250 Hz. For each subject, a 75-150 min experiment was performed to change CO and
other hemodynamic parameters, with a subset of following interventions: infusions of volume,
phenylephrine, dobutamine, isoproterenol, esmolol, nitroglycerine, and progressive hemorrhage.
Different infusion rates were implemented followed by brief recovery periods.
Off-line analysis was first applied to the measured waveforms which were resampled to 90 Hz.
Second, the proportional CO trends were estimated from the femoral ABP by the long time interval
analysis. Third, two PTTs were estimated by the system identification technique for comparison:
one is determined from the aorta-radial pair (rPTT) and the other is identified from the aortafemoral pair (fPTT). In order to acquire high resolution time delay, we estimated PTTs using data at
their original sampling frequency (250Hz). Last, the corresponding reference CO was established
by averaging the flow probe trend over the identical time interval.
For the original technique, the proportional CO trend was first scaled to the reference CO trend
by equalizing their mean values for each individual animal over the entire experiment. Then,
the root-mean-squared-normalized-error (RMSNE) of the scaled CO estimates was computed as
a metric. For the corrected technique, the proportional CO trend is divided by PT T 2 (from both
rPTT and fPTT separately), followed by scaling based on the mean value of the reference CO
signal. The RMSNE was also computed for comparison. Next, log-transformation was utilized to
the RMSNE values for improving uniformity, followed by paired t-test to determine the statistical
significance level between the original technique and the corrected technique. In addition, in order
to evaluate the benefits of the introduction of PTT, the value of calibrated new CO was determined
in situation where there were huge changes in ABP.

3.4.3.1

Results

Table 3.4 lists the characteristics of segments and compares results of original and corrected techniques for every individual subject. The ABP range was wide, with the average of 77.4 ± 16.9
mmHg. Without PTT correction, the average RMSNE of the original technique was 14.9 ± 4.3
%. Comparing with the original technique, the estimation error with fPTT correction was reduced

70

Table 3.4: Characteristics of ABP and RMSNE values of original and corrected techniques for
every individual subject.
ABP [mmHg]
Animal

Mean ± Std

1
2
3
4
5

57.2 ± 16.9
76.4 ± 19.0
88.6 ± 13.5
87.3 ± 17.6
77.6 ± 17.5

Average

77.4 ± 16.9

CO RMSNE [%]
Corrected Technique
Original Technique
fPTT
rPTT
20.9
16.6
17.9
12.6
13.2
14.8
16.0
14.0
12.6
9.3
7.6
9.2
15.7
13.8
10.5
13.0 ± 3.3 13.0 ± 3.5
14.9 ± 4.3
(p = 0.055) (p = 0.25)

Table 3.5: RMSNE values of original and corrected techniques for segments at two extremes in
every individual subject.
Animal

Max ABP-Min ABP

1
2
3
4
5

[mmHg]
71.2
73.4
50.5
53.1
56.2

Average

60.8 ± 10.6

CO RMSNE [%]
Corrected Technique
Original Technique
fPTT
rPTT
81.0
52.1
29.4
34.6
6.1
21.0
60.2
9.1
19.3
16.8
16.0
15.5
36.7
11.5
2.2
19.0 ± 18.9 17.5 ± 9.9
45.9 ± 25.0
(p = 0.042) (p = 0.076)

to 13.0 ± 3.3 % (p=0.055). On the other hand, the estimation error with rPTT correction was
decreased to 13.0 ± 3.5 %. But the difference was not significant (p=0.25).
Table 3.5 compares results of original and corrected techniques for segments with greatest ABP
change in every individual subject. To evaluate the estimation, we picked the segment with either
largest or smallest ABP in one subject. The average range of ABP change was 60.8 ± 10.6 mmHg.
The RMSNE of the uncorrected technique was 45.9 ± 25.0 %. The error was reduced to 19.0
± 18.9 % (p = 0.042) with fPTT correction and 17.5 ± 9.9 % (p = 0.076) with rPTT correction,
respectively.
Figure 3.11 illustrates trends in CO values of the measured reference (solid), uncorrected estimation (dashed) and fPTT corrected estimation (dot dashed). Note during the intervention of

71

10
CO [L/min]

Phenylephrine
5

0

20

40

60
80
Time [min]

100

120

Figure 3.11: CO trends of the measured reference (solid), uncorrected estimation (dashed) and
fPTT corrected estimation (dot dashed).

phenylephrine, the corrected method is apparently closer to the uncorrected method.

3.4.3.2

Discussion

In summary, we employed PTT measurements in an attempt to correct the relative CO change
estimates of our long time interval radial ABP waveform analysis technique for any AC change.
We tested this corrected technique using previously collected data from swine during various drug
and volume interventions. Our results showed that the technique was able to reduce the calibrated
CO estimation error by 18% relative to the uncorrected technique.
Our available data included only invasive PTT measurements. Thus, the results here demonstrate proof-of-concept. In practice, PTT could be measured non-invasively using, for example,
arterial tonometry or pulse oximetry. Further, the average standard deviation of MAP over all the
animals was ∼15 mmHg. We suspect that the corrected technique will afford greater improvements
in CO estimation accuracy during more severe changes to MAP and other modes of hemodynamic
instability. Future testing to address both of these issues would be worthwhile.

