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Assessing
pressure
wave
components
for
aortic
stiffness
monitoring
through
spectral
regression
learning
Arian
Aghilinejad
* and Morteza
Gharib
Division
of
Engineering
and
Applied
Science,
California
Institute
of
Technology,
1200
E
California
Blvd,
Pasadena,
CA
91125,
USA
Received
22
February
2024;
revised
2
May
2024;
accepted
10
May
2024;
online
publish-ahead-of-print
21
May
2024
Handling
Editor:
Thomas
Kahan
Aims
The
ageing
process
notably
induces
structural
changes
in
the
arterial
system,
primarily
manifesting
as
increased
aortic
stiff
-
ness,
a precursor
to
cardiovascular
events.
While
wave
separation
analysis
is a robust
tool
for
decomposing
the
components
of
blood
pressure
waveform,
its
relationship
with
cardiovascular
events,
such
as
aortic
stiffening,
is incompletely
understood.
Furthermore,
its
applicability
has
been
limited
due
to
the
need
for
concurrent
measurements
of
pressure
and
flow.
Our
aim
in
this
study
addresses
this
gap
by
introducing
a spectral
regression
learning
method
for
pressure-only
wave
separation
analysis.
Methods
and results
Leveraging
data
from
the
Framingham
Heart
Study
(2640
individuals,
55%
women),
we
evaluate
the
accuracy
of
pressure-
only
estimates,
their
interchangeability
with
a
reference
method
based
on
ultrasound-derived
flow
waves,
and
their
association
with
carotid-femoral
pulse
wave
velocity
(PWV).
Method-derived
estimates
are
strongly
correlated
with
the
reference
ones
for
forward
wave
amplitude
(
R
2
=
0
.
91),
backward
wave
amplitude
(
R
2
=
0
.
88),
and
reflection
index
(
R
2
=
0
.
87)
and
moderately
correlated
with
a time
delay
between
forward
and
backward
waves
(
R
2
=
0
.
38).
The
proposed
pressure-only
method
shows
interchangeability
with
the
reference
method
through
covariate
analysis.
Adjusting
for
age,
sex,
body
size,
mean
blood
pressure,
and
heart
rate,
the
results
suggest
that
both
pressure-only
and
pressure-flow
evalua
-
tions
of
wave
separation
parameters
yield
similar
model
performances
for
predicting
carotid-femoral
PWV,
with
forward
wave
amplitude
being
the
only
significant
factor
(
P
<
0.001;
95%
confidence
interval,
0.056–0.097).
Conclusion
We
propose
an
interchangeable
pressure-only
wave
separation
analysis
method
and
demonstrate
its
clinical
applicability
in
capturing
aortic
stiffening.
The
proposed
method
provides
a valuable
non-invasive
tool
for
assessing
cardiovascular
health.
* Corresponding
author.
Tel:
+1
626
395
4450,
Email:
aghili@caltech.edu
©
The
Author(s)
2024.
Published
by
Oxford
University
Press
on
behalf
of
the
European
Society
of
Cardiology.
This
is
an
Open
Access
article
distributed
under
the
terms
of
the
Creative
Commons
Attribution
License
(
https://creativecommons.org/licenses/by/4.0/
), which
permits
unrestricted
reuse,
distribution,
and
reproduction
in
any
medium,
provided
the
original
work
is
properly
cited.
European
Heart
Journal
Open
(2024)
4
,
oeae040
https://doi.org/10.1093/ehjopen/oeae040
ORIGINAL
ARTICLE
Hypertension
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Graphical
Abstract
Keywords
Blood
pressure
•
Haemodynamics
•
Aortic
stiffening
•
Pulse
wave
analysis
Introduction
Aortic
stiffness
increases
with
age
and
is
one
of
the
earliest
pathological
changes
within
the
arterial
wall,
affecting
the
wave
dynamics
in
the
vasculature.
1–8
Nevertheless,
there
remains
considerable
ambiguity
re
-
garding
the
contributions
of
various
components
of
blood
pressure
waveform
and
wave
reflection
to
aortic
stiffness.
In
classical
pressure
wave
analysis,
wave
reflection
is
frequently
assessed
through
the
augmentation
index
(AIx).
9
The
clinical
significance
of
AIx
has
been
highlighted
in
recent
work
by
Yofoglu
et
al
.,
10
demonstrating
its
corre
-
lations
with
left
ventricle
mass.
However,
a limitation
of
AIx
lies
in
its
dependency
not
solely
on
the
magnitude
but
also
on
the
timing
of
wave
reflection.
