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This is to certify that the
thesis entitled

IDENTIFICATION OF THE TOTAL PERIPHERAL
RESISTANCE BAROREFLEX

presented by
YING LI

has been accepted towards fulﬁllment
of the requirements for the

Master of degree in Department of Electrical
Science Enmeering

 

 

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2/05 c:/C'l—RC/Da_teDue.indd-p.'" '1'5’

‘—

 

IDENTIFICATION OF THE TOTAL PERIPHERAL
RESISTANCE BAROREFLEX

By

Ying Li

A THESIS

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

MASTER OF SCIENCE

Department of Electrical Engineering

2005

ABSTRACT

Identification of the Total Peripheral Resistance Baroreﬂex

By

Ying Li

Feedback control of total peripheral resistance (TPR) by the arterial and
cardiopulmonary baroreﬂex systems is a well-known mechanism for short-term blood
pressure regulation. Conventional methods for measuring this TPR baroreﬂex mechanism
aim to quantify only the static gain value of one baroreflex system as it operates in open-
loop conditions. As a result, the normal, dynamic functioning of the arterial and
cardiopulmonary baroreﬂex control of TPR remains to be fully elucidated. To this end,
we introduce a signal processing algorithm to identify the TPR baroreﬂex impulse
response (and the dominant time constant of the systemic arterial tree) by analysis of
small, beat-to-beat ﬂuctuations in arterial blood pressure, cardiac output, and stroke
volume. The algorithm may therefore provide a complete linear dynamic characterization
of the TPR baroreﬂex under normal, closed-loop conditions from totally non-invasive
measurement methods (e.g., arterial tonometry and Doppler ultrasound). .We also
demonstrate the validity of the algorithm with respect to realistic simulated data with
known dynamic properties and conscious canine data before and after chronic arterial
baroreceptor denervation. With further successful experimental testing, the signal
processing algorithm may ultimately be employed to advance the basic understanding of

the TPR baroreﬂex in both humans and animals in health and disease.

ACKNOWLEDGMENTS

Here I would like to thank all the people who have helped me in this work.

First, I am very grateful to my advisor: Dr. Ramakrishna Mukkamala. Dr. Mukkamala
helps me ﬁnish this very interesting thesis research and always gives me suggestions.

I would also like to thank J. K. Kim, J. Sala-Mercado, R. L. Hammond and D. S.
O’Leary from Wayne State University School of Medicine for providing the
experimental data used in the evaluation.

I also thank my colleagues Zhenwei Lu and Rafat Inayat Elahi for their advice.

iii

TABLE OF CONTENTS

 

 

 

1. INTRODUCTION ' 1
1.1 MOTIVATION ........................................................................................................ 1
1.2 AIMS .................................................................................................................... 2
1 .3 ORGANIZATION .................................................................................................... 3

2. BACKGROUND 4
2.1 BAROREFLEX PHYSIOLOGY .................................................................................. 4
2.2 PREVIOUS METHODS FOR MEASURING THE TPR BAROREFLEX .............................. 5

3. SIGNAL PROCESSING ALGORITHM 9
3.1 ESTIMATION OF THE STATIC GAINS OF THE ARTERIAL AND CARDIOPULMONARY
TPR BAROREFLEX SYSTEMS ............................................................................................. 9

3.2 ESTIMATION OF THE IMPULSE RESPONSE OF THE ARTERIAL TPR BAROREFLEX.... 17
3.3 ESTIMATION OF THE IMPULSE RESPONSE OF THE CARDIOPULMONARY TPR

 

 

BAROREFLEX ................................................................................................................. 19
3.4 IMPLEMENTATION OF THE SIGNAL PROCESSING ALGORITHM .............................. 19

4. EXPERIMENTS AND RESULTS 24
4.1 SIMULATED DATA .............................................................................................. 24
4.1.1 Data generation objective ......................................................................... 24

4.1.2 Results ....................................................................................................... 27

4.2 EXPERIMENTAL DATA ........................................................................................ 29
4.2.1 Experimental methods .............................................................................. 29

4.2.2 Results ....................................................................................................... 3O

5. CONCLUSIONS AND FUTURE WORK -- 33
5.1 CONCLUSIONS .................................................................................................... 33
5.2 FUTURE WORK ................................................................................................... 33
BIBLIOGRAPHY 35

 

iv

LIST OF FIGURES

Figure 1: Block diagram deﬁning the total peripherial resistance(TPR) baroreﬂex system

to be analyzed ................................................................................................................... 11
Figure 2: Diagram indicating how arterial blood pressure (ABP) would change over time
in response to a step change in cardiac output (CO) ......................................................... 13
Figure 3: Block diagram indicating step 1 of signal processing algorithm ...................... 14
Figure 4: Block diagram indicating step 2 of signal processing algorithm ...................... 16
Figure 5: A ﬁrst order RC circuit to represent the systemic arterial tree at low
ﬁ'equencies ........................................................................................................................ 1 8
Figure 6: Estimation of the RC time constant of the systemic arterial tree ..................... 18

Figure 7: Block diagram summarizing a previously developed human cardiovascular

simulator ........................................................................................................................... 25
Figure 8: Simulated and human radial ABP waveforms ................................................. 26
Figure 9: Power spectra of heart rate (HR) from the Simulated and human experimental

data .................................................................................................................................. 26
Figure 10: Actual and estimated arterial TPR baroreﬂex impulse responses ................... 28

Figure 11: Sample power spectra before and after chronic arterial baroreceptor
denervation from a Single dog ........................................................................................... 31

Figure 12: Group average arterial and cardiopulmonary TPR baroreﬂex gain values
before and after chronic arterial baroreceptor denervation in seven conscious dogs. ...... 32

LIST OF TABLES

Table 1: Conventional methods for measuring the TPR baroreﬂex ................................... 8
Table 2: Actual and estimated Gc and T values ................................................................ 28
Table 3: Segments chosen to analyze in conscious dog data ............................................ 30
Table 4: Group average hemodynamic values of conscious canine data .......................... 31

vi

1. Introduction

1.1 Motivation

The total peripheral resistance (TPR) baroreﬂex is one of the most important factors to
regulate short-term arterial blood pressure (ABP) on a time scale of seconds to minutes
and thus is critical to maintain arterial pressure in response to changing demands on the
cardiovascular system.

The traditional techniques used to characterize the TPR baroreﬂex system involve
perturbing the blood pressure with an external stimulus as the input signal, measuring the
TPR response as the output signal, and then plotting the stimulus-response curve whose
slope indicates the system gain. The external stimuli that have been employed may be
broadly classiﬁed as selective or non-selective. Selective stimuli only excite one
baroreﬂex system while the non-selective stimuli excite both arterial and
cardiopulmonary baroreflex systems simultaneously.