72

3.4.4

Technique evaluation in a human lbnp study

We proposed another investigation of the new physiologic waveform analysis techniques for early
detection of hemorrhage during transport and higher echelon medical care of combat casualties.
The materials and data analysis have been described in previous chapters. Briefly, 129 subjects
were secured in a sealed chamber with progressively negative pressure. Blood was sucked into
the lower body in order to simulate central hypovolemia. ECG, ABP and ICG were recorded for
analysis. The algorithm of LTIA was performed identically as previously described. We estimated
PTT from a black-box model system with input of zero-mean ICG and output of zero-mean ABP.
The PTT was determined as the maximal 2nd derivative of the impulse response of the system.

3.4.4.1

Results

Figure 3.12 shows the results of original and corrected techniques of LTIA comparing with the
reference measurement. The introduction of PTT greatly decreased the CO estimation during
LBNP. Therefore, the corrected LTIA is a more sensitive marker of the simulated hemorrhage.

3.4.5

Discussion

During the experiment of LBNP, a decrease of MAP would result in an increase of PTT, whereas
the increasing resistance due to hemorrhage would reduce the PTT. From results in our experiment,
the resistance should be the dominant factor in determining PTT.
In this chapter, we demonstrated preliminary results of two techniques with PTT correction.
With PTT correction, the accuracy of the techniques was found qualitatively enhanced. However,
the preliminary results need further evaluations in the following areas: (a) Statistical tests for
significance level should be performed; and (b) Quantitative metrics should be evaluated, such as
RMSE, or ROC AUC analysis. In sum, PTT is verified as an indicator for reflecting AC variation
and it can be used to eliminate the estimation errors of pulse contour analysis techniques.

73

Group Average Results

CO Estimation [%]

100

90

80

70

Original LTIA
Corrected LTIA
Modelflow
ICG

60
Baseline

-15

-30
-45
LBNP Level [mmHg]

-60

Recovery

Figure 3.12: Comparison of the candidate techniques for estimating CO. LTIA was corrected with
PTT for the changing AC.

74

Chapter 4
CARDIAC OUTPUT MONITORING FROM PERIPHERAL ARTERIAL BLOOD
PRESSURE BY SHORT TIME INTERVAL ANALYSIS

4.1 Introduction
Techniques described in previous chapters require the measurement of waveform over multiple
heart beat cycles. Empirically, the length of the waveform should be longer than 1 minute. In
this chapter, we will introduce a method which permits to estimate CO beat by beat. The method
develops a tube-load model with an adaptive transfer function, which can reconstruct the central
arterial blood pressure waveform from a peripheral arterial blood pressure waveform.

4.2 The technique
To estimate CO from a peripheral ABP waveform, we introduced a previously developed tube-load
model. The principle of the model has been described in Chapter 1. Briefly, we first reconstructed
the central ABP waveform from a peripheral ABP waveform. Then we applied the Windkessel
model to he reconstructed central ABP to get an estimate of CO. The accuracy was even improved
with PTT for correcting AC.

4.2.1

Central blood and flow waveform reconstruction from a peripheral arterial blood
pressure waveform

The idea of the technique is to define the transfer function relating peripheral ABP to central ABP
with a distributed model, which accounts for confounding wave reflections, and to then estimate
the unknown model parameters by exploiting pre-knowledge of aortic flow. Like all of the new
techniques here, the technique is adaptive by virtue of updating the parameters of the transfer
function each time a new segment of the peripheral ABP waveform becomes available for analysis.