9
,
11
This
timing
is
influenced
by
a
range
of
physical
and
physiological
factors,
including
subjects’
height
and
heart
rate.
11
,
12
To
provide
a
more
comprehensive
evaluation
of
wave
reflection,
wave
separation
analysis
has
been
employed.
13
This
method
decom
-
poses
the
pressure
pulse
into
a
forward
pressure
wave,
travelling
from
the
heart
to
the
periphery,
and
a reflected
pressure
wave,
travel
-
ling
backward
towards
the
heart.
14
,
15
Zamani
et
al
.
16
,
17
highlighted
the
clinical
significance
of
wave
separation
analysis
by
showing
its
ability
to
correlate
with
all-cause
mortality
in
individuals
initially
free
of
clinically
evident
cardiovascular
disease.
In
the
Framingham
Heart
Study
(FHS),
Cooper
et
al
.
18
associated
forward
pressure
wave
amplitude
with
inci
-
dent
cardiovascular
disease,
whereas
mean
arterial
pressure
and
global
wave
reflection
did
not
show
similar
associations.
Despite
the
compelling
evidence
supporting
the
importance
of
wave
separation
analysis,
its
full
integration
into
clinical
practice
is hindered
by
the
requirement
for
simultaneous
measurements
of
pressure
and
flow
waveforms.
Although
approximate
approaches
based
on
triangular
flow
profiles
or
Windkessel-based
methods
enable
wave
separation
analysis
using
only
pressure
measurements,
implementing
these
proto
-
cols
in
clinical
settings
is
challenging,
and
their
applicability
has
faced
dif
-
ficulties
in
large
heterogeneous
populations.
12
,
19–22
Notably,
the
study
by
Kips
et
al
.
23
in
the
Asklepios
population
suggested
substantial
differ
-
ences
in
results
between
pressure-based
approximative
methods
and
those
using
both
pressure
and
flow
information.
In
this
study,
utilizing
data
from
the
population-based
FHS,
our
objec
-
tives
are
to:
(i)
evaluate
the
accuracy
of
pressure-only
estimates
for
wave
separation
parameters
through
the
application
of
the
proposed
spectral
regression
learning
method,
(ii)
conduct
a
covariate
analysis
to
investigate
the
interchangeability
between
the
proposed
pressure-
only
method
and
the
reference
method,
and
(iii)
investigate
the
associ
-
ation
between
wave
separation
parameters
(using
the
reference
as
well
as
the
proposed
pressure-only
method)
and
aortic
stiffness,
as
mea
-
sured
by
carotid-femoral
pulse
wave
velocity
(PWV).
The
selection
of
carotid-femoral
PWV
as
a validation
metric
is
based
on
its
crucial
role
in
governing
wave
dynamics
within
the
cardiovascular
system,
along
with
its
well-established
pathophysiological
association
with
the
early
arrival
of
pressure
wave
reflections.
24–28
Methods
Participants
and data
In
this
investigation,
we
employed
data
from
the
FHS,
a population-based
epidemiological
cohort
analysis.
Details
are
provided
in
the
previous
works.
15
,
18
,
28–30
The
sample
was
drawn
from
the
eight-examination
cycle
of
an
offspring
cohort.
The
characteristics
of
the
participants,
including
a
2
A.
Aghilinejad
and
M.
Gharib
heterogeneous cohort of
n
=
2640 individuals (comprising 1201 males and
1439 females, aged between 40 and 91 years), are presented in
Table 1
. All
participants provided written informed consent, and the study protocols
received approval from the Boston University Medical Campus and
Boston Medical Center Institutional Review Board. Initially, the clinical
data set is split into the training and testing data for all regression learning
analyses. The models are strictly trained on the training population, and
the testing data set is used only once to evaluate the accuracy of the model.
The characteristics of these two data sets are also presented in
Table 1
. All
participants underwent a thorough and non-invasive evaluation of central
haemodynamics, resulting in a comprehensive collection of tonometry re
-
cordings for carotid pressure waveforms. Aortic flow waveforms were ac
-
quired through two-dimensional echocardiography of the left ventricular
outflow tract, followed by pulsed Doppler from an apical five-chamber
view to acquire the aortic flow waveform. Additionally, tonometry data
were digitized at a rate of 1000 Hz during the primary acquisition process,
and the waveforms were signal-averaged using the electrocardiogram
R-wave as a fiducial point. Calibrated carotid pressure served as a surrogate
for central pressure. Carotid-femoral PWV was used as a metric for aortic
stiffness, as previously described.
