Listening to heart sounds through
the pressure waveform
Alessio
Tamborini
& Morteza
Gharib
Non-invasive diagnostic modalities are integral to cardiovascular care; however, current systems
primarily measure peripheral pressure, limiting the breadth of cardiovascular prognostication. We
report a novel approach for extracting left side heart sounds using a brachial cuff de
vice. The technique
leverages brachial cuff device enhanced signal resolution to capture pressure fluctuations generated
by cardiohemic system vibrations, the sound pressure waveform. We analyze left heart catheterization
data alongside simultaneous brachial cuff device measurements to correlate sound pressure waveform
features with left ventricle (LV) contractility. The extracted sound pressure waveform reveals two
prominent oscillatory wave packets, termed WP1 and WP2, originating from cardiac structure
vibrations associated with LV contractions and relaxation. We demonstrate that WP1 originates
from LV contraction during systolic blood ejection through the aortic valve (AV) and is correlated
with LV isovolumetric contraction, clinically measured by LV dPdt-max (Pearson-R
=
0.65, p
<
0.001).
Additionally, we show that WP2 comes from LV elongation required for blood flow deceleration at the
end of systole, causing AV closure, and is correlated with LV isovolumetric relaxation, measured by
LV ndPdt-max (Pearson-R
=
0.55, p
<
0.001). These findings highlight the value of cuff sound pressure
waveforms in providing insights about dynamic coupling of the LV-Aorta complex for non-invasive
assessment of LV contractility.
Keywords
Brachial cuff, Heart sounds, Sound pressure waveform, Left ventricular contractility
The generation of heart sounds is a complex physiological process arising from the energy of cardiac contractions
and the interaction of pressure gradients, blood flow, and valvular function
1
. During the cardiac cycle, heart
chamber contract to generate positive pressure gradients, open heart valves, and generate forward flow. These
forceful contractions bring about abrupt accelerations and decelerations of blood flow that send the entire
cardiohemic system (heart and aorta (AO)) into a transient state of vibration. In clinical cardiology, heart sounds
are commonly auscultated with a stethoscope as a non-invasive diagnostic indicator for heart valve disease,
such as stenosis or regurgitation
2
. However, these sounds encompass a wealth of information about the heart
beyond valvular function
3
. The capability of the heart to generate forceful contractions and relaxations, clinically
referred to as contractility, is fundamental for the correct functionality of this muscular organ
4
. Inability to
generate these pressure differences leads to heart failure. Given the increasing prevalence of left-sided heart
failure in the population, there is an unmet need for a non-invasive and rapid method to assess left side heart
functions
5
,
6
.
The left ventricle (LV) is responsible for pumping blood out of the heart to the arterial system. At the start
of LV systole, the LV undergoes a rapid pressure rise during isovolumetric contraction, which causes the aortic
valve (AV) to open forcefully. The energy input for the forceful acceleration of blood into the aorta AO generates
transient pressure vibrations referred to as aortic ejection sounds (AES), a component of the first heart sound
7
–
9
.
At the end of systole, the LV undergoes a rapid pressure drop during isovolumetric relaxation, which rapidly
decelerates blood flow and causes the AV to close. The rapid change in momentum of flow generates transient
cardiac vibrations that are the origin of the second heart sound
9
–
15
. These cardiac system vibrations produce
complex pressure waveforms whose characteristics are dependent on the underlying system properties
9
. These
complex vibrational waveforms are composed of lower and higher frequency content
9
. The higher frequency
content radiates from the cardiac tissue into the chest wall and can be auscultated with a stethoscope. On the
other hand, the lower frequency content, the sound pressure waveform, is embedded and superimposed in the
cardiac pressure waveform
9
. Yet, given the significantly smaller relative amplitude of the signal, this information
is hidden by the dominant frequencies of the cardiac pressure wave.