75

More specifically, the arterial tree is modeled as a parallel arrangement of m distributed, uniform tubes terminated by lumped parameter loads. By building the peripheral ABP to central
ABP transfer function, the central ABP is reconstructed, which is less affected by wave reflection.
Then, the time constant τ is estimated in the Windkessel model by fitting the diastolic decay of
the reconstructed central ABP. The SV can be derived and the corresponding CO is achieved by
SV·HR.
Our adaptive transfer function technique is illustrated in figure 4.1. Briefly, the arterial tree is
modeled as m parallel, uniform, and frictionless tubes with terminal loads. The ith tube represents
the wave travel path between the central aorta and the ith peripheral artery. Each tube has constant
characteristic impedance (Zci ) and allows waves to travel along the entire tube with constant time
delay (Tdi ). The ith terminal load represents the arterial bed distal to the ith peripheral artery. Each
terminal load has frequency-dependent impedance characterized by peripheral resistance (Ri ), peripheral compliance (Ci ), and Zci . According to this model, a peripheral ABP waveform (p pi (t))
is related to the central ABP waveform (pc (t)) through a transfer function defined in terms of Tdi ,
RiCi , and ZciCi .
The three unknown parameters are estimated from p pi (t) by exploiting the fact that central
aortic blood flow (ABF) is negligible during diastole. Thus, the flow at each tube entrance in the
model (central ABF component (qci (t))) may likewise be small during this time interval. That
is, according to the model, p pi (t) is related to qci (t) through a transfer function also defined in
terms of Tdi , RiCi , and ZciCi (see peripheral ABP central ABF transfer function in Fig. 2). These
common parameters are estimated by finding the peripheral ABP central ABF transfer function,
which when applied to p pi (t), optimally fits qci (t) (scaled by Zci ) to zero over its diastolic intervals.
This optimization is achieved via a nonlinear least squares search over a physiologic range of the
parameters. The optimization is facilitated with an initial measurement of Tdi (i.e., pulse transit
time between the central aorta and peripheral artery measurement site), which sets the search range
for this key parameter.
Finally, the peripheral ABP central ABP transfer function with the estimates of Tdi , RiCi , and

76

Td1
qc1(t)

Zc1

qp1(t)

Zc1

pp1(t)
C1

Central ABF

qci(t)

Tdi
Zci

pc(t)

qpi(t)

Zci

R1

Zi(ω)

ppi(t)
Ci

Tdm
qcm(t)

Zcm

Ri

qpm(t) Zcm
ppm(t)
Cm

Rm

Peripheral ABPÆCentral ABP

ppi(t)

· jωTdi
§ 1
1
1
-jωTdi
¸
¨

e
¨ R C  2Z C  jω¸ e
2ZCiCi
Ci i
¹
© i i
1
1

 jω
RiCi ZCiCi

pc(t)

Peripheral ABPÆCentral ABF

ppi(t)

·
§ 1
1
1
-jωTdi
¨

 jω¸ ejωTdi 
e
¸
¨ R C 2Z C
2ZCiCi
Ci i
¹
© i i
1
1

 jω
RiCi ZCiCi

Zciqci(t)
= 0 during diastole

Figure 4.1: Structure of the tube-load model and the model transfer functions.

77

ZciCi is applied to p pi (t) so as to derive pc (t).

4.2.2 Stroke volume estimation from a central blood pressure waveform
The reconstructed central ABP was then applied to a Windkessel model for an estimation of SV.
Amongst techniques estimating SV from pressure waveforms, perhaps Bourgeois et al. performed
the most compelling study. They developed a more intricate technique which had no assumption
about the cardiac ejection time [9]. They introduced the Windkessel model for the representation
of the arterial tree, which can account for the lumped compliance of the large arteries and the total
peripheral resistance of the small arteries. According to this model, central ABP should decay like
a pure exponential during each diastolic interval with a time constant (τ ) equal to the product of
TPR and AC. The technique is able to provide an estimation of proportional SV for each beat via
the governing Windkessel model equation:
∫ tee

t pa (t)dt
SV ∝ pa (tee ) − pa (tbe ) + be
.
τ

(4.1)

4.3 Materials and analysis
4.3.1

Experimental data

De-identified physiologic data from humans subjected to a well-established LBNP protocol to
simulate hemorrhage and resuscitation were studied [87]. The data collection procedures were
approved by the Institutional Review Board of the Brooke Army Medical Center. The procedures
pertinent to this particular study are briefly described as follows. 129 young, healthy humans in the
supine posture were secured in an LBNP chamber. Instruments were positioned for measurement
of various physiologic variables including a non-invasive impedance cardiography (ICG) waveform and a non-invasive finger ABP waveform (Finometer, TNO-TPD Biomedical Instrumentation,
Amsterdam, The Netherlands). For comparison, The physiologic variables were recorded at a sampling frequency of 500 Hz during a five-minute baseline period and following sequential exposure
78

to increasing levels of LBNP up to at least 60 mmHg for five minutes each. After termination
of LBNP and a five-minute equilibration period, the physiologic variables were recorded for an
additional five-minute recovery period.
In this study, we also introduced PTT for correction the varying AC. The algorithm has been
described in the previous chapter. Briefly, we developed a black-box whose transfer function can
be characterized as a standard form of ARX system. The input and the output of the system
are zero-mean differentiated impedance cardiography and zero-mean peripheral arterial pressure,
respectively. The PTT can be determined as the maximal 2nd derivative of the impulse response of
the system.

4.3.2

Data analysis

The adaptive transfer function technique was applied to the peripheral ABP waveforms during the
baseline period, each LBNP level, and the recovery period. Central and peripheral PP were then
respectively determined from the derived and measured ABP waveforms. SV was also estimated
from the derived central ABP from the Bourgeois’ technique.