15,18,31
Wave separation analysis
Wave separation analysis, which facilitates the breakdown of arterial pres
-
sure waves into forward and backward wave components, has been previ
-
ously outlined.
32
This approach involves quantifying information about
forward and backward waves through principles of fluid dynamics in com
-
pliant tubes.
12,33–36
Flow and pressure data were utilized to compute for
-
ward and backward pressure waveforms using the linear wave separation
technique, initially described by Westerhof
et al
.,
32
and details are provided
in the
Supplementary Material
. The input impedance of the artery is calcu
-
lated using Fourier analysis as the ratio of
P
(
t
) and
Q
(
t
) harmonics in the fre
-
quency domain.
15
To evaluate the time delay (TD) between forward
pressure wave amplitude (Pf) and backward pressure wave amplitude
(Pb), the method introduced by Qasem and Avolio
22
is used.
Wave separation analysis via spectral
regression learning
A pressure-only estimation of wave separation can be achieved through the
hybrid spectral regression learning methodology introduced by Aghilinejad
et al
.,
37
and further details are provided in the
Supplementary Material
. In
this approach, Fourier series (spectral) decomposition is employed for in
-
put feature selection. Initially, the carotid pressure waveforms from tono
-
metry measurements are sampled at a rate of 1000 Hz, resulting in 1000
data points per single pressure measurement in a cycle size of 1 s. The
high dimensionality of the input signal poses limitations on naive regression
model constructs for practical applications. To address this, in our study, we
utilized Fourier-based spectral analysis, specifically employing the Fast
Fourier Transform (FFT), to transform data from a high-dimensional space
to a low-dimensional one. This approach preserves meaningful properties
of the original data, while reducing input dimensionality. The advantage of
using FFT-based input reduction lies in the fact that high-frequency compo
-
nents do not provide significant additional physiological information for
computing the wave separation parameters.
13
The regression model is subsequently trained on features derived from
the Fourier decomposition of the pressure waveform. These models are
trained with the Fourier modes of the central pressure waveforms as input
and the Fourier modes of the central flow waveforms as output. Following
training, the testing data set is utilized once to assess the accuracy of the
model. The carotid waveform in the testing data set undergoes spectral
mode decomposition and is then input to the regression model. The output
of the regression models, representing the estimated modes of the corre
-
sponding central flow waveform, is inverse-Fourier-transformed to the
time domain using the computed modes and the length of the signal. As
demonstrated in previous studies, there is no need to calibrate the flow
profile.
21
The estimated flow waveform from the regression model is
then used to conduct the wave separation analysis. The steps for the model
implementation are presented in
Figure 1
. In addition to the proposed wave
separation analysis of this study, we also conducted pressure-only wave
separation based on the generic triangular flow profile approximation
20,21
for comparison in this study.
Statistical analysis
Table 1
illustrates the baseline characteristics of the study sample, with con
-
tinuous variables from the sample data summarized as mean
±
standard de
-
viation (SD). Key parameters, including Pf, Pb, reflection index (RI), and TD
between forward and backward pressure waves, were selected to assess
the efficacy of the proposed pressure-only wave separation analysis. The
reference values for wave separation in all cases were determined using
central flow measurements in conjunction with carotid pressure measure
-
ments, serving as a surrogate for central pressure. To evaluate the accuracy
of the proposed method, we compared the estimated values with those ob
-
tained through an exact wave separation analysis using Pearson correlation
coefficients (
r
), the coefficient of determination, and root mean square er
-
rors. The agreement and bias between the exact wave separation variables
and the estimated ones were further examined using a Bland–Altman ana
-
lysis, presenting mean differences along with limits of agreement (mean bias
±
1.96 SD of the differences). Multivariate regression was used to explore
the influence of clinical covariates on each wave separation variable as well
as aortic stiffness (quantified by carotid-femoral PWV). The proportion of
variability in the dependent variable explained by the model was presented
as
R
2
. Additionally, regression coefficients (beta coefficients) were reported
along with their 95% confidence intervals. Continuous variables were com
-
pared between the groups using the Kruskal–Wallis rank-sum test.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 1
Baseline characteristics of total patient data (
n
=
2640), the training subpopulation (
n
=
1848), and the testing
subpopulation (
n
=
792)
Variable
Total (
n
=
2640)
Training (
n
=
1848)
Test (
n
=
792)
Age, years
66
±
9
66
±
9
66
±
9
Women,
n
(%)
1439 (55)
1000 (54)
439 (55)
Height, cm
167
±
10
167
±
10
167
±
9
Weight, kg
78
±
17
79
±
18
78
±
17
Body mass index, kg/m
2
27.9
±
5.1
27.9
±
5.1
27.9
±
5.1
Heart rate, b.p.m.