However, these traditional techniques have limitations. The selective stimuli methods
Open the feedback loop between the baroreﬂex and circulation and thereby preclude the
study during normal physiologic conditions. In contrast, non-selective stimuli methods
preserve normal closed-loop conditions, but the unique contribution of each baroreﬂex
system cannot be distinguished from a simple stimulus-response curve. Multiple
regression analysis (MRA) [McCullagh et a1, 1989] can distinguish the individual gain
values of arterial and cardiopulmonary TPR baroreﬂex systems. However, it requires a
sophisticated experimental preparation in which both heart rate (HR) and blood volume

are perturbed. As a result, its applications are limited. In addition, the traditional

techniques only provide a static characterization of the TPR baroreﬂex without
explaining the dynamic properties. Thus, a practical technique is needed to characterize
the normal, dynamic functioning of the arterial and cardiopulmonary TPR baroreﬂex

systems.

1.2 Aims

To this end, we previously developed a signal processing algorithm to identify the
static gains of the arterial TPR baroreﬂex (GA) and cardiopulmonary TPR baroreﬂex (Gc)
by mathematical analysis of the small beat-to—beat ﬂuctuations in ABP, cardiac output
(CO), and stroke volume (SV). In this thesis, we aim to extend the signal processing
algorithm so as to identify the impulse response characterizing the TPR baroreﬂex. The
extended technique may therefore provide a complete linear dynamic characterization of
the TPR baroreﬂex under normal, closed-loop conditions without application of an
external stimulus and from totally non-invasive measurement methOds (e.g., Finger-cuff
photoplethysmography [Imholz et a1, 1998] and Doppler ultrasound [Eriken et a1, 1990]).
The technique speciﬁcally identiﬁes the impulse responses relating the ﬂuctuations in CO
to ABP and the ﬂuctuations in SV to ABP and then represents the identiﬁed impulse
responses with physiologic models so as to estimate the arterial TPR baroreﬂex impulse
response, Gc, as well as the dominant time constant (T) of the systemic arterial tree (i.e.,
the product of TPR and the lumped arterial compliance (AC)).

In this thesis, we also aim to evaluate the technique with respect to both simulated and
experimental data. First, we applied the technique to the realistic beat-to-beat variability

generated by a cardiovascular simulator whose actual dynamic properties are precisely

determined. Then, we applied the technique to the spontaneous beat-to-beat variability
measured from seven conscious dogs before and after chronic arterial baroreceptor

denervation.

1.3 Organization

This thesis is organized as follows. Chapter 2 provides an overview of the TPR
baroreﬂex systems and the conventional measurement methods. Chapter 3 discusses the
signal processing algorithm we developed and its implementation. Chapter 4 describes
the simulated and experimental evaluation studies and results. Chapter 5 summarizes the

works carried out in this thesis and suggests future directions of study.

2. Background

2.1 Baroreflex Physiology

The arterial and cardiopuhnonary baroreﬂex systems contribute to the regulation of
blood pressures over Short time scales of seconds to minutes. The maintenance of blood
pressure is vital to the proper functioning of organs such as the brain, heart, and others.
Thus, understanding the functioning of these baroreﬂex systems is very important.

The baroreﬂex systems operate through negative feedback control of the circulation
in which the sensed variables are blood pressures and the controlled variables are
circulatory parameters such as HR, TPR, and ventricular contractility (V C). The arterial
baroreﬂex senses ABP via baroreceptors that lie in the wall of the bifurcation region of
the carotid arteries in the neck and also in the arch of the aorta in the thorax. The arterial
baroreﬂex system responds to an increase in pressure at its receptors by, for example,
decreasing HR, TPR, and VC so as to maintain ABP. The cardiopulmonary
baroreceptors reside mostly in the cardiac chambers but also in the walls of the
pulmonary artery [Bishop et al, 1983] and are very responsive to changes in central
venous pressure (CVP) [Desai et al, 1997; Raymundo et al, 1989]. The cardiopulmonary
baroreﬂex responds to an increase in pressure at its receptors by decreasing TPR [Mancia
et a1, 1983; Raymundo et a1, 1989]. An increase in CVP also leads to an increase in HR
in dogs [Bainbridge, 1915], but an opposite change may occur in humans [Desai et al,
1997]. The cardiopulmonary baroreﬂex is more complicated and is less understood

compared to the arterial baroreﬂex.

The control of HR by the arterial baroreﬂex is the most extensively studied baroreﬂex
mechanism due to the relative ease of measuring HR and ABP. Previous researchers have
studied the HR baroreﬂex in diabetes mellitus (e.g., [Mukkarnala et al, 1999]), heart
failure (e.g., [Thames et al, 1993]), and hypertension [Moreira et al, 1992]. However, the
HR baroreﬂex may not be the most important regulator of ABP. Guyton showed that
venous return is nearly saturated at normal right atrial pressures due to the collapse of the
large veins entering the thorax and thus, ABP can only be enhanced by about 15-20% by
increasing only HR (see Figure 4 in [Guyton et al, 1957]). In contrast, all TPR changes
are directly transmitted to ABP via Ohmic effects so that the TPR baroreﬂex may be a

more important short-time regulator of ABP.

2.2 Previous Methods for Measuring the TPR

Baroreﬂex

Among the previous studies of the TPR baroreﬂex, most employed an external
stimulus and followed three steps for characterizing this feedback mechanism: 1) perturb
the baroreceptors with an external stimulus; 2) measure the steady-state TPR response;
and 3) plot the stimulus-response curve whose slope indicates the system gain. The
external stimuli that have been employed may be broadly classiﬁed as selective or non-
selective. Selective stimuli such as carotid sinus pressure control [Olivier et al, 1993;
Schmidt et al, 1971] and lower body negative pressure [Johnson et al, 1974; Zoller et al,
1972] only excite one set of baroreceptors and thus only the system response
corresponding to this speciﬁc baroreﬂex system may be determined. However, the

selective stimuli approach opens the feedback loop between the baroreﬂex and

circulation and thereby precludes its study during normal physiologic conditions. In
addition, the tenet that only one set of baroreceptors has been perturbed may not always
be valid.

The non-selective stimuli such as upright tilting [Waters et a1, 2002] excite both
arterial and cardiopulmonary baroreﬂex systems simultaneously. The advantage of the
non-selective stimulus approach is that it preserves normal closed-loop conditions.
However, the relative contributions of the arterial and cardiopulmonary baroreceptors to
the total system response cannot be distinguished without a more sophisticated analysis.