4.4 Results
Figure 4.2 illustrates a sample of the derived central and measured peripheral ABP waveforms.
Consistent with known physiology, central PP was appreciably smaller than peripheral PP. Figure 4.3 illustrates the group average results. When central PP and peripheral PP were multiplied
with HR to obtain CO surrogates, only CO derived from central PP demonstrated a decline with
progressive LBNP. Hence, central PP provided a considerably more accurate and sensitive indication of reduced SV than peripheral PP.
The estimated CO derived with Bourgeois’ algorithm was consistently lower than the estimated
central PP·HR during the LBNP. The result was as expected since the algorithm had no assumption
of the cardiac ejection time. Therefore, it yielded more accurate estimation of CO. Further, when

79

Central

Peripheral
Arterial Pressure
Forward Wave
Backward Wave

Figure 4.2: Sample plot of measured arterial blood pressure (solid) and computed forward (short
dash) and backward (dash dot) waves in the central aorta and a peripheral artery.

the PTT was introduced for correcting AC, the corrected CO was significantly reduced and thus it
was an earlier indicator of simulated hemorrhage.

4.5 Discussion
In summary, there is a profound need for early and convenient detection of hemorrhage in both
civilian and military medicine. Central PP - as a surrogate of SV - can provide an early marker of
blood loss, but only peripheral PP is convenient to measure.
We tested our previously developed adaptive transfer function technique for deriving the central
ABP waveform from a peripheral ABP waveform in healthy humans subjected to a LBNP protocol.
In this laboratory procedure, negative pressure is applied to the abdomen and lower extremities
through a pressure chamber with an airtight seal so as to cause blood to pool in the lower body. A
chamber pressure of -40 mmHg causes about a one liter shift of blood from the upper body to lower
body [25]. As a result, similar to early hemorrhage, CO declines markedly even though mean ABP
is maintained [49]. Our results showed that the derived central PP provided an earlier and more
sensitive marker of LBNP and a far more accurate measure of reduced SV than measured peripheral
PP. As predicted by wave reflection theory, the drop in peripheral PP due to a declining SV was

80

Group Average Results
110

CO Estimation [%]

100

90

80

70

Peripheral PP HR
Central PP HR
CO-STIA

60

Corrected CO-STIA
Modelflow
ICG

50
Baseline

-15

-30
-45
LBNP Level [mmHg]

-60

Recovery

Figure 4.3: Group average results of reconstructed central pulse pressure vs. measured peripheral
pulse pressure.

buffered by the compensatory vasoconstriction that occurred during LBNP. However, central PP
was much less impacted by the rise in total peripheral resistance, presumably due to the significant
time delay between the forward and backward waves in the central aorta.
This study improves upon our previous efforts to estimate SV and CO by long time interval
analysis of a peripheral ABP waveform [87]. In particular, that technique estimates average CO
over approximately 30-60 sec intervals. The technique described in the current study can potentially estimate beat-to-beat SV and could therefore detect rapid changes during hemorrhage and
other physiologic conditions.

81

The assumption of PP to be a surrogate of SV is instantaneous cardiac ejection. In practice, it
occurs over finite time for the heart to eject blood from the central aorta to the periphery. Therefore,
we tried to circumvent this assumption by estimating the Windkessel time constant via fitting an
exponential to the diastolic decay of the derived central ABP waveform, which is less complicated
by wave reflection than a peripheral ABP waveform. The SV estimated by Bourgeois’ method
showed earlier indication of hemorrhage than the estimated central PP.
The group average of PTT was progressively decreasing during the LBNP experiment. In principle, decreasing ABP should lead to an increase of PTT. On the other hand, increasing resistance
due to hemorrhage will change PTT to the other direction. From the result in our experiment, the
decreasing PTT indicated that the resistance is the dominant factor.
In future, we will quantitatively evaluate the techniques with statistical analysis, such as ROC
AUC. The discrimination between the low-tolerant and high-tolerant subjects will be investigated
as well.

82

Chapter 5
CARDIAC OUTPUT MONITORING FROM PULMONARY ARTERIAL PRESSURE BY
LONG TIME INTERVAL ANALYSIS

5.1 Introduction
Cardiac output (CO), which represents the total blood flow rate in the circulation, can also be
monitored from a measurement of pulmonary arterial pressure waveform. Meanwhile, left atrial
pressure (LAP), which generally indicates the blood pressure attained in the left ventricle during
the cardiac filling phase, can be simultaneously tracked with the pulmonary arterial pressure waveform. As two of the most important quantities, the information of CO and LAP collected from
critically ill patients can facilitate the diagnosis, monitoring, and treatment of various disease processes such as left ventricular failure, mitral valve disease, and shock of any cause. For example,
patients with left ventricular failure often have symptom of a decrease in CO and an increase in
LAP, whereas a decrease in CO while LAP is falling may indicate that the patient is going into
hypovolemic shock.
So far, the use of the balloon-tipped, flow-directed pulmonary artery catheter is the gold standard method for measuring CO and LAP in critically ill patients [61, 106]. As previously
discussed, CO is specifically estimated according to the thermodilution method. This method involves injecting a bolus of cold saline in the right atrium, measuring temperature downstream in
the pulmonary artery, and computing the average CO based on conservation laws. LAP is estimated through the pulmonary capillary wedge pressure (PCWP) method. This method involves
advancing the catheter into a branch of the pulmonary artery, inflating the balloon, and measuring
the resulting steady-state PCWP. In theory, PCWP should nearly equal LAP, since flow has ceased
through the branch.
A major limitation of the catheterization method is that it requires an operator, which therefore
does not permit continuous monitoring. Moreover, risks exist in the implementation such as partial