62
±
10
62
±
10
62
±
10
Brachial blood pressure, mmHg
Systolic
141
±
20
140
±
20
141
±
20
Diastolic
69
±
9
69
±
9
69
±
9
Pulse
72
±
19
71
±
19
72
±
18
All values are (mean
±
standard deviation) except as noted.
Regression learning and aortic stiffening
3
Statistical significance was defined as
P
<
0.001. All mathematical and statis
-
tical analyses of the clinical data were performed using custom-written
codes implemented in Python (Python Software Foundation, Python
Language Reference, version 3.11).
Results
Accuracy of wave separation parameters
Table 2
presents correlations and errors between pressure-only esti
-
mates of wave separation parameters and reference values, as well as
measures of RI (an indicator of the relative significance of backward
pressure wave amplitude) and TD (an indicator of the time lag between
the forward and the backward wave components of the pressure wave
-
form). These results are demonstrated within the testing subset of the
initial population. From the initial testing population of 792 individuals,
39 patients were excluded due to the failure in PWV measurement, re
-
sulting in 753 subjects in
Table 2
. The last column presents estimates
derived based on flow estimation from the spectral regression learning
proposed in this study. The accuracy of the uncalibrated estimated flow
profiles, used to conduct pressure-only wave separation through spec
-
tral regression learning, is presented in
Supplementary material online,
Table S1
.
Figure 2
illustrates six sample cases from the blind testing set,
where the uncalibrated flow profile is estimated using spectral regres
-
sion learning and overlaid on the measured flow profile.
Supplementary
material online,
Figure S1
demonstrates scatter and Bland–Altman plots
indicating the agreement between the measured and the estimated un
-
calibrated averages of the mean flow profile, revealing the method’s
ability to capture the shape of the flow profile. In
Table 1
, the estimated
pressure-only wave separation parameters using conventional triangu
-
lar flow estimation are also provided for comparison. In
Supplementary
material online,
Table S2
, average values for all wave separation para
-
meters in different age groups based on pressure and flow measure
-
ments are tabulated for reference.
Figure 3
illustrates scatter and Bland–Altman plots indicating agree
-
ment in forward and backward pressure wave amplitudes between
measured (using pressure and flow) and estimated (using pressure-only
spectral regression learning) values. The coefficient of determination is
also presented for all the wave separation parameters in these plots.
The distributions of the residuals between reference and estimated
variables with respect to age are also presented in
Supplementary
material online,
Figure S2
.
Analysis of covariates for wave separation
parameters
Table 3
presents a regression analysis of covariates for measured
(reference) and estimated forward and backward pressure wave ampli
-
tudes. Values for backward pressure wave amplitude (Pb) are inde
-
pendently
related to age, height, heart rate, and mean blood pressure
(
R
2
=
0.904).
Weight and sex do not contribute significantly (
P
>
0.001). The estimated pressure-only models for backward pressure
wave amplitude using spectral regression learning show similar results
to the measured values (
R
2
=
0.873), except in terms of the signifi
-
cance level for height. An analysis of covariates for forward pressure
Figure 1
A description of the proposed spectral regression learning approach for a pressure-only wave separation analysis. The process starts with a
non-invasive pressure waveform measurement, followed by a Fourier-based decomposition of the waveform. The wave components of the flow profile
are then estimated by regression learning and then composed to reconstruct the uncalibrated flow profile. The estimated flow waveform, along with
the measured pressure waveform, will be used to conduct a wave separation analysis.
4
A. Aghilinejad and M. Gharib
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table
2
Mean
values,
errors,
and correlations
between
pressure-only
estimates
of wave
separation
parameters
and
reference
values
(
n
=
753)
Variables
Reference
(pressure
and flow)
Triangular
flow estimation
Pressure-only
estimation
of this study
Pb
(mmHg)
56
(8.2)
67
(10.4)
56
(8.3)
NRMSE
(Pb
exact
−
Pb
est
) (%)
—
21.6
5.4
r
(Pb
exact
vs.
Pb
est
)
—
0.94
0.94
Pf
(mmHg)
92
(16.6)
91
(18.8)
93
(14.3)
NRMSE
(Pf
exact
−
Pf
est
) (%)
—
7.5
4.8
r
(Pf
exact
vs.
