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Harnessing the Manifold Structure of Cardiomechanical Signals for Physiological Monitoring During Hemorrhage

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Objective: Local oscillation of the chest wall in response to events during the cardiac cycle may be captured using a sensing modality called seismocardiography (SCG), which is commonly used to infer cardiac time intervals (CTIs) such as the pre-ejection period (PEP). An important factor impeding the ubiquitous application of SCG for cardiac monitoring is that morphological variability of the signals makes consistent inference of CTIs a difficult task in the time-domain. The goal of this work is therefore to enable SCG-based physiological monitoring during trauma-induced hemorrhage using signal dynamics rather than morphological features. Methods: We introduce and explore the observation that SCG signals follow a consistent low-dimensional manifold structure during periods of changing PEP induced in a porcine model of trauma injury. Furthermore, we show that the distance traveled along this manifold correlates strongly to changes in PEP (δPEP). Results: δPEP estimation during hemorrhage was achieved with a median R2 of 92.5% using a rapid manifold approximation method, comparable to an ISOMAP reference standard, which achieved an R2 of 95.3%. Conclusion: Rapidly approximating the manifold structure of SCG signals allows for physiological inference abstracted from the time-domain, laying the groundwork for robust, morphology-independent processing methods. Significance: Ultimately, this work represents an important advancement in SCG processing, enabling future clinical tools for trauma injury management.
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1
Harnessing the Manifold Structure of
Cardiomechanical Signals for Physiological
Monitoring during Hemorrhage
Jonathan Zia, Student Member, IEEE, Jacob Kimball, Student Member, IEEE,
Christopher Rozell, Senior Member, IEEE, and Omer T. Inan, Senior Member, IEEE
AbstractObjective: Local oscillation of the chest wall in
response to events during the cardiac cycle may be captured
using a sensing modality called seismocardiography (SCG), which
is commonly used to infer cardiac time intervals (CTIs) such as
the pre-ejection period (PEP). An important factor impeding
the ubiquitous application of SCG for cardiac monitoring is
that morphological variability of the signals makes consistent
inference of CTIs a difficult task in the time-domain. The goal
of this work is therefore to enable SCG-based physiological moni-
toring during trauma-induced hemorrhage using signal dynamics
rather than morphological features. Methods: We introduce and
explore the observation that SCG signals follow a consistent low-
dimensional manifold structure during periods of changing PEP
induced in a porcine model of trauma injury. Furthermore, we
show that the distance traveled along this manifold correlates
strongly to changes in PEP (PEP). Results:PEP estimation
during hemorrhage was achieved with a median R2of 92.5%
using a rapid manifold approximation method, comparable to an
ISOMAP reference standard, which achieved an R2of 95.3%.
Conclusion: Rapidly approximating the manifold structure of
SCG signals allows for physiological inference abstracted from
the time-domain, laying the groundwork for robust, morphology-
independent processing methods. Significance: Ultimately, this
work represents an important advancement in SCG processing,
enabling future clinical tools for trauma injury management.
Index Terms—Seismocardiogram, manifold, ISOMAP, pre-
ejection period, signal quality
I. INTRODUCTION
SINCE its early description in the 1960s, the seismocardio-
gram (SCG) has emerged as a promising sensing modality
for the noninvasive assessment of cardiomechanical function
[1]. Typically captured using chest-mounted inertial measure-
ment units, the SCG measures local oscillation of the chest
wall occurring in response to underlying hemodynamic events
[2]. Prior literature has demonstrated a strong relationship
between time-domain features of the SCG signal and cardiac
time intervals (CTIs), most notably the pre-ejection period
(PEP) and left ventricular ejection time (LVET), essential
indicators of cardiac preload and contractility [3], [4]. Coupled
This material is based on work supported by the Office of Naval Research
under Grant N000141812579, by NSF grant CCF-1409422, and by NSF
CAREER award CCF-1350954.