The sound pressure waveform has been previously measured in the ascending AO and LV by using invasive
catheter methods
7
,
10
. These studies demonstrated that the pressure vibration amplitudes generated by the LV-AV
interactions closely correlate to the rates of pressure change in the LV. It has been reported that increased LV
Department of Medical Engineering, California Institute of Technology, Pasadena, CA, USA.
email:
atambori@caltech.edu
OPEN
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| (2024) 14:26824
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| https://doi.org/10.1038/s41598-024-78554-5
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isovolumetric contraction produces a faster pressure rise and results in AES of greater amplitude
7
. Similarly, the
amplitude of the second heart sound has been shown to be directly correlated to the rate of pressure fall during
LV isovolumetric relaxation
16
–
24
. While these studies discovered and characterized this signal, the invasive nature
of the catheter limited the applicability of such measurements. In contrast, a non-invasive method capable of
measuring the sound pressure waveform could present a valuable tool for assessing LV contractile and relaxation
rates. However, it is noteworthy that stethoscopes cannot be a substitute as they are unable to capture the low
frequency component of the sound pressure waveform
9
,
17
,
25
.
This study introduces a cuff-based method to extract the sound pressure waveform for non-invasive
assessment of the LV-AV coupling, focusing on evaluating LV contractility. The small amplitude of the sound
pressure waveform has only recently become measurable with cuff-based devices thanks to advancements in high-
resolution signal acquisition. Using invasive catheter measurements as reference, this study aims to demonstrate
that the proposed method can reliably capture the sound pressure waveform non-invasively. First, the high-
resolution cuff-based system is used to extract the sound pressure waveform from brachial measurements
26
. The
method is then evaluated in a clinical study against simultaneous invasive catheter recordings. Finally, sound
pressure waveform features are correlated with LV maximal contraction rate (dPdt-max) and maximal relaxation
rate (ndPdt-max), assessing isovolumetric contraction and relaxation strength
4
,
27
.
Results
Study population
The invasive study enrolled 202 subjects who were referred and pre-scheduled for left heart catheterization.
Notably, 159 recordings from this population satisfied the device hardware requirements. Following the
exclusion criteria, 43 individuals were excluded: 5 for severe atrial fibrillation, 3 for incorrect procedure, and 32
for apparatus malfunction (14 catheter failures, 7 brachial cuff failures, and 11 data acquisition faults), and 3 for
abnormal catheter pressure signals (LV pressure always smaller than the AO pressure upon catheter retraction).
Algorithmic filtering excluded an additional 10 individuals for low quality recordings in the suprasystolic blood
pressure (sSBP) hold. Participant inclusion is summarized in Fig.
S1
using a flowchart.
The population (n
=
106) was composed of 65% men, the average age was 66 years, and the average BMI
was of 29.1. In the study population, 81% reported hypertension, 31% reported diabetes, and 75% reported
hyperlipidemia. High prevalence of heart valve disease was present: 23% reported heart valve disease, 6%
reported aortic stenosis and 5% reported aortic regurgitation. Table
1
summarizes the main characteristics of
the study population.
Va r i a b l e
Quantity (n
=
106)
Clinical characteristics
Age, (years)
66
±
9
Men, n (%)
69 (65%)
Weight, (kg)
86.1
±
18.9
Body mass index, (kg/m^2)
29.1
±
5.6
Left arm circumference, (cm)
31.8
±
4.0
White, n (%)
77 (73%)
Comorbidities
Hypertension, n (%)
86 (81%)
Diabetes, n (%)
33 (31%)
Thyroid, n (%)
17 (16%)
Hyperlipidemia, n (%)
80 (75%)
Smoker, n (%)
18 (17%)
Cardiovascular disease
Carotid artery disease, n (%)
25 (24%)
Cardiomyopathy, n (%)
12 (11%)
Heart failure, n (%)
19 (18%)
Heart valve disease, n (%)
24 (23%)
Aortic stenosis, n (%)
6 (6%)
Aortic regurgitation, n (%)
5 (5%)
Heart surgery, n (%)
10 (9%)
Left ventricular dysfunction, n (%)
15 (14%)
Myocardial infarction, n (%)
16 (15%)
Peripheral vascular disease, n (%)
20 (19%)
Pacemaker, n (%)
3 (3%)
Stroke, n (%)
2 (2%)
Ta b l e 1
. Characteristics of study participants. Data in table summarizes the clinical characteristics of the
population used in this study; the data is mean
±
standard deviation, unless otherwise stated.