Pf
est
)
—
0.91
0.96
RI
0.38
(0.03)
0.43
(0.04)
0.38
(0.02)
NRMSE
(RI
exact
−
RI
est
) (%)
—
25.5
5.4
r
(RI
exact
vs.
RI
est
)
—
0.74
0.93
TD
(ms)
64
(19)
63
(28)
64
(18)
NRMSE
(TD
exact
−
TD
est
) (%)
—
30.5
15.9
r
(TD
exact
vs.
TD
est
)
—
NC
0.62
NRMSE
indicates
the
normalized
root
mean
square
errors
by
the
range
of
the
variable.
The
values
given
in
the
parentheses
denote
standard
deviation.
NC
indicates
not
correlated
(
r
<
0.2).
Figure
2
Typical
sample
cases
of
the
estimated
and
measured
central
flow
waveform
profile.
The
blue
waveform
(dashed
line)
demonstrates
the
measured
flow
profile
using
ultrasound
and
the
red
one
(solid
line)
demonstrates
the
estimated
one
using
the
spectral
regression
learning
method.
Regression
learning
and
aortic
stiffening
5
Figure
3
Scatter
and
Bland–Altman
plots
for
wave
separation
parameters.
The
parameters
are
forward
pressure
wave
amplitude
(Pf),
backward
pressure
wave
amplitude
(Pb),
reflection
index
(RI),
and
time
delay
(TD)
between
forward
and
backward
pressure
wave
amplitudes.
The
plots
are
demonstrated
for
the
test
data
(
n
=
753).
6
A.
Aghilinejad
and
M.
Gharib
wave amplitude suggests that
values for Pf are independently related to
age and mean blood pressure (
R
2
=
0.551). Heart rate, height, weight,
and sex do not contribute significantly to forward pressure wave amp
-
litude. The estimated pressure-only model for forward pressure wave
amplitude suggests similar results to the same significant parameters
(i.e. age and mean blood pressure;
R
2
=
0.627). Both types of models
(based on measured and estimated wave separation parameters)
show that the proportion of variance in wave separation variables
based on common physiological parameters is better explained for
backward pressure wave amplitudes (Pb) than forward pressure
wave amplitudes (Pf).
Wave separation associations with aortic
stiffening
Figure 4
presents unadjusted analysis comparing measures of aortic stiff
-
ness in various carotid-femoral PWV groups. In this analysis, subjects
with elevated aortic stiffness demonstrate a higher forward pressure
amplitude compared with those with lower levels of aortic stiffness
(
P
<
0.001), whereas the increase in backward pressure wave amplitude
is less significant, especially between the group with a carotid-femoral
PWV of 8–16 m/s and the one with carotid-femoral PWV
>
16 m/s.
The between-group comparison is similar using either estimated or
measured wave separation parameters. The RI is lower for partici
-
pants with higher levels of aortic stiffness (
P
<
0.001), while the
change in time delay is not significant between the group
with a
carotid-femoral PWV of 8–16 m/s and the one with carotid-femoral
PWV
>
16 m/s.
Table 4
presents the statistical contribution of forward, backward,
and TD between pressure waves to carotid-femoral PWV based on
measured (using pressure and flow measurements) and estimated
(using pressure-only spectral regression learning) wave separation
values. A base model not including the wave separation variables is pre
-
sented as
Supplementary material online,
Table S3
(
R
2
=
0.383). When
forward pressure wave amplitude enters the model, the
R
2
increases to
0.428 for the model with an exact forward wave amplitude (based on
pressure and flow measurement) and
R
2
increases to 0.413 for the
model with estimated forward pressure wave amplitude (based on
pressure-only measurement). When the Pb and time delay enter the
model (as demonstrated in
Table 4
), increments to the model
R
2
are
not significant.
Discussion
In this study, we comprehensively investigate the accuracy of a novel
wave separation analysis using spectral regression learning and single
pressure waveform measurements and investigate the associations
with aortic stiffness. A primary finding of our study is that the wave sep
-
aration parameters, estimated through the proposed spectral regres
-
sion learning approach, outperform those based on the triangular
flow approximation used conventionally in previous studies.
21
This is
due to the ability of our approach in capturing flow waveform morph
-
ology, as demonstrated in
Figure 2
and
Supplementary material online,
Table S1
.