83

wedging and balloon over-inflation [54, 67]. Indeed, the developers of the PCWP method and
the pulmonary artery catheter each reported that they could properly measure PCWP only about
75% of the time [106]. Similar technical problems can also be encountered in implementing the
thermodilution method. Perhaps, as a result of these shortcomings, the clinical benefit of the
pulmonary artery catheter is still controversial [93].
On the other hand, continuous monitoring of pulmonary artery pressure (PAP) is available with
the invention of the pulmonary artery catheter. Since CO and LAP are both known to be significant
determinants of PAP, it should, in principle, be possible to continuously monitor these two critical
hemodynamic variables by mathematical analysis of a PAP waveform. Such an approach could be
utilized in critically ill patients to, for example, assess the effects of interventions in real-time, provide an early indicator of deleterious hemodynamic events, save precious time in the busy intensive
care unit (ICU), as well as circumvent the aforementioned technical problems in implementing the
standard measurement methods.
To our knowledge, only four papers are found in the literature for monitoring CO by PAP
waveform analysis [21, 32, 107, 116]. These papers described techniques that analyzed intrabeat PAP variations in which highly complex wave and inertial effects are prominent [73]. On
the other hand, there is substantial literature on estimating LAP through the end-diastolic PAP
(e.g., [61, 45]). However, this simple analysis is not as accurate as PCWP [45] and is known to
be unreliable during pulmonary hypertension [61]. One paper in the literature was found which
involves training a neural network to predict PCWP from a PAP waveform [30]. However, the
accuracy of technique was limited by its training group. Thus, no advanced technique has been
introduced in the literature which can both monitor LAP and CO by mathematical analysis of a
PAP waveform.
In this chapter, we evaluate a technique for continuous monitoring of both CO and LAP by
mathematical analysis of a PAP waveform over time scales greater than a cardiac cycle in which
the confounding effects of wave and inertial phenomena are attenuated [73]. The technique has
been proposed in a previous animal study. In this study, we evaluated the technique with respect to

84

pulmonary artery catheterization data from 180 critically ill patients.

5.2 The technique
Our technique for monitoring CO and LAP from a PAP waveform is extended from a technique
we previously developed for estimating CO from an arterial blood pressure waveform by long time
interval analysis [59, 69]. The method can be briefly described as follows:
The novel technique is based on the Windkessel modeling of the pulmonary system in Figure 5.1(a). The pulmonary system consists of a resistor, a capacitor and a constant voltage source.
The resistor represents the pulmonary arterial resistance (PAR), and the capacitor stands for the
pulmonary arterial compliance (PAC). The constant voltage source describes the left atrial pressure. According to the circuit theory, during each diastolic interval, the PAP should exponentially
decay to the average LAP, rather than zero pressure. The time constant τ of the decay should be
the product of PAR and PAC. By fitting an exponential function to the PAP waveform, both τ and
LAP can be determined. Then CO can be subsequently derived with a scale factor of 1/PAC by
subtracting LAP from mean PAP (MPAP) and dividing the difference by τ .
However, pure exponential diastolic decay is often obscure to observe in experimental PAP
waveforms (Figure 5.1(b)) [107] due to complex wave reflections and inertial effects in the pulmonary circulation [73]. On the other hand, our previous study has indicated that the confounding
wave and inertial effects may be faster than the exponential Windkessel dynamics. This concept
implies that if pulsatile activity abruptly ceased, then PAP would eventually decay like a pure exponential and ultimately equilibrate to LAP once the faster wave and inertial dynamics vanished.
Thus, the Windkessel model of Figure 5.1(a) is a more valid representation of the long time scale
or beat-to-beat variations in the PAP waveform.
Our technique therefore analyzes the PAP waveform over long time intervals (seconds to minutes) in order to determine the pure exponential decay and equilibrium pressure that would eventually result if pulsatile activity suddenly ceased. More specifically, average LAP and the response
of PAP minus average LAP to a single, solitary cardiac contraction (h(t) in Figure 5.2) are simulta85

(a)
CO

(b)

PAP

W

PAR
PAC

PAP [mmHg]