Raymundo et a1 introduced their approach to measure the TPR baroreﬂex [Raymundo
et al, 1989], which improved upon previous efforts. The central idea of their technique
was to perturb all of the baroreceptors by changing the ventricular pacing rate and blood
volume which are both non-selective stimuli. Then, they employed the MRA approach to
distinguish the contributions of the arterial and cardiopulmonary baroreﬂex. To be
speciﬁc, these investigators developed a conscious canine model utilizing the ventricular
pacing (50-160 bpm aﬁer atrioventricular (AV) block) and blood volume perturbations
(i10%) to vary mean CVP and mean ABP independently of each other. That is, changes
in the blood volume cause mean CVP and mean ABP to vary in the same direction, while
changes in the ventricular pacing rate cause the two pressures to vary in the opposite
direction (e.g., [Barcroﬁ et al, 1944; Fisher et al, 1984; Raymundo et al, 1989]). Thus, by
combining these two perturbations, a data set was created in which ABP and CVP were
orthogonal. With this orthogonal data set, the contribution of the resulting changes in
mean CVP and mean ABP to mean TPR (as determined with an aortic ﬂow probe CO

measurement) was accurately assessed by MRA in which the two pressures were treated

as the independent variables and mean TPR was considered as the dependent variable.
The coefﬁcient associated with mean ABP (GA) indicated the steady-state TPR change
that would occur if the arterial baroreﬂex was stimulated by a unity step increase in ABP
when CVP remained constant, while the coefﬁcient associated with mean CVP (Gc)
indicated the steady-state TPR change that would occur if the cardiopulmonary
baroreﬂex was stimulated by a unity step increase in CVP when ABP remained constant.
Raymundo et a1 evaluated their technique in ﬁve animals during baseline conditions
and also under conditions of chronic arterial baroreceptor denervation and then vagal
block. Under baseline conditions, both arterial and cardiopulmonary baroreﬂex systems
contributed signiﬁcantly to TPR control. After arterial baroreceptor denervation, the
magnitude of GA was reduced essentially to zero, while the magnitude of Gc increased
nearly three-fold probably to compensate for the diminished arterial baroreﬂex.
Subsequent vagal block reduced the magnitude of Gc to zero as well (i.e., all TPR
responses were eliminated). Thus, in their conscious canine model, the sympathetic
afferent nerves contributed negligibly to TPR control. Additionally, these investigators
extended the MRA to include nonlinear terms (e.g., mean ABP*CVP as an independent
variable whose associated coefﬁcient represents the gain value of the nonlinear TPR
baroreﬂex interaction) but found no statistical evidence of nonlinear baroreﬂex effects or
interactions for each of the three experimental conditions. This particular ﬁnding
indicates that nonlinear TPR baroreﬂex behaviors may be insigniﬁcant under each
investigated condition and over the physiologic range imposed by the ventricular pacing
rate and blood volume perturbations. However, the ﬁnding does not necessarily preclude

nonlinear or more complex behaviors under a different set of physiologic conditions.

While the technique of Raymundo et al provides an effective means to quantify each
TPR baroreﬂex, it requires a sophisticated experimental preparation to change the
ventricular pacing rate and blood volume. It is very time-consuming too. Moreover,
because of its invasive nature, the technique is essentially limited to animal studies and
has not been subsequently employed for further examination of the TPR baroreﬂex.

Based on what we have discussed above, we summarize the conventional methods to
measure the TPR baroreﬂex and their limitations in Table 1.

Table 1. Conventional methods for measuring the TPR baroreﬂex

 

 

gﬁgﬁlﬁgg DISAVDANTAGE OF THE TECHNIQUE
MEASUREMENT WITH RESPECT TO THE PROPOSED
TECHNIQUE SIGNAL PROCESSING ALGORITHM
l) instrumentation needed to excite carotid sinus
baroreceptors
carotid sinus pressure/nerve 2) TPR baroreﬂex feedback loop is opened
stimulation 3) cardiopuhnonary baroreceptors may also be

stimulated

4) only GA may be determined
1) lower body negative pressure muipment needed
2) invasive CVP required
3) TPR baroreﬂex feedback loop is disturbed
4) arterial baroreceptors may also be stimulated
5) only GC may be determined
1) cannot distinguish changes in GA ﬁom changes
in GC
2) cannot determine changes in GA and GC due to
postural changes
1) ventricular pacing electrodes and atrio-
MRA ventricular block needed
[Raymundo et a1, 1989] 2) hemorrhage and volume infusions needed
3) invasive CVP required

 

lower body negative pressure
(< 20 mmHg)

 

upright tilting

 

 

 

 

 

Thus, the integrated, dynamic functioning of the TPR baroreﬂex remains to be fully

explained. To this end, a practical technique is needed to measure these dynamics during

normal, closed-loop conditions.

3. Signal Processing Algorithm

Mukkamala et a1 previously developed a Signal processing algorithm to quantify the
static gains (integral of the impulse response) of the arterial'TPR baroreﬂex (GA) and the
cardiopulmonary TPR baroreﬂex (Gc) [Mukkamala et al, 2002]. Here, we extend this
algorithm to identify the impulse response characterizing the TPR baroreﬂex by
analyzing the naturally occurring, beat-to-beat ﬂuctuations in CO, SV, and ABP, which
can be measured non-invasively in humans using, for example, Doppler ultrasound and
arterial tonometry. The algorithm thus characterizes the dynamics of the TPR barorﬂex
under normal closed-loop conditions and requires non-invasive measurements.

System identiﬁcation is one of the key concepts employed in this signal processing
algorithm. System identiﬁcation iS a useful engineering approach to build models
characterizing the unknown system from measured input and output data. Compared to
the power spectral analysis, which only characterizes the system output response, system
identiﬁcation characterizes the system itself, and thus distinguishes changes in actual
system fImctioning from changes in the system input [Ljung, 1987]. Employed in
physiologic systems, system identiﬁcation can estimate the dynamic system properties

(input-output transfer relationship) of the physiologic mechanisms.