Table 2
and
Figure 3
indicate a significant correlation between
forward pressure wave amplitudes and the reference forward pressure
wave amplitude (
R
2
of 0.91) with negligible systemic bias. The normal
-
ized error associated with the spectral regression learning method for
forward pressure wave amplitude is 5.4%, which is considerably better
than the 21.6% error associated with the triangular flow approximation
method. While the spectral regression learning method outperforms
the triangular flow approximation method in terms of Pb, the differ
-
ence in the error is less significant (4.8 vs. 7.5%). Following Qasem
and Avolio,
22
we also assess the TD between forward and backward
pressure waves using a cross-correlation technique. Our results also
suggest that, unlike the triangular flow approximation method, the pro
-
posed spectral regression learning method in this study provides accur
-
ate estimates of the TD between forward and backward pressure
waves, with a correlation as high as 0.62 and a moderate
R
2
of 0.38.
These results align with findings from other studies, such as the one
by Kips
et al
.,
23
which demonstrated that TD could not be accurately
captured using the triangular flow approximation method in a large
population due to an overestimation in wave components. Our ap
-
proach utilizes Fourier-based wave decomposition to analyse pressure
signals, enabling an accurate estimation of flow wave morphology and a
subsequent separation of pressure waves. By leveraging harmonic con
-
tent, we effectively decode the periodic and oscillatory waves present
in the cardiovascular system. While previous methods, such as those
employing multi-Gaussian decomposition,
38
have shown efficacy in
smaller data sets or virtual ones, our approach stands as one of the
few to be successfully applied in a large, diverse cohort, building upon
the valuable contributions of existing research.
The results further suggest that the regression analysis of covariates
and determinants reveals no significant difference between the refer
-
ence wave separation parameters and those derived from the
pressure-only estimates using the spectral regression learning method
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 3
Regression analysis of covariates for measured
(reference) and estimated forward (Pf) and backward
(Pb) pressure wave amplitudes (
n
=
753)
Variables
β
SE (
β
)
CI (
β
)
P
-value
Pb (mmHg) derived from both pressure and flow measurements, adjusted
R
2
=
0.904
Age, years
0.039
0.011
(0.017, 0.062)
<
0.001
Height, cm
−
0.143
0.041
(
−
0.224,
−
0.063)
<
0.001
Heart rate, b.p.m.
−
13.03
0.571
(
−
14.15,
−
11.91)
<
0.001
Mean blood
pressure, mmHg
0.644
0.008
(0.629, 0.660)
<
0.001
Pb (mmHg) derived from the proposed pressure-only measurement,
adjusted
R
2
=
0.873
Age, years
0.095
0.013
(0.069, 0.121)
<
0.001
Height, cm
−
0.089
0.047
(
−
0.183, 0.004)
<
0.01
a
Heart rate, b.p.m.
−
8.86
0.664
(
−
10.166,
−
7.558)
<
0.001
Mean blood
pressure, mmHg
0.638
0.009
(0.621, 0.657)
<
0.001
Pf (mmHg) derived from both pressure and flow measurements, adjusted
R
2
=
0.551
Age, years
0.506
0.049
(0.406, 0.602)
<
0.001
Height, cm
−
0.171
0.178
(
−
0.526, 0.175)
<
0.5
a
Heart rate, b.p.m.
−
5.175
2.493
(
−
10.10,
−
0.308)
<
0.1
a
Mean blood
pressure, mmHg
0.901
0.035
(0.833, 0.971)
<
0.001
Pf (mmHg) derived from the proposed pressure-only measurement,
adjusted
R
2
=
0.627
Age, years
0.388
0.039
(0.312, 0.465)
<
0.001
Height, cm
−
0.173
0.140
(
−
0.448, 0.102)
<
0.5
a
Heart rate, b.p.m.
−
4.735
1.958
(
−
8.579,
−
0.892)
<
0.1
a
Mean blood
pressure, mmHg
0.858
0.027
(0.805, 0.912)
<
0.001
CI, confidence interval; SE, standard error.
a
A non-significant parameter.
Regression learning and aortic stiffening
7
(
Table
3
). These
results
indicate
that
the
variation
in
backward
pressure
wave
amplitude
is
well
explained
by
age,
heart
rate,
height,
and
mean
blood
pressure
for
both
the
reference
and
the
estimated
methods,
with
R
2
values
of
0.904
and
0.873,
respectively.
Although
the
R
2
values
based
on
the
same
covariates
are
smaller
for
forward
pressure
wave
amplitude,
there
is no
significant
difference
between
the
measured
ref
-
erence
and
the
estimated
values
for
forward
pressure
wave
amplitude
(
R
2
of
0.551
and
0.627,
respectively).
