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LIBRARY
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SYSTEM IDENTIFICATION OF NEURAL
CARDIOVASCULAR CONTROL MECHANISMS

presented by

XIAOXIAO CHEN

has been accepted towards fulfillment
of the requirements for the

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SYSTEM IDENTIFICATION OF NEURAL
CARDIOVASCULAR CONTROL MECHANISMS

By

Xiaoxiao Chen

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Electrical Engineering

2009

.F-.. ‘ 1‘ (‘HALE

ABSTRACT

SYSTEM IDENTIFICATION OF NEURAL CARDIOVASCULAR
CONTROL MECHANISMS ‘

By
Xiaoxiao Chen

One of the most important functions of neural cardiovascular regulation is to
maintain arterial blood pressure (ABP) within a narrow range in order to protect
blood flow to the brain, heart and other vital organs. The autonomic nervous system
is primarily responsible for extrinsic cardiovascular regulation over short time scales
of seconds to minutes usually through mediation of the arterial and cardiopulmonary
baroreflex. When changes in ABP or central venous pressure increase/decrease the
stretch of the arterial or cardiopulmonary baroreceptors and afferent signals are
transmitted to the brain, the brain responds to keep ABP near its normal operating
level by adjusting heart rate (HR), ventricular contractility (V C), total peripheral
resistance (TPR) and systemic venous unstressed volume. Improper functioning of
the neural cardiovascular control mechanisms could cause numerous diseases such as
postural tachycardia syndrome, congestive heart failure and diabetic autonomic
neuropathy. Therefore, it is important to be able to quantify neural cardiovascular
regulation in order to better understand its functioning in both health and disease and
to guide patient therapy.

The research addressed in this dissertation is an effort to quantitatively
characterize the neural cardiovascular control mechanisms via system identification

and advanced signal processing techniques. We derived specific parasympathetic and

sympathetic nervous system indices from identified HR baroreflex impulse response
via non-invasive cardio-respiratory variability, developed a model-based technique to
estimate the arterial TPR baroreflex impulse response through potentially non-
invasive measurements, and investigated the dynamic control mechanisms of VC via
the baroreflex and force-frequency relation. Our results, obtained from animal/human
experiments and as well as realistic computer simulated data, either correctly predict
the known effects after autonomic interventions or provide new insight in the neural

cardiovascular regulation.

To my Mom

iv

ACKNOWLEDGEMENTS

I would like to express my sincere appreciation to my advisor Dr.
Ramakrishna Mukkamala for his guidance and support throughout my Ph.D. study.
He not only taught me the knowledge and research skills, but also set a great example
of how to conduct first-class research, from which I can benefit for the rest of my life.

I would like to thank my committee members Dr. Gregory Fink, Dr. Selin
Aviyente and Dr. Lalita Udpa for their valuable discussions during each of my
presentation and also for their patience and support every time I had changes in my
course plan.

I would like to express my gratitude to my collaborators in Wayne State
University, Dr. Robert Hammond, Dr. Javier Sala-Mercado and Dr. Donal O’Leary,
for their great effort in every experiment and their patience and kindness whenever I
had a question to ask. Also, I would like to thank Dr. Xinshu Xiao in University of
California, Los Angeles for her help and guidance in my selective quantification of
the autonomic nervous system project.

I would like to extend my appreciations to my dear colleagues Rafat I Elahi,
Zhenwei Lu, Ying Li, Kabi Padhi, Da Xu, Federico Aletti, Gokul Swamy, Soroor
Soltani, Guanqun Zhang, and Anton Khomyakov for their help during my research

and for the good times we spent together.

In addition, I would like to take this opportunity to thank all my friends,
especially Erica Chen and Erica Tseng, for letting me share my ups and downs with
them and for their support and patience when I am in a bad mood.

The last individual I wish to thank is the one to whom I dedicate this
dissertation, my Mom Zhenxiu Chen. I would like to send her my most sincere
gratitude for raising me up on her own, supporting me unconditionally and loving me

as who I am. Thank you, Mom!

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................... ix
LIST OF FIGURES ...................................................................................... x
CHAPTER 1. INTRODUCTION ................................................................ l
1.1 Motivation and Objective ........................................................................................ 1
1.2 Scope and Organization of the Dissertation ............................................................ 4
CHAPTER 2. BACKGROUND ................................................................... 6
2.1 Neural Cardiovascular Regulation ........................................................................... 6
2.1.1 The Cardiac Autonomic Nervous System ....................................................... 6
2.1.2 Baroreflex Control of Arterial Blood Pressure ............................................... 7
2.2 The System Identification Method .......................................................................... 8
2.2.1 Overview ......................................................................................................... 8
2.2.2 The Exogenous Input Model ......................................................................... 12
2.2.3 The Autoregressive Exogenous Input Model ................................................ 14

CHAPTER 3. SELECTIVE QUANTIFICATION OF THE CARDIAC
SYMPATHETIC AND PARASYMPATHETIC NERVOUS SYSTEMS
BY MULTISIGNAL ANALYSIS OF CARDIORESPIRATORY

VARIABILITY. .......................................................................................... 17
3.1 Abstract .................................................................................................................. 17
3.2 Introduction ............................................................................................................ 18
3.3 Multi-Signal Analysis of Cardio-Respiratory Variability ..................................... 21
3.4 Materials and Methods ........................................................................................... 28

3.4.1 Experimental Data ......................................................................................... 28

3.4.2 Data Analysis ................................................................................................ 29
3.5 Results .................................................................................................................... 30
3.6 Discussion .............................................................................................................. 41
3.7 Appendix ................................................................................................................ 49

CHAPTER 4. ESTIMATION OF THE TOTAL PERIPHERAL
RESISTANCE BAROREFLEX IMPULSE RESPONSE FROM

SPONTANEOUS HEMODYNAMIC VARIABILITY ........................... 51
4.1 Abstract .................................................................................................................. 51
4.2 Introduction ............................................................................................................ 52
4.3 Materials and Methods ........................................................................................... 55

4.3.1 Extended Mathematical Analysis Technique ................................................ 55

4.3.2 Technique Evaluation ................................................................................... 64
4.4 Results .................................................................................................................... 68

vii

4.5 Discussion .............................................................................................................. 74
4.6 Appendix A ............................................................................................................ 80
4.7 Appendix B ............................................................................................................ 83

CHAPTER 5. DYNAMIC CONTROL OF MAXIMAL
VENTRICULAR ELASTAN CE VIA THE BAROREFLEX AND
FORCE-FREQUENCY RELATION IN AWAKE DOGS BEFORE

AND AFTER PACIN G INDUCED HEART FAILURE ........................ 90
5.1 Abstract .................................................................................................................. 90
5.2 Introduction ............................................................................................................ 91
5.3 Materials and Methods ........................................................................................... 94

5.3.1 Hemodynamic Data ....................................................................................... 94

5.3.2 Data Analysis ................................................................................................ 95
5.4 Results .................................................................................................................. 100
5.5 Discussion ............................................................................................................ 107

CHAPTER 6 CANINE INVESTIGATION OF THE
CARDIOPULMONARY BAROREFLEX CONTROL OF

VENTRICULAR CONTRACTILITY .................................................... 114
6.1 Abstract ................................................................................................................ 114
6.2 Introduction .......................................................................................................... 114
6.3 Methods ............................................................................................................... 116

6.3.1 Data Collection ........................................................................................... 116

6.3.2 Data Analysis .............................................................................................. 117
6.4 Results .................................................................................................................. 120
6.5 Discussion ............................................................................................................ 121
CHAPTER 7 CONCLUSIONS AND FUTURE WORK ...................... 124
7.1 Accomplishments and Conclusions ..................................................................... 124
7.2 Future Work ......................................................................................................... 125
REFERENCES .......................................................................................... 127

viii

LIST OF TABLES

Table 4.1 Theoretical evaluation results of the extended mathematical analysis
technique in which two of the estimated parameters (mean i SE) from the
cardiovascular simulator are shown along with the actual reference values and
corresponding quantitative errors. ............................................................................... 71

Table 4.2 Experimental evaluation results of the extended mathematical analysis
technique in which the group averages of the estimated parameters (mean i SE) from
the seven conscious dogs are shown before and after chronic arterial baroreceptor
denervation along with level of statistical significance. .............................................. 74

Table 5.1 Group average mean hemodynamic variables from five conscious dogs
before and after pacing induced heart failure (HF) .................................................... 100

Table 5.2 Group average gain values and overall time constants of the transfer
functions relating beat-to-beat fluctuations in ABP to Emax (ABP—)Emax) and beat-to-

beat fluctuations in HR to Emax (HR—>Emax) from the five conscious dogs before and
after HF. ..................................................................................................................... 106

ix

LIST OF FIGURES

Figure 2.1 The system identification loop. Adapted from Ref (46). ........................... 9

Figure 2.2 The block diagram of a typical closed-loop 8180 system: h(t) represents
the impulse response of the feedforward system; g(t) represents the impulse response
of the feedback system; u(t) and y(t) denote the system input and output, respectively;
and n(t) represents the unknown noise disturbance. .................................................... 12

Figure 3.1 Models of transfer functions relating fluctuations in instantaneous lung
volume to heart rate (ILV—)HR) and fluctuations in arterial blood pressure to HR
(ABP—)HR) upon which the multi-signal analysis of cardio-respiratory variability is
based. ........................................................................................................................... 23

Figure 3.2 Block diagram illustrating the estimation of the ILV—>HR and ABP—>HR
impulse responses by application of parametric system identification to resting beat-
to-beat fluctuations in HR, ABP, and ILV ................................................................... 26

Figure 3.3 Group average results (mean i- SE) for the estimated ILV—)HR impulse
responses and the corresponding P1 and SI indices fiom 14 human subjects before

(control) and after vagal, B-sympathetic, and double (vagal+[3-sympathetic) blockade
in the standing posture. ................................................................................................ 31

Figure 3.4 Group average results (mean i SE) for the estimated ABP—)HR impulse

responses and the corresponding P2 and $2 indices from 14 human subjects before

(control) and after vagal, B-sympathetic, and double (vagal+B-sympathetic) blockade
in the standing posture. ................................................................................................ 32

Figure 3.5 Group average results (mean t SE) for the conventional HF power of HR

variability and the P1 and P2 indices of the PNS. The symbol # indicates p<O. 10; *,
p<0.05; §, p<0.01; T, p<0.005; and I, p<0.001. .......................................................... 34

Figure 3.6 Group average results (mean ._+. SE) for the conventional LF/HF ratio and
normalized LF power of HR variability and the SI and 82 indices of the SNS. The

symbol # indicates p<0.10; *, p<0.05; §, p<0.01; T, p<0.005; and I, p<0.001. .......... 38
Figure 4.1 Step 1 of the mathematical analysis technique. ......................................... 58
Figure 4.2 Step 2 of the mathematical analysis technique. ......................................... 60
Figure 4.3 Step 3 (extension) of the mathematical analysis technique. ...................... 63

Figure 4.4 Theoretical evaluation results of the extended mathematical analysis

technique in which the estimated arterial TPR baroreflex impulse response h A(t)
(mean (dashed) E SE (dashed-dotted)) is illustrated along with the corresponding

actual reference h A(t) (solid) for three different simulator TPR baroreflex gain values.
...................................................................................................................................... 69

Figure 4.5 Theoretical evaluation results of the extended mathematical analysis

technique in which the estimated arterial TPR baroreflex impulse response hA(t)
(mean (dashed) 3: SE (dashed-dotted)) is illustrated along with the corresponding

actual reference hA(t) (solid) for three different simulator TPR baroreflex overall time
constant values. ............................................................................................................ 70

Figure 4.6 Experimental evaluation results of the extended mathematical analysis

technique in which the group average estimated h A(t) (mean (solid) i SE (dashed))
from the seven conscious dogs is illustrated before and after chronic arterial
baroreceptor denervation. ............................................................................................ 73

Figure 5.1 Method for estimating spontaneous beat-to-beat maximal ventricular

elastance (Emax) variability fi'om left ventricular pressure and volume (LVP and LW)

measurements during transient vena cava occlusion (left panel) and a baseline period
(right panel) .................................................................................................................. 97

Figure 5.2 Block diagram for identifying the transfer functions relating fluctuations
in arterial blood pressure (ABP) to Emax (ABP—mum) and fluctuations in heart rate

(HR) to Emax (HR—)Emax) from spontaneous beat-to-beat ABP, HR, and Ema.x
variability. .................................................................................................................... 99

Figure 5.3 Group average power spectra of the spontaneous beat-to-beat ABP, HR,

and Emax fluctuations (meaniSE) from five conscious dogs before and after pacing
induced heart failure (HF) .......................................................................................... 101

Figure 5.4 Group average ABP—)Emax and HR—>Emax transfer functions in terms of
magnitude and phase responses as well as step responses (meant SE) from the five
conscious dogs before and after HF. .......................................................................... 103

Figure 6.1 Block diagram for identifying the CVP—9Emax, ABP—>13max and
HR—)Emax transfer functions from beat-to-beat fluctuations in CVP, ABP, HR, and

Em. .......................................................................................................................... 120

Figure 6.2 Group averaged transfer fimctions in terms of step responses during the
control and propranolol conditions .................................................................................. 121

xi

CHAPTER 1. INTRODUCTION

1.1 Motivation and Objective

One of the most important functions of global or extrinsic cardiovascular
regulation is to maintain arterial blood pressure (ABP) within a narrow range via
multiple negative feedback and control systems in order to protect blood flow to the
brain, heart, and other vital organs (33). The autonomic nervous system (ANS) is
primarily responsible for this type of regulation over short time scales of seconds to
minutes to reduce the minute by minute variation in ABP usually through mediation
of the arterial and cardiopulmonary baroreflex mechanisms. The “buffer” fimction of
arterial baroreflex operates as follows. Changes in ABP increase or decrease the
stretch of the arterial baroreceptors and then the signals are conveyed to the brainstem
via afferent nerve fibers. The brain responds in order to keep ABP near its normal
operating level by adjusting heart rate (HR), ventricular contractility (V C), total
peripheral resistance (TPR) and systemic venous unstressed volume (SVUV). The
cardiopuh'nonary baroreflex operates analogously except that its sensory receptors
seem to be very responsive to changes in pressures in low-pressure areas of the
circulation caused by changes in blood volume.

Proper functioning of the neural cardiovascular control mechanisms is most
critical during physiologic perturbations such as exercise and postural changes. For

instance, upon standing from supine position, the arterial pressure in the head and

upper body tends to fall, and the falling pressure at the baroreceptor sites elicits an
immediate reflex, resulting in strong ANS reaction throughout the body to minimize
the decrease in pressure in the head and upper body. Should the baroreflex work
dysfunctionally, marked reduction of this pressure can cause loss of consciousness.
In addition, there are numerous diseases (e.g., congestive heart failure (50)) of or
affecting neural cardiovascular regulatory function. Therefore, it is important to be
able to quantify neural cardiovascular control mechanisms in order to better
understand its functioning in both health and disease, and to improve patient
monitoring as well as to guide patient therapy.

The conventional methods for quantifying neural cardiovascular regulation
involve perturbing the circulation with an external stimulus, measuring the regulatory
response and usually plotting the stimulus-response curve. The external stimuli that
have been employed may be broadly classified as selective or nonselective (48). In
principle, selective stimuli (e.g., carotid sinus pressure control) excite and permit the
study of only one particular feedback mechanism (e. g., arterial baroreflex) with no
confounding contributions from other feedback mechanisms (e.g., cardiopulmonary
baroreflex). However, these stimuli open or disturb the closed-loop feedback system
and thereby prevent study during normal physiologic conditions. On the other hand,
nonselective stimuli (e. g., head-up tilting) excite all feedback mechanisms
simultaneously and can preserve normal closed-loop operation, except that the
relative contribution of each feedback mechanism to the total system response cannot
be distinguished with the simple plotting method. Furthermore, the conventional

methods could only quantify the steady-state gain values of the feedback mechanisms

with their dynamic characteristics such as overall time constants and delays
undiscovered.

Since the advent of modern digital signal processing in 1965, it has become
well recognized that short-term, beat-to-beat variability of cardiovascular signals
represent the dynamic interplay between ongoing perturbations to the cardiovascular
system and the compensatory response of the neural regulatory system. Over the last
three decades, investigators have successfully applied numerous quantitative
techniques for the analysis of beat-to-beat variability in single cardiovascular signals,
the principal advantage of which is to be able to quantify neural cardiovascular
regulation without application of an external stimulus and therefore during normal
physiologic conditions. One good example of such studies is selective quantification
of the sympathetic and parasympathetic nervous activities through power spectral
analysis of HR variability (2). While single signal analysis techniques have greatly
contributed to the basic understanding of cardiovascular regulatory functioning, these
techniques are significantly limited in that they characterize only the output response
of the system under study rather than the system itself. To be more specific, the
alterations in the output response may be due to changes of the system and/or
variations in the input, while it is the system itself that should actually be sought for
characterization. On the other hand, if a simultaneous measurement of the input
signal is obtained, then the problem becomes: given input and output, what should the
system be like? This is the system identification problem, which is solvable under

more general conditions (46). Hence, system identification provides a means to

characterize the neural regulatory mechanisms responsible for generating the beat-to-
beat fluctuations rather than the variability that is generated (112).

The principal objective of this dissertation is to investigate the neural
cardiovascular control mechanisms via the technique of system identification.
Respectively, we seek to quantitatively characterize the baroreflex control of HR,
TPR and VC in order to advance the basic understanding of the neural cardiovascular
regulatory functioning and to establish new patient monitoring system. More
specifically, for the HR baroreflex project, we aim to develop selective indices for the
cardiac sympathetic and parasympathetic nervous systems by analyzing cardio-
respiratory variability. For the TPR baroreflex project, the specific aim is to estimate
the arterial TPR baroreflex impulse response from spontaneous hemodynamic
variability which can be obtained via potentially noninvasive measurements. For the
VC baroreflex project, our goal is to study the linear dynamic control of maximal
ventricular elastance in conscious dogs before and after pacing-induced heart failure
and as well as to investigate the cardiopulmonary baroreflex control of VC. Although
the baroreflex system also controls SVUV, the beat-to-beat fluctuation of this signal

is difficult to measure and thus excluded in our current study.

1.2 Scope and Organization of the Dissertation

There are seven chapters in this dissertation. Chapter 1 and 2 are the
introduction and background, including brief description of neural cardiovascular
regulatory system and system identification method. Chapters 3 to 6 serve as the

main content. Chapter 3 presents our work of selective quantification of the cardiac

sympathetic and parasympathetic nervous systems by multi-signal analysis of cardio-
respiratory variability. Chapter 4 describes our novel mathematical algorithm of
estimating the arterial TPR baroreflex impulse response from spontaneous
hemodynamic variability. Chapter 5 is devoted to our investigation of short-terrn VC
control mechanisms via arterial baroreflex and force-frequency relation. Chapter 6
adds in central venous pressure as a third contributor to further investigate the
cardiopulmonary VC baroreflex. Lastly, Chapter 7 summarizes major

accomplishments and points out future work.