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Evaluation of sound pressure digital filtering method
The method to extract the sound pressure waveform from the brachial cuff recording, as outlined in Fig.
1
, was
successfully applied to the sSBP pulse waveform signals from the entire study population (n
=
106). The digital
filter for sound pressure waveform extraction was optimized for filter type and cutoff frequency (Fig.
S2
and
Note
S1
). Optimal signal reconstruction was obtained with a 4th order elliptic high-pass filter with 20 Hz cutoff
frequency. These filtering characteristics are used throughout the rest of the study. Future device iterations can
integrate in analog format the filter specified for onboard sound pressure waveform measurement.
The cardiac cycle in the extracted sound pressure waveforms consistently featured two distinct oscillatory
patterns or wave packets, termed WP1 and WP2, followed by a long quiescent interval. The foot of the cardiac
pressure waveform marked the start of the cardiac cycle. Figure
2
A shows example segments of sound pressure
waveform signals extracted in the sSBP hold from three subjects in the study population. All signals consistently
displayed this double peak nature characteristic of the sound pressure waveform as described in the literature.
The cuff sound pressure waveform feature timing in cardiac cycle is illustratively compared with respect to the
invasive catheter in the AO location adjusted for wave propagation time (Fig.
2
B). The WP1 oscillations occur
at the onset of AO systole. The start of the WP1 oscillations coincides with the pressure rise in the AO, which
physiologically represents the opening of the AV and the acceleration of blood in the AO. The WP2 oscillations
occur between the end of systole and the onset of diastole. The start of the WP2 oscillations is simultaneous to
the rapid pressure deflections at the dicrotic notch in the AO pressure signal which physiologically marks the
closing of the AV and deceleration of blood flow in the AO.
Signal comparison with stethoscope
Simultaneous stethoscope and brachial cuff sound pressure waveforms in the sSBP hold were captured for five
young-healthy individual (n
=
5) in a non-invasive study at Caltech. Signals from both the cuff sound pressure
and the stethoscope showed waveforms with two peaks followed by a quiescent period (Fig.
3
A and B). In the
stethoscope signal, the first peak, conventionally denoted as S1, is the closure of atrioventricular valves and the
second peak, conventionally denoted as S2, is the closure of semilunar valves.
The timing interval between the peaks in the stethoscope and cuff sound pressure waveform was compared
on a beat-to-beat basis. Figure
3
C reports a median S1 to WP1 peak time delay of 132 ms, 123 ms, 114 ms,
127 ms, and 150 ms and a median S2 to WP2 peak time delay of 80 ms, 76 ms, 80 ms, 67 ms, and 96 ms for the
five subjects in this analysis. In all individuals the S1 to WP1 peak time delay is longer than the S2 to WP2 peak
time delay; the average difference between the median time delays is of 49
±
10 ms for the five subjects. The time
delays present between the stethoscope and cuff measurement originates from the difference in wave propagation
speed. In cuff measurements, sound pressure waveforms propagate embedded within the cardiovascular pulse
waveform at the characteristic speed of the arterial pressure wave, the pulse wave velocity. In stethoscope
measurements, the signal travels through the chest cavity at the speed of sound, which is significantly larger than
pulse wave velocity
28
.
The sound pressure signals were analyzed for instantaneous frequency (IF) around the oscillatory pressure
peaks: WP1, WP2, S1, and S2. As reported in Fig.