Previous
studies
have
demon
-
strated
that
forward
pressure
wave
amplitude
serves
as
a
measure
of
proximal
aortic
geometry
and
stiffness,
while
mean
arterial
pressure
and
backward
(reflective)
wave
amplitudes
are
more
correlated
with
the
resistance
of
vessel
structure
and
function.
18
Consequently,
the
in
-
clusion
of
mean
arterial
pressure
as
a determinant
in
the
multivariate
regression
significantly
improves
the
Pb
model
more
than
the
forward
pressure
wave
amplitude,
thereby
explaining
the
higher
R
2
. The
re
-
semblance
in
the
covariate
regression
models
for
both
Pf
and
Pb
be
-
tween
the
reference
and
the
estimated
values
implies
a comparable
physiological
interpretation
of
the
parameters
obtained
through
the
spectral
regression
learning
method
and
the
measured
ones.
It
is
worth
noting
that
Hametner
et
al
.
20
demonstrated
that
drawing
a
similar
conclusion
is
not
possible
when
employing
the
triangular
flow
approximation
or
average
flow
method
for
pressure-only
wave
separation.
In
our
current
investigation
into
the
associations
of
wave
separation
parameters
with
aortic
stiffness,
participants
were
categorized
into
groups
with
carotid-femoral
PWV
<
8,
8–16,
and
>
16
m/s
(
Figure
4
).
Both
the
reference
and
the
estimated
measures
of
the
wave
separation
parameters
yielded
consistent
trends;
forward
pressure
wave
ampli
-
tudes
differed
significantly
among
the
different
groups
(
P
<
0.001),
while
the
backward
pressure
wave
component
and
the
time
delay
did
not
exhibit
the
same
variations.
Changes
in
the
RI
were
also
signifi
-
cant
among
different
groups,
yet
this
change
could
be
attributed
solely
to
the
forward
component.
Additionally,
we
employed
a multivariate
model
considering
both
Pf
and
Pb,
as
well
as
the
TD
between
these
two
waves
(
Table
4
).
The
results
indicated
that
forward
pressure
wave
amplitude
remained
significant,
whereas
Pb
and
TD
did
not.
These
findings
are
consistent
with
prior
studies
suggesting
that
for
-
ward
wave
amplitude
is
associated
with
the
pulsatile
load
in
the
car
-
diovascular
system,
while
Pb
is
more
associated
with
the
steady
load
component.
13
,
18
,
39
Our
findings
further
suggest
that
incorporating
forward
pressure
wave
amplitude
into
the
base
model
enhances
the
model’s
R
2
using
reference
measures.
By
utilizing
the
estimate
of
forward
pressure
wave
amplitude
from
the
spectral
regression
learning
method,
the
model’s
R
2
improves
analogously.
These
results
suggest
that
forward
pressure
wave
amplitude
plays
a role
in
elevating
carotid-femoral
PWV
(an
indicator
of
vascular
stiffening),
and
these
adverse
effects
can
be
effectively
captured
using
the
proposed
spectral
regression
learning
method
for
wave
separation
based
solely
on
pressure
measurements.
Ultimately,
this
platform
provides
valu
-
able
information
for
assessing
cardiovascular
health
that
can
be
incor
-
porated
in
a wide
range
of
non-invasive,
inexpensive,
and
easy-to-use
devices.
40–45
Figure
4
Boxplots
for
wave
separation
parameter
distributions
for
different
levels
of
aortic
stiffness.
Unadjusted
comparisons
of
forward
pressure
wave
amplitude
(Pf),
backward
pressure
wave
amplitude
(Pb),
reflection
index
(RI),
and
time
delay
(TD)
between
participants
with
carotid-femoral
pulse
wave
velocity
<
8,
8–16,
and
>
16
m/s.
Wave
separation
parameters
are
determined
using
the
reference
(pressure
and
flow)
and
spectral
regres
-
sion
learning
(pressure-only)
methods.
8
A.
Aghilinejad
and
M.
Gharib
Study limitations and future work
The major limitation in this study is that we do not have invasively mea
-
sured aortic pressure waveforms for determining the exact central
pressure waveform. Future studies employing invasive clinical measure
-
ments can further expand the applicability of the proposed spectral re
-
gression learning for the wave separation analysis. However, our choice
of using the carotid pressure waveform as a surrogate for aortic pres
-
sure is well-established and shown in the previous studies.