CHAPTER 2. BACKGROUND

2.1 Neural Cardiovascular Regulation

2.1.1 The Cardiac Autonomic Nervous System

The nervous system controls the cardiovascular system almost entirely through
the autonomic nervous system (ANS) (33). By far the most important part of the
ANS for regulating the circulation is the sympathetic nervous system (SNS), while
the parasympathetic nervous system (PNS) also contributes specifically to regulation
of the heart.

The SNS takes effect by innervating the blood vessels and as well as the heart.
The SNS passes to the circulation via two routes: (i) through specific sympathetic
nerves that innervate mainly the vasculature of the internal viscera and the heart, and
(ii) almost immediately into peripheral portions of the spinal nerves and distributed to
the vasculature of the peripheral areas (33). The innervation of the small arteries and
arterioles allows sympathetic stimulation to increase the resistance to blood flow and
thereby to increase the blood pressure. One the other hand, the innervation of the
large vessels, particularly of the veins, makes it possible for sympathetic stimulation
to decrease the volume of these vessels. This can thus translocate blood into the heart
and thereby play a major role in the regulation of heart pumping. In addition,

sympathetic fibers also go to the heart directly by innervating the sinoatrial (SA) node

and cardiac muscle, and increase the activity of the heart by both elevating the heart
rate (HR) and the ventricular contractility (V C).

The PNS plays a minor role in regulation of the circulation by mainly
adjusting the heart function through innervation of the SA node and the PNS fibers
are carried to the heart via the vagus nerves. Principally, stimulation of PNS causes

marked decease in HR.

2.1.2 Baroreflex Control of Arterial Blood Pressure

One of the most important roles of neural cardiovascular regulation is to
maintain the arterial blood pressure (ABP) at or near its normal operating level and
almost all of these mechanisms belong to negative feedback reflex, which is well
known as baroreceptor reflex or simply baroreflex (33). Baroreceptors are spray-type
nerve endings that usually lie in the walls of the arteries, and they are stimulated when
stretched. One type of baroreceptors, known as arterial baroreceptors, is extremely
abundant in the wall of the carotid sinus and the aortic arch; while the other type,
known as low-pressure or cardiopulmonary baroreceptors, is spread in the walls of the
atria and the pulmonary arteries.

The arterial baroreflex, which is the much more understood mechanism,
operates as follows. Changes in ABP increase or decrease the stretch of the arterial
baroreceptors and then the signals are transmitted to the brainstem via afferent nerve
fibers. Blood pressure change at carotid sinus is transmitted through the very small
Hering’s nerve to the glossopharyngeal nerve and then to the brain, while signals

from aortic arch are transmitted through the afferent vagus nerves instead. The brain

then responds to keep ABP variation in a tight range near its normal value by
communicating with (a) the SA node via efferent parasympathetic and fi-sympathetic
nerve fibers to adjust HR; (b) the ventricles via efferent B-sympathetic nerve fibers to
adjust VC; (c) the arterioles via efferent (Jr-sympathetic nerve fibers to adjust total
peripheral resistance (TPR) and (d) the veins via efferent (Jr-sympathetic nerve fibers
to adjust system venous unstressed volume (SVUV). For example, the net feedback
response of the arterial baroreflex to an increase in ABP would be a decrease in HR,
VC and TPR and an increase in SVUV. These adjustments would, in turn decrease
ABP back towards its normal operating level via mechanical feedforward effects.

It has been shown that cardiopulmonary baroreflex is responsive to changes in
right atrial pressure or central venous pressure (CVP) (25, 85). However, this
mechanism is much less understood. The cardiopulmonary baroreflex responds to a
change in CVP by inducing an opposite change in TPR (59, 85). One the other hand,
an increase in CVP could lead to an increase in HR (i.e., Bainbridge effect) in dogs
(8), but an opposite change may occur in humans (25). Furthermore, the effect of

cardiopuhnonary VC and SV U V baroreflex is yet to be elucidated.

2.2 The System Identification Method

2.2.1 Overview

Generally speaking, the system identification method is a “black box” process
for estimating the dynamic system under study using simultaneously measured input

and output data. The procedure is typically iterative and consists of three basic steps:

(a) data generation/collection, (b) model determination and (c) model validation (see
Figure 2.1).

Pfior
Knowledge

 

Data
Generation/Collection

 

 

 

Model Determination

I

I

Candidate :
Models :

l

I

Criterion '
of Fit :

+ :

I

I

I

I

I

I

I

 

 

 

 

 

 

 

v 1 I

Model Estimation

 

 

 

 

 

Mode, I Not 3K:
Validation I Revise

 

10K: Use it!

Figure 2.1 The system identification loop. Adapted from Ref (46).

For the data generation/collection step, it not only involves choosing which
signals are to be measured and by what means but also designing the experiments so
that the measured signals are sufficiently informative for the subsequent procedures.
More specifically, for nonparametric models, which do not assume any particular

structure, the input signals should contain all the frequencies of the system under

study. On the other hand, for parametric models, which assume a particular structure
(see below), the input signals should contain at least as many frequency components
as the number of parameters characterizing the system in question (112). For multi-
input systems, “sufficiently informative” also means that the input signals are
different enough (ideally uncorrelated) from each other. Otherwise, it would be
difficult or impossible to distinguish the respective contribution from each input to the
output. While spontaneous variability may nevertheless be sufficiently informative
for a particular system identification task, the experimental design may include the
application of external randomized perturbations in order to ensure enough
information or, at least, to enhance the measured information for a better system
identification accuracy.

Model determination is the step to choose a model that “best” couples the
input-output data fiom a pool of candidates. Although nonparametric models are
attractive in the sense that they do not assume any particular mathematical structure
and are relatively easy to estimate, they are only applicable to systems operating in
open-loop conditions, which are, unfortunately, not the case in neural cardiovascular
regulation. Therefore, parametric models are more often used for analyzing neural
cardiovascular regulatory mechanisms. Another key question that must be addressed
in establishing a set of candidate models is: can the system under study be represented
with a linear and time-invariant (LTI) model? The complex neural cardiovascular
regulatory system is generally nonlinear and time-varying. However, LTI models
may be nearly valid when the data are collected during short time periods of stable,

unchanging experimental conditions, and such models can be considered as

10

approximating small signal system behavior around a given operating point (112).
After an optimal model is chosen, its parameters are usually determined by
minimizing the variance of the unobserved stochastic disturbance. This least squares
estimation (LSE) approach is appropriate when the unobserved disturbance is
normally distributed, which may often be the case due to central limit theorem
arguments.

Once the model is determined, a final step remains as to demonstrate the
validity of the model for its intended purpose (112). The most obvious approach for
model validation would be to obtain an independent measure of the system dynamics
(without the use of system identification) against which the estimated model may be
compared. For instance, to evaluate an estimated impulse response, an impulse
change would have to be applied to an appropriate point in the neural regulatory
system while all other contributing inputs are held constant. However, such an
evaluation procedure would require precise control of the studied inputs, which could
be very difficult to achieve from experimental procedures. Another highly
convincing evaluation would be directly comparing system identification results with
high-fidelity, independent reference quantities. Again, such a procedure may involve
highly complex experiments that are not easy to conduct. A more realizable approach
for model validation could be readily conducted using a cardiovascular simulator with
precisely known system properties. Of course, this type of theoretical evaluation
would only be as meaningful as the extent to which the simulator coincided with an
experimental system. Alternatively, an experimental evaluation in terms of detecting

changes in the estimated quantities to a known intervention (e. g., selective autonomic

11

blockade) could be more easily achieved. Finally, if the model is not supported by
any of the above or alternative evaluation means, then the previous system
identification steps should be modified and repeated until the model validation criteria
are achieved.

Among the three basic steps of system identification loop, we will briefly
introduce two parametric models that are extensively employed in this dissertation.
In the upcoming discussion, we will focus on the single-input single-output (8180)
(see Figure 2.2) system while expecting that extensions to multi-input single-output

form will be naturally clear.

n(t)

 

 

' ht t
u(t)>| () % yr)

Figure 2.2 The block diagram of a typical closed-loop 8180 system: h(t) represents the

impulse response of the feedforward system; g(t) represents the impulse response of the

feedback system; u(t) and y(t) denote the system input and output, respectively; and n(t)
represents the unknown noise disturbance.

2.2.2 The Exogenous Input Model

Among the simplest parametric models, the exogenous input (El) model is
used to represent an LTI system (see Figure 2.2) with a finite impulse response (FIR).
Hence, the input-output relationship can be represented with linear convolution as

below:

12

y(t) = Z u(t — i)h(i) + n(t)

ile ’
(2.1)
where u(t) and y(t) are the system input and output, respectively, h(t) represents the

impulse response with a duration of [N1, Nu] and n(t) is the unknown noise
disturbance. Note that one advantage of parametric models is that strict causality can

be imposed here by not allowing N1 to be less than 1, so that the feedforward system

under study can be disentangled from the feedback system and thus be solved in an
open-loop form. Writing Equation (2.1) in matrix form, the E1 model can be
represented as follows:

y = Uh + n,

(2.2)

where U is the input data matrix defined as

_ u(t-Nl) u(t-Nl-l) u(t-Nu) 7
u(t-N1+1) u(t-Nl) u(t-Nu+1)

 

 

Lu(t-NI+K) u(t-Nl-1+K) u(t-Nu+K)

‘

y is the measured output vector: y = [y(t), y(t+1), ..., y(t+K)]T; and n is the

unobserved, additive noise vector: 11 = [n(t), n(t+1), ..., n(t+K)]T, which is

13

uncorrelated with the input. The column vector h represents the unknown parameters

that specify the FIR.

By applying LSE, the solution of Equation (2.2) is as follows:
h = (UTUr‘UTy,
(2.3)
where h is the estimated impulse response. Note that the LSE solution may involve
ill-conditioned matrix inversion when h has a large duration. In this case, more

sophisticated algorithms, such as weighted-principal component regression method,

should be considered for efficient impulse response estimation (110).
2.2.3 The Autoregressive Exogenous Input Model

The autoregressive exogenous input (ARX) model is perhaps the most widely
employed parametric model in system identification thanks to its ability of estimating
infinite impulse response (IIR) effectively via only a few parameters. The ARX

model with input u(t) and output y(t) is given as follows:

Y(t) = i aiY(t - i) + N2 b.11(t - i) + W(t)

i=N1 ’

(2.4)

where w(t) is an unobserved, white noise disturbance that is uncorrelated with the

input u(t). The unknown coefficients {ai} and { bi } are respectively referred to as

the autoregressive (AR) and moving average (MA) parameters, and the summation

14

limits M, N1 and N11 specify the model order. Similarly, by writing in matrix form,

the ARX model can be represented as:
y = (1)9 + w ,
(2.5)

where (D is the matrix containing both output and input information and expressed

as (I) : [Qy9q)u] , y is the measured output vector: y = [y(t), y(t+1), ...,
y(t+K)]T;w is the unobserved, additive white noise vector: w = [w(t), w(t+1), ...,

w(t+K)]T and 0 contains the unknown AR and MA parameters with

(i=[a1 a2...aM b1,,1b1\,1+1...bN]T

 

 

u . (by and (1)“ are
further defined as follows:
y(t-l) y(t-2) y(t-M) “
(I) _ y(t) y(t-l) y(t+1-M)
y_ o o o
I 1 Z and
Ly(t+K-1) y(t+K-2) y(t+K-‘M)_
— u(t-Nl) u(t-Nl-l) u(t-Nu) T
(I) __ .u(t-N1+1) u(t-Nl) u(t-Nu+1)
_u(t-N1+K) u(t-N1-1+K) u(t-Nu+K)_

 

 

Again, by utilizing the LSE, Equation (2.5) can be solved:

15

6 = <<I>T<I>>"<I>Ty.
(2.6)

where 5 is the estimated AR and MA parameters. Thereafter, the system function of

the ARX model is obtained via z-transform:

N

u

 

(2.7)

Applying inverse z-transform to H(z), the impulse response h(t) is thus obtained.

16

CHAPTER 3. SELECTIVE QUANTIFICATION OF THE
CARDIAC SYMPATHETIC AND PARASYMPATHETIC
NERVOUS SYSTEMS BY MULTISIGNAL ANALYSIS OF
CARDIORESPIRATORY VARIABILITY

3.1 Abstract

Heart rate (HR) power spectral indices are limited as measures of the cardiac
autonomic nervous systems (CANS) in that they neither offer an effective marker of
the [II-sympathetic nervous system (SNS) due to its overlap with the parasympathetic
nervous system (PNS) in the low frequency (LF) band nor afford specific measures of
the CANS due to input contributions to HR (e.g., arterial blood pressure (ABP),
instantaneous lung volume (ILV)). We derived new PNS and SNS indices by multi-
signal analysis of cardio-respiratory variability. The basic idea is to identify the
autonomically mediated transfer functions relating fluctuations in ILV to HR
(ILV—>HR) and fluctuations in ABP to HR (ABP—>HR) so as to eliminate the input
contributions to HR and then separate each estimated transfer function in the time
domain into PNS and SNS indices using physiologic knowledge. We evaluated these
indices with respect to selective pharmacological autonomic nervous blockade in 14
humans. Our results showed that the PNS index derived from the ABP—)HR transfer
function was correctly decreased after vagal and double (vagal+B-sympathetic)

blockade (p<0.01) and did not change after B-sympathetic blockade, while the SNS

index derived from the same transfer function was correctly reduced after [3-

17

sympathetic blockade in the standing posture and double blockade (p<0.05) and
remained the same after vagal blockade. However, this SNS index did not
significantly decrease after [i-sympathetic blockade in the supine posture. Overall,
these predictions were better than those provided by the traditional high frequency

(HF) power, LF/HF ratio, and normalized LF power of HR variability.

3.2 Introduction

Over two decades ago, Cohen and co-workers demonstrated that power
spectral analysis of resting heart rate (HR) variability could provide more specific
measures of the cardiac autonomic nervous systems (CANS) than a basic single time
statistical analysis (e.g., mean and standard deviation) (1, 2, 79). Using selective
pharmacological autonomic nervous blockade, these investigators demonstrated that
the low fi'equency (LF, 0.04-0.15 Hz) fluctuations in HR are jointly mediated by the
parasympathetic nervous system (PNS) and the B-sympathetic nervous system (SNS),
whereas the high frequency (HF, 0.15-0.4 Hz) fluctuations are solely mediated by the
PNS. It therefore directly followed that the HF power of HR variability could serve
as a simple quantitative index of the PNS. Shortly thereafter, Malliani, Cerutti, and
colleagues proposed the ratio of the LF power to the HF power of HR variability
(LF/HF ratio) as an index of sympathovagal balance as well as normalized LF and HF
powers as indices of the CANS independent of the total power or variance (71).
Since then, these easily obtainable indices have been extensively studied under a wide

variety of pathophysiologic conditions (101), having most notably been shown to be

18

associated with mortality in various patient classes (e.g., post-myocardial infarction
(16), cardiac arrest (26), and critically ill (109)) as well as to be altered by various
disease processes (e.g., diabetic autonomic neuropathy (31, 72), congestive heart
failure (17, 91), and hypertension (34, 44). Today, the HF power of HR variability is
generally accepted as a useful index of the PNS, while the LF/HF ratio and
normalized LF power are sometimes considered to be indices of sympathovagal
balance or the SNS (101).

Despite their widespread use and established association with disease, the HR
power spectral indices are quite controversial in terms of being actual measures of the
CANS (47, 73). Part of this controversy simply stems from the common
misconception that these indices should be indicative of basal or mean autonomic
outflow when they are, in fact, intended to reflect the fluctuations in autonomic
outflow about the mean value. The remaining part of the controversy surrounding the
HR power spectral indices is based on their intrinsic limitations as measures of such
fluctuations. One of the major limitations is that the HR power spectral indices,
including the LF/HF ratio and normalized LF power, generally cannot provide an
effective marker of the SNS (i.e., fluctuations in SNS outflow), because the LF power
is mediated by both CANS as shown in the initial studies by Cohen and co-workers
and verified in subsequent studies (74). Another major limitation, alluded to above, is
that none of the HR power spectral indices is truly specific to the CANS, since HR is
just an output of these systems. For example, it is well known that the ultimate source
of the HF power of HR variability is respiration. Thus, changes in the HF power

could also reflect changes in the respiratory input. Similarly, changes in the LP

19

power of HR variability could also reflect changes in arterial blood pressure (ABP)
fluctuations, which may cause the HR fluctuations through the baroreflex (1). So, for
example, the HF power may not provide a useful means to monitor the PNS during
exercise (47), while the LF/HF ratio may not be an effective indicator of
sympathovagal balance when local vasomotor activity alters the variability of the
ABP input (1, 113).

As a result, investigators have recently sought improved indices of the CANS
by employing more sophisticated analyses of beat-to-beat cardiovascular variability.
Vetter et al. proposed to selectively quantify the PNS and SNS using a blind source
separation analysis of HR and ABP variability (105) as well as HR and QT interval
variability (106). Chon and co-workers then introduced a principal dynamic mode
analysis of HR variability to separately characterize the two CANS (113, 114). The
common idea underlying each of these analyses is to distinguish the SNS from the
PNS by invoking some sort of independence or orthogonality assumption, which is
generally untenable. Despite this assumption, the results of these analyses were quite
promising and sparked our own interest in pursuing improved indices of the PNS and
SNS.

In this paper, we derive indices of the PNS and SNS based on a multi-signal
analysis of the beat-to-beat variability in potentially non-invasively measured HR,
ABP, and instantaneous lung volume (ILV). The basic idea of the analysis, which
was briefly proposed by us with co-Workers in (111) (see Discussion section), is to
identify the transfer functions relating the fluctuations in ILV and ABP to HR so as to

effectively eliminate the input contributions to HR and then separate the estimated

20

transfer functions in the time domain into PNS and SNS indices using physiologic
insight rather than any independence or orthogonality assumption. We then show that
these new indices are better than the traditional HR power spectral indices in terms of
predicting the known effects of selective pharmacological autonomic nervous

blockade on the two CANS in 14 healthy human subjects.

3.3 Multi-Signal Analysis of Cardio-Respiratory Variability

Our multi-signal analysis of cardio-respiratory variability aims to derive
specific indices of the PNS and SNS from the dynamic coupling relating fluctuations
in ILV to HR (ILV—>HR), which represents the autonomically mediated respiratory
sinus arrhythmia phenomena (64), and the dynamic coupling relating the fluctuations
in ABP to HR (ABP—>HR), which characterizes the autonomically mediated HR
baroreflex (64). (Note that ILV—>HR coupling is actually non-causal perhaps due to
coupling between the respiratory and HR control centers in the brain (64, 92, 102).)
The analysis specifically invokes two key linearity assumptions that are justified by
previous physiologic findings. The first assumption is that the ILV—)HR and
ABP—>HR couplings may be well approximated with linear and time-invariant
transfer functions for small, resting fluctuations. This assumption is supported by the
work of Chon et al. who showed that 70-7 5% of the variance of resting HR variability
could be explained by linear couplings, while only an additional 10-15% of the
variance could be attributed to second-order nonlinear couplings (22). The second

assumption is that the ILV—>HR and ABP—)HR transfer functions may each be

21

modeled in its time domain impulse response form as the superposition of an early
and fast PNS component and a delayed and sluggish SNS component, as initially
observed by Triedman et al. (102). This assumption is buttressed by known
physiology and the comparison shown in Figure 3.1 of the impulse responses relating
pure vagal and sympathetic stimulation to HR fluctuations that were experimentally
determined by Berger et al. in dogs (13) with typical ILV—)HR and ABP—>HR
impulse responses that were identified by analysis of cardio-respiratory fluctuations
fi'om humans at rest (64). (Note that the data of Berger et a1. actually reveal that the
sympathetic impulse response is delayed by about two seconds with respect to the
vagal impulse response (13).) It should be further noted that the comparison in the
figure effectively represents an extrapolation of the efferent autonomic nervous limbs
in dogs to the afferent, central, and efferent autonomic nervous limbs in humans.