3.1 Estimation of the Static Gains of the Arterial and

Cardiopulmonary TPR Baroreflex Systems

The block diagram in Figure 1 is based on the work of Raymundo et a1 and speciﬁes

the arterial and cardiopulmonary TPR baroreﬂex systems that we seek to characterize. AS

shown in Figure 1 and discussed in Chapter 2, the arterial TPR baroreﬂex couples ABP
ﬂuctuations to TPR ﬂuctuations, and the cardiopuhnonary TPR baroreﬂex couples
central venous transmural pressure (CVTP) (which is the difference between CVP and
intrathoracic pressure (lTP)) ﬂuctuations to TPR ﬂuctuations. (Because CVP is relatively
small, CVTP is a more appropriate index of the sensing pressure of the cardiopulmonary
baroreﬂex.) The block diagram also includes an unmeasured perturbing noise source
NTpR, which reﬂects the residual variability in TPR that is not accounted for by the
baroreﬂex mechanisms. Such variability may be due to, for example, the autoregulation
of local vascular beds and the release of endothelium-derived relaxing factors [Guyton et
al, 1996]. However, we note that NTpR may be small with respect to the total TPR
ﬂuctuations, as Raymundo et a1 observed no signiﬁcant changes in TPR despite
variations in ABP, CVP, and CO after arterial baroreceptor denervation and vagal block.
The block diagram in Figure 1 also assumes that only linear TPR baroreﬂex dynamics are
present, as Raymundo et a1 suggested that nonlinear TPR baroreﬂex behaviors may be
insigniﬁcant under the investigated condition and over the physiologic range imposed by
the ventricular pacing rate and blood volume perturbations.

In principle, one would obtain beat-to-beat measurements of ABP, CVTP, and TPR in
order to identify the impulse responses characterizing the arterial TPR baroreﬂex and
cardiopuhnonary TPR baroreﬂex and the power spectrum of NTpR based on Figure 1.
However, in practice, techniques for directly measuring beat-to-beat ﬂuctuations in TPR
are not available. Furthermore, invasive procedures are required to measure CVTP. All
these facts indicate that this direct identiﬁcation algorithm needs to be modiﬁed to be

more practical.

10

 

anenal

 

ABP ——>

 

 

 

 

TPR baroreﬂex l
CVTP cardiopulmonary I T

 

 

TPR baroreﬂex I

 

Figure 1. Block diagram deﬁning the total peripheral resistance (TPR) baroreﬂex
system to be analyzed

The measurement of CVTP is very invasive, so we make the assumption that the
ﬂuctuations in SV, which can be obtained by dividing CO by HR, are adequate surrogates
for the ﬂuctuations in CVTP. In general, changes in left ventricular (LV) SV are caused
by changes in LV preload (left atrial (transmural) pressure; LAP), LV aﬁerload (ABP),
and VC. However, Suga and Sagawa showed that spontaneous ﬂuctuations in VC are
very small at rest [Sagawa et a1, 1977]. By accordingly regarding the contribution of
resting VC changes to SV changes to be relatively small, we are now able to argue that
steady-state SV changes are determined solely by CVTP changes. The pulmonary
circulation is a low-pressure circuit with an average pulmonary artery pressure (PAP) of
normally 10-15 mmHg. Moreover, PAP is insensitive to CO and LAP over a wide range
due to recruitment and distension [Coumand, 1956]. Since the right ventricular (RV) end-
systolic elastance is about one mmHg/ml [Dell’Italia et a1, 1988], even moderate changes
in PAP (RV aﬁerload) would have only a small effect on RV SV. Thus, in steady-state,
RV SV is usually determined by only RV preload (CVTP). Since LV SV must equal RV
SV on average, steady-state SV changes are therefore determined by only CVTP changes.
Although the beat-to-beat LV SV changes are not determined by just CVTP changes, our

assumption is Speciﬁcally that the present CVTP ﬂuctuation is determined by a future LV

11

SV ﬂuctuation as well as present and past LV SV ﬂuctuations. Note that, by inversion,
this assumption may be interpreted as the present LV SV ﬂuctuation is determined by the
past CVTP ﬂuctuations. Thus, all of these CVTP ﬂuctuations may at least partly account
for LV preload and aﬁerload variability.

A straight forward method to estimate the TPR ﬂuctuations is to compute the ratio of
average ABP to average CO over intervals in which TPR changes little and net ﬂow
through the large compliant arteries is small. It is possible to choose such intervals
because the dominant time constant of the systemic arteries (~2 s [Sato et al, 1974]) is
smaller than the time constant governing changes in TPR (~ 10 s [Berger et al, 1989]).
And we take SV ﬂuctuations as the surrogate for CVTP ﬂuctuations as discussed above,
so we can directly estimate the arterial and cardiopulmonary TPR baroreﬂex through
Figure 1. However, a previous study [Mukkamala et al, 2003] has shown that this direct
estimation of TPR ﬂuctuations imposes a nonphysiological relationship between the

direct identiﬁcation inputs and the direct identiﬁcation output as follows

ATPR AABP
T—PR (t)~ 2E0 (t)-—S=——(t)-—(t) (1)

 

 

where each fractional quantity here reﬂects relative ﬂuctuations with respect to mean
values. This relationship erroneously suggests that the arterial TPR baroreﬂex and
SV—iABP step responses are unit step functions scaled by 1 and -1, respectively.

To account for the unmeasured TPR ﬂuctuations, our Signal processing algorithm
therefore employs the concept that the dynamic relationship between the ﬂuctuations in
ABP and. CO reﬂects the ﬂuctuations in TPR caused by the baroreﬂex. Suppose that the
cardiopuhnonary TPR baroreﬂex is inactive (i.e., Gc = 0) and there is a step change in

CO, as shown in the top panel of Figure 2. If the arterial TPR baroreﬂex is also inactive

12

(i.e., GA =0), then, by Ohm’s law, the steady-state fractional change in ABP would equal

the fractional change in CO (i.e., A3431) = A5? ). In contrast, if the arterial TPR

ABP CO

 

baroreﬂex is active (i.e., GA <0), then the steady-state fractional change in ABP would be

less than that of CO due to the accompanying drop in TPR (i.e. %P< % ). The

 

difference between these two situations indicates the functioning of the arterial TPR
baroreﬂex. That gives us the conceptual basis to characterize the arterial TPR baroreﬂex

by identifying the relationship between ﬂuctuations in CO and ABP.

_ ACO
co

M h:

 

 

 

 

 

 

 

 

arterial TPR arterial TPR
baroreflex inactive baroreflex active

11 ABP MBP g ACO ABP AABP ACO

ABP co ABP co

due to
bamt'lex

_ AABP _

ABP ABP MBP

t t

 

Figure 2. Diagram indicating how arterial blood pressure (ABP) would change over
time (t) in response to a step change in cardiac output (CO), if both the arterial TPR
baroreﬂex and cardiopulmonary TPR baroreﬂex were inactive (lower left panel)
and if only the arterial TPR baroreﬂex were active (lower right panel)

13

Finally, the block diagram indicating our signal processing algorithm is shown in
Figure 3 (step 1 of signal processing algoritlun), which accounts for the unmeasured TPR
and CVTP ﬂuctuations as discussed above. Here we assume that the measured
ﬂuctuations in CO, SV, and ABP are sufﬁciently small and stationary so that the
autonomic coupling mechanisms may be represented by linear time-invariant (LTI)
transfer functions. NAB]: reﬂects the residual variability in ABP ﬂuctuations that is not
accounted for by the CO and SV ﬂuctuations. We employed the system identiﬁcation
approach to estimate the impulse response of from C0 to ABP and ﬁ'om SV to ABP.
Figure 4 (step 2 of signal processing algorithm) indicates the physiologic models that
couple CO to ABP and from SV to ABP. We calculated the static gains of arterial and

cardiopulmonary TPR baroreﬂex, i.e., GA and Gc, based on these models.