3
D the cuff sound pressure signal had a median WP1 IF of
14.2 Hz, 12.5 Hz, 12.2 Hz, 13.2 Hz, and 12.5 Hz and a median WP2 IF of 14.7 Hz, 13.4 Hz, 13.5 Hz, 11.4 Hz, and
12.8 Hz for the five subjects, respectively. The stethoscope sound pressure signal had a median S1 IF of 28.1 Hz,
25.9 Hz, 18.4 Hz, 31.4 Hz, and 32.4 Hz and a median S2 IF of 31.1 Hz, 33.8 Hz, 27.5 Hz, 32.5 Hz and 29.3 Hz
(Fig.
3
E). The larger variance in the stethoscope results comes from the measurement sensitivity to device
Fig. 1
. Method for sound pressure waveform extraction with brachial cuff. Step-by-step method for extracting
the cardiovascular sound pressure waveform from a high-resolution brachial cuff device with inflate and hold
capabilities. Part of the figure were generated with a modified picture from Servier Medical Art, provided by
Servier, licensed under a Creative Commons Attribution 4.0 Unported License.
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placement. These results confirm the cuff sound pressure waveform captures the low frequency component
while the stethoscope captures the high frequency component of the cardiac structure vibrations.
Both findings, namely the difference in the time delays and IFs, highlight that WP1 and WP2 in the cuff
represent different time intervals and physiological events to the S1 and S2 peaks detected by the stethoscope.
The well-established fact that the stethoscope primarily detects the closure of heart valves, coupled with the
observation from our study regarding the delayed appearance of the first pressure oscillation in the cuff,
strengthens the correlation between the peaks of the cuff-based sound pressure waveform and the opening and
closing of the AV
29
. These results further suggest that the stethoscope measurement is not a substitute of the cuff
sound pressure waveform information.
Effect of cuff hold pressure on sound pressure waveform morphology
The target pressure in the inflate-and-hold approach varies the pressure-flow relationship in the brachial artery.
It has been previously shown that the pulse waveform shows significant morphological changes with hold
pressure
26
. The method to extract the sound pressure waveform from the brachial cuff recording was applied
at the signals captured in the diastolic blood pressure (DBP), mean arterial pressure (MAP), and sSBP holds.
Figure
4
shows overlayed average pressure and extracted sound pressure waveforms for all holds in four subjects
from the clinical study. Pulse waveforms between the DBP, MAP, and sSBP hold show significant differences for
both morphology and amplitude. On the other hand, sound pressure waveforms displayed compatible features
amongst the holds. WP2 oscillations had consistent amplitude, shape, and frequency between all holds. WP1
oscillations had same frequency and shape, yet variable amplitude. Following the WP2 oscillations, all sound
pressure waveforms have a flat steady signal.
Fig. 2
. Sound pressure waveforms from brachial cuff device extracted in a clinical study. (
A
) The three
panels of the illustration show the sound pressure waveform extracted in the sSBP hold pressure for different
individuals in the study. Catheter pressure signals (black) shown serve as a timing reference for the signals. (
B
)
shows the cardiovascular signals timing intervals during a single cardiac cycle inclusive of cuff-based sound
pressure waveform (red) and catheter aortic pressure (blue). The sound pressure waveform WP1 and WP2
peaks are labeled for reference. Acoustic pressure waveform has been time shifted using the calculated time
delta to correct for wave propagation delay.
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Beyond flow induced pressure vibrations, the morphology of the sound pressure waveform should be
independent of the hold pressure. Indeed, the WP2 oscillations perfectly overlapped in all three holds as no flow
is expected at this instance of the cardiac cycle. In contrast, the WP1 oscillations were incrementally affect by
local flow. In the presence of flow, arterial restrictions cause arterial wall flutter and local turbulence, known as
Korotkoff sounds
30
. Korotkoff sounds are maximal at the MAP hold pressure and the waveform morphologies
shown in Fig.
4
align with these expectations. Yet, upon full occlusion of the artery in the sSBP hold, flow is
blocked and Korotkoff sounds disappear. Korotkoff sounds can be measured using a stethoscope on the brachial
artery under the distal end of the cuff from the heart. In Fig.