This figure therefore suggests that the frequency dependency of the ILV—)HR and

ABP—>HR impulse responses can be largely attributed to efferent autonomic nervous

limbs and that the CANS of dogs can well represent the CANS of humans. Based on
these two linearity assumptions, the multi-signal analysis of cardio-respiratory

variability is employed in three steps.

22

Figure 3.] Models of transfer functions relating fluctuations in
instantaneous lung volume to heart rate (ILV—>HR) and fluctuations in
arterial blood pressure to HR (ABP—>HR) upon which the multi-signal

analysis of cardio-respiratory variability is based.

23

bpmlliter-sec

4
2
0
-2

lV»HR

 

i 6 iii 6 '
time[sec]

bpmlmmHg-sec

ABR+HR
an

em
//,#,
an xéfisz

-0.50
-0.75
-1.00

 

b i A s a
time [sec]

 

 

[Canine sinoatrial (SA) node discharge rate]
pure vagal stimulation

 

 

 

 

 

 

 

 

 

 

 

=3 e'
e I
Q -3 r r r r l #1
.o -40 -20 20 40
time [sec]
pure sympathetic stimulation
£05
EeL F\\M_
a. L I r r r r 1
-° -40 -20 0 20 40
time [sec]
A ll
PNS—>P1 time
/ _ : PNS—>P2
time
Figure 3.1

u

In the first step, the ILV—>HR and ABP—>HR impulse responses are estimated
by applying parametric system identification to resting beat-to-beat fluctuations in HR,
ABP, and ILV according to the block diagram of Figure 3.2. In this way, the known
correlation between the ILV and ABP inputs is accounted for by simultaneously
considering the contributions of both inputs to HR (i.e., dual-input identification), and
the feedback baroreflex effects of fluctuations in ABP on HR may be disentangled
from the feedforward mechanical effects of fluctuations in HR on ABP through the

imposition of causality (i.e., open-loop identification of closed-loop systems) (108).

The block diagram also includes a perturbing noise source NHR, which is also

estimated and represents the residual HR variability not accounted for by the two
inputs. This step is mathematically achieved with the following double exogenous
model with autoregressive input (XXAR) (80) originally proposed by Baselli et al. (9,

10):

HR[n] = i g[i]ILV[n — i] + 51:: h[i]ABP[n — i] + NHR [n]

i=1

Nam = iariiNHRin - i] + Warn],

(3.1)

where n is discrete time. The sets of unknown finite impulse response (FIR)

parameters {g[i], h[i]} respectively define the ILV—)HR and ABP—)HR impulse

responses, while the unmeasured residual white noise error WHR and the set of

25

unknown AR parameters {a[i]} specify NHR. The terms m, M, and N represent the

maximum expected durations of the FIRs, while P limits the number of AR
parameters. Note that causality of the ABP—>HR impulse response is enforced here
by virtue of setting the h[i] parameters to zero for negative values of i, while non-
causality of the ILV—)HR impulse response is accounted for by setting m to a
negative value. The parameter sets are estimated from approximately six-minute

intervals of zero-mean fluctuations in HR, ABP, and ILV sampled at 1.5 Hz based on

least squares minimization of WHR using a weighted-principal component regression

method (110) (see Appendix). Prior to the application of this method, HR and ABP
are normalized by their mean values and ILV is normalized by its standard deviation
as described in (111). Thus, the identified impulse responses will have units of
inverse seconds and represent the relationship between relative fluctuations in the

input about its mean value and relative fluctuations in the output about its mean value.

a ILV -) HR

ILV

    
   

 

ABP ABP -) HR

Figure 3.2 Block diagram illustrating the estimation of the ILV—)HR and ABP-9HR
impulse responses by application of parametric system identification to resting beat-to-
beat fluctuations in HR, ABP, and ILV.

26

In the second step, the estimated ILV—>HR and ABP—>HR impulse responses
are each separated into PNS and SNS components as generally indicated in Figure 3.1.
More specifically, the typical ILV—)HR impulse response here indicates that, in
response to an impulse increase in ILV at time zero, HR would first increase due to
early (noncausal) and fast parasympathetic withdrawal and then decrease due to
delayed and sluggish B-sympathetic withdrawal. Thus, the PNS and SNS components
are of opposite direction in amplitude and delayed in time with respect to each other.
As a result, the PNS component of the ILV—)HR impulse response is precisely
determined as the initial portion of the impulse response extending up to the first zero
crossing (as this marker specifies the amplitude direction change) following the time
of the peak amplitude that occurs within the first five seconds (as the PNS is fast),
while the SNS component is specified as the remaining latter portion of the impulse
response (as the SNS is slow and delayed). The typical ABP—)HR impulse response
in Figure 3.1 indicates that, in response to an impulse increase in ABP at time zero,
HR would decrease first due to early (causal) and fast parasympathetic activation and
then due to delayed and sluggish B-sympathetic withdrawal. Thus, the PNS and SNS
components here are also delayed in time with respect to each other but are of the
same direction in amplitude. As a result, the separation procedure is not as
straightforward for the ABP—+HR impulse response. In particular, the initial
downstroke of this impulse response is regarded as the first part of the PNS
component. The time interval of the initial downstroke is precisely defined up to the

minimum amplitude that occurs within the first five seconds (as the PNS is fast). The

27

remaining part of the PNS component (i.e., the return of this stable component to
zero), which may be obscured by the subsequent SNS component, is assumed to be
symmetric to the visible first part as suggested by the data of Berger et al. in Fig. l.
The SNS component is then established by subtracting the total PNS component from
the entire ABP—>HR impulse response (as the SNS is slow and delayed). Note that
the separation procedure for the ILV—)HR impulse response assumes that the PNS
and SNS components do not overlap in time, while this separation procedure makes
no such assumption.

In the third step, scalar indices of the PNS and SNS are determined from the
corresponding components of the ILV—)HR and ABP—)HR impulse responses.

Specifically, the two-norms (i.e., square root of the energy) of the PNS and SNS

components are calculated to arrive at a pair of PNS and SNS indices denoted as P1

and 81 as determined from the ILV—)HR impulse response and P2 and 82 as

determined from the ABP—)HR impulse response. Note that these indices will be

dimensionless due to the aforesaid signal normalization.

3.4 Materials and Methods

3.4.1 Experimental Data

We evaluated the P1 and P2 indices of the PNS and the S1 and S2 indices of

the SNS with respect to a previously collected human cardio-respiratory dataset. The

materials and methods utilized in the collection of this dataset are described in detail

28

elsewhere (92). Briefly, 14 healthy male subjects (ages 19-38 years) participated.
Surface ECG, ABP (radial artery catheter), and ILV (chest-abdomen inductance-
plethysmography) were continuously recorded at a sampling rate of 360 Hz.
Throughout the recordings, the subjects initiated each respiratory cycle on cue to a
sequence of audible tones spaced at random intervals of 1-15 seconds with a mean of
five seconds (12). The purpose of this random-interval breathing protocol was to
produce a broadband ILV signal so as to enhance the reliability of subsequent system
identification analyses, especially pertaining to the estimation of couplings involving
ILV as the input. Approximately 13-minute intervals of the random-interval
breathing cardio-respiratory measurements were recorded for each of six
experimental conditions. First, control measurements were recorded from the
subjects in the supine and standing postures. Then, seven of the subjects received
atropine at 0.03 mg/kg i.v. (vagal blockade), and the measurements were recorded
from the subjects in the two postures. Finally, these subjects received propranolol at
0.2 mg/kg i.v. (IS-sympathetic blockade) to achieve total cardiac autonomic nervous
blockade (double blockade), and the measurements were again recorded fi'om the
subjects in both postures. The remaining seven subjects were studied similarly but
received the drugs in reverse order. A five-minute period for hemodynamic

equilibration was allowed between each experimental condition.
3.4.2 Data Analysis

As described in (1 1, 92), ABP and ILV were digitally filtered and decimated

to 1.5 Hz, and synchronized 1.5 Hz HR tachograms were constructed from the surface

29

ECGs. The PNS and SNS indices were then derived as described above from two
non-overlapping intervals of each ~13-minute record in the cardio-respiratory dataset.
The resulting pairs of each index fi'om each data record were then averaged. For
comparison, the HF power, the LF/HF ratio, and the normalized LF power
(LF/(LF+HF)) of the HR tachograms were analogously computed for each data record
using AR power spectral analysis (101) with post-filtering (11). (The HF and LF
bands were defined here to range from 004-015 Hz and 0.15-0.40 Hz, respectively
(101).) For each of the seven investigated indices, outliers defined to be greater than
two SDs from the mean value were removed, wherein the mean and SD were robustly
estimated with the Gaussian-based method of Armoundas et al. (4). Finally, paired t-
tests were performed to determine if the indices were significantly altered from the

control condition to each drug condition.
3.5 Results

Figures 3.3 and 3.4 show the group average results (mean :I: SE) for the

estimated ILV—>HR and ABP—>HR impulse responses, along with the corresponding

P1 and P2 indices of the PNS and 81 and 82 indices of the SNS, before (control) and
after vagal, B-sympathetic, and double blockade in the standing posture. Generally
speaking, it can be seen visually that the early and fast PNS components of the two

impulse responses were blunted much more following vagal and double blockade

than B-sympathetic blockade, while the delayed and slower SNS components were

30

more strongly attenuated after B-sympathetic and double blockade than vagal

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

blockade.
control vagal blockade

0,04. 0.04

0 03 _ P1 = 0.023 :1: 0.003 s1 = 0.015 :I: 0.003 0 03 p1 = 0,013 i 0,005 $1 = 0,003 i 0.002
0.02-

PH
:2. 0.01 ~
of .-. " ‘
-0.01»
‘ ' -0.0" . - . .
1o 15 ‘-5 0 5 10 15
time [sec] time [590]
B—sympathetic blockade double blockade
0 04 0 Ml
0.03 ~91 = 0.017 :I: 0.002 51 = 0.009 :I: 0.003 0.03 P1 = 0.005 1 0.001 51 = 0.004 :I: 0.0005
0.02.»
H
3'“ 0.01 -
-0.01 [
. J . 2 . . . J
10 15 '0 0 -5 0 5 10 15
time [see] time [see]

Figure 3.3 Group average results (mean i SE) for the estimated ILV—)HR impulse

responses and the corresponding P1 and $1 indices from 14 human subjects before

(control) and after vagal, B-sympathetic, and double (vagal+[3-sympathetic) blockade in
the standing posture.

31

control vagal blockade

 

 

 

0.4- 0 4
0.2- O 2
_ 4:. ~— 0 W ~—
7" ~02
.22.
-0.4’

 

v
-0-6’ P2 = 0.54 :l: 0.04 s; = 0.45 :l: 0.03 -0.6- P; = 0.28 :I: 0.04 52 = 0.33 :I: 0.08
-0.8t . . . -0.e

 

 

 

 

 

 

 

0 5 10 15 o 5 1'0 15
time [see] time [sec]
B-sympathetic blockade double blockade
04- 0.4-
0.2- 0.2-
..-- ° w
:2. -0.2-
-0.4r

 

-0.6 P; = 0.49 a; 0.06 52 = 0.25 a: 0.03 .05. P2 = 0.26 :I: 0.04 s; = 0.22 r: 0.03
_0.8 1 1 n . J . n
0 5 10 15 '0 80 5 10 15
time [sec] time [sec]

 

 

 

Figure 3.4 Group average results (mean i SE) for the estimated ABP—)HR impulse

responses and the corresponding P2 and $2 indices from 14 human subjects before

(control) and after vagal, B-sympathetic, and double (vagal+B-sympathetic) blockade in
the standing posture.

Figure 3.5 summarizes the group average results (mean :t SE) for the two PNS
indices, P1 and P2, derived from the estimated ILV—)HR and ABP—>HR impulse

responses and the conventional HF power of HR variability. As expected, the HF
power generally performed well in predicting the known effects of the
pharmacological autonomic nervous blockade agents on the PNS. In particular, this

index was virtually abolished following vagal and double blockade with p<0.05.

32

Further, the index did not change after B-sympathetic blockade in the supine posture.

However, counter to expectation, the PNS index did decrease following 0-
sympathetic blockade in the standing posture with p<0.05. Overall, the P1 index was

better in predicting the known drug effects on the PNS. That is, this index reduced

considerably after vagal and double blockade with p<0.10 and did not change

following B-sympathetic blockade in either posture. The P2 index provided even

better predictive capacity in that it decreased after vagal and double blockade with
p<0.01 while remaining unchanged after B-sympathetic blockade. However, the

extent of the reductions was not as marked as the other indices.

33

Figure 3.5 Group average results (mean i SE) for the conventional HF

power of HR variability and the P1 and P2 indices of the PNS. The
symbol # indicates p<0.10; *, p<0.05; §, p<0.01; 1', p<0.005; and I,
p<0.001.

34

 

El control
I drug

 

 

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, - .§ .........................
4 7 7 7,7, if 7;
"E
33 TTTGIT 4“”
a:
2- ,,E,,,-L.-
1. A 7 #
0 B-sympathetic double vagal B-sympathetrc double
[blockade ”955mg blockade I I blockade “9“an blockade.
supine standing
P
1 ldru-
.05
0.045'v7 —'i‘—— ‘—
0.04-~~ ~ A-»7 7
0.035% 31—h- * #
g 0.03—
50.025?
C
3 0.023? ~7 7
0.015% ——-
0.01%
.00“ ~77
B-sympathetic double vagal B-sympathetic double
jblockade hlggkagg blockadel lblockade 919;};ng blockade.

 

supine

standing

 

35

 

Figure 3.5 (cont’d).

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

P Dcontrol
2 Idrug
1.2
17§1 777 7
0.8 , i , a e i i i i i
In
8
508 ---, 7 7777,11
C
3
0.4 - 74- ~ 7
0.277 7 7 7777 7
0 I I i I
vagal B-sympathetic double vagal B-sympathetic double
|bIockade plggkadg blockade. |bIockade blggkadg blockade.
supine standing

 

Figure 3.6 summarizes the group average results (mean t SE) for the two SNS
indices, S. and 82, derived from the two estimated impulse responses and the

conventional LF/I-IF ratio and normalized LF power of HR variability. As expected,
the LF/HF ratio did not perform as well in predicting the known effects of the
autonomic nervous blockade drugs on the SNS as the HF power did in predicting the
drug effects on the PNS. While the LF/HF ratio did decrease following [3-
syrnpathetic blockade with p<0.05 and did not change after vagal blockade, it did not
diminish after double blockade. In fact, this index actually increased following
double blockade in the standing posture with p<0.10. The LF/HF ratio appeared to be

a somewhat better index of sympathovagal balance, as it doubled following vagal

36

blockade, albeit not to any level of statistical significance. Overall, the normalized
LF power did not provide an improved ability to predict the drug effects on the SNS.
This index did decrease after double blockade with p<0.10 and alter B-sympathetic
blockade in the standing posture with p<0.001 but did not diminish after [3-
sympathetic blockade in the supine posture. Further, the extent of the reductions was
always very small. In addition, in contrast to expectation, the index increased after

vagal blockade in the supine posture but not the standing posture with p<0.05. The
S. index likewise did not offer enhanced predictive capacity. This index did
substantially decrease after double blockade with p<0.005 but did not change after B-
sympathetic blockade in both postures. Moreover, the SNS index actually decreased

after vagal blockade in the supine posture with p<0.10. On the other hand, the 82

index afforded overall improved ability in predicting the drug effects on the SNS. In
particular, this index did not change after vagal blockade and decreased after double
blockade in both postures and fl-sympathetic blockade in the standing posture with
p<0.05. Its only blemish was that the decrease after B-sympathetic blockade in the

supine posture was not statistically significant.

37

Figure 3.6 Group average results (mean i SE) for the conventional
LF/HF ratio and normalized LF power of HR variability and the S. and

$2 indices of the SNS. The symbol # indicates p<0.10; *, p<0.05; §,
p<0.01; T, p<0.005; and I, p<0.001.

38

 

LF/HF ratio

 

     

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

20
187 77 7777777777
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0 vagal BLsympathetic double vagal B-sympathetic double
|bIockade plgglsagg blockade. |bIockade plggkggg blockade.
supine standing
normalized LF power
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oi}
g 0.
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S 0.47
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0.177
G vagal B-sympathetic double ' vagal H-sympathetic double

supine standing

 

39

 

Figure 3.6 (cont’d).

 

s
1 Idru-

 

 

 

 

  

 

 

  

 

 

 

 

vagal Ssymmthetic double ‘ vagal B-sympathetic double

supine standing

 

S Dcontrol
2 I (IN:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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.5 . ..u- h
l .1 T
0-5"—‘ *
8
2 0.477 777
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c 0.37
3
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vagal B-sympathetic double T vagal B-sympathetic double
|b|gg|gade blgckade hlggkggm |h|ggkadg blgckgde plggkgge.
supine standing

 

 

 

40’

3.6 Discussion

Conventional HR power spectral indices are indisputably of significant
physiologic and prognostic value but suffer from limitations as measures of the
CANS. Most notably, these indices neither offer an effective marker of the SNS due
to its joint mediation with the PNS in the LF band nor afford specific measures of the
CANS due to the input contributions to HR (e.g., ILV and ABP). In this study, we
aimed to overcome these limitations by deriving indices of the PNS and SNS via
multi-signal analysis of cardio-respiratory variability. More specifically, first, we
applied parametric system identification to resting beat-to-beat fluctuations in HR,
ABP, and ILV so as to estimate the autonomically mediated ILV—>HR and ABP—>HR
transfer functions (see Figure 3.2). Then, we separated each estimated transfer
function in the time domain into an early and fast PNS component and delayed and
sluggish SNS component (see Figure 3.1). Finally, we computed scalar indices of the
PNS and SNS fiom the respective time domain or impulse response components. In
this way, the overlap of the SNS and PNS in the frequency domain may be
circumvented, and the input contributions to HR may be eliminated. Analogous to
the HR power spectral indices, the derived indices represent the responses of the
CANS to unity changes in their inputs about the mean value and therefore do not
reflect basal autonomic tone. While there have been many studies of the ILV—)HR
and ABP—)HR couplings (see, e.g., (112)), this study goes one step further by
attempting to separately quantify the two CANS from the couplings. We note that

this basic idea was initially introduced by us with co-workers in the appendix of (111).

41

In that study, we specifically proposed the method described herein to separate the

ILV—)HR impulse response into PNS and SNS indices (P. and 8.). In this study, we

introduced a method to decompose the less straightforward ABP—)HR impulse
response into PNS and SNS indices (P2 and S2). In addition, and significantly, we

evaluated, for the very first time, both pairs of indices, specifically in the context of
selective pharmacological autonomic nervous blockade in 14 human subjects. Our

results showed that, at the expense of requiring additional measurements, the newly

derived indices, particularly P2 and 82, were better than the HF power, LF/HF ratio,

and normalized LF power of HR variability in correctly predicting the known drug
effects on the PNS and SNS (see Figures 3.5 and 3.6).