46,47
The FHS
data used in this study were composed primarily of White participants
of Western European descent with a mean (range) age of 66 (40–91)
years. Future studies can aim to include training data from multi-centre
data sets to further examine and expand the usage of the proposed
spectral regression learning method. The comparison between the
parameters derived from the reference wave separation and our pro
-
posed pressure-only method is based on cross-sectional data. Future
studies could benefit from clinical validation using mortality data and as
-
sessing the predictive performance of the pressure-only approach on
cardiovascular events.
Conclusions
This study presented a comprehensive evaluation of a novel spectral re
-
gression learning method for pressure-only wave separation analysis in
a population-based FHS. We demonstrated the method’s accuracy by
comparing wave separation parameters with a reference method em
-
ploying Doppler ultrasound-derived flow waves and tonometry-
measured pressure waveforms. The proposed pressure-only method
showed interchangeability with the reference method in a large, het
-
erogeneous cohort and its associations with carotid-femoral PWV as
a marker of vascular ageing. Our investigation into carotid-femoral
PWV highlighted the significance of forward pressure wave amplitude,
with the proposed spectral regression learning method demonstrating
similar performance to that of the reference approach. These findings
emphasize the clinical applicability and accuracy of the proposed
pressure-only wave separation analysis, providing a valuable non-
invasive tool for assessing cardiovascular health.
Lead author biography
Arian Aghilinejad, PhD, currently serves as
a postdoctoral research associate at the
Division of Engineering and Applied
Science at the California Institute of
Technology (Caltech). He is interested in
studying fluid physics in the cardiovascular
system and developing engineering-based
monitoring solutions for cardiovascular
disease patients. He is the recipient
of the American Heart Association
Fellowship Award, as well as a finalist for
the 2024 Young Investigator Award at
the American College of Cardiology. He
completed his PhD at the University of Southern California and earned
his bachelor’s degree from Sharif University of Technology.
Data availability
No new clinical data were generated in support of this research. The sec
-
ondary data analysis codes will be available upon reasonable request to
the corresponding author.
Supplementary material
Supplementary material
is available at
European Heart Journal Open
online.
Acknowledgements
The FHS was conducted and supported by the National Heart,
Lung, and Blood Institute (NHLBI) in collaboration with Boston
University (Contract No. N01-HC-25195, HHSN268201500001I,
and 75N92019D00031). This manuscript was not prepared in collabor
-
ation with the investigators of the FHS and therefore does not neces
-
sarily reflect the opinions or views of the FHS, Boston University, or the
NHLBI.
Funding
The authors received no particular funding for this study.
Conflict of interest
: none declared.
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 4
Haemodynamic correlates of the
carotid-femoral pulse wave velocity using reference and
pressure-only estimates of wave separation parameters
(
n
=
753)
Variables
β
SE (
β
)
CI (
β
)
P
-value
Model for carotid-femoral PWV based on the measured WSA, adjusted
R
2
=
0.430
Sex
1.113
0.315
(0.495, 1.732)
<
0.001
Age, years
0.177
0.014
(0.149, 0.204)
<
0.001
Mean blood
pressure, mmHg
0.059
0.029
(0.002, 0.116)
<
0.05
a
Heart rate, b.p.m.
2.715
0.852
(1.041, 4.389)
<
0.01
a
Pf, mmHg
0.077
0.010
(0.056, 0.097)
<
0.001
Pb, mmHg
−
0.094
0.046
(
−
0.184,
−
0.004)
<
0.05
a
TD, ms
−
4.502
7.505
(
−
19.235, 10.232)
<
0.6
a
Model for carotid-femoral PWV based on the proposed pressure-only
WSA, adjusted
R
2
=
0.414
Sex
1.047
0.346
(0.422, 1.672)
<
0.001
Age, years
0.178
0.014
(0.151, 0.206)
<
0.001
Mean blood
pressure, mmHg
0.019
0.025
(
−
0.030, 0.069)
<
0.5
a
Heart rate, b.p.m.
3.463
0.751
(1.989, 4.937)
<
0.001
Pf, mmHg
0.081
0.014
(0.054, 0.108)
<
0.001
Pb, mmHg
−
0.042
0.044
(
−
0.129, 0.045)
<
0.5
a
TD, ms
−
13.061
7.954
(
−
28.676, 2.554)
<
0.2
a
CI, confidence interval; PWV, pulse wave velocity; SE, standard error; TD, time delay
between the forward and the backward waves; WSA, wave separation analysis,
respectively.
a
A non-significant parameter.
Regression learning and aortic stiffening
9