 

 

 

 

 

LE)... co ABP
CO "’
AABP
N _=
ABP ABP
ASV
—_———> SV—>ABP
SV

 

 

 

Figure 3. Block diagram indicating step 1 of signal processing algorithm
The mechanism coupling CO to ABP, which is indicated by CO—iABP, includes the
dynamic properties of the arterial TPR baroreﬂex as well as the systemic arterial tree
according to Figure 4 (a). This feedback hierarchy shows that an increase in CO will
initially cause ABP to increase via the systemic arterial tree. This will excite the arterial

TPR baroreﬂex/systemic arterial tree are to decrease TPR to maintain ABP.

l4

The static gain of the arterial TPR baroreﬂex (GA) can be computed from the static
gain of CO—->ABP, because the static gain of the systemic arterial tree is identical to one
due to the normalization of all signals with their respective mean values. Also due to this
normalization, the static gains of CO——>ABP and arterial TPR baroreﬂex will be unitless.
GA indicates the steady-state percent change in TPR (with respect to its mean value) that
would occur, if the arterial TPR baroreﬂex was Simulated by an X percent step change in
ABP (with respect to its mean value) through the product of X and GA

The mechanism coupling SV to ABP, which is indicated by SV—PABP, includes the
dynamic properties of the arterial TPR baroreﬂex and cardiopulmonary TPR baroreﬂex
as well as the inverse heart-lung unit and systemic arterial tree according to Figure 4 (b).
The heart-lung unit is deﬁned to precisely couple CVTP ﬂuctuations to SV ﬂuctuations
(according to the above assumption) [Hemdon et al, 1969]. So the inverse heart-lung unit
precisely couples SV ﬂuctuations to CVTP ﬂuctuations. The feedback hierarchy in
Figure 4 (b) Shows that an increase in SV will initially cause CVTP to increase via the
inverse heart-lung unit. This CVTP increase will excite the cardiopulmonary TPR
baroreﬂex to decrease TPR. This decrease in TPR will then excite the arterial TPR
baroreﬂex/systemic arterial tree arc to increase TPR to maintain ABP.

The static gain of the cardiopuhnonary TPR baroreﬂex can be computed from the
static gains of arterial TPR baroreﬂex and SV—->ABP because the static gains of the
systemic arterial tree and inverse heart-lung unit are identical to one due to the
normalization of the signals with their respective mean values. Similarly, the static gains
of SV—>ABP and cardiopulmonary TPR baroreﬂex are also unitless due to the

normalization. Gc indicates the steady-state percentage change in TPR (with respect to its

15

mean value) that would occur, if the cardiopulmonary TPR baroreﬂex was simulated by

an X percent step change in CVTP (with respect to its mean value) through the product of

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

X and Ge,
. systemic
arterial tree
ATPR
ASP TPR> systemic
CO arterial tree
arterial ,
TPR baroreﬂex
(a)
inverse
heart-lung unit
ATPR
ACVTP TPR systemic
ASV CVTP arterial tree
S__V cardiopulmonary
TPR baroreﬂex
anenal
TPR baroreﬂex

 

 

 

 

 

 

 

(b)

AABP
»

ABP

AABP

ABP

Figure 4. Block diagrams indicating step 2 of signal processing algorithm. The two
block diagrams are physiologic models of the internal dynamics of (a) CO-—)ABP
and (b) SV—)ABP in Figure 3

16

3.2 Estimation of the Impulse Response of the Arterial

TPR Baroreﬂex

To extend this signal processing algorithm to estimate the TPR baroreﬂex impulse
response, we reconsider the physiologic model of Figure 4 (a). It implies that the impulse
response of the arterial TPR baroreﬂex can be computed through the feedback hierarchy,
if both the impulse response of CO-—)ABP and the impulse response of the systemic
arterial tree are known. The impulse response of CO—>ABP can be obtained by system
identiﬁcation as described in Section 3.1. So we extended the algorithm to estimate the

impulse response of the systemic arterial tree also from the observed beat-to-beat

ﬂuctuations in CO and ABP.

We know ﬁ'om physiology that: 1) the distributed systemic arterial tree may be
regarded as a lumped system as Shown in Figure 5, which is characterized by a single
time constant I (’C is equal to the product of TPR and AC) for the slow, beat-to-beat
ﬂuctuations considered here [Noordergraaf et al, 197 8] and 2) TPR baroreﬂex dynamics
are delayed with respect to, and slower than, systemic arterial tree dynamics [Mukkamala
et a1, 2003]. The extended algorithm therefore aims to estimate the value of 1: and then the

impulse response of the systemic arterial tree which is given by

—t
Irma) =le . u(t) (2)
T

where u(t) is the unit step function.

17

ABP

 

 

CO T == AC ' TPR

 

 

Figure 5. A ﬁrst order RC circuit to represent the systemic arterial tree at low
frequencies

Figure 6 shows the estimation of T by the least square ﬁtting of the systemic arterial
tree step response (which is the integral of the impulse response in Equation 1) to the

initial upstroke of the CO——)ABP step response in which the TPR baroreﬂex has not taken

 

 

 

 

effect (see Figure 2).
A ABP AABP
__ P(t=) (1— e )u(t)
due to
baroreﬂex
ABP due to systemic
arterial tree AABP
»

t

Figure 6. Estimation of the RC time constant of the systemic arterial tree

According to the feedback hierarchy in Figure 4 (a), the impulse response of the

arterial TPR baroreﬂex (h A TPR) can be computed from the impulse responses of

CO—->ABP (hC0—> ABP) and the systemic arterial tree (hsys ).