J. Zia, J. Kimball, C. Rozell, and O. T. Inan are with the School of Electrical
and Computer Engineering at the Georgia Institute of Technology, Atlanta,
GA, USA (email: zia@gatech.edu).
Copyright (c) 2020 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending an email to pubs-permissions@ieee.org.
Infer
Hemodynamic
Changes
Quality
Indexing
Manifold-Level Dynamics
Compute
Displacement
Exercise, Injury,
Stimulus, etc.
Manifold
Approx.
ISOMAP
Seismocardiogram Signals
Hemorrhage
Decompensation
Baseline
Resuscitation
PEP (+)
(-)
Fig. 1. Overview of this work. Hemodynamic changes such as modulation of
PEP are reflected in the SCG signal. After an initial step of quality indexing
to remove noisy signals, the remaining SCG signals are confined to a low-
dimensional manifold. The distance traveled by the signal along the manifold
may be used to infer changes in hemodynamic indicators such as PEP in a
manner that is abstracted from time-domain features.
with the advent of wearable microelectronics, such physi-
ological insights suggest that the SCG may enable cardiac
monitoring systems of the future to assess cardiomechanical
function noninvasively [5]–[7]. This would prove invaluable
for the diagnosis and management of diseases which affect
cardiomechanical function, from chronic illnesses such as
heart failure [8] and hypertension [9], [10] to acute conditions
such as ischemic events [11] and hemorrhage [12].
In particular, the focus of this work is physiological mon-
itoring during hemorrhage and subsequent fluid resuscitation
via PEP estimation, one of several key indicators of cardiome-
chanical function. Hemorrhage is a common complication of
trauma injury, which accounted for 5 million deaths globally
in the year 2000 at an economic burden of $117 billion in the
U.S. alone [13]. For patients suffering from trauma-induced
hemorrhage, timely and appropriate care are essential for
preventing hypovolemic shock, which comprises the majority
2
of preventable fatalities [14]. As an estimated 1 in 4 trauma
fatalities are preventable, it is incumbent upon healthcare
providers to rapidly assess the severity of hemorrhage and
titrate care appropriately [15]. Toward the development of
clinical tools to aid healthcare providers, recent literature has
indicated that tracking cardiomechanical indicators such as
PEP via SCG may enable providers to track the progression of
hemorrhage and provide individualized treatment [12], [16].
A significant limitation which has prevented the ubiquitous
application of SCG technology is the morphological variability
of the signals, which is highly patient-specific, transient, and
dependent upon sensor placement [2], [17]. This makes it
difficult to consistently extract time- and frequency-domain
features of the signal for PEP estimation [18], [19]. Even
so, prior literature has typically focused on identification and
extraction of time-domain features in spite of this variabil-
ity, which may then be related to PEP [17]. Though such
approaches have demonstrated success in PEP estimation,
they are inherently subject to the transient time-frequency
characteristics of the signal.
The goal of this work is to introduce an approach to PEP
estimation from SCG signals which is abstracted from the
time-domain, focusing instead on the inherent dynamics of
the signal. Namely, we will demonstrate that SCG signals
exhibit a consistent low-dimensional manifold structure during
periods of hemodynamic change, and that displacement along
the manifold is linearly-related to changes in PEP. To obtain
an accurate estimate of displacement along the manifold, we
begin by using the classic ISOMAP algorithm; however, as this
approach is computationally complex and thereby impractical
for wearable systems, we then show that high performance
may still be achieved with a rapid manifold approximation
approach [20]. Manifold approximation algorithms have his-
torically be used to map data to nonlinear subspaces in an
efficient yet robust manner [21].