In theory, the HF power of HR variability, which is mediated solely by the
PNS, should be a useful vagal index, unless there is a significant change in respiratory
effort. The experimental results of the present study confirm this theory. In particular,
the HF power was able to correctly predict the effects of vagal and double blockade in
the supine and standing postures and B-sympathetic blockade in the supine posture
wherein no significant change in the HF power of ILV fluctuations occurred.
However, this PNS index actually decreased after B-sympathetic blockade in the
standing posture likely due to the significant reduction (p<0.05) in the HF power of
ILV fluctuations. The change in HF power of ILV fluctuations during only this
particular condition may be related to postural factors, bronchoconstriction resulting

from B-sympathetic blockade, and/or the random-interval breathing protocol.

42

Regardless of the mechanism, this result suggests that the HF power will be an

ineffective marker of the PNS in situations where breathing is altered (e. g., exercise).

As discussed above, a basic idea of the P. and P2 indices is to eliminate the

contributions of respiration so as to result in more specific measures of the PNS. Our

results showed that both of these indices were, in fact, able to correctly predict the

effects of all studied autonomic nervous blockade conditions. The P2 index was a

better predictor than the P. index in terms of statistical significance but did not

decrease as much after vagal and double blockade.

In theory, without confounding input alterations, the LF/HF ratio of HR
variability should generally be a good measure of the SNS when only the SNS
changes or the SNS and PNS change in opposite directions and a poor marker when
only the PNS changes or both CANS change in the same direction. Indeed, our
results showed that this index was able to correctly predict the effects of B-
sympathetic blockade but not double blockade on the SNS. The index even showed a
tendency to increase after double blockade in the standing posture. In addition, the
LF/HF ratio increased by a factor of two after vagal blockade, though not to any level
of statistical significance due to the large variance resulting from a division by zero-
like effect. Overall, the LF/HF ratio appeared to be a somewhat better marker of
sympathovagal balance in the present study, which is consistent with its original
intention (71). However, we note that even if it were a perfect index of
sympathovagal balance and the HF power were a perfect index of the PNS, they could

not, in general, be utilized in tandem to quantify the SNS. For example, if the LF/HF

43

ratio increased while the HF power decreased, this could indicate that the SNS was
enhanced, remained the same, or was diminished but not to the extent of the PNS.

The normalized LF power of HR variability differs from the LF/HF ratio in
that it includes LF power in the denominator (i.e., LF/(LF+HF) (101)). In theory, this
extra term should improve the ability to predict the effects of double blockade on the
SNS (as the term will not go exactly to zero in practice) and should markedly blunt
changes following vagal and [ii-sympathetic blockade. Consistent with this theory, the
normalized LF power was superior to the LF/HF ratio in predicting the effects of
double blockade on the SNS and inferior in predicting the effects of B-sympathetic
blockade. Moreover, the normalized LF power did not change as much as the LF/HF
ratio after vagal blockade. However, the increase in the former index following vagal
blockade in the supine posture actually showed statistical significance because of the
reduced variance due to the presence of the extra denominator term. Overall, the
normalized LF power appeared to be a better index of the SNS than sympathovagal
balance in our study.

Like the HF power of HR variability, the predictive capacity of both the
LF/HF ratio and normalized LF power can, in theory, be adversely affected by
alterations in the inputs to HR. In our study, the LF and HF powers of the ABP and
ILV input fluctuations did significantly decrease during some of the experimental
conditions. However, the contributions of these input changes to the LF/HF ratio and

normalized LF power were generally more difficult to interpret.

44

As discussed above, the basic idea of the S. and 82 indices is to circumvent

the frequency domain overlap of the SNS and PNS, while eliminating input
contributions, by separating autonomically mediated transfer functions in the time

domain using physiologic knowledge and thereby arrive at more effective markers of
the SNS. Indeed, the S. index decreased to a larger degree after double blockade and

with a greater level of statistical significance than the normalized LF power.

However, this SNS index did not decrease following B-sympathetic blockade and
actually decreased after vagal blockade in the supine posture. Thus, the S. index did

not provide an overall improved measure of the SNS in our study. On the other hand,

the 82 index did enhance the ability to predict the known drug effects on the SNS.

This index correctly decreased following double blockade in both postures and B-
sympathetic blockade in the standing posture and did not change after vagal blockade
in the two postures. It was only unable to identify a statistically significant decrease
after B-sympathetic blockade in the supine posture, perhaps because sympathetic
nervous outflow is very low in this posture (79). Note that even the LF/HF ratio only

slightly decreased during this experimental condition. We hypothesize that the
improved performance of the S2 index over the S. index was due to differences in the
fi'equency content of ABP and ILV. In particular, the LF ILV fluctuations may have
been insufficient to accurately identify the sluggish SNS component of the ILV—)HR

impulse response. That is, even though the ILV fluctuations here were induced by a

random-interval breathing protocol, the probability density of the respiratory intervals

45

decreased exponentially with interval length (12). In contrast, the naturally occurring
LF ABP fluctuations appear to have been enough for more reliable estimation of the
SNS component of the ABP—)HR impulse response.

The major aim of this study was to highlight the enhanced ability of our multi-
signal analysis of cardio-respiratory variability over HR power spectral analysis in
correctly predicting large changes in the CANS induced by selective pharmacological
autonomic nervous blockade. However, our results also revealed the capacity of these
indices to predict postural changes. In particular, all three PNS indices correctly
decreased upon standing in the control condition (see Figure 3.5), while only the

LF/HF ratio and normalized LF power correctly increased upon standing in the

control condition (see Figure 3.6). This result further suggests that the S. and S;

indices may not be as sensitive to smaller SNS changes. This insensitivity could be
partly due to any non-autonomic nervous contributions to the ILV—+HR and
ABP—>HR impulse responses such as mechanical modulation of the sinoatrial node
by respiration (14) and variations in baroreceptor and sinoatrial node responsiveness
(81). Future attempts to eliminate non-autonomic nervous contributions from the
impulse responses (e.g., as proposed by Porta et al. (81)) may increase the sensitivity
of the indices.

Random-interval breathing was employed in this study to enhance the
reliability of the estimated ILV—>HR and ABP—>HR impulse responses. This
protocol is not utilized in standard HR variability analysis and could have negatively

impacted the performance of the HR power spectral indices. However, as described

46

above, the results of these indices reported herein are consistent with expectation
based on previous spontaneous or controlled breathing studies. We therefore believe
that these results are generally representative of what would have been obtained with
conventional breathing protocols. However, we do speculate that some of the detailed
aspects of the results may have been affected. For example, conventional breathing
may have reduced the variance of the LF/HF ratio during vagal blockade and
therefore result in a statistically significant increase in this index following vagal
blockade. This result would have made the LF/HF ratio a much better index of

sympatho-vagal balance but an even poorer index of the SNS and thereby better

demonstrate the superiority of the 82 index as a marker of the SNS.

Our multi-signal analysis of cardio-respiratory variability has certain
advantages and disadvantages with respect to other recently proposed analyses
mentioned above aiming to likewise derive improved indices of the PNS and SNS.
The blind source separation analyses of HR and ABP variability as well as HR and
QT interval variability by Vetter et al. (105, 106) are based on the generally invalid
assumption that the two CANS operate independently of each other. Our multi-signal
analysis is theoretically advantageous in that it makes no assumption about the
relationship of the PNS and SNS. However, the blind source separation analyses
have the practical advantage of requiring fewer measurements. The principal
dynamic mode analysis of HR variability by Chon and co-workers (113, 114) is based
on a nonlinear expansion. Remarkably, these investigators were able to show that the

first two principal dynamic modes of the estimated first- and second-order Volterra

47

kernels (calculated by invoking orthogonality) just happened to correspond to the
PNS and SNS in their random-interval breathing datasets. Our multi-signal analysis
is theoretically advantageous in that it is physiologically based. Further, it potentially
has the practical advantage of not being reliant on random-interval breathing, since it
is not a nonlinear analysis, which generally has more stringent demands on the
frequency content of the inputs (51), employs the parsimonious weighted-principal

component regression method (see Appendix), and is most effective with respect to

the ABP—)HR impulse response (i.e., the P2 and $2 indices). On the other hand, the

principal dynamic mode analysis has the practical advantage of requiring only a
surface ECG measurement and may be theoretically advantageous in terms of
extracting nonlinear information fi'om HR variability. Future comparisons of our
multi-signal analysis with the blind source separation and principal dynamic mode
analyses during spontaneous breathing and random-interval breathing are certainly
warranted.

Potential applications of our multi-signal analysis of cardio-respiratory
variability include any research or clinical setting in which continuous ABP, HR, and
ILV or at least continuous ABP and surface ECGs are available (as ILV may
potentially be estimated from surface ECGs (57)). An example of such a clinical
setting is the intensive care unit wherein HR power spectral indices, as mentioned
above, have been shown to be predictive of patient outcome (109). Further
demonstrations of the multi-signal analysis in providing improved markers of the

PNS and SNS as well as enhanced association with mortality and disease are needed,

48

particularly under spontaneous breathing conditions, to ultimately realize these

applications.
3.7 Appendix

The weighted-principal component regression method utilized herein to
estimate the parameter sets specifying the ILV—)HR and ABP-)HR impulse
responses in the Equation (3.1) is described in detail in (110). We briefly review the
major steps of this method below.

First, the AR parameters ({a[i]}) in the Equation (3.1) are initialized to zero,
and the terms m, M, and N are set to values that are believed to encompass the actual
durations of the ILV—>HR and ABP—>HR impulse responses (i.e., FIRs). (In this
study, we set m, M, and N to 77, 42, and 50, respectively, thereby assuming that each
FIR is no greater than 50 samples in duration and accounting for the noncausality of
the ILV—)HR impulse response.) Then, the upper model in the Equation (3.1) is
formed into a matrix equation by stacking each individual equation, corresponding to
each discrete time 11, one on top of the other as follows: y = X11 + w, where y, b, and
w are vectors respectively comprising the samples of HR, the two FIRs to be
estimated ({g[i], h[i]}), and Wax, while X is a matrix consisting of samples of
delayed versions of ILV and ABP. Next, the matrix X is post-multiplied by a
diagonal matrix W whose diagonal elements decay exponentially so as to assume that
the current output sample is more dependent on recent input samples than distant

input samples. Then, the principal components of the matrix XW (“weighted-

49

principal components”) are added into a regression structure, one at a time, in order of
descending principal components and regressed on to the vector y until the Minimum
Description Length criterion is minimized (46) so as to arrive at an estimate of the
vector x (i.e., the two FIRs). This calculation is repeated for various exponential

weighting decay rates, with the one minimizing the vector w in the least squares sense

ultimately selected. Next, NHR is calculated (i.e., y - X11), and the AR parameters are

estimated by standard linear least squares minimization of WHR in the lower model in

the Equation (3.1) (46). (For simplicity, in this study, P was set to 20. This value was

justified by observing that WHR was indeed generally white via standard

autocorrelation analysis.) Finally, HR, ABP, and ILV are pre-filtered using the
estimated AR parameters, and the above steps are repeated until the estimated FIRs
converge. Importantly, this method effectively represents the FIRs, asymptotically,
with damped sinusoidal basis functions that reflect the dominant frequency content of
the inputs. Thus, only a small number of basis functions (or weighted-principal
components) should be needed, thereby decreasing the number of parameters to be
estimated and thus the estimation error. (In this study, 20-25 basis functions were
nominally used, which represents a > 75% reduction in the number of estimated

parameters).

50

CHAPTER 4. ESTIMATION OF THE TOTAL
PERIPHERAL RESISTANCE BAROREFLEX IMPULSE
RESPONSE FROM SPONTANEOUS HEMODYNAMIC
VARIABILITY

4.1 Abstract

We have previously developed a mathematical analysis technique for

estimating the static gain values of the arterial total peripheral resistance (TPR)

baroreflex (GA) and the cardiopulmonary TPR baroreflex (GC) from small,

spontaneous beat-to-beat fluctuations in arterial blood pressure, cardiac output, and

stroke volume. Here, we extended the mathematical analysis so as to also estimate

the entire arterial TPR baroreflex impulse response (hA(t)) as well as the lumped

arterial compliance (AC). The extended technique may therefore provide a linear
dynamic characterization of the TPR baroreflex systems during normal physiologic
conditions from potentially non-invasive measurements. We theoretically evaluated
the technique with respect to realistic spontaneous hemodynamic variability generated

by a cardiovascular simulator with known system properties. Our results showed that

the technique reliably estimated hA(t) (error = 30.2i2.6% for square root of energy

(EA), 19.7il.6% for absolute peak amplitude (PA), 37.3i2.5% for GA, and

33.1i4.9% for overall time constant) and AC (error = 17.6i4.2%) under various

simulator parameter values and reliably tracked changes in Gc. We also

51

experimentally evaluated the technique with respect to spontaneous hemodynamic
variability measured from seven conscious dogs before and after chronic arterial

baroreceptor denervation. Our results showed that the technique correctly predicted

the abolishment of hA(t) (EA = 1.0:t0.2 to 0.3i0.1, PA = 0.3:l:0.1 to 0.1100 s", and

GA = -2.lfl:0.6 to 03320.2 (p<0.05)) and the enhancement of GC (-O.7:I:0.44 to -

1.81:0.2 (p<0.05)) following the chronic intervention. Moreover, the technique
yielded estimates whose values are consistent with those reported with more invasive

and/or experimentally difficult methods.
4.2 Introduction

The total peripheral resistance (TPR) baroreflex is a well-appreciated feedback
control mechanism for rapid arterial blood pressure (ABP) regulation. Consistent
with negative feedback, the arterial TPR baroreflex is widely known to respond to a
step increase (decrease) in ABP by decreasing (increasing) steady-state TPR.
Similarly, the cardiopulmonary TPR baroreflex has been shown to respond to a step
increase (decrease) in central venous pressure (CVP) by decreasing (increasing)
steady-state TPR (85). In this way, the cardiopulmonary TPR baroreflex is able to
anticipate and thereby quickly buffer the imminent change in ABP that will arise from
the preload alteration.

Much of our knowledge of the TPR baroreflex systems is owed to open-loop
studies in which the steady-state or static gain properties of one baroreflex was

experimentally determined by selectively exciting it and measuring the steady-state

52

TPR response via Ohm’s law (i.e., mean ABP divided by mean cardiac output (C0))
(see, e.g., (68, 94)). Indeed, we find only a handful of studies aiming to individually
quantify each of the TPR baroreflex systems while they are simultaneously active,
presumably because of the need for complex experimental methods and data analysis.
In. the first of these studies conducted two decades ago, Raymundo et al. determined
the individual static gain values of both TPR baroreflex systems through multiple
regression analysis of steady-state ABP, CVP, and TPR measurements obtained
during a set of step perturbations to the ventricular pacing rate and total blood volume
(85). Although this method is fundamentally sound, it is complex and has yet to be
repeated. Further, we find few studies related to quantification of the dynamic
properties of the TPR baroreflex (e. g., the time course TPR takes to reach its steady-
state value in response to step excitation), perhaps due to the inability to measure
sufficiently rapid TPR changes in which Ohm’s law may no longer be valid as well as
the enhanced demands on experimentation and/or data analysis. In the earlier studies,
Rosenbaum et al. and other investigators experimentally maintained flow or pressure
to a particular regional circulation so as to measure peripheral resistance changes
through pressure or flow' at that region and then quantified the dynamic properties of
one baroreflex by applying step excitation, sinusoidal stimulations at various
frequencies, or randomized perturbation in conjunction with system identification
analysis of the measured variations (23, 86, 93). However, this approach is obviously
difficult and not as relevant to overall ABP regulation as those studies that have
observed TPR. In the very recent studies, Aljuri et al. and Hughson et al. estimated

TPR changes from beat-to-beat measurements of ABP, CVP, and CO and then sought

53

to identify, for the very first time, the individual linear dynamic properties of both
simultaneously active TPR baroreflex systems (3, 37). In particular, Aljuri et al.
essentially generalized the approach of Raymundo et al. by applying dual-input
system identification analysis to fluctuations in ABP, CVP, and estimated TPR
obtained during randomized pacing and venous occlusion, whereas Hughson et al.
applied a similar analysis to these fluctuations as obtained during randomized lower
body negative pressure. However, these methods are also difficult and, as we have
previously shown in (62), estimation of TPR fluctuations could introduce artifact in
the identified TPR baroreflex. Thus, a more convenient technique is needed to fully
elucidate the integrated, dynamic functioning of the arterial and, cardiopulmonary
TPR baroreflex systems.

To this end, in a previous study, we introduced a technique for estimating the
static gain values of the arterial and cardiopulmonary TPR baroreflex systems by
mathematical analysis of beat-to-beat fluctuations in ABP, CO, and stroke volume
(SV) (62). Rather than estimating TPR fluctuations, the technique accounts for these
variations by physiologic modeling of identified systems relating the measured
fluctuations. In that study, we theoretically validated the technique with respect to
realistic hemodynamic variability generated by a cardiovascular simulator with
exactly known system properties. In a follow-up study, we experimentally validated
the technique by applying it to spontaneous hemodynamic variability measured from
seven conscious dogs before and after chronic arterial baroreceptor denervation and
showing that the estimated TPR baroreflex static gain values changed in the expected

manner following the chronic intervention (59). In this study, we extended the

54

mathematical analysis so as to estimate the TPR baroreflex impulse response (i.e., the
time derivative of the step response) as well as the lumped arterial compliance (AC).
In contrast to the previous methods, the extended technique may therefore provide a
linear dynamic characterization of the TPR baroreflex systems during normal
physiologic conditions using potentially non-invasive transducers (e.g., Doppler
ultrasound and applanation tonometry). In addition, we theoretically and
experimentally evaluated this technique with respect to spontaneous hemodynamic
variability obtained from the aforementioned cardiovascular simulator and seven

conscious dogs.

4.3 Materials and Methods

4.3.1 Extended Mathematical Analysis Technique

Our initial mathematical analysis technique for estimating the static gain
values of the arterial and cardiopulmonary TPR baroreflex systems from beat-to-beat
fluctuations in ABP, CO, and SV is described in detail, including justification of its
underlying assumptions, in (59, 62). We briefly review this technique below and then
describe an extension of the mathematical analysis so as to also estimate the TPR
baroreflex impulse response and AC.

The initial technique is based on the compelling study of Raymundo et al. (85).
These investigators defined the arterial TPR baroreflex as the system that couples
fluctuations in ABP to TPR and the cardiopulmonary TPR baroreflex as the system

that couples fluctuations in central venous transmural pressure (CVTP) to TPR.