18

3.3 Estimation of the Impulse Response of the

Cardiopulmonary TPR Baroreflex

According to the feedback hierarchy in Figure 4 (b), the impulse response of the
cardiopulmonary TPR baroreﬂex can be calculated, if given the impulse responses of
SV—)ABP, systemic arterial tree, arterial TPR baroreﬂex, and inverse heart-lung unit.
However, we do not propose a method to estimate the impulse response of the inverse
heart-lung unit. So, the direct estimation of the cardiopulmonary TPR baroreﬂex impulse
response through Figure 4 (b) is not possible. However, we know that both arterial and
cardiopulmonary TPR baroreﬂex systems are governed by the (IL-sympathetic nervous
system. So, it might be reasonable to assume that they have the same dynamics. That is,
the impulse response of the cardiopuhnonary TPR baroreﬂex may be identical to that of
the arterial TPR baroreﬂex in shape but sealed in magnitude. Based on the static gain
values of arterial and cardiopulmonary TPR baroreﬂex (GA and Gc) and the impulse
response of arterial TPR baroreﬂex we already obtained, we could therefore calculate the

impulse response of the cardiopuhnonary TPR baroreﬂex by sealing the impulse response

of the arterial TPR baroreﬂex bygi.

A

3.4 Implementation of the Signal Processing Algorithm

The block diagram Shown in Figure 3 can be mathematically represented by an

autoregression moving average (ARMA) equation as follows

19

AABP m

—A—BY)—(t)= (Ea-AA -=BP—(t—i)+ 2b,? ——00-(t"i)+ 20 _(t_i)+WABP(t)
(3)

ACO ASV and AABP
C_O ’ S—v E

 

in Equation 3 represent the measured beat-to-beat

ﬂuctuations in these signals. The three sets of unknown parameters {a,-, b,-, c,-} deﬁne the

impulse responses of CO—->ABP and SV—vABP. The terms m, n, p limit the number of
parameters (model order), and WABP is the unmeasured residual error. This residual

error together with the set of parameters {a,-} fully deﬁnes the power spectrum of NABp.

Because the original signals we have are the continuous recordings of ABP, CO and
SV. So we ﬁrst averaged these Signals by replacing their values for current cardiac cycles
by the average values of the three previous and three subsequent cardiac cycles. We then
resampled the averaged Signals at 0.5 Hz with an anti-aliasing ﬁlter whose impulse
response is unit-area boxcar of four seconds’ duration. Finally, we subtracted the means
ﬁ'om these Signals and divided them by the means to obtain the deviations of the Signals
from their mean values. Through the above steps, we normalized the Signals by their
mean values and obtained the ﬂuctuations of these signals, which are used as the inputs
and outputs of Equation 3.

Starting from using a maximal model order 3 (i.e., m=n =p=3) and employing a
previously developed system identiﬁcation algorithm [Perrott et a1, 1996] which
intelligently reduces the model order, we estimate the three sets of parameters {ab bi, Cf}.

Then, according to the physiologic models in Figure 4, the static gains of the arterial
and cardiopulmonary TPR baroreﬂex, i.e., GA and Gc, are computed from the parameter

sets {a,, b,-, c,-} as follows

20

GA :[Zbi +Zai —1)/Zbi (4)
i=0 i=1

i=0

CC = EC.- Zb.~ . (5)
i=0 '=

In principle, this algorithm will be effective provided that spontaneous HR variability
is present. If HR variability is deemed to be insigniﬁcant with respect to CO variability
(e.g., <5%), then only the CO—)ABP impulse response may be reliably identiﬁed (via a
single-input ARMA equation). However, in this case, the model of this physiologic

system becomes the sum of the block diagrams in Figure 4 with a static gain (GL) given

 

as follows
1+

GL = GC . (6)
1 — G A

Thus, when HR variability is virtually absent, the algorithm estimates GL and
therefore cannot distinguish between the functioning of the arterial TPR baroreﬂex and
cardiopulmonary TPR baroreﬂex. However, note that GL provides a quantitative measure
of the lumped functioning of the two TPR baroreﬂex mechanisms.

By transferring all the impulse responses to the z-domain, we obtain the z—transform of

the impulse response of the arterial TPR baroreﬂex , denoted as H A TPR (z) , as follows

H - H
HA TPR (z) = C0—->ABP (Z) sys (Z) (7)
HC0—)ABP (Z)Hsys (2)

where H ATPR(Z) , HC0—4ABP(Z) and H ”3(2) are the z-transform of h ATPR ,

 

hCO _, A 3p and hsys , respectively.

21

Due to noise, we noticed that some zeros of the estimated H CO _, ABP (z) reside
outside of the unit circle. These zeros will cause system instability in H ATPR (z)

[Oppenheim et al, 1997] because all the zeros of H CO _, A 3,; (2) becomes the poles of
H ATPR (2) according to Equation 7.

To solve this instability problem, we tracked these zeros outside of the unit circle in

H CO _, A 3p (2) and found that they were corresponding to the high frequency

components in CO—)ABP impulse response. So we employed a low pass ﬁlter to remove
these high frequency components and thus remove all the zeros outside of the unit circle
to make the system invertible. The cut-off frequency of this low pass ﬁlter is chosen to be
0.1 Hz [Berger et a1, 1989]. We employed this low pass ﬁlter on the CO——>ABP impulse
response obtained from the system identiﬁcation, and then compensated the phase delay
caused by this ﬁlter to realize a zero-phase ﬁltering.

To obtain the impulse response of the systemic arterial tree, I we integrated the
estimated impulse response of CO—>ABP before the low pass ﬁltering to obtain the step
response of CO—)ABP (solid line in Figure 6). According to the analysis in Section 3.2,
the initial upstroke of the ﬁrst three seconds in this step response is only governed by the
systemic arterial tree since the slower TPR baroreﬂex has not taken effect yet. This initial
upstroke corresponds to the ﬁrst two samples in the step response of CO—->ABP since our
sampling frequency is 0.5 Hz. We ﬁt the systemic arterial tree step response to these two
samples through the minimum mean square error (MMSE) method to ﬁnd the best
estimation of the time constant I . Then the impulse response of the systemic arterial tree

is generated through Equation 1.

22

We also low pass ﬁltered the impulse response of the systemic arterial tree through

the same zero phase ﬁlter employed on the impulse response of CO—>ABP.

Finally, the impulse response of the arterial TPR baroreﬂex (hATPR) is calculated
according to Equation 7 and we also low pass ﬁltered h A TPR by the same zero phase
ﬁlter employed before.