The overall process proposed in this work is illustrated in
Figure 1; SCG signals are first obtained from a chest-mounted
accelerometer during periods of hemodynamic change. In this
study, changes in PEP are induced via simulated hemorrhage
and fluid resuscitation in a porcine animal model. The critical
benefit of using a porcine model in this work is that (1) large
changes in blood volume could be induced, better simulating
clinical use-cases while closely approximating human cardio-
vascular physiology [22]; and (2) this allowed for collect-
ing gold-standard measurements of PEP from direct cardiac
catheterization [23], [24]. To estimate these induced changes
in PEP, the first step is to remove low-quality signals using a
signal quality index (SQI). Following this, the SCG signals
are nonlinearly-mapped to positions on a low-dimensional
manifold, which may in turn be linearly-mapped directly to
changes in PEP.
This manuscript is organized as follows. We begin by
describing the experimental protocol, in which changes in
PEP are induced in a porcine animal model. After formulating
the quality indexing and manifold mapping methods used in
this work, the relationship between manifold displacement and
changes in PEP are analyzed. Ultimately, inferring cardiome-
chanical indicators such as PEP in a manner that is abstracted
from the time-domain may serve as a harbinger for robust,
morphology-independent methods of both processing and un-
derstanding SCG signals. Doing so represents a critical step in
enabling reliable noninvasive monitoring of cardiomechanical
function in clinical and outpatient environments using SCG.
Specifically, the contributions of this work include:
1) Demonstrating that SCG signals exhibit a low-
dimensional manifold structure during complex physi-
ological processes such as changes in blood volume;
2) Inferring changes in PEP from these manifolds, abstract-
ing SCG processing from the time domain.
II. ME TH OD S
A. Experimental Protocol and Hardware
The following experimental protocol was conducted with
approval from the Institutional Animal Care and Use Commit-
tees (IACUC) of the Georgia Institute of Technology, Trans-
lational Training and Testing Laboratories Inc. (T3 Labs), and
the Department of the Navy Bureau of Medicine and Surgery
(BUMED) and included six Yorkshire swine (3 castrated male,
3 female, Age: 114–150 days, Weight: 51.5–71.4kg) under-
going induced hypovolemia followed by fluid resuscitation.
Anaesthesia was first induced in the animal with xylazine and
telazol and maintained with inhaled isoflurane during mechan-
ical ventilation, and intravenous heparin was administered to
prevent the coagulation of blood during the protocol. The ani-
mals’ total blood volume was estimated using Evans blue dye
administration [25], [26], following which hypovolemia was
induced by draining blood passively through an arterial line
into a sterile container at up to four levels of blood volume loss
(BVL): 7%, 14%, 21%, and 28% [27]. Following each level of
blood loss, exsanguination was paused for approximately 5-10
minutes to allow the cardiovascular system to stabilize. The
procedure was followed until a safety threshold was reached,
namely a 20% drop in mean arterial pressure (MAP). Upon
reaching this threshold, fluid resuscitation was performed by
re-infusing the stored blood through the arterial line at the
same levels of blood volume loss, pausing again for 5-10
minutes between each level. Figure 2(a) shows the PEP derived
from the aortic root catheter during the experimental protocol
for Pig 1, the calculation of which will be detailed below.
During the experiment, aortic root pressure was recorded by
inserting a fluid-filled catheter through a vascular introducer in
the right carotid artery. The vascular introducer was connected
via a pressure monitoring line to an ADInstruments MLT0670
pressure transducer (ADInstruments Inc., Colorado Springs,
CO, USA), with pressure data continuously recorded with an
Animal Max BVL No. of Instances
Pig 1 21% 18,916
Pig 2 28% 16,985
Pig 3 21% 10,956
Pig 4 21% 9,210
Pig 5 14% 13,400
Pig 6 28% 16,146
TABLE I
MAX IMU M BVL AN D AVAI LAB LE N UMB ER O F INS TANC ES FO R EAC H
AN IMA L IN T HE PRO TOC OL.