30
20
10

LAP

CO v

LAP

PAP - LAP
W

0
10

11

W PAR˜PAC

12
13
Time [sec]

14

15

Figure 5.1: (a) Windkessel model of the pulmonary artery pressure (PAP) waveform. (b)
Experimental PAP waveform and diastolic decay fitting.
neously estimated by optimal fitting or prediction of ∼6 min contiguous segments of a PAP waveform. Then, the Windkessel time constant τ is determined by fitting a mono-exponential function
to the tail end of h(t) once the faster wave and inertial effects have vanished (Figure 5.2). Finally,
proportional CO is computed via Ohm’s law (Figure 5.2). The technique, which is illustrated in
Figure 5.2, is specifically implemented in four mathematical steps.
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 of y(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 input equation with constant term c:

86

PAP
h(t)

25

1

20
15 PPj-1 PPj PP
j+1
10

0.5

y(t) [mmHg]

x(t) [mmHg]

25

W

5
0

Rj+1
Rj-1 Rj
0
0.5 1
1.5
Time [sec]

PPj-1 PPj

PPj+1

20
15
10
5

Rj-1 Rj

Rj+1

LAP

0
0

2

1
Time [sec]
CO v

00

0.5
1 1.5
Time [sec]

y(t)-LAP
W

Figure 5.2: Illustration of how the mathematical analysis technique determines the time constant
τ of the Windkessel model in Figure 5.1, average left atrial pressure (LAP), and proportional
cardiac output (CO) from a pulmonary artery pressure (PAP) waveform.

m

k=1

y(t) = c +

n

k=l

∑ ak y(t − k) + ∑ bk x(t − k) + e(t).

(5.1)

where e(t) is the unmeasured residual error, ak , bk are unknown parameters, and m and n limit the
number of these parameters (model order) [58]. For a fixed model order, the parameters including
c are estimated from x(t) and y(t) through the least-squares minimization of e(t), which has a
closed-form solution [58]. With the estimated parameters, average LAP and h(t) are computed as
follows:

LAP = c/(1 −
ˆ

m

∑ aˆk ).

(5.2)

k=1
m

k=1

h(t) =

n

k=l

∑ aˆk h(t − k) + ∑ bˆk δ (t − k).

(5.3)

where ^ indicates estimates and δ (t) is the impulse function.
Next, τ is determined over the interval of the estimated h(t) ranging from one to two seconds
following the time of its maximum value based on the exponential equation:

87

h(t) = Ae−t/τ + w(t).

(5.4)

The parameters A and τ are estimated through the least squares minimization of the unmeasured
residual error w(t), which has a closed-form solution after log transformation of h(t). In principle,
accurate determination of τ as well as average LAP is achieved by virtue of h(t) reliably coupling
the long time scale variations in x(t) to y(t)-LAP.
Finally, proportional CO is computed by dividing MPAP-LAP with τ . Note that the continuous
proportional CO provided by the technique may be conveniently calibrated to continuous absolute
CO with a single thermodilution measurement.

5.3 Materials and analysis
5.3.1

Pulmonary artery catheterization data

The pulmonary artery catheterization data utilized here for the mathematical analysis were obtained from the MIMIC II (Multi-parameter Intelligent Monitoring for Intensive Care II) database,
which is described in detail elsewhere and freely available on the web. Briefly, this database includes 247 critically ill patient records that were archived from patient monitors in 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 PAP and surface ECG leads as well as
one-minute trends such as thermodilution CO, PCWP, and heart rate (HR). 180 of the 247 patient records were applicable for technique evaluation, as they included a PAP waveform and more
than one reference thermodilution CO measurement (as the technique estimates changes in CO)
and/or at least one PCWP measurement. Within each of these records, CO as well as PCWP were
naturally changing due to disease progression and therapy.
Based on these 247 MIMIC patient records, we created a data set for technique evaluation as
follows. First, we downloaded from these records all of the distinct, one-minute thermodilution
CO and PCWP measurements and corresponding three-minute segments of the PAP waveforms.
88

Then, we visually examined each of the PAP waveform segments and extracted the artifact-free
records. A total of 87 pairs of artifact-free PAP waveform segments and reference PCWP from
27 patient records and a total of 1211 pairs of artifact-free PAP waveform segments and reference thermodilution CO from 180 patient records remained for the subsequent evaluation of our
technique.

5.3.2

Data analysis

After applying the technique to all 1211 PAP waveform segments, the resulting proportional CO
and absolute LAP estimates were quantitatively compared with their respective reference thermodilution CO and PCWP measurements as follows. First, the proportional CO estimates were scaled
to have the same mean as the reference thermodilution CO within each patient record. Then, the
root-mean-squared-normalized-errors (RMSNEs) between the calibrated CO and their respective
reference measurements were computed. For comparison, the RMSNE between MPAP, PP·HR
and the reference CO were also computed.
On the other hand, the root-mean-squared-errors (RMSE) between the absolute LAP estimates
and the reference PCWP were calculated. For comparison, the RMSE between the mean enddiastolic PAP (EDPAP) and their reference PCWP measurements was also computed.
In our previous study, we found that our technique was more robust to challenging physiologic
conditions than conventional techniques. We also performed similar analysis in this study. To be
more specific, for the CO estimates, we investigated the CO estimation accuracy of the investigational techniques as a function of minimum thermodilution CO change magnitude. The magnitude
was increased from baseline up to 40%.