S3
, we show how the sSBP and MAP hold pressure
can be combined to extract the Korotkoff sound pressure waveform. The extracted waveform from the brachial
cuff closely matches the Korotkoff waveform at the distal end of the brachial cuff measured with the digital
stethoscope.
Fig. 3
. Sound pressure signal comparison between simultaneous cuff and stethoscope. (
A
) Shows a ten-
second segment of simultaneous stethoscope and sSBP hold sound pressure waveforms. (
B
) Shows the average
waveform for the cuff and stethoscope highlighting the time shift between the WP1 and WP2 peaks. (
C
) The
calculated beat-to-beat time delay between the cuff and stethoscope peaks showing a clear difference between
the WP1 and WP2 time deltas. (
D
) shows the Instantaneous Frequency analysis for the WP1 and WP2 cuff
sound pressure signal. (
E
) shows the Instantaneous Frequency analysis for the S1 and S2 stethoscope signal.
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These findings indicate that the WP1 oscillations from AES are present at all hold pressures but, at non-
occlusive pressures, these oscillations are combined with local flow vibrations. These results confirm that the
sound pressure waveform is independent of the hold pressure and the measured pressure oscillations are a
property of the LV-AV coupling. Although, a direct representation of the sound pressure waveform free from
local flow vibrations can be optimally obtained at the sSBP hold.
Validation of sound pressure waveform content with aortic catheter
An invasive catheter placed in the ascending AO is the method reported in the literature to measure the sound
pressure waveform
7
. To validate the content of the cuff sound pressure waveform, we compared our methodology
to sound pressure waveforms extracted from the catheter signal. For both the catheter and cuff, the digital filter
discussed above was applied to the pressure time signals during the sSBP hold pressure segments to generate a
simultaneous sequence of sound pressure waveforms. Figure
5
A shows the sound pressure waveforms extracted
from simultaneous cuff and catheter recordings in a subject from the study population. Both signals display a
first pressure oscillation after the foot of the cardiac waveform, close to the beginning of systole, and second
subsequent pressure oscillation, followed by a large interval of steady signal. A time delay is observed between
the catheter and cuff sound pressure waveforms corresponding to the time delay of wave propagation in the
cardiovascular system from central to brachial artery.
The time interval from WP1 to WP2 peaks was compared between the cuff and catheter sound pressure
waveforms. The WP1 to WP2 peak time interval between catheter and cuff exhibited a strong measurement
agreement (ICC
=
0.69 [0.58, 0.78]) for the entire population (n
=
106) (Fig.
5
B). The average time delay
measured between the catheter and cuff sound pressure waveform signal was of 58
±
16 ms (Fig.
5
C). These
values align with expected wave propagation speeds for a population with these demographics
31
,
32
.
The IF analysis was applied to the cuff and catheter sound pressure signals and the mean IF values around
the oscillatory peaks, WP1 and WP2, were extracted for each subject. The mean cuff IF values for the study
population was of 16.4 (3.1) Hz for WP1 and 15.8 (2.8) Hz for WP2 (Fig.
5
D). The mean catheter IF values
for the study population was of 17.3 (3.1) Hz for WP1 and 18.0 (1.9) Hz for WP2 (Fig.
5
E). WP1 and WP2
Fig. 4
. Effect of the hold pressure on the sound pressure waveform morphology. Comparison between the
pulse waveform and sound pressure waveform pairs for three holds: DBP (black), MAP (red), and sSBP (blue).
Top row shows the characteristic pulse pressure waveforms, and the bottom row shows the extracted sound
pressure waveforms. Each column represents a distinct individual from the clinical study.
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distributions closely overlapped for catheter and cuff measurements. The within subject differences on WP1 and
WP2 for the cuff and catheter measurements are reported in Fig.