3
100
150
ECG
Aortic PressureSCG
PEP LVET
(c)
ECG Lead
ECG Ground
SCG Sensor
(mid-sternum)
ECG Axis
Carotid
Arteries
A
(1) Aortic Root Catheter
Introducer Location
A
(b)
Q
R
S
AO
AC
PEP (ms)
(a) Exsanguination Re-Infusion
time
Fig. 2. (a) The PEP computed for each heartbeat during the protocol from the aortic pressure waveform of Pig 1. Darker red shading indicates higher blood
volume loss (7%, 14%, and 21% respectively). (b) Sensor setup for the experimental protocol. ECG sensors are configured in Einthoven Lead II configuration.
(c) Tracings from an example heartbeat from Pig 1. The ECG QRS complex is labeled along with the AO point derived from the aortic pressure waveform.
As shown, the ECG R-peak and AO points are used to compute the PEP. The corresponding point on the SCG signal is labeled for illustration, though SCG
feature points were not used for AO estimation in this work. Prior studies have used SCG signals to compute LVET as well via AC estimation, since the
second high-energy complex of the SCG has been shown to correspond with the onset of diastole [4]; an example is provided in the figure for illustration,
though LVET is not explored in this work.
ADInstruments Powerlab 8/35 data acquisition system (DAQ)
sampling at 2kHz. Concurrent electrocardiogram (ECG) and
SCG data was also captured using a wearable sensing system.
As will be described, ECG was collected in order to segment
the SCG signal on a heartbeat-by-heartbeat basis. ECG signals
were captured using a three-lead system of adhesive-backed
Ag/AgCl electrodes interfacing with a BIOPAC ECG100C
amplifier. SCG signals were captured using an ADXL354
accelerometer (Analog Devices, Inc., Norwood, MA, USA)
placed on the mid-sternum, interfacing with a BIOPAC
HLT100C transducer interface module. Signals from these
sensors were continuously recorded using a BIOPAC MP160
DAQ (BIOPAC Systems, Inc., Goleta, CA, USA) sampling at
2kHz. A 1Hz square wave output from the BIOPAC and fed
into the Powerlab in order to commence recording simulta-
neously and ensure that both systems remained synchronized
throughout the experiment. The configuration of the sensing
system is detailed in Figure 2(b).
B. Signal Pre-Processing
Only the dorso-ventral axis of SCG acceleration was used in
this study [2]. All signals were first filtered with finite impulse
response (FIR) band-pass filters with Kaiser window, both in
the forward and reverse directions. Cutoffs were 0.5–40Hz
for the ECG, 1–40Hz for the SCG [17], and 0.5–10Hz for
the aortic pressure signal [28]. Subsequently, the SCG and
aortic pressure waveforms were segmented using the ECG
R-peaks as a reference. The resulting signal segments were
abbreviated to a length of 1,000 samples (500ms) from the R-
peak, since this was shorter than the shortest R-R interval in
the protocol while remaining long enough to capture systolic
ejection. All SCG signals were then amplitude-normalized
with mean-centering and unit variance.
The interval between the ECG R-peak and aortic opening
(AO) is typically used as the PEP reference value [29], [30].
As illustrated in Figure 2(c), AO was estimated from the aortic
pressure waveform as the point of maximum second derivative,
indicating the onset of the pressure upswing associated with
systolic ejection; as the signals were R-peak-separated, the
time elapsed from the beginning of each signal segment to
the AO point was itself the PEP interval for each respective
heartbeat. All processing in this work was performed with
MATLAB 2018b (The Mathworks, Inc., Natick, MA, USA).
As it pertains to the assessment of arterial pressure and
CTIs, catheter-based systems allow for the direct measurement
of pressure gradients and the changes thereof during the
cardiac cycle. Though infrequently used to measure PEP due
to the difficulty in obtaining these signals, the relationship
between AO and the upstroke of the arterial pressure wave-
form has long been established [24]. For this reason, cardiac
catheterization was selected as the reference standard for
PEP in this work. Notably, impedance cardiography (ICG) is
another common method of estimating CTIs, however recent
literature has suggested