5.4 Results
Table 5.1 summarizes the results of the evaluation of the technique with respect to the MIMIC II
database. This table shows that the technique achieved an overall CO RMSNE of 17.6% (after a

89

Table 5.1: Overall cardiac output estimation accuracy of the investigational techniques.
Technique

RMSE (%)

Limits-of-Agreement (L/min)

LTIA
MPAP
PP·HR

17.60
22.48
19.67

-1.84/+1.84
-2.19/+2.19
-1.94/+1.94

Wilcoxon Signed-Rank
Test (p)
<0.001
0.30

Table 5.2: Overall left atrial pressure estimation accuracy of the investigational techniques.
Technique
LTIA
EDPAP

RMSE (mmHg)
4.9
5.9

Limits-of-Agreement (mmHg)
-8.58/+10.57
-3.83/+12.31

Paired t-Test (p)
<0.001

single calibration), whereas the errors of MPAP and PP·HR were 22.48% and 19.67%, respectively.
Figure 5.3 shows the results with increasing CO magnitude. The LTIA technique was least affected
by the change. The overall LAP RMSE has the error of 4.9 mmHg, which is significantly better
than the conventional EDPAP technique with the error of 5.9 mmHg, as illustrated in Table 5.2.

5.5 Discussion
The technique was validated in our previous study. We now evaluated the technique with respect
to the MIMIC II database, which includes fully annotated hemodynamic records from thousands
of ICU patients. The analysis was performed from 180 critically ill patients and have compared
the resulting CO and LAP estimates with standard operator-dependent thermodilution CO and
PCWP measurements, respectively. Comparing with conventional techniques, our technique is
more accurate in estimating CO and LAP. When the patient condition becomes more challenging,
the advantage between our technique and other conventional techniques is more significant.
One potential limitation of our technique is the assumption of constant PAC. In future, the accuracy might be improved with the measurement PTT. With future successful testing, the technique
may ultimately be employed in critically ill patients so as to effectively automate the pulmonary
artery catheter.

90

Number of CO Measurements (and Patients)
65

CO RMSNE [%]

55

180 (1211) 147 (582)

84 (184)

37 (56)

12 (16)

20

30

40

MAP
PP·HR
LTIA

45

35

25

15

0

10

Minimal CO Change Magnitude [%]
Figure 5.3: Illustration of how the mathematical analysis technique determines the time constant
τ of the Windkessel model in Figure 5.1, average left atrial pressure (LAP), and proportional
cardiac output (CO) from a pulmonary artery pressure (PAP) waveform.

91

Chapter 6
CONCLUSIONS

6.1 Summary
In this report, we proposed several novel physiologic waveform analysis techniques, which will
prove both reliable and superior to previous techniques, for monitoring cardiac output. The long
time interval analysis can remove the reflection confounding issue by estimating the cardiac output over multiple beats. The technique was evaluated on a large, medical/surgical ICU patient
dataset. Our proposed technique was comparative with other traditional methods at the baseline
level and the technique became increasingly superior to others with more challenging cardiac output changes. We also introduced pulse transit time to overcome the estimation error by varying
arterial compliance. With the pulse transit time correction, we validated our technique in an animal
study and a human lower body negative pressure experiment. The decreasing pulse transit time excellently compensated the arterial compliance variation, the corrected techniques overlapped with
the reference method, while other methods all overestimated the cardiac output during the LBNP
process. In addition, we compared the effects of pulse transit time and pulse arrival time, in terms
of their capabilities in tracking blood pressure. We implemented high-fidelity, invasive measurements over wide hemodynamic conditions. From our results, we concluded that the pulse arrival
time is not an adequate surrogate for pulse transit time and we only recommended future research
should focus on pulse transit time.
In addition, we employed the tube-load model with adaptive transfer function to estimate CO
from a peripheral ABP waveform. In order to identify unknown parameters of the model, we
exploited the fact that central flow should be negligible during diastole. This technique permits
beat-by-beat estimation and thus it can facilitate the real-time CO monitoring. The PTT was also
introduced to overcome the influence of AC.

92

Further, we adapted our LTIA model to estimate CO from a pulmonary artery pressure. The
Windkessel model was modified with an additional constant term. This novel technique is able to
simultaneously estimate CO and left atrial pressure, which are two important physiologic variables.