S10
. The mean IF frequencies for WP1 and
WP2 were compared to physiological characteristics of subjects in the study population. Figure
5
F and
G
show
a moderate negative linear relationship between height and the corrected WP1 IF (Pearson-R
=
-0.44, p
<
0.001)
and a strong negative linear relation between height and the corrected WP2 IF (Pearson-R
=
-0.54, p
<
0.001),
respectively.
To rationalize the observed results, we model the cardiac structure transient vibrations using the mass-spring-
damper subjected to external forcing by a Dirac delta function. In an underdamped system, the mass-spring-
damper solution exhibits an exponentially decaying oscillatory behavior, with oscillatory frequency determined
Fig. 5
. Comparison between cuff and catheter sound pressure waveforms. (
A
) shows a simultaneous cuff
(red line) and catheter (blue line) sound pressure waveform segment from a subject in clinical study. Catheter
pressure signal (black) is provided as a timing reference. (
B
) scatter plot comparing the WP1 and WP2 peak
time intervals between the cuff and catheter signals. (
C
) shows the average time delays of cuff sound pressure
signal compared to catheter sound pressure signal. (
D
) and (
E
) show the Instantaneous Frequency analysis for
the sound pressure signal WP1 and WP2 in the cuff and catheter, respectively. (
F
) and (
G
) show scatter plots
for the correlation of the height with the corrected Instantaneous Frequency of the WP1 and WP2, respectively.
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by the damped natural frequency term. The damped natural frequency
(
f
d
)
, in units of Hz, can be expressed in
terms of mass (m), damping (c), and stiffness (k) as shown in Eq. (
1
),
f
d
=
1
2
π
√
k
m
−
c
2
4
m
2
(1)
For the cardiac system, the parameters of Eq. (
1
) can be related to physiological parameters. ‘k’ denotes the
combined stiffness of the heart and aorta, approximated as
k
≈
k
aorta
+
k
heart
. The stiffness of an elastic tube can
be expressed as
k
=
Eh/r
, where E represents elasticity, r is the radius, and h is the wall thickness. ‘m’ represents
the momentum mass, comprising the masses of the blood-filled aorta and heart, roughly
m
≈
m
aorta
+
m
heart
.
The mass of the blood-filled aorta is proportional to
L
(
ρ
blood
A
ID
+
ρ
wall
(
A
OD
−
A
ID
))
, where L is the segment
length,
ρ
blood
is the density of blood,
ρ
wall
is the aortic wall density,
A
ID
is the aortic internal diameter, and
A
OD
is the aortic outer diameter. The mass of the heart can be simplified as,
m
heart
∝
ρ
heart
V
heart
, with
ρ
heart
representing heart density, and
V
heart
denoting heart volume. ‘c’ is the damping term which is challenging to
directly relate with system properties.
This decomposition reveals that the damped natural frequency of the system correlates directly with its
stiffness
(
f
d
∝
√
k
)
and inversely with its dimensions, the diameter ‘d’,
(
f
d
∝
d
−
1
)
. Previous studies have
established a relationship between height and aortic root diameter, allowing height to serve as a proxy for aortic
diameter
33
,
34
. The findings in the literature align with this study’s observed inverse relationship between height
and IF. Interestingly, when extending the analysis to correlate age and weight as surrogate for stiffness, weak
linear relationships were observed at best (Pearson-R
<
0.25, p
>
0.01) (Fig.
S4
). Additionally, regression analysis
indicated no significant associations between height, age, or their interaction with WP1 and WP2 parameters,
results are summarized in Table S2. This outcome is not surprising given this population has a high prevalence
of cardiovascular conditions as reported in Table
1
and therefore the impact of age and weight on stiffness is
s e c on d ar y.
Sound pressure assessment of left ventricular contractility
Prior to the beat-to-beat analysis of LV contractility with cuff sound pressure waveform parameters, we evaluated
the impact of the catheter placement through the AV on the measured signal. Subject-averaged comparison of the
cuff sound pressure waveform parameters performed with the catheter in the LV and the AO recording showed
good agreement for both morphology and features (Fig.