55

(Note that fluctuations in CVTP are nearly equal to fluctuations in right atrial
transmural pressure, which may represent the more precise input to the
Cardiopulmonary baroreflex.) They demonstrated that these TPR baroreflex systems
may be regarded as linear and time-invariant (LTI) over a wider hemodynamic range
than that attained by the resting variability considered herein. To estimate the static
gain values of the two TPR baroreflex systems as just defined from only beat-to-beat
measurements of ABP (mean), CO and SV, the initial technique first identifies
impulse responses coupling the beat-to—beat measurements (step 1) and then computes
the static gain values based on physiologic models of the identified impulse responses

(step 2). Importantly, prior to executing these two steps, each beat-to-beat
measurement (X) has its mean value (R) removed (AX = X 7)?) and is then divided

by the mean value so as to arrive at normalized, beat-to-beat fluctuations (AX/ R ).

More specifically, in step 1 of the technique, the impulse responses coupling

AGO/CO to AABP/ABP (CO—)ABP) and ASV/S_\7 to AABP/ABP (SV—>ABP)

are identified, as indicated in the block diagram of Figure 4.1. In the process, the

noise term N ABP in the block diagram, which reflects the residual variability in

AABP/ ABP not accounted for by the two inputs, is also estimated. This step is

mathematically achieved with the following dual-input, autoregressive exogenous

input (ARX) model:

56

 

 

 

AABP__[11] _Zai AABP[n 11+ Pib achn i]
ABP1_ ABP H,

 

(4.1)

where n and square brackets indicate discrete time. The three sets of unknown

coefficients {a., b., c.} completely specify the CO—>ABP and SV—>ABP impulse

responses, while the unmeasured residual error WABp together with the set of

coefficients {a.} fully define N ABP (46). The unknown model order parameters m, p,

and q limit the number of coefficients retained in the ARX model. The coefficient

sets are estimated from five to ten minute intervals of AABP/ ABP , AGO/E , and

ASV/SV sampled to 0.5 Hz by least squares minimization of WABp in conjunction

with a model order reduction algorithm (75). (Typically, this algorithm selects each
model order parameter to be between three and five.) Note that an implicit
assumption here is that the two inputs are uncorrelated enough for reliable
identification. This assumption will be violated when heart rate (HR) variability is
absent or tightly correlated to CVTP fluctuations (and thus SV fluctuations (59)) via,

for example, a potent Bainbridge reflex.

57

 

aco
(Y) —» CO—sABP 77——

 

 

 

 

AABP
NABP TV”

 

ASV
-S—\7 —> SV—>ABP

 

 

 

Figure 4.1 Step 1 of the mathematical analysis technique.

In step 2 of the technique, the static gain values of the arterial TPR baroreflex
(G A) and the cardiopulmonary TPR baroreflex (GC) are computed by representing the
identified CO-)ABP and SV—)ABP impulse responses with the physiologic models
of Figure 4.2. In these models, the systemic arterial tree is defined to be the system
that couples AGO/E and ATPR/fi to AABP/A_BP , while the inverse heart-lung

unit is defined to be the system that couples ASV/SV to ACVTP/CVTP. A key
point is that each of these two systems, which are likewise assumed to be LTI, has a
static gain value of unity due to its input and output reflecting normalized fluctuations.

(For example, it is easy to show this property for the systemic arterial tree through

Ohm’s law.) As a result, GA and GC may be specifically computed from the static

gain values of the identified CO—~)ABP and SV—)ABP impulse responses based on

58

the physiologic models of Figure 4.2. This step is achieved with the following

formulas involving the ARX coefficient sets estimated from step 1:

GA: ibfiiai-l :bi GC=:ci :br
i=0 i=1 i=0 i= i=

(4.2)

See Appendix A for a derivation of these two formulas.

59

(a)

 

 

 

systemic arterial tree

 

 

 

 

 

 

 

 

 

AABP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ABP

AABP

 

 

 

 

 

 

 

(hSAT(t))
ATPR +
£3 TPR ’l systemic arterial tree .
CO “IS/n(t)) I
arterial TPR baroreflex
(h(t)) I
(b)
’l inverse
heart-lung unit
ATPR .
ACVTP TPR systemic arterial
ASV __ CVTP tree (1817(0)
W cardiopuhnonary
TPR baroreflex
arterial TPR
baroreflex (hA(t))

 

 

 

 

 

Figure 4.2 Step 2 of the mathematical analysis technique.

5.—

ABP

To extend the technique so as to estimate the arterial TPR baroreflex impulse

response (step 3), as indicated in Figure 4.28, the systemic arterial tree impulse

response must likewise be known. However, while the static gain value of the

systemic arterial tree is known to be unity, its system dynamics are generally

60

unknown and must first be estimated. To do so, the following two assumptions are
made based on known physiology. First, as justified in (61, 67), the systemic arterial

tree is assumed to be well represented by a lumped parameter model governed by a

single time constant IS AT equal to the product of TPR and AC for the slow, beat-to-

beat fluctuations considered herein. In other words, the sampled systemic arterial

tree impulse response is assumed to take on the following form:

1 1
F 2 —t

S

11min] = leTu(t)dt,
1 1 T

(4.3)
where t and round brackets indicate continuous time; u, the unit step function; and PS,

the sampling frequency likewise set to 0.5 Hz. Note that the integrand here represents
the continuous-time systemic arterial tree impulse response (with unity static gain)

that arises from the above assumption, while the integration preserves unity static

gain after sampling (by virtue of the sum of hSAfln] being one for all physical 1:5 AT)

as well as attenuates any artifact in the sampling process. Second, as justified from
(13, 19, 20, 86), TPR baroreflex dynamics are assumed to be delayed and slower than

systemic arterial tree dynamics. Thus, as shown in Figure 4.3, the initial (< 5 sec)

time evolution of the CO—-)ABP impulse response (which represents the AABP/ ABP

61

response to a transient unit increase in AGO/CO) may be attributed solely to the

systemic arterial tree, as the more sluggish arterial TPR baroreflex has yet to be

activated. So, in step 3 of the extended technique, ISA. in Equation (4.3) is first
solved for by fitting hSATIOI to the corresponding sample of the identified 0.5 Hz
CO—-)ABP impulse response (hCOEABp[n]). In this way, hSA—dn] is fully defined,
and AC may be determined via ISAT/(mean ABP/mean CO). Then, the sampled
arterial TPR baroreflex impulse response (hA[n]) is calculated from hSAT[n] and

hCOaABPIIl] through the following formula arising from the physiologic model of

Figure 4.2a:

hA [n] = (hSA'l'l:r‘1]® hCO—eABP [I‘D-1 ®(hco—1ABP[n] " hSAT [11]) ,

(4.4)
where (8 is the convolution operation governing the input-output relationship of LTI
systems and the indicated inverse is defined as h[n]<8>h[n]'l = h[n]’l ®h[n] = 6[n]
with 6 representing the unit impulse function. ‘While hA[n] here may be determined

through standard computation of the involved inverse or exactly solved via an ARX

formulation, any error or noise in the estimates of hSATln] and hCOaABPIZII] would be

greatly amplified by either of these naive inversion calculations. Thus, hA[n] in

Equation (4.4) is computed through a noise robust method that we developed in which

the impulse response is compactly represented with damped sinusoidal basis functions

62

whose parameters are estimated using regularized least squares with the constraint

that its static gain value is equal to GA from Equation (4.2). Finally, the estimated

hA[n] is converted to physical units via hA(t)=FshA[tFS] (70). See Appendix B for a

complete mathematical specification of the extension.

0.3

0.25

P
N

0.15

TPR baroreflex activated

0.05

U

hCO-MBPIt): hSATIt) [3'1]
O

 

-0.05 -

 

 

'0-1 I I l l l
0 10 20 30 40 50

Time[sec]

Figure 4.3 Step 3 (extension) of the mathematical analysis technique.

Note that the inverse heart-lung unit impulse response is neither known nor
estimated. The extended technique therefore does not provide a direct estimate of the
cardiopulmonary TPR baroreflex impulse response. However, since both TPR baroreflex

systems are governed by the a-sympathetic nervous system (33), it may be reasonable to

63

assume that their dynamic properties are quite similar. To the extent that this assumption

holds, an estimate of the cardiopulmonary TPR baroreflex impulse response may then be

obtained by scaling the estimated h A(t) to have a static gain value equal to Gc from

Equation (4.2).

4.3.2 Technique Evaluation

Theoretical Evaluation. We theoretically evaluated the extended
mathematical analysis technique based on a cardiovascular simulator, which, in
contrast to an experimental system, offers precisely known TPR baroreflex system
properties and AC values for direct comparison of the estimates. We specifically
employed a cardiovascular simulator that we previously developed, demonstrated to
generate realistic short-term, b'eat-to-beat variability, and utilized to theoretically
validate our initial technique. The simulator is described in detail in (58, 62). Briefly,
the major components of the simulator are a circulatory system, a short-term
regulatory system, and resting perturbations. The circulatory system consists of
contracting left and right ventricles, systemic and pulmonary arterial trees, and
systemic and pulmonary veins. Each of these six compartments is specifically
modeled as a first-order system accounting for both viscous and compliant effects.
The regulatory system comprises arterial and cardiopulmonary baroreflex control of
HR, TPR, systemic venous unstressed volume, and maximum ventricular elastance as
well as a direct neural coupling between respiration and HR. Each of the baroreflex
effector systems is specifically modeled as a static nonlinearity to account for

saturation phenomenon followed by LTI dynamics. The resting perturbations include

64

spontaneous respiratory activity, which impinges on the circulatory system through a
first-order model of the airways and lung as well as the direct neural coupling, low
fi'equency disturbances to TPR and systemic venous unstressed volume, and a I/f
disturbance to HR. These three disturbances are randomly generated. Thus, each
simulator run or realization will actually differ under the same set of simulator
parameter values. For the present study, we replaced the first-order model of the
systemic arterial tree with a well-known third-order model accounting for inertial
effects in addition to viscous and compliant effects (32, 49). (This modification, for
example, has the effect of introducing a bump in the diastolic interval of the simulated
ABP waveform.) In this way, the systemic arterial tree of the simulator was more
complex than what is assumed by the technique.

For this theoretical evaluation, our specific aim was to determine if the

technique could reliably estimate hA(t), GC, and AC when applied to hemodynamic

variability simulated under different TPR baroreflex static gain values (implemented
via system amplitude scaling), TPR baroreflex overall time constant values
(implemented via system time scaling), and AC values. To achieve this aim, first, we
established the actual reference quantities against which the estimates could be

compared for each investigated set of simulator parameter values. More specifically,

we determined the actual reference h A(t) by separating the arterial TPR baroreflex

model from the simulator, applying an impulse input to the isolated model, and

measuring the output response (see (62) for details); the actual reference GC value by

first establishing the actual reference cardiopulmonary TPR baroreflex impulse

65

response in an analogous manner and then computing its sum; and the actual
reference AC value by summing the two individual compliances in the systemic
arterial tree model. Then, we applied the technique to 25 different realizations of
ABP, CO, and SV simulated under each investigated set of simulator parameter

values in order to determine the mean and standard error (SE) of the estimates. Next,

we succinctly characterized the estimated and actual reference h A(t) in terms of the
following parameters: E A (square-root of the energy of hA(t)), PA (absolute peak

amplitude of hA(t)), GA (sum of hA(t)), and TA (overall time constant of hA(t)

determined with a robust rectangular-based method (45)). Finally, we quantitatively

compared the estimates of these four impulse response parameters as well as GC and

AC with their actual reference quantities in terms of the root-mean-square (RMS) of
the error (E) normalized (N) by the actual reference quantity (i.e., RMSNE).
Experimental Evaluation. We also experimentally evaluated the extended
technique based on canine hemodynamic data, which were originally collected by us
to address different specific aims and previously utilized to experimentally validate
our initial technique. The materials and methods used in the collection of these data
are described in detail in (41). As we have done in (59), we briefly describe the most
relevant aspects of the experimental procedures below. All procedures were reviewed
and approved by the Wayne State University Animal Investigation Committee. We
studied seven conscious dogs (20-25 kg) of either gender. For each dog, we installed

chronic instrumentation through a series of aseptic surgeries for measurement of

66

continuous ABP (via an aortic catheter, Abbott Laboratories), CO (via an aortic flow
probe; Transonic Systems), HR, as well as other hemodynamic variables. After
recovery from the instrumentation surgeries, we recorded the hemodynamic variables
on a beat-to-beat basis for ~10 min while the dog was standing quietly. Then, we
achieved complete baroreceptor denervation by transection of the aortic depressor and
carotid sinus nerves. We verified the completeness of the arterial baroreceptor
denervation by observing essentially no HR response to an intravenous bolus infusion
of phenylephrine, which increased mean ABP by ~40 mmHg. Finally, about two
weeks after completion of the arterial baroreceptor denervation surgeries, we likewise
recorded the beat—to-beat hemodynamic variables.

For this experimental evaluation, our main specific aim was to determine if the
technique could detect the alterations in TPR baroreflex functioning that are known to
occur following the chronic intervention. To address this aim, first, we applied the
technique to the beat-to-beat ABP, CO, and SV (= CO/HR) recorded from each dog

before and after the chronic intervention. Then, we again parameterized each

estimated hA(t) with the E A1 P A, G A1 and TA. Finally, we performed paired t-tests to

determine if the group averages of the impulse response parameters as well as

estimated GC and AC and measured mean TPR were significantly altered by the

chronic arterial baroreceptor denervation. We considered a p-value < 0.05 to be

statistically significant.

67

4.4 Results

Theoretical Evaluation. Figures 4.4 and 4.5 respectively illustrate the

estimated hA(t) (mean 1: SE) along with the actual reference hA(t) for three different

simulator TPR baroreflex static gain values (but with the same overall time constant)

and three different simulator TPR baroreflex overall time constants (but with the same
static gain value). Visually, the estimated h A(t) closely agreed with the reference hA(t)
for each of the investigated simulator parameter values. Quantitatively, this
agreement corresponded to overall EA, PA, GA, and TA RMSNEs of 30.2i2.6%,
19.7:1.6%, 37.3i2.5%, and 33.1i4.9%, respectively. Table 4.1 shows the estimated
Gc and AC (mean i SE) and their corresponding actual reference values for three

different simulator TPR baroreflex static gain values and AC values, respectively.

The overall GC RMSNE was 48.4:12.0%, while the overall AC RMSNE
wasl7.6i-4.2%. Although the estimated GC was the least accurate, it was able to

reliably detect changes in the simulator Gc value. In other words, the Gc RMSNE

had a significant bias component.

68

RMSNE
EA: 26.78%
PA: 25.36%
GA: 30.34%
TA: 20.82%
0.02

-0.02

-0.04 7

[8"]

-0.06 7

-0.08 -

-0.1 -

 

0 25 50

0.02

-0.02

-0.04

RMSNE
EA: 30.69%
PA: 17.55%
61.1 35.49%
TA: 37.88%

F

 

-0.06 - .

-0.08 -

-0.1 .

 

—l—_l

- 12
0 25 50

Time [sec]

0.02 -

-0.02

-0.04

-0.06

-0.08

-0.1

2
0

RMSNE

I 36.170/0
: 18.59%
: 45.03%
: 44.28%

EA
PA
GA
1711

 

 

25 50

Figure 4.4 Theoretical evaluation results of the extended mathematical analysis

technique in which the estimated arterial TPR baroreflex impulse response h A(t) (mean
(dashed) i SE (dashed-dotted)) is illustrated along with the corresponding actual
reference h A(t) (solid) for three different simulator TPR baroreflex gain values.

69

0.02

0

-0.02

-0.04

‘2

-0.06

-0.08

-0.1 -
-0.1 2

RMSNE
EA: 34.88%
PA: 16.15%
GA: 35.10%
TA: 22.06%

 

 

_—7

 

 

 

0 25 50

-0.02

-0.04

-0.12

RMSNE
EA: 30.69%
PA: 17.55%
GA: 35.49%
TA: 37.99%

 

 

0

25 50

Time [sec]

0.02

-0.02

-0.04

-0.06 -

-0.08 7

-0.12

RMSNE
EA: 22.26%
PA: 20.72%
GA: 40.58%
TA: 40.58%

 

 

0 25 50

Figure 4.5 Theoretical evaluation results of the extended mathematical analysis

technique in which the estimated arterial TPR baroreflex impulse'response hA(t) (mean
(dashed) i SE (dashed-dotted)) is illustrated along with the corresponding actual

reference hA(t) (solid) for three different simulator TPR baroreflex overall time constant
values.

70

Table 4.1 Theoretical evaluation results of the extended mathematical analysis technique
in which two of the estimated parameters (mean i SE) from the cardiovascular simulator
are shown along with the actual reference values and corresponding quantitative errors.

 

 

GC AC
Estimated Actual RMSNE Estimated Actual RMSNE
[unitless] [unitless] [%] [ml/mmHg] [ml/mmHg] [%]
-014 i 0.01 -037 ‘ 61.46 1.20 :h 0.01 1.1 10.91
-0.31 :l: 0.01 -0.55 45.88 1.83 i 0.03 1.6 16.51
-0.49 d: 0.02 -0.74 37.92 2.60 :l: 0.04 2.1 25.46

 

GC is the static gain value of the cardiopulmonary total peripheral resistance (TPR)
baroreflex; AC, arterial compliance; and RMSNE, root-mean—squared—normalized-error.

Experimental Evaluation. Figure 4.6 illustrates the group average estimated
hA(t) (mean i SE) from the seven conscious dogs before and after chronic arterial
baroreceptor denervation. Before the baroreceptor denervation (i.e., the control
condition), the group average estimated hA(t) indicated that, in response to a

hypothetical impulse increase in ABP at time zero, TPR would immediately decrease

and then return towards baseline via a small amplitude oscillation, with 'c A equal to

7.6 5. Following the baroreceptor denervation, the group average estimated h A(t) was

blunted essentially to zero and therefore indicated that TPR would remain virtually

unaltered in response to an ABP change. Table 4.2 shows the group averages (mean

i SE) of three parameters of the estimated hA(t) (E A1 P A. and G A), estimated GC and

AC, and measured mean TPR from the dogs before and after chronic arterial

baroreceptor denervation. (Note that 13A is not included in this table, because it not

71

well defined when hA(t) is nearly zero.) The group average estimated E A1 P A1 and

G A were all significantly blunted following the baroreceptor denervation, thereby

statistically buttressing the visual results of Figure 4.6. In addition, the magnitude of

the group average estimated GC was significantly enhanced after the chronic

intervention. (Note that the G A and GC results here were reported earlier in the

context of experimentally evaluating our initial technique (59).) On the other hand,
the group average estimated AC was reduced but not to a level of statistical
significance after the baroreceptor denervation, with a value of 2.69 i 0.44 ml/mmHg
over both conditions. The group average measured mean TPR was likewise not

significantly altered.

72

Chronic Arterial Baroreceptor Denervation
Before After

0.1

 

 

 

-0.5

 

 

'0 12.5 25 37.5 50
Time [sec]

0 12.5 25 37.5 50

Figure 4.6 Experimental evaluation results of the extended mathematical analysis

technique in which the group average estimated hA(t) (mean (solid) i SE (dashed)) from
the seven conscious dogs is illustrated before and after chronic arterial baroreceptor
denervation.

73

Table 4.2 Experimental evaluation results of the extended mathematical analysis
technique in which the group averages of the estimated parameters (mean E SE) from the
seven conscious dogs are shown before and after chronic arterial baroreceptor
denervation along with level of statistical significance.