By employing the same ﬁlter on hCO _) A BP’ hsys and h ATPRa we cancel the effects
of these low pass ﬁlters ideally at the end and make Equation 7 hold exactly. To be

speciﬁc, suppose the z-transform of this low pass ﬁlter is G(z), then H CO _, A BP (2)

becomes H CO _, ABP(Z)G(Z) and H m (2) becomes H sys (Z)G(z) aﬁer ﬁltering.
Substitute H CO _, ABP(z) by H CO _, ABP(z)G(z) and H WS (2) by H W (z)G(z) in

Equation 7 and the output H . ATPR (2) becomes

HC0—)ABP (2)0(2) — Hsys (2)6(2) __ HC0—)ABP (Z) — Hsys (Z)

(HC04A3P(Z)G(Z))(Hsys (z)G(z» "' HC0—>ABP(Z)Hsys (Z>G<z>
(8)

 

 

H'ATPR (2):

As described before, we also employed the same low pass ﬁlter on H ' ATPR (z) . So

the output of this ﬁlter, which is the z-transform of our estimated h A TPR , becomes

. H — H
H ATPR (Z)=H ATPR(Z)G(Z)= COT/WC?) ”3(2) (9)

HC0—)ABP (Z)Hsys (Z)

 

which is exactly the same as the one without low pass ﬁltering. So we canceled the

impact of the low pass ﬁlter and exactly followed the algorithm that we developed above.

23

4. Experiments and Results

4.1 Simulated Data

4.1.1 Data Generation Objective

We generated Six-minute intervals of simulated data with beat-to-beat variability from
a previously developed computational simulator of human cardiovascular system
[Mukkamala et al, 2003]. We applied our signal processing algorithm to these data to
estimate the static gains of the arterial and cardiopulmonary TPR baroreﬂex, the impulse
response of the arterial TPR baroreﬂex, and the time constant of the systemic arterial tree.
Independently, we applied an arbitrary narrow unit-area input to the appropriate point in
the cardiovascular simulator to establish the gold standard impulse responses of the
arterial and cardiopulmonary TPR baroreﬂex.

The block diagram shown in Figure 7 illustrates the major components of this
cardiovascular Simulator. It includes three major components: a pulsatile heart and
circulation, a short-term regulatory system, and resting physiological perturbations. The
circulatory system consists of contracting left and right ventricles, systemic arteries and
veins, and puhnonary arteries and veins. The systemic arteries are speciﬁcally modeled
as a third-order system accounting for viscous, compliant, and inertial effects. The
regulatory system comprises arterial and cardiopulmonary baroreﬂex control of HR,
TPR, systemic venous unstressed volume (SVUV), and VC as well as a direct neural
coupling between respiration and HR. Each baroreﬂex effector system is speciﬁcally

modeled as a static non-linearity to account for saturation followed by linear dynamics.

24

The resting perturbations include respiratory activity, stochastic disturbances to TPR and

SV UV, and l/f HR ﬂuctuations.

      
  
   

BAROREF LEX
SATU RATION

  
  
 

ASP
I3max

Pa P39

 

  
  
   

Pth

   
 
      

AIRWAYS AND F
LUNGS [a P Sp

Palv " ra

 
      
   
  

(I
QV SYSTEM 5
PU LM
CIRCULATIONS

     
    
   
 

Ra

BAROREFLEX

CARDIOPULMONARY

BAROREFLEX

Figure 7. Block diagram summarizing a previously developed human
cardiovascular simulator [Mukkamala et al, 2003]

As shown in Figure 8, the simulated ABP waveform resembles human radial ABP
waveform, which demonstrates the cardiovascular simulator can generate realistic signal
waveforms. Figure 9 illustrates that the power spectrum of HR from the simulated data
resembles that of the human data, which demonstrates the cardiovascular simulator can

generate realistic beat-to-beat variability of Signals.

25

120’ Simulated ABP

[mmHg]

 

 

0 K 7 115 it
Time [sec]

 

 

120‘ Human radial ABP
110
100

E

E 90’

E 80
70
60»

2.5 “”1 ofs i {5 é 25'
Time [sec]

Figure 8. Simulated and human radial ABP waveforms

    

 

-— Human (average)
— Human (95% conﬁdence intervals)

' ' ' Model

0:4 0.5

oz 0.3
Frequency [Hz]

Figure 9. Power spectra of heart rate (HR) from the simulated and human

experimental data

Our speciﬁc goal was to determine if the technique can accurately estimate, and

detect changes in the impulse response of the arterial TPR baroreﬂex, the static gain

26

value of the cardiopulmonary TPR baroreﬂex, Gc, and the dominant time constant 1 of
the systemic arterial tree. In order to achieve this goal, we conducted a series of
simulations under different sets of parameter values. For each set of parameter values,
we repeated the simulation 50 times to determine the mean and 95% conﬁdence intervals
of the estimates. To evaluate the estimates, we established the corresponding actual I
value by taking the product of the total AC and the mean TPR and the actual arterial and
cardiopulmonary TPR baroreﬂex impulse responses by isolating these systems from the
simulator, applying an impulse input to each system, and measuring the TPR response.

The areas of these impulse responses were then computed so as to establish the actual GA

and Gc values.

4.1.2 Results

Figure 10 illustrates the actual and estimated arterial TPR baroreﬂex impulse
responses for different simulator GA values. Table 2 shows the actual and estimated Gc
for different simulator Gc values as well as the actual and estimated T for different
simulator total AC values.

These results show that the technique is able to accurately estimate, and detect
changes in, the arterial TPR baroreﬂex impulse response and 1'. Because SV ﬂuctuations
do not perfectly represent CVTP ﬂuctuations, the results also indicate that the technique

has consistently underestimated GC. However, the algorithm is able to detect changes in

the simulator Gc value.

27

-0.1

0.02 -
l

-0.02

-0.04

 

-0.06 ~

 

 

25 50

 

 

—1—J '0.1 _J——J _0_1 ____*l

25 50 25 50

Time [sec]

Figure 10. Actual (solid) and estimated (mean (dash) i 95% conﬁdence intervals
(dash-dot» arterial TPR baroreflex impulse responses

Table 2. Actual and estimated (meani95% conﬁdence intervals) GC and r values

 

 

 

 

 

 

Gc [unitless] 1 [sec]
ACTUAL ESTIMATE ACTUAL ESTIMATE
-O.37 -0.15:t0.02 1.06 1.13-J:0.02
-0.55 -0.29i0.02 1.56 1.64i0.03
-0.74 -0.50i0.03 2.08 2.19i0.05

 

 

 

 

 

28

4.2 Experimental Data

4.2.1 Experimental methods

We analyzed the experimental data from seven conscious dogs before and after
chronic arterial baroreceptor denervation. We applied our signal processing algorithm to
these data to speciﬁcally identify the arterial and cardiopuhnonary TPR baroreﬂex gain
values.