S5
) for: the WP1 to WP2 time interval (ICC
=
0.87
[0.82, 0.91]), WP1 amplitude (ICC
=
0.92 [0.88, 0.94]), and WP2 amplitude (ICC
=
0.79 [0.71, 0.85]). These
results confirm that the catheter in the LV, which passes through the AV, does not affect the sound pressure
waveform signal as measured with the cuff, and therefore can be used for this beat-to-beat analysis.
The portion of the measurement with the catheter in the LV was analyzed to assess the correlation of cuff
sound pressure waveform parameters to LV contractility. The LV contractility analysis utilizing the sound pressure
waveform required a population free of heart valve disease. A pressure gradient analysis was implemented to
measure the LV to AO pressure gradient and identify undiagnosed AV disease. The pressure gradient analysis
successfully estimated the AV pressure gradient in all 106 individuals. The calculated pressure gradients ranged
from
−
19 to 35 mmHg; the negative pressure gradients are non-physiological and originate from methodology
related limitations. Figure
S6
summarized the results from the pressure gradient analysis.
Within the study population, 71 subjects passed all eligibility criteria for the LV contractility analysis. A total
of 14 subjects were excluded for AV disease (9 reported from the patient questionnaire and 5 detected with the
pressure gradient analysis) and 21 were excluded for lacking beat-to-beat segments longer than 5 sequential
pulsations. This population subset (n
=
71) was composed of 63% men with average age of 65 years. In the study
population, 82% reported hypertension, 27% reported diabetes, and 72% reported hyperlipidemia. Table S1
summarizes the main characteristics of this population subset.
Simultaneous LV pressure and cuff sound pressure time sequences are used for pulse waveform analysis.
Figure
6
A shows an example of a five second time segment of LV pressure and cuff sound pressure waveforms.
The simultaneous signals show that WP1 occurs after the LV pressure rise, upon opening of the AV, and WP2
develops with the LV pressure drop, upon closure of the AV. The LV isovolumetric contraction rate, dPdt-max,
showed the highest positive linear correlation with the WP1 peak-to-peak amplitude corrected with a surrogate
of arterial elasticity (Pearson-R
=
0.65, p
<
0.001) (Fig.
6
B). The LV isovolumetric relaxation rate, ndPdt-max,
showed the highest positive linear correlation with the WP2 peak-to-peak amplitude corrected for a surrogate of
arterial elasticity (Pearson-R
=
0.55, p
<
0.001) (Fig.
6
C). Correction for arterial elasticity was performed using
wave propagation time from central to peripheral arteries; Fig.
S7
shows the correlation between subject age
and wave propagation time. The correlations for the full WP1 and WP2 parameter set, and LV contractility
parameters are shown in Fig.
S8
in the form of a correlation matrix. As reported in Fig.
6
D, the measure of
pressure wave intensity, p
rms
, showed good correlation between the LV pressure wave and the cuff sound pressure
wave (Pearson-R
=
0.73, p
<
0.001). The moderate yet statistically significant (p
<
0.001) correlation observed
between WP1 and ndPdt-max, as well as WP2 and dPdt-max, arises from the physiological interdependence
in LV contractile functions. Despite being distinct mechanisms, they are inherently connected within the same
physical structure. The results presented above show that the sound pressure waveform method is capable of
non-invasively measuring the LV-AV coupling which directly correlates with LV contractility.
Regression analysis was performed to adjust the dPdt-max and ndPdt-max models for age, gender, systolic
blood pressure (SBP), and heart rate (HR). The dPdt-max model explained 52.4% of the variance (R
2
=
0.524),
with the WP1 parameter providing the largest contribution to the model (β
=
176.54, p
<
0.001). Additionally,
SBP (β
=
67.87, p
=
0.022) and HR (β
=
79.54, p
=
0.009) were significant predictors. The model did not report
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