 

Chronic Arterial Baroreceptor Denervation

 

Parameters [units] p-value

 

Before After
E A [unitless] 0.98zt0.24 0.31:1:0.05 0.0227
P A [5“] 0.27i0.08 0.06:t0.01 0.0372
G A [unitless] -2.07i0.61 0.25:1:0.15 0.0154
Gc [unitless] -0.70fl:0.44 -1.82i0.18 0.0481
AC [ml/mmHg] 3.26:1:055 2.1 1i0.64 0.2933
TPR [mmHg-sec/ml] 1.32i0.06 1 .50i0.10 0.2258

 

E A is the energy of the estimated arterial TPR baroreflex impulse response (hA(t)); P A,

the absolute peak amplitude of h A(t); and G A1 the static gain value or sum of hA(t). See
Table 4.1 caption for remaining abbreviations.

4.5 Discussion

In two previous studies (59, 62), we introduced and demonstrated the validity

of a technique based on system identification analysis and physiologic modeling for

estimating the static gain values of the arterial TPR baroreflex (G A) and the

cardiopulmonary TPR baroreflex (GC) from spontaneous beat-to-beat fluctuations in

ABP, CO, and SV (see Figures 4.1 and 4.2). In the present study, we extended this

technique through additional physiologic modeling and analysis so as to estimate the

entire arterial TPR baroreflex impulse response (hA(t)) as well as the lumped arterial

compliance (AC) (see Figure 4.3). In addition, with the assumption that the two or-
sympathetically mediated TPR baroreflex systems have the same dynamic properties,

the cardiopulmonary TPR baroreflex impulse response may then be estimated by

74

scaling hA(t) to have a static gain value equal to Gc. However, we have left

investigation of the veracity of this assumption for the future.

The extended technique introduced herein is closely related to a few
mathematical methods proposed very recently in the cardiovascular physiology
literature. As discussed above, Aljuri et al. and Hughson et al. also proposed to
estimate the linear dynamic properties of both simultaneously active TPR baroreflex
systems. Potential advantages of the extended technique are that it does not require
invasive measurements (i.e., CVP), any external perturbations, or estimation of heat-
to-beat fluctuations in TPR, which, as mentioned above, could introduce artifact in
the identified TPR baroreflex impulse response. On the other hand, with a CVP
measurement, direct estimation of the cardiopulmonary TPR baroreflex impulse
response is, in principle, feasible. In addition, Quick et al. proposed to estimate AC
by likewise exploiting slow, beat-to—beat fluctuations in ABP and CO via the
calculated impedance of the systemic arterial tree (83). The extended technique here
is different in that it attempts to be more precise by also accounting for baroreflex
dynamics.

To evaluate the extended technique, ideally, the estimated h A(t) (with a static

gain value of G A)1 Gc, and AC from an experimental system would be directly

compared to high fidelity, independent reference quantities. However, as we have

argued in (58), it would be very difficult to establish such reference quantities. For

example, to experimentally determine reference hA(t), beat-to-beat TPR would have

75

to be measured in response to an impulsive change in ABP while CVTP was held
constant. On the other hand, a direct comparison could be readily conducted using a
cardiovascular simulator with precisely known system properties. However, this
theoretical evaluation would only be as meaningful as the extent to which the
simulator coincided with an experimental system. Alternatively, an experimental
evaluation in terms of detecting changes in the estimated quantities to a known
intervention could be more easily achieved. Although this sort of experimental
evaluation would not establish the extent to which the estimated quantities are correct,
it would at least demonstrate the utility of the technique with respect to real data.
Thus, in this study, we performed theoretical and experimental evaluations of the
technique to reap the advantages of both types of evaluations.

We first theoretically evaluated the extended technique with respect to a
cardiovascular simulator that we previously developed and demonstrated to generate

realistic spontaneous beat-to-beat variability. Our results showed that, under various
simulator parameter values, the technique was able to reliably estimate hA(t) and AC
(see Figures 4.4 and 4.5 and Table 4.1), even though the simulator included more

complex dynamics than those assumed by the technique (e.g., baroreflex saturation,

inertial effects in the systemic arterial tree). However, the technique did

underestimate the magnitude of Gc (see Table 1) due to the fact that the SV

fluctuations did not entirely account for the CVTP fluctuations in the simulator, as
assumed in the physiologic model of Figure 4.2b (see (59) for further discussion of

this assumption). Importantly, the underestimation was consistent, and the technique

76

was therefore able to reliably track changes in the simulator Gc value. These

theoretical evaluation results help validate various aspects of the mathematical
extension introduced herein. In particular, the results indicate that l) the specific

sampling method in Equation (4.3) is justified; 2) the basis function representation for

hA(t) in Equation (B43) is flexible enough under variations to the TPR baroreflex

static gain value and overall time constant; and 3) the bias introduced by the use of
regularization (see last paragraph of Appendix B), which is needed to reduce the error
variance due to noise amplification resulting fi'om the inversion in Equation (4.4), is
modest.

We then experimentally evaluated the extended technique with respect to
spontaneous hemodynamic variability measured fi'om seven conscious dogs during a
control condition and following chronic arterial baroreceptor denervation. Our results
generally showed that the technique was able to correctly predict the changes in TPR
baroreflex functioning that are known to occur following the chronic intervention as
well as yield estimates whose values are consistent with those previously reported

with more invasive and/or experimentally difficult methods.

More specifically, the group average estimated hA(t) from the control

condition indicated negative feedback dynamics (see Figure 4.6), which is congruent
with known baroreflex physiology. Moreover, the overall time constant of this group
average impulse response of 7.6 s is consistent with the value of 9 s reported in the
study by Rosenbaum et al. referred to above. However, the lack of a delay in the

impulse response is not supported by current evidence (12, 19). Poor agreement

77

A. .1' ¢'-( J."

 

$1.1.

between estimated hSAT(t) and hcoaABpUI) at t = 2 s (in which the TPR baroreflex

should yet to be activated; see Figure 4.3) due to imperfect estimation of the latter
impulse response (i.e., step 1 of the technique) certainly contributed to the lack of
delay. However, note that this estimation error was partially attenuated by averaging
the estimates over all the dogs. Another contributing factor may have been imperfect
estimation in step 3 of the technique, as the time delay was also missed during the

theoretical evaluation (see Figures 4.4 and 4.5) wherein the agreement between

hSAT(t) and hCO_)ABp(t) at t = 2 s was excellent.

The control group average estimated hA(t) appears similar to the one

determined by Aljuri et al. in conscious sheep in terms of reflecting negative feedback
dynamics, overall time constant, and general shape, but different in detail with a
smoother initial downstroke and a somewhat larger overshoot. On the other hand, the
impulse response reported here is grossly different from the one obtained by Hughson

et al. in humans, which reflected positive feedback dynamics that were attributed to a

myogenic response. Differences between our control group average estimated hA(t)

and the ones previously reported could be entirely due to variations in experimental
preparations. As discussed above, it is also possible that imperfect estimation of TPR
fluctuations could have rendered their impulse response estimates to be different.

Following the chronic arterial baroreceptor denervation, the group average

estimated h A(t) along with its parameters (EA, P A1 and G A) were largely abolished, as

expected (see Figure 4.6 and Table 4.2). (Note that a GA value of zero does not

78

necessitate that hA(t) be zero for all t but rather that only its sum over t be zero.) In

addition, the magnitude of the group average estimated GC was increased after the
chronic intervention, perhaps as a result of a central compensatory mechanism (see

Table 4.2). These changes are entirely consistent with the pattern of alterations in G A

and GC reported in the aforementioned study by Raymundo et al. after the same

intervention in conscious dogs.

On the other hand, the group average estimated AC did not change following
the chronic arterial baroreceptor denervation (see Table 4.2). This lack of change is
consistent with the belief that the baroreflex only controls HR, TPR, ventricular
contractility, and systemic venous unstressed volume (33). To give further credence
to this result, the group average estimated AC over both conditions of 2.69 i 0.44
ml/mmHg is on par with the previously reported value of ~2 ml/mmHg determined
with the flow stop method (20). Finally, the group average measured mean TPR did
not change after the baroreceptor denervation (see Table 4.2), as baroreflex
functioning does not affect mean hemodynamic values (3 3).

In conclusion, we have introduced a novel technique to mathematically
estimate linear dynamic properties of the arterial and cardiopulmonary TPR
baroreflex systems as well as AC fi'om spontaneous hemodynamic variability that
could potentially be measured non-invasively. We have demonstrated the validity of
the technique using both realistic simulated data and experimental measurements. In

the future, we plan to continue evaluating the technique in animals as well as begin

79

testing in humans with interventions of known effect. Ultimately, we hope that the
practical technique is employed to advance the basic understanding of the normal,
integrated, and dynamic functioning of the TPR baroreflex systems in humans and

animals in health and disease.

4.6 Appendix A

We derive below the formulas for the TPR baroreflex static gain values (G A

and GC) in Equation (4.2). These formulas generally arise by equating the static gain

values of the CO—)ABP and SV—-)ABP impulse responses expressed in terms of the
dual-input ARX model of Equation (4.1) to the corresponding static gain values
expressed with the physiologic models of Figure 4.2 through application of basic

linear systems theory (45, 70, 82).

To derive the G A formula, first, the z-transform is applied to the dual-input

ARX model to compute the system function of the CO—>ABP impulse response

 

(HCOQABp(z)) as follows:
P
2 b 1 Z fl
__ i=0
Hco—mBP (Z) — m
1 _ z a I Z —1
i=1

(A41)

80

Then, the static gain value of the CO—)ABP impulse response (GCOAABP) is

expressed in terms of the ARX coefficients by evaluating HCO7>ABP(Z) at z = l as

 

 

follows:
P
Zbi AABP ACO
GCO—eABP = HCO—9ABP (1) = Pom —

liafii‘fifi '66.

(A42)
Note that the right-most equality here merely indicates that the static gain value is
defined to be the steady-state output response divided by the steady-state input. Next,
linear systems theory is applied to the physiologic model of Figure 4.28 to give the

following steady-state relationships:

AABP _ ACO + ATPR

ABP CO TPR

(A43)

ATPR _ G AABP
TPR A ABP 7

 

(A4.4)
where unity static gain has been invoked for the systemic arterial tree in Equation
(A4.3). Then, Equation (A4.3) , is substituted into Equation (A44) to give the

following expression:

81

 

 

1
GA :17
AABP ACO
ABP CO
(A4.5)
Finally, Equation (A42) is substituted into Equation (A45) so as to arrive at the a.

formula for G A in Equation (4.2)

To derive the Gc formula, first, the static gain value of the SV—)ABP impulse

 

response (GSV—1ABP) is similarly expressed in terms of the ARX coefficients as

follows:

E“ =AABP ASV
l-Za- E W

 

 

(A46)
Then, linear systems theory is applied to the physiologic model of Figure 4.2b to give

the following steady-state relationships:

AABP _ ATPR
ABP TPR

(A47)

82

ATPR ACVTP AABP

 

 

_ = G +GA
TPR CVTP ABP
(A48)
ACVTP ASV
_CT/ffi :37
I (A49)

where unity static gain has again been invoked for systemic arterial tree in Equation
(A47) as well as for the inverse heart-lung unit in Equation (A49). Next, Equations
(A47) and (A49) are substituted into Equation (A48) to give the following

expression:

Gc =AABPP/ASSVV (1_ GA)

(A410)

Finally, the G A formula in Equation (4.2) and Equation (A46) is substituted into

Equation (A410) so as to arrive at the formula for CC in Equation (4.2)

4.7 Appendix B

We outline below a complete mathematical description of step 3 of the

extended technique. See Refs. 8, 22, and 28 for related background material.

First, hSAfin] is estimated from the identified hCOAABp[n] based on

physiologic knowledge (see Extended Mathematical Analysis Technique section). In

83

particular, hSATIn] in Equation (4.3) is determined by numerically searching for the
value of Ts AT over a physiologic range (0.1-10 s) that equates hSATIOI to

hCQAABpm]. Then, hSAT[n] in Equation (4.3) is computed from n = 0 to n = N-l,

where N represents its effective length (i.e., the number of samples or time duration

for which the impulse response is essentially non-zero).

Second, hA[n] is computed from the newly estimated hSAT[n] and the
identified hCO—sABPInl according to the physiologic model of Figure 4.2a. More

specifically, hCOAABpm], which is strictly of infinite length due to the ARX

representation in Equation (4.1), is truncated from n = 0 to n = M-l, where M

likewise represents its effective length. In addition, hA[n] is assumed to be

effectively of finite length and non-zero from n = 1 to n = L. (The value of L is set to

50 so that h A(t) can extend up to 100 3.) Now, invoking the definitions of the inverse

and convolution, Equation (4.4) may be rewritten as follows:

2:: h A[1]g[n— i=] hCO—>ABP Ini— hSAT In] + e[n]

(B41)

where g[n] = hSAfin] <8) hCO—sABPInla and e[n] has been introduced to account for

any estimation and/or modeling error. This equation represents a linear set of

equations with N+M+L~2 equations corresponding to the discrete times n e [1,

84

 

N+M+L-2] for which the equation is non-zero and L unknowns corresponding to the

samples of hA[n]. Since the static gain value of hA[n] has already been estimated in

step 2 to be G A in Equation (4.2), the following additional equation arises:

ihfin] =GA.

(B42)

Taken together, Equations (B41) and (B42) represent a linear set of equations with

 

N+M+L-1 equations and L unknowns. This set of equations may be conveniently
solved based on least squares minimization of e[n] via the closed-form linear least
squares solution with Tikonov regularization to attenuate any noise amplification in
the involved inverse calculation. However, since L is relatively large, the resulting
estimates of the unknowns may still appear to be noisy.

To reduce the number of unknowns so as to improve the estimation accuracy,
hA[n] is further assumed to be compactly represented with damped sinusoidal basis

functions as follows:

h A [n] = Z A: (dkcos[(0kn] + fksin[00kn])
k=1 ’

(B43)

where {3...} is a set of unknown damping parameters, {dk, fk} is a set of unknown

coefficient parameters, {am} is a set of unknown fiequency parameters, and r is an

85

unknown number of basis functions. This assumption is similar to representing hA[n]

with an ARX equation, which was previously done by Aljuri et al. (3) and Hughson et
al. (37) and generally permits a significant reduction in the number of parameters to
be estimated. Substituting Equation (B43) into Equations (B41) and (B42) yields

the following equations:

r L r L
2 6k 2 A].cos[(0ki]g[n - 1] +2 1, Z Aiksin[0)ki]g[n -1]
11:1 i=1 k=1 i=1

= hCO—>ABP [n] ' hSAT In] + e[n]
r L r L
n n ' _
(1k 2 Akcos[(0kn] + Z fk Z Aks1n[0)kn] — G A
k=1 n=1 k=1 n=1
(B44)
These equations represent a nonlinear set of equations with N+M+L-l equations and
4r unknowns corresponding to the basis function parameters. This set of equations

may also be estimated by regularized least squares minimization of e[n]. However,

this optimization problem is considerably more difficult, because the equations are

nonlinear particularly in the unknown parameter sets {71.0 (0k)- To simplify this
problem, each damping factor in the parameter set {7...} is assumed to be equal to A =
exp(-3/L) so that hA[n] approximately decays to zero, while the frequencies in the

parameter set {01k} are allowed to take on only discrete values according to the

Fourier Series (i.e., 27tl/L for l=0,l,...,ceil((L-1)/2), where ceil(x) is the smallest

86

 

integer 2 x). Then, for each set of frequency parameters {01k} considered (see below),

the corresponding coefficient parameter sets are estimated through the linear least
squares solution with Tikonov regularization. More specifically, Equation (B44)
may be expressed in matrix form by stacking each individual equation, corresponding

to each 11, one on top of the other as follows:

[G1 YG,] f: 7
A .

 

 

 

hCO-+ABP[1] - hSATII]

hC07>ABP[N+M+L-2]-hSAT[N+M+L-2]

 

 

 

 

 

 

_ GA _
13
CD]
+ :

e[N+M+L-2]

_e[N+M+L-1]_
‘e' ,

(B45)

87

 

where

 

 

' g[O] 0 0 0
g[l] g[O] O 0
g[L-ll BIL-2] BIL-3] g[0]
(3.: gm g[L-ll g[L-2] gm
0 0 g[N+M-2] g[N+M-3]
0 0 0 g[N+M-2]
L 1 1 1 1 J

' A‘fII-col] A‘fll-wq] '
AZfIZocol] AszZ-mq]
x A3f[3-60.] 7.3fI3-00q]

 

 

L L
3» tum-41 1 tum-41
with j = 1, 2 and fix] = cos[x] for j = 1 and sin[x] for j = 2. Then, after scaling the last
row of the matrix A and vector b by a factor of ten so as to ensure that the estimated

hA[n] will have a static gain value of nearly G A1 the regularized linear least squares

estimate of the vector x comprising the coefficient parameters is obtained via

71
x = (ATA + OLI) ATb, where or represents the regularization factor and I is the
2rx2r identity matrix. (The value of ct was empirically set to two, which essentially
eliminated spurious noise in hA[n]. However, hA[n] was not very sensitive to this

specific value.) Amongst all such estimates computed for each considered set of

88

 

 

frequency parameters {wk} , the one that results in the least squares value of the vector
Ax-b is selected so as to provide the optimal estimate of the parameter set {dk, fk,

wk}. Finally, the number of basis functions r is determined iteratively by starting

with a single basis function representation and then adding one basis function at a

time until the least squares value of the vector Ax-b no longer decreases by > 5%.

For further simplicity, in the kth iteration, only the frequency parameter of the newly

added basis function is added with the frequency parameters of the previous (k-l)

. . . . . . th
_ bas1s functrons set to the estimates obtained from the (k-l)th iteration. In the k

iteration, the number of sets of frequency parameters considered is therefore (ceil((L-

1)/2))-k+2).