6.2 Future work
In future, an extension can be performed to the tube-load technique. The extended model can estimate relative change in end-diastolic volume (EDV) from the central ABP waveform, which may
be derived from a peripheral ABP waveform with the preceding adaptive transfer function technique. EDV is considered as an earlier marker of hypovolemia than SV. The idea of the technique
is to build upon the Windkessel technique by modeling the left ventricle in addition to the arterial
tree so as to split an SV estimate into its cardiac end-systolic volume (ESV) and EDV components.
The basic steps are to (1) represent both the ejection and diastolic intervals of the central ABP
waveform with a lumped parameter model; (2) estimate the lumped model parameters to with a
constant AC scale factor by fitting the model to each beat of the waveform; and (3) use the proportional parameter estimates for each beat to compute beat-to-beat EDV and ESV to within the same
scale factor.
More specifically, first, the entire central ABP waveform is represented with a modified Windkessel model of the left ventricle and arterial tree (see electrical analog in Figure 6.1). In the model,
the left ventricle is characterized by the well-known variable elastance (reciprocal of compliance)
model whose elastance (ventricular elastance, VE) is time-varying (E(t)) [101, 92]. Assuming
absence of valve disease, the aortic valve is modeled by an ideal diode. The arterial tree is represented with the Windkessel model as justified above. In addition to compliance, the left ventricle
(and large arteries) is parameterized with an unstressed volume (ventricular unstressed volume,
VUV). Then, the model parameters can be derived from the following discretized governing equation:

93

(b)

Pa(t)

Ra

Ca

τ

Teje

Emax
Elv(t)Elv(t)
[mmHg/ml]

Elv(t)

Pa(t) [mmHg]
Pa(t) [mmHg]

(a)

Elv(0)

Ts 1.5Ts

t

Time [s]
Figure 6.1: New technique for monitoring EDV by analysis of the central ABP waveform, which
may be derived from a peripheral ABP waveform. (a) Lumped parameter model of the left
ventricle and arterial tree upon which the technique is based. (b) The unknown model parameters
(in gray) are estimated by fitting the model to the ejection and diastolic intervals of each beat of
the ABP waveform so as to compute relative change in beat-to-beat EDV.

t
pa (t)
T
pa (tbe )
[pa (k) + pa (k − 1)],
−
= pa (t) − pa (tbe ) +
AC · E(tbe ) AC · E(t)
2τ k=t∑+1

tbe ≤ t ≤ tee , (6.1)

be

where T is the sampling period, and tbe and tee are the beginning and end times of the ejection
interval. Both T and pa (t) for tbe and tee are known, while the proportional model parameters,

τ = TPR· AC and AC· E(t) for tbe ≤ t ≤ tee , need to be determined. Equation 6.1 represents an
under-determined set of equations with N equations and N + 2 unknowns, so it does not provide
a basis for uniquely determining these parameters. In order to find solutions to the equations,
94

a parametric function is assumed to succinctly characterize the time-varying VE as justified by
previous studies. In particular, Senzaki et al. showed that experimental VE functions, normalized
in both amplitude and time, were remarkably consistent in 87 patients despite wide variations in
their ventricular states (see discrete values in the lower panel of Figure 6.1) [94]. Heldt et al. then
showed that these normalized VE data could be well fitted, especially during the relevant ejection
interval (i.e., the higher elastance range), by a parametric raised cosine function (Figure 6.1) [42].
Substituting this parametric function into (6.1) reduces the number of unknowns to four, namely τ ,
AC · Emax , AC · E(tbe ), and Ts (Figure 6.1). These four parameters then can be estimated for each
beat in two steps. First, τ is estimated by fitting an exponential to the diastolic interval of pa (t)
(see Figure 6.1). Second, the estimated τ is substituted into (6.1), and AC·Emax , AC·E(tbe ), and Ts
are estimated from pa (t) over the ejection interval by optimally fitting both sides of this equation
to each other. This optimization is achieved via a nonlinear least squares search over a physiologic
range of the three parameters.
Finally, the beat-to-beat proportional EDV can be derived from the estimated proportional VE
function over the ejection interval, AC·E(t) for tbe ≤ t ≤ tee , and the central ABP waveform pa (t),
via the following governing equation:

EDV ∝

pa (tbe )
VUV
+
AC · E(tbe )
AC

(6.2)

VUV/AC is much smaller than EDV in normal subjects such as soldiers [47], so VUV/AC may
be neglected or set to a nominal value (e.g., 15 mmHg in dogs [9, 101]), rather than estimated. This
value can be measured for patients with dilated hearts by obtaining EF via imaging and finding the
value of VUV/AC. In this case, the EF estimated from the ABP waveform should equal to the
independent EF measurement.
Given the available reconstructed central ABP, EDV and EF can be estimated by this approach.
We expect that EDV would be a more acute marker of hemorrhage than SV. The technique will be
evaluated with the data in the LBNP study.

95

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