Researchers at the Wayne State University School of Medicine collected the
hemodynamic data utilized in our evaluation, and the materials and methods were
described in detail in a very recently published study [Kim et al, 2005]. We described
here the most basic aspects of the experimentation that were relevant to our evaluation.
Seven conscious dogs (20-25 kg) of either gender were studied according to the
following protocol. Chronic instrumentation was installed in each dog to measure central
ABP, CO, HR, and other hemodynamic variables. After recovery from the surgery, the
beat-to-beat hemodynamic data were recorded for about ten minutes while the dog was
standing quietly. Then, surgical denervation of the carotid sinus and aortic arch receptors
was performed. The completion of the baroreceptor denervation was conﬁrmed by
observing the lack of any HR response to an intravenous bolus infusion of phenylephrine,
which increased ABP by ~40 mmHg. Finally, approximately two weeks after the
completion of the baroreceptor denervation, the beat-to-beat hemodynamic data were
again recorded for about ten minutes while the dogs were standing quietly.

We choose the segments shown in Table 3 of the experimental data of each dog
visually to include as much “clean data” as possible before and after chronic arterial

baroreceptor denervation. “End” indicates the end of the individual data set.

29

Table 3. Segments chosen to analyze in conscious dog data

 

 

 

 

 

 

 

 

 

3:22.253“ Cm.
BO 70:end 50:end
CHI 61 :274 1:170
CR 70:end 1:410
HAS lzend 40:end
LU 852end 300:end
MO 601end lzend
ROK 602280 lzend

 

 

 

 

 

4.2.2 Results

Table 4 illustrates that the group mean hemodynamic values did not change in
response to chronic arterial baroreceptor denervation. The “blindness” of the mean
hemodynamic values to baroreﬂex functioning is consistent with the notion that the
baroreﬂex is not important in long-term blood pressure regulation. The standard deviation
of ABP signiﬁcantly increased from 2.9 mmHg to 10.2 mmHg after the chronic arterial
baroreceptor denervation. The power spectra in Figure 11 show that the ﬂuctuations of
the hemodynamic variables about their mean values were altered by chronic arterial
baroreceptor denervation, especially the ﬂuctuations in ABP increased signiﬁcantly. This
is because the chronic arterial baroreceptor denervation reduced the ability to maintain
blood pressure. However, it is still impossible to “see” the effects of the denervation

speciﬁcally on TPR baroreﬂex functioning.

3O

Table 4. Group average hemodynamic values (meani95% confidence intervals) of
conscious canine data

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

HEMO— CHRONIC ARTERIAL BARORECEPTOR
DENERVATION
DYNAMIC BEFORE AFTER
VARIABILITY
MEAN STDEV MEAN STDEV
ABP
[MMHG] 105.9i12.3 2.93.0.7 11721140 10.2:1:4.5
CO
[ML/S] 80.6i9.9 6.2:t3.0 79.7i13.5 5.3:t1.8
sv
[ML] 46.1i6.0 2,412.9 37.7i4.9 2.0:t0.6
HR
[BPS] 1.8:t0.2 0.2:l:0.1 2.11:0.3 0.11.0.1
chronic arterial baroreceptor denervation
E- 1500 . before 1500 _ after
%’ 1000» 1000
E. 5001 500 .
E _
< 0o 0.1 0.2 0o _ 0.1 0.2
£ 1500 . 1500
if 1000 1000
3
E 500 km 500
5' _
0 0o o 1 0.2 00 0.1 0.2
if 40 40
N-l
E 201 20 »
U)
0 \...\ O
0 0.1 0.2 o 0.1 0.2
Frequency [Hz] Frequency [Hz]

Figure 11. Sample power spectra before and after chronic arterial baroreceptor
denervation from a single dog

31

 

Figure 12 illustrates the group average estimates of GA and Gc (meanistdev) before
and after chronic arterial baroreceptor denervation by employing our algorithm on these
canine data. It indicates that our algorithm predicted that chronic arterial baroreceptor
denervation caused the magnitude of GA to reduce to nearly zero (i.e., arterial TPR
baroreﬂex functioning was lost) and the magnitude of GC to more than double (i.e.,
cardiopulmonary TPR baroreﬂex functioning was enhanced) to compensate. Both
changes were statistically signiﬁcant. These results are consistent with the very invasive
MRA method for quantifying the TPR baroreﬂex gain values [Raymundo et a1, 1989].
The estimated GA and GC values in Figure 12 are, on average, roughly 2-3 times as large
as the values reported by Raymundo et a1. These differences may be due to different

postures and signal normalization schemes as well as inter-subj ect variability.

 

 

 

 

 

 

 

 

 

 

 

 

 

_ arterial TPR baroreﬂex 0 5_cardiopulmonary TPR baroreﬂex
o __ i_, 0..
-0 5 —0.5
'5' '5'
(I)
g _1 . g _1 .
.5. s
0< -1.5~ (Do-1.5-
-2 . .__, -2. I
-2.5 ~ -2 5
p=0.015 q p=0.048
- before after before after

chronic arterial baroreceptor denervation

Figure 12. Group average arterial and cardiopulmonary TPR baroreﬂex gain values
before and after chronic arterial baroreceptor denervation in seven conscious dogs

32

5. Conclusions and Future Work

5.1 Conclusions

In this thesis, we discussed the theoretical fundamental and the implementation of a
signal processing algorithm, which can be employed on the continuous measurements of
CO, ABP and SV to identify the dynamic ﬁmctioning of the TPR baroreﬂex. It is a
noninvasive technology and keeps the normal, closed-loop conditions of the TPR
baroreﬂex systems. We also covered the evaluation of this algorithm by both simulated
data generated from a cardiovascular simulator and experimental data collected from
seven conscious dogs.

The main contributions of this research are as follows:

1) It developed a signal processing algorithm to estimate the impulse response of the

arterial TPR baroreﬂex from the continuous measurements of CO, ABP, and SV.

2) It validated the signal processing algorithm by simulated data and experimental

data.

5.2 Future Work

The impulse response of the TPR baroreﬂex of the conscious dogs remains
undetermined in this thesis. And we do not have the corresponding gold standard
dynamics against which we can compare our results with.

In the future, we will study the conscious dogs to compare the TPR gain values
determined by our algorithm with the ones obtained by applying MRA to ABP, CO and

CVTP measured during a set of adjustments to the ventricular pacing rate and blood

33

volume [Raymundo et al, 1989]. We will also evaluate the ability of our algorithm in
determining the subtle changes in TPR baroreﬂex functioning. Those changes, which
may be excited by the usage of medicine, will be a practical test conditions for our
algorithm.

With further successful experimental testing, the technique presented in this thesis
may ultimately be employed to advance the basic understanding of the TPR baroreﬂex in

both humans and animals in health and disease.

34

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