89

 

CHAPTER 5. DYNAMIC CONTROL OF MAXIMAL
VENTRICULAR ELASTANCE VIA THE BAROREFLEX
AND FORCE-FREQUENCY RELATION IN AWAKE DOGS
BEFORE AND AFTER PACING INDUCED HEART
FAILURE

5.1 Abstract

We investigated the dynamic control of maximal ventricular elastance (Emax)

via the arterial baroreflex and force-frequency relation in five conscious dogs before
and after rapid chronic pacing induced heart failure (HF) by mathematical analysis of

spontaneous beat-to-beat hemodynamic variability. First, we determined ventricular

unstressed volume (V 0) from left ventricular pressure and volume (LVP and LW)

measurements during vena cava occlusion using traditional linear regression. Then,

we estimated beat-to—beat Emax during a baseline period via the maximum of
LVP/(LVV-Vo) over each beat. Finally, we jointly identified the transfer functions
relating beat-to-beat fluctuations in arterial blood pressure (ABP) to Emax

(ABP—>Emax) and beat-to-beat fluctuations in heart rate (HR) to Emax (HR—)Emax) to

characterize the dynamic properties of the arterial baroreflex and force-frequency

relation, respectively. During the control condition, the ABP—)Emax transfer function

revealed that ABP perturbations caused opposite direction Emax changes with a gain

90

 

value of -0.023:t:0.012 ml'l, whereas the HR—)Emax transfer function indicated that

HR alterations caused same direction Emax changes with a gain value of 0.013i0.005

mmHg/ml-bpm. Both transfer functions behaved as lowpass filters. However, the

ABP—)Emax transfer function was more sluggish than the HR—eEmax transfer

function with overall time constants of 11.2:l:2.8 and 1.7:t0.5 sec (p < 0.05),

respectively. During the HF condition, the ABP—>Emax and HR——)Emax transfer

functions were markedly depressed with gain values reduced to —0.0002:l:0.007 ml-1

and -0.001:t0.004 mmHg/ml-bpm (p < 0.1). These results provide perhaps the first

data on dynamic Emax control during normal closed-loop operation in health and the'

presence of HF.
5.2 Introduction

The control of ventricular contractility (V C) contributes importantly to the
modulation of cardiac output and therefore cardiovascular homeostasis. Specific
control mechanisms involved include the arterial baroreflex and force-frequency
relation (i.e., the Treppe or Bowditch effect). Both of these mechanisms may occur
simultaneously. For example, in response to a fall in arterial blood pressure (ABP),
there will be a baroreflex mediated sympatho-excitation, which could increase
inotropic state. The concurrent tachycardia could also increase inotropic state
independently via the force-frequency relation. Previous studies have described

these mechanisms through various indices of VC including Frank-Starling curves (27,

91

39, 90), cardiac sympathetic nerve discharge (28), maximal temporal derivative of

ventricular pressure (24, 39, 55, 104), and maximal ventricular elastance (Emax) (6, 7,

30, 42, 52, 53, 56, 98). However, Emax is generally recognized as the most specific
index available.
Nearly all investigations of Ema.x control have focused on its steady state

performance (e.g., gain values). To our knowledge, only two studies have examined

its dynamic behavior (e.g., time constants and delays). Sunagawa and colleagues
characterized the dynamic properties of the baroreflex control of Emax by identifying
the transfer function relating randomly perturbed carotid sinus pressure to estimated

beat-to-beat fluctuations in Emax of anesthetized, vagotomized dogs (42). Their

identified transfer function exhibited the expected negative feedback dynamics with
an overall time constant indicative of sympathetic nervous mediation and could be

parameterized as a second-order delay system. This same group then characterized
the dynamic properties of Emax control via the efferent baroreflex limb, while also

obtaining information about the force-frequency relation, by identifying the transfer

functions relating randomized left and right stellate ganglion stimulations to estimated

beat-to-beat fluctuations in Emax of isolated canine hearts with and without atrial

pacing (56). Their identified transfer functions could also be represented with

second-order delay systems and suggested that Emax is controlled by the left

sympathetic nerve through direct inotropic action and by the right sympathetic nerve

92

via both direct inotropic action and indirect chronotropic effects. While these two
studies provide unique insights, they were performed in either isolated hearts or

anesthetized animals with acute surgical trauma, which may markedly affect the

dynamic control of Emax. The open-loop approach may also alter the compensatory
mechanisms. Further, the studies did not examine Emax control in the presence of

disease such as congestive heart failure (HF), wherein steady-state control of Emax is

markedly reduced. The cardiac response to tachycardia and inotropic agents as well

as global baroreflex function are depressed (6, 15, 68). To what extent the dynamic

properties of Emax control are altered in HF is unknown.

In this study, we aimed (1) to separately characterize the dynamic control of
Emax via the arterial baroreflex and force-frequency relation during normal closed-
loop operation in conscious, chronically instrumented animals and (2) to determine in

what way the two dynamic Emax control mechanisms are altered by HF. To

accomplish these aims, we mathematically analyzed naturally occurring, beat-to-beat
hemodynamic variability from fully conscious dogs before and after rapid chronic

pacing induced HF. First, rather than using single beat methods (95, 100) to estimate

the spontaneous Em...x fluctuations on a beat-to-beat basis as previously done, we

employed a simple and potentially more reliable method in which the ventricular
unstressed volume was assumed to be relatively constant and determined with the

traditional multiple beat method during vena cava occlusion. Then, we jointly

93

identified the transfer function relating beat-to-beat fluctuations in ABP to Emax
(ABP—>Emax) to characterize the dynamic properties of the arterial baroreflex and the
transfer function relating beat-to-beat fluctuations in heart rate (HR) to Emax

(HR—)Emax) to characterize the dynamic properties of the force-frequency relation.

Finally, we compared the results before and after HF. A preliminary version of this

study has been reported in abbreviated form (21).
5.3 Materials and Methods

5.3.1 Hemodynamic Data

The collection of the hemodynamic data for analysis in this study are
described in detail elsewhere (88). Below, we briefly describe the instrumentation
employed and the relevant aspects of the executed protocol. All procedures were
approved by the Wayne State University Animal Investigation Committee and
conformed to the National Institutes of Health guidelines.

We studied five healthy adult mongrel dogs (~20-25 kg). We installed chronic
instrumentation in each dog through two recovery surgeries. The instrumentation
included a fully implanted, high fidelity pressure transducer (Data Sciences
International) for left ventricular pressure (LVP) measurement; two pairs of

sonomicrometry crystals (Sonometrics) for LV short axis and long axis dimensions

(D3 A and DLA) measurement and subsequent computation of LV volume (LVV) via

the modified ellipsoid formula (1t/6)xDSAxDSAxDLA; a fluid-filled catheter that was

94

connected to a standard extracorporeal pressure transducer (Abbott Laboratories) for
ABP measurement; an ultrasonic flow probe (Transonic Systems) for aortic flow rate
measurement; two hydraulic vascular occluders (In Vivo Metrics) for superior and
inferior vena cava occlusion; and three stainless steel sutures (Ethicon) that served as
electrodes for ventricular pacing. (For studies unrelated to the present investigation,
we also instrumented each dog during the second surgery for measurement of
hindlirnb blood flow via a retro-peritoneal approach (88)). After each dog fully
recovered from the surgeries, we continuously recorded the hemodynamic data during
a baseline period and multiple transient vena cava occlusions while the dog was
standing quietly. Thereafter, we connected the ventricular pacing leads to a
pacemaker set at a rate of 240 bpm for ~30 days to induce a moderate level of HF.
We then discontinued the ventricular pacing and likewise recorded the hemodynamic

data.

5.3.2 Data Analysis

Determination of Spontaneous Beat-to-Beat Variability. We estimated Emax

on a beat-to-beat basis from the hemodynamic data during the baseline periods

according to the method illustrated in Figure 5.1. First, we employed the traditional

multiple beat method for determining Emax, that is, linear regression on the end-

systolic LVP-LVV points during transient vena cava occlusion (87). The slope and x-

intercept of the resulting line respectively represent the average Emax and the LV

unstressed volume (V0). Then, assuming constant V0, we computed the LV elastance

95

(LVE) waveform from the LVP and LVV waveforms during the baseline periods by

dividing the former waveform by the difference between the latter waveform and V0

(averaged over the respective multiple transient vena cava occlusions to reduce

noise). Finally, we established beat-to-beat Emax by identifying the maximum of the

LVE waveform over each beat.

96

Transient Vena Cava Occlusion Baseline

 

 

 

 

 

 

 

160 3200
I
3 E
a E
5.80 3 °
1:. Time [sec]
3 1—1 70
E
o _____________ n—a
V0 5 55
1 40 80 7‘ M
LW [ml] '"' Time [sec]
\\
Ir 4Q\
88 ~ A)
v
a LVE(t) = LVP(t)I[LW(t)-Vo]
E
or
I
E
.§.
1.11 0
>
-' Time [sec]
:- metn] = maleVE(t)}
g 4.
U
I . ,
E . . .
if
E 4.-‘.
I“ Beat number n

Figure 5.1 Method for estimating spontaneous beat-to-beat maximal ventricular elastance

(Emu) variability from left ventricular pressure and volume (LVP and LVV)
measurements during transient vena cava occlusion (left panel) and a baseline period
(right panel).

We calculated the corresponding HR and ABP on a beat-to-beat basis by
detecting each heat from the aortic flow rate waveform and averaging the ABP

waveform over each beat during the baseline periods. We then converted the

97

spontaneous Emax, ABP, and HR beat sequences to 1 Hz time series as described in

(11).

Identification of Transfer Functions. From these three time series, we

identified the ABP—-)Emax and HR—>Emax transfer functions according to the block
diagram shown in Figure 5.2. The perturbing noise source NE...ax in the block
diagram is also estimated and represents the residual variability in Emax due to, for

example, Emax estimation error as well as other control mechanisms such as the

cardiopulmonary baroreflex. We mathematically represented the block diagram with

the following dual-input, autoregressive exogenous input (ARX) model:

Emax (t) = : aiEmax (t - i) + :biABPG - i) + i ciI-IR(t - i) + WBum (t) .

i=0
(5.1)

Here, t indicates discrete time; the three sets of unknown parameters (8., hi, ci} define
the ABP-—>Emax and HR—)Emax transfer functions; the unmeasured residual error

WE...ax together with the set of parameters {3.} specify NEmax; and the unknown

model order terms, p, q, r, and m, limit the number of parameters to be estimated (46).

For a fixed model order, we estimated the parameters in closed-form from 3-6 min

stationary intervals of zero-mean fluctuations in the ABP, HR, and Emax time series

by linear least squares minimization of WE...ax (46). We established the model order

by setting p and r to, respectively, two and q (i.e., second-order delay representation

98

 

of the arterial Emax baroreflex) according to the data of Sunagawa and colleagues (see

above) and determining q and m via minimization of the standard MDL criterion (46).

ABP—DI ABP—> Emam

 

max Emax

FIR—Fl FIR—’Emax

Figure 5.2 Block diagram for identifying the transfer functions relating fluctuations in
arterial blood pressure (ABP) to Emax (ABP—)Emax) and fluctuations in heart rate (HR)
to Ema, (HR—)Emax) from spontaneous beat-to-beat ABP, HR, and Em...x variability.

 

Statistical Comparisons. We computed the mean values and power spectra

(via standard autoregressive modeling (46)) of the ABP, HR, and Emax time series.

We then parameterized the computed power spectra in terms of low frequency (0.04-
0.15 Hz), high frequency (0.15-0.5 Hz), and total powers and the identified transfer
functions in terms of gain value, time delay, and overall time constant (determined
with a robust rectangular-based method (45)). Finally, we employed paired t-tests to
compare the scalar parameters mainly before and after HF but also within an

experimental condition.

99

 

5.4 Results

Table 5.1 and Figure 5.3 show the group average mean and power spectra of

the ABP, HR, and Emx time series as well as the group average V0 before and after

pacing induced HF. Mean ABP and mean Emax decreased, while mean HR and V0

increased, from the control condition to the HF condition. (Mean Em, as

determined with the traditional multiple beat method during vena cava occlusion,

revealed a similar result.) The Eum spectra were more narrowband than their ABP

and HR counterparts. All of the power spectra were depressed following the
induction of HF. The corresponding low frequency, high frequency, and total powers
all decreased, but only the low frequency power of the ABP spectrum reached the p =
0.1 level of significance.

Table 5.1 Group average mean hemodynamic variables from five conscious dogs before
and after pacing induced heart failure (HF).

 

 

Hemodynamic Variable Control HF p value
ABP [mmHg] 1 11.4i2.3 86.6i1.5 0.002
HR [bpm] 109.4d:5.9 128.3d:3.9 0.013
Emax [mmHg/ml] 5.5:1:O.1 3.13:0.1 0.011
V0 [ml] 10.5:t4.7 23.3i10.4 0.025

 

Values are meaniSE. ABP is arterial blood pressure; HR, heart rate; Em, maximal
ventricular elastance; and V0, ventricular unstressed volume.

100

 

Control HF

 

 

 

 

 

 

'3? 500 500
E '.
N
ABP g 250 250
E
E. 0 ' 0
0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5
’Fi"
=5.
N
HR E
a . .
a 0 1..1....1., 0
0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5
:3 1 1
"A
E
E m ax .5 0.5 05
I
E o 0
g 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5
Frequency [Hz] Frequency [Hz]

Figure 5.3 Group average power spectra of the spontaneous beat-to-beat ABP, HR, and

Emu fluctuations (meaniSE) from five conscious dogs before and after pacing induced
heart failure (HF).

Figure 5.4 illustrates the group average ABP—>Emax and HR—)Emax transfer

functions in terms of magnitude and phase responses as well as intuitive step
responses before and after HF. Table 5 .2 provides the gain values and overall time
constants of these transfer functions. The transfer functions during the control
condition are precisely defined as follows:

1 70.0013e'2j“)
14.385861“) +0.4585e'2jw

 

HABP—eEmax (0))

101

 

HHR—>E ((1)) =
max

70.0038 + 0.011361“) - 0.0055641"D - 0.0016e'3j‘” + 0.0004241“) + 0.0004e'5j‘” .
1-1385861” + 0.4585e'2j‘”

 

(5.2)

where 60 indicates normalized frequency.

102

 

Figure 5.4 Group average ABP—)Emax and HR—)Emax transfer functions
in terms of magnitude and phase responses as well as step responses
(meand: SE) fi'om the five conscious dogs before and after HF.

103

ABP—*Emax

Control HF
,7" 10'1 . 10:.

 

.5
°.
N

 

 

Magnitude [ml
3
6.1

 

 

 

   

 

 

10'4 7 7 7
10-3 10'2 10-1
'5'
i
O
O
P.
O
O
a
S . '
(L -130. 7 - ~ - s . - . - . .
10-3 10-2 10'1 10° 10:3 10'2 10-1 10°
Frequency [Hz] Frequency [Hz]

 

 

 

20 30 40 50

 

Time [see] Time [sec]

104

Figure 5.4 (cont’d).

 

 

 

 

 

 

 

 

      

 

   

 

 

5. Control HF

2 .0-1. .01

E

U

I

E 104. ................ f‘

2' ............... -

'3

9g 10-3 . . 10-3 . . .

g 10-3 10'2 10'1 10° 10'3 10'2 10'1 10°

2

v;- 180.

O

2

O

O

.2. 0‘

O

a

N

S

a. -180 . . '100 . . ' - .
10'3 10'2 10'1 10° ”-3 .0-2 .0-1 100

Frequency [Hz] Frequency [Hz]

cl.-
ooooooooooooooooooo

 

 

   

[mmHgImI-bpm]

20 30 40 20 30 40 50
Time [see] Time [sec]

105

Table 5.2 Group average gain values and overall time constants of the transfer functions
relating beat-to-beat fluctuations in ABP to Emax (ABP—)Emax) and beat-to-beat
fluctuations in HR to Emax (HR—)Emax) from the five conscious dogs before and after

 

 

HF.
Transfer F unctron Control HF p value
Parameters
GABPAEM [1111"] -0.023 I 0.012 -00002 :t 0.007 0.088
GHR-fimax 0 013 :l: 0 005 -0 001 1: 0 004 0 082
[mmHg/nfl-bpml ' ' ' ' '
TABP—namax [860] 1 1'2 i 2'8 ] p=0.039 * '
{HR—)Emax [SEC] 1'7 i 0'5 '

 

Values are meaniSE. G is gain value, and 1: is overall time constant. See Table 5.1
caption for remaining abbreviations. *The parameter I was not well defined due to the
small transfer function magnitude (see Figure 5.4).

During the control condition, the ABP—9E“...x and HR—-)Emax transfer

functions exhibited negative and positive gain values, respectively. Thus, Emax

would decrease (increase) in the steady state in response to an increase (decrease) in

mean ABP but in absence of any change to mean HR as a result of the arterial

baroreflex, whereas Emax would increase (decrease) in the steady state in response to

an increase (decrease) in mean HR without any change to mean ABP due to the force-

frequency relation. The two transfer functions were similar in that they both behaved

as lowpass filters. Thus, Emax would reach steady state without oscillating in

response to a change in mean HR or mean ABP. However, the ABP—-)Emax transfer

function was more sluggish. This transfer function showed a notable time delay and

an overall time constant that was over five times as large as that of the HR——)Em,,.x

106

transfer function. Thus, Emax would reach steady state faster in response to a change

in mean HR than a perturbation to mean ABP.

During the HF condition, the ABP—>Emax and HR—>Emax transfer functions

were markedly blunted, except for the higher frequency regime of the latter transfer
function. The gain values of the two transfer functions were, in particular, reduced to

negligible values. (Note that the time constants and delays were not well defined due

to the small transfer function magnitudes.) Thus, Emax would not change much

transiently and especially in the steady state in response to a variation in either mean

ABP or mean HR.

5.5 Discussion

This study is the first to examine the dynamic control of VC in conscious
animals before and after induction of HF. Through mathematical analysis of
spontaneous beat-to-beat hemodynamic variability, we were able to reveal
quantitatively the strength and temporal (or frequency) characteristics of the arterial
baroreflex and force-frequency relation in modulating VC during normal closed-loop

operation in healthy and pathophysiologic conditions.

We employed Emax as the quantitative index of VC, thereby assuming that the

ventricular end-systolic pressure-volume relationship was linear. Although
nonlinearity has been observed over wide pressure and volume ranges (66, 103), the

relationship indeed appears to be linear over more physiologic pressure and volume

107

ranges in conscious dogs (96, 97) as well as humans in health (54) and with severe

HF (5).

We utilized V0 determined with the traditional multiple beat method during

vena cava occlusion to estimate the requisite beat-to—beat Emax during the

corresponding baseline period (see Figure 5.1). We therefore assumed that V0 was

constant within an experimental condition of 8 dog (i.e., not modulated by control

mechanisms). This assumption originates from the classic studies of Suga and

Sagawa demonstrating that inotropic agents selectively alter Emax (e.g., (87)) as well

as subsequent work showing that average Emax: but not V0, is controlled over a wide
HR range via the force-fiequency relation (53). Although single beat methods for
estimating EImx on a beat-to-beat basis do not involve such a constant V0 assumption,

they are based on other, seemingly more stringent assumptions such as the LVE
function, normalized in amplitude and time over each beat, is invariant (95) or peak
isovolumic pressure at end-diastolic volume can be extrapolated from isovolumic

phase LVP of ejecting beats (100). These methods have been verified during large

perturbations to Emax but not smaller, spontaneous Emax changes. We did attempt to

implement several variants of the single beat method based on an invariant

normalized LVE function to estimate beat-to-beat Emax but were not able to obtain

physiologic results.

108

We characterized dynamic Emax control via the arterial baroreflex and force-

frequency relation through the ABP——>Emax and PER—)Emax transfer firnctions,

respectively. Thus, we assumed that these control mechanisms were linear and time-
invariant. Sunagawa and colleagues showed that the coherence of the transfer

functions relating randomly perturbed carotid sinus pressure and randomized left and

right stellate ganglion stimulations to estimated beat-to-beat fluctuations in Emax

during stable conditions was between 0.5 and 0.8 over the lower frequency regime
(42, 56). Since the spontaneous hemodynamic fluctuations considered herein were
smaller and likewise obtained at rest, our linearity and time invariant assumption

appears to be quite tenable.

Finally, we jointly identified the ABP—)Em...x and HR-eEmax transfer

functions from spontaneous beat-to—beat ABP, HR, and Em fluctuations using a

dual-input ARX model (see Figure 5.2). We therefore assumed that the ABP and HR
fluctuations, though related, have a sufficient uncorrelated component and at least as
many frequency components as the number of ARX model parameters. Indeed, it is
well known that ABP and HR variability arise from fluctuations in variables other
than each other such as total peripheral resistance and respiration, and a significant
uncorrelated component has been shown in previous studies on multi-signal analysis
of beat-to-beat variability including those by us (60, 64). Further, we limited the
ARX model to only a small number of parameters (< 10) in accordance with the

results reported by Sunagawa and colleagues (43, 56).

109

The mean values of ABP, HR, and Emax as well as V0 changed in the expected

directions following the induction of HF (see Table 5.1). Further, the power spectra

of the beat-to-beat ABP, HR, and Emax fluctuations all showed a tendency to decrease

during the pathophysiologic condition (see Figure 5.3). A number of previous studies
have shown that HR variability is reduced in HF including after rapid chronic pacing
in conscious dogs (76) due to aberrant autonomic nervous system functioning, and at

least one study has demonstrated that ABP variability is smaller in HF patients than

control subjects (84). We are not aware of any previous study addressing Emax

variability during HF. The lack of statistical significance of the reductions in spectral

powers in our study may be due to the smaller sample size as well as error in the beat-
to-beat Ermx estimates. Importantly, however, the identified transfer functions
coupling the beat-to-beat fluctuations were able to reveal greater levels of statistical

significance perhaps because beat-to-beat Emax estimation error independent of the

ABP and HR fluctuations was ascribed to the perturbing noise term NEmax rather than
the transfer functions (see Figure 5.2).
The ABP-—)Emax transfer function showed negative feedback dynamics during

the control condition (see Figure 5.4), which is consistent with the arterial baroreflex

mechanism. More specifically, the transfer firnction behaved as a lowpass filter (see
Figure 5.4) with a time delay and overall time constant of 2.6:05 and 11.2i2.8 sec,

respectively (see Table 5.2). These dynamics are indicative of the well-known

110

 

sympathetic nervous mediation of the arterial Emax baroreflex (l3). Sunagawa and

colleagues reported that the transfer function relating randomly perturbed carotid

sinus pressure to beat-to-beat Em...x fluctuations in anethestized, vagotomized dogs

similarly exhibited lowpass frequency characteristics with a time delay and overall

time constant of 2.3 and 11 sec, respectively (42). However, the gain value of 70.085

ml'1 that they found is nearly four times as large as the -0.023:h0.012 ml‘l ABP—>Emax

gain value that we obtained (see Table 5.2). This difference is in accord with a

previous study showing that the VC baroreflex gain value was smaller in conscious

than anesthetized dogs (104).

The ABP—)Emax transfer function including its gain value was blunted

essentially to zero following induction of HF (see Figure 5.4 and Table 5.2). This
alteration is likely due to both depressed sympathetic nervous responsiveness as well
as diminished total baroreflex arch functioning in HF (36, 65, 107). Thus, not only
are baroreflex mediated changes in HR smaller in HF, but the abolition of any change
in VC will further act to attenuate the strength of the arterial baroreflex in the control

of ABP as baroreflex mediated changes in cardiac output will be depressed (38).

The HR—>Emax transfer function indicated that HR changes cause directionally

the same Emax changes during the control condition (see Figure 5.4), which is

consistent with the force-frequency relation. In particular, compared to the

ABP—)Emax transfer function, this transfer function likewise acted as a lowpass filter

(see Figure 5.4) but with minimal time delay and a significantly smaller overall time

111

 

 

constant of 1.7i0.5 sec (see Table 5.2). These dynamics are coherent with the belief
that the force-frequency relation is mediated by fast intracellular calcium handling

mechanisms (though the more sluggish sympathetic nervous system does appear to

set its operating point and thus its gain value) (69, 78). Moreover, the HR—>Emax

gain value of 0013:0005 mmHg/ml-bpm (see Table 5.2) is not far from the 0.03
mmHg/ml-bpm gain value previously obtained from isolated canine hearts at the
same mean HR (53). Deviations in these values are likely due at least in part to the

different experimental conditions.

The HR—>Emax transfer function and especially its gain value were depressed

following the induction of HF (see Figure 5.4 and Table 5.2). Several previous
studies have shown that the force-frequency relation was reduced or even inverted in
the steady state in isolated myocardium from failing human hearts (29, 63), conscious,
but autonomically blocked, dogs following pacing induced HF (6), and HF patients
(29, 35). The mechanisms involved appear to be abnormal intracellular calcium
handling (77). Another potential mechanism for the diminished strength of the force-
frequency relation in our study may be the significant increase in mean HR (i.e., shift

in operating point; see Table 5.2) as previously shown in isolated canine hearts (53).

The abolishment of the ABP—)Emax transfer function and the marked attenuation of

the HR—>Emax transfer function coupled with lower baroreflex control of HR likely

contribute to the markedly attenuated baroreflex control of cardiac output in HF (38,

68).

112

In summary, we have identified the ABP—->Emax and HR-—)Emax transfer

functions, which respectively characterize the dynamic properties of the arterial VC
baroreflex and force-frequency relation, by mathematical analysis of spontaneous
beat—to-beat hemodynamic variability from awake dogs before and after pacing

induced HF. Our results provide perhaps the first data on the dynamic control of

Emax during normal closed-loop operation in health and HF. In the future, we plan to

apply our mathematical analysis to investigate dynamic Emax control via the arterial

baroreflex and force-fi'equency relation during other pathophysiologic conditions and
extend the analysis to elucidate additional control mechanisms such as the

cardiopulmonary baroreflex.

113

 

 

CHAPTER 6. CANINE INVESTIGATION OF THE
CARDIOPULMONARY BAROREFLEX CONTROL OF
VENTRICULAR CONTRACTILITY

6.1 Abstract

We performed a novel investigation of the cardiopulmonary baroreflex control
of ventricular contractility in four conscious dogs. We specifically measured
spontaneous beat-to-beat hemodynamic variability before and after the administration

of propranolol. We then identified the transfer function relating beat-to-beat

fluctuations in central venous pressure (CVP) to maximal ventricular elastance (me)

to characterize the cardiopulmonary baroreflex control of ventricular contractility,

while accounting for the influences of arterial blood pressure fluctuations on Emax via

the arterial baroreflex and heart rate fluctuations on Emax via the force-frequency

relation. Our major finding is that the cardiopuhnonary baroreflex responds to an

increase (decrease) in CVP by increasing (decreasing) Emax via the B-sympathetic

nervous system.
6.2 Introduction

The baroreflex systems are primarily responsible for maintaining blood
pressures over short time scales of seconds to minutes. It is well known that the

arterial baroreflex senses arterial blood pressure (ABP) via baroreceptors lying in the

114

carotid sinus and aortic arch and buffers a decrease (increase) in ABP by increasing
(decreasing) heart rate (HR), total peripheral resistance, and ventricular contractility
(VC). However, the cardiopulmonary baroreflex is less understood. The sensory
receptors of this system are more complex, residing mainly in the cardiac chambers
but also in the walls of the pulmonary artery (18). These receptors have been shown
to be very responsive to central venous pressure (CVP) (25, 85). The
cardiopulmonary baroreflex responds to a change in CVP by inducing an opposite
change in total peripheral resistance (59, 85). An increase in CVP also leads to an
increase in HR (i.e., Bainbridge effect) in dogs (8), but an opposite change may occur
in humans (25).

To our knowledge, the cardiopulmonary baroreflex control of VC has not been
elucidated. A change in CVP could induce a same directional change in VC so as to
maintain CVP, much like the Bainbridge effect. On the other hand, a change in CVP
could cause an opposite change in VC in order to blunt the forthcoming change in
ABP due to the altered preload, much like the cardiopulmonary baroreflex control of
total peripheral resistance.

We performed a novel canine investigation of the cardiopulmonary baroreflex
control of VC. More specifically, we measured spontaneous beat-to-beat
hemodynamic variability from four conscious dogs during control conditions and as
well as after the administration of propranolol to abolish the neural control of VC.

We then identified the transfer function relating beat-to-beat fluctuations in CVP to

maximal ventricular elastance (Emax), which is perhaps the best available index of VC

115

(40, 97, 99), while accounting for other influences on Emax including ABP

fluctuations via the arterial baroreflex.

6.3 Methods

6.3.1 Data Collection

We collected hemodynarrric data for this study from four adult dogs (20-25 kg)
in the context of performing experiments to address unrelated specific aims. We
describe only those aspects of the experimental procedures that were relevant to the
present study. All procedures were reviewed and approved by the Wayne State
University Animal Investigator Committee.

We studied each dog on three experimental. days with suitable recovery
periods in between as follows. On the first day, we performed a midline stemotomy
under sterile conditions. We installed instrumentation including two pairs of
sonomicrometry crystals (Sonometrics) on the left ventricular (LV) endocardium for
continuous LV volume (LVV) as described in (89); a fully implanted system with a
micromanometer-tipped catheter (Data Sciences International) in the left ventricle
(LV) for continuous LV pressure (LVP); an ultrasonic flow probe (Transonic
Systems) around the ascending aorta for continuous cardiac output; and hydraulic
vascular occluders (In Vivo Metrics) on the superior and inferior vena cava to
diminish cardiac preload. Then, on the second day, we installed additional
instrumentation under sterile conditions including fluid-filled catheters in the terminal

aorta for continuous ABP and in the right atrium for continuous CVP. Finally, on the

116

third day, we recorded the cardiovascular measurements during a baseline period of
5-8 min and transient vena cava occlusion while the dogs were standing quietly.
Lastly, for each dog, we administered propranolol to achieve complete B-sympathetic

nervous blockade and likewise recorded the measurements.

6.3.2 Data Analysis

We analyzed the hemodynamic data of the four dogs as follows. First, we

determined Emax and CVP, along with ABP and HR, on a beat-to-beat basis from the

continuous measurements during the baseline period. Then, we identified the transfer

function relating the spontaneous beat-to-beat fluctuations in CVP to Emax

(CVP—)Emax), while effectively eliminating the known influences of beat-to-beat

ABP and HR fluctuations on Emax.

More specifically, as described in Chapter 5 of dynamic Emax control before

and after heart failure, we estimated beat-to-beat Emax during the baseline period

according to the procedure shown in Figure 5.1. First, we applied the traditional

method for determining Emax by performing linear regression on the end-systolic

LVP-LVV points during the transient vena cava occlusion (96). The slope of the

resulting line represents the average Emax, while the x-intercept indicates the LV

unstressed volume (V0). Then, assuming constant V0, we computed the time-varying

LV elastance (LVE) curve from the continuous LVP and LVV during the baseline

117

period by dividing the former measurement by the difference between the latter

measurement and V0. Finally, we determined Emax on a beat-to-beat basis by

identifying the maximum of the LVE curve over each beat.
We computed beat-to-beat CVP and ABP by respectively time averaging the
continuous CVP and ABP over each beat during the baseline period and identified

beat-to-beat HR from the continuous cardiac output during the same period. We then

re-sampled the Emaxa CVP, ABP, and HR beat series to time series at a sampling

frequency of 1 Hz as described in (l 1).

We identified the CVP—) Emax transfer function by analyzing all four of the

time series according to the block diagram illustrated in Figure 6.1. As indicated in

this diagram, we simultaneously identified the transfer function relating beat-to-beat

fluctuations in ABP to Emax (ABP—)Emax), which characterizes the arterial baroreflex,

and the transfer function relating beat-to-beat fluctuations in HR to Emax (HR—>Emax),

which characterizes the force-frequency relation. In this way, the influence of heat-

to-beat fluctuations in CVP on Emax was isolated from other major confounding
factors. We also estimated the perturbing noise source NEmax in the block diagram,

which represents the residual variability in Em...x not explained by the analyzed

fluctuations. In particular, we mathematically represented the block diagram with the

following autoregressive exogenous input structure:

118

P r
4.01724 E (t-i>+2 b. ~CVP(t-i)
i=1

i=q

+2 ci ABM—n+2 di -HR(t-i)+WEmax (t)’

i=0
(6.1)
where t is discrete time; the four sets of unknown parameters {a., b., c., d.} fully

define the three transfer functions; the unmeasured residual error WEmax together

with the set of parameters {8.} specify NEW; and the unknown model order, p, q, r, s,

m, and n, limit the number of parameters (46). For a fixed model order, we

analytically estimated the parameters from zero-mean fluctuations in the 1 Hz CVP,

ABP, HR, and Emax time series by linear least squares minimization of WEB...1x (46).

We set p, r, and m to two, q, and s, respectively, on the basis of a compelling previous

study demonstrating that the arterial baroreflex control of Emax could be well

represented as a second-order delay system (42). We determined q, s, and n by

minimization of the popular minimum description length criterion (46).

119

 

cardiopulmonary

CVP VC baroreflex

 

 

arterial
ABP VC baroreflex Em“

 

 

HR force-frequency

. NE
relation m“

 

Figure 6.] Block diagram for identifying the CVP—eEmax, ABP—>Emax and HR—)Emax
transfer functions from beat-to-beat fluctuations in CVP, ABP, HR, and Ema...

6.4 Results

Figure 6.2 illustrates the group averaged (meaniSE) CVP—)Emax,

ABP—)Emax, and HR—)Emax transfer functions in terms of intuitive step responses,

respectively, before and after the administration of propranolol. During the control

condition, the CVP—)Emz.x step response indicates that Emax would increase in

response to a step increase in CVP. Quantitatively, the average gain value and

dominant time constant during control condition are 0.0859i0.0638 ml'1 and
9.0892ztO.7704 sec. The corresponding pairs of ABP—)Emax and HR-—>Emax step
responses show that Emax would decrease and increase, respectively, in response to

step increases in ABP and HR. The average gain value of the ABP—9Emax step

120

response and the average dominant time constant of the HR—)Emax step response are
smaller than those of the CVP—9E...x step response. During the propranolol
condition, the CVP—> Emax step response indicates that Emax would not change in

response to a step increase in CVP. The corresponding ABP—>Emax and HR——>Emax

step responses similarly reveal blunted responses to steps increases in ABP and HR.

 

 

 

 

 

 

 

 

Control Propranolol
0 2 0.2
-- 0.1» ,7’” 0 1
CVP-+Emax '- / ..................
E. of o .. ......................
-O 1 -0.1
0 10 20 30 40 50 0 10 20 30 40 50
0.01» 0.01- 1 __________________
7"" -0.01’ \\ 001 ‘~ ------------------
ABFL"Emax E 41.02. \‘ .................. 43.02.
.003 » ‘~~- ________________ -0.03-

 

 

 

 

 

 

 

Tlme [see] Time [see]

Figure 6.2 Group averaged transfer functions in terms of step responses during the
control and propranolol conditions.

6.5 Discussion

In summary, we have investigated the cardiopuhnonary baroreflex control of

VC in terms of Em...x in four conscious dogs before and after the administration of

121

propranolol. Our results suggest that, similar to the Bainbridge effect, the

cardiopulmonary baroreflex responds to an increase (decrease) in CVP by increasing

(decreasing) Ema... This mechanism appears to be mediated by the B-sympathetic

nervous system, as the Emax response to a change in CVP was abolished following

the administration of propranolol. These results may be amongst, if not, the first to

illustrate how the cardiopuhnonary baroreflex controls VC.

Further, our ancillary results here on the Ema... response to changes in ABP and

HR are consistent with known physiology. In particular, we found that an ABP

change produces an opposing change in BM, which is consistent with the negative
feedback dynamics of the arterial baroreflex, while a HR change induces the same

directional change in BM, which is congruent with the force-frequency relation.

Moreover, the Emax response to a HR change was markedly faster than to an ABP

change. This result is in accord with the force-frequency relation being mediated by

fast mechanical effects and the arterial baroreflex being governed by the sluggish

sympathetic nervous system. Finally, as expected, the Emax response to a change in

ABP was eliminated after the administration of propranolol. (However, it is unclear

why the Emax response to a HR change was also blunted after the drug administration.)

These physiologically consistent results add confidence to our new findings on the

cardiopulmonary baroreflex control of VC.

122

Our future efforts will focus on confirming the results reported herein in a
larger number of animals and using more sophisticated system identification models.
Ultimately, we believe that this line of research will translate to a significant advance

in the understanding of baroregulatory physiology.

123

CHAPTER 7. CONCLUSIONS AND FUTURE WORK

7.1 Accomplishments and Conclusions

In conclusion, we have investigated the heart rate (HR), total peripheral
resistance (TPR) and ventricular contractility (V C) baroreflex respectively by
applying system identification and advanced signal processing techniques. In the HR
baroreflex study, we derived specific neural indices to selectively quantify the cardiac
sympathetic and parasympathetic nervous functioning from the estimated HR
baroreflex impulse response via non—invasive cardio-respiratory variability. Our
indices statistically outperform the conventional HR variability power spectral
analysis and can be used for patient monitoring under even wider physiologic
conditions, such as breathing pattern being altered. In the TPR baroreflex project, we
developed a potentially non-invasive technique to mathematically estimate the arterial
TPR baroreflex impulse response, and demonstrated its validity using both realistic
simulated data and experimental measurements. In the investigation of linear

dynamic control of VC, we identified the transfer functions coupling beat-to-beat

fluctuations in HR to maximal ventricular elastance (Emax) and ABP to Em, and

obtained corresponding gain values and time constants in conscious dogs before and
after pacing-induced heart failure (HF). Our results expand the basic understanding

of the short-term VC control mechanisms and provide perhaps the first data on

dynamic Emax control during normal closed-loop operation in health and the presence

124

of HF. In addition, we extended this study by including central venous pressure (CVP)

as a third input to investigate the cardiopulmonary baroreflex control of VC in terms

of Em...x before and after the administration of propranolol and our results may be

amongst the earliest to illustrate the cardiopulmonary VC baroreflex mechanism. In
future, we hope that our novel techniques are implemented to advance the
understanding of the normal, integrated and dynamic functioning of the cardiac
baroreflex systems in animals and humans in health and disease, and to establish new

patient monitoring systems.

7.2 Future Work

To complete the study described in Chapter 4, our future effort will be to
further validate the proposed mathematical algorithm by comparing it to an existing
experimental method proposed by Raymundo et al. (85). Our goal includes
comparison of the arterial and cardiopuhnonary TPR baroreflex gain values from the
two methods and as well as their alteration after the administration of digoxin and
prazosin.

In Chapter 6, we investigated the cardiopulmonary VC baroreflex by

identifying the CVP——>Emax impulse response in four conscious dogs. We used a

second-order delay system model to describe the mechanism based on a previous
compelling study (42) and discovered that similar to the Bainbridge effect, the

cardiopulmonary baroreflex responds to an increase (decrease) in CVP by increasing

(decreasing) Ema... However, the model we used here may have constrained the

125

impulse response shape and thus prejudiced the result. Future work should contain
exploring different system identification models and conducting more animal
experiments.

As mentioned in Background, the neural cardiovascular regulation also adjusts
systemic venous unstressed volume (SVUV). Due to difficulties in measuring beat-
to-beat SVUV, the SVUV baroreflex mechanisms are much less understood. We
would definitely like to extend our techniques to investigate the SVUV baroreflex,
provided its beat-to-beat measurements become available.

Lastly, as justified in Background and within each study, linear and time-
invariant (LTI) models were predominantly used through our research. Since the
neural regulatory system is not LTI in a more general sense, we would like to exploit

its nonlinear and time-varying behavior in future work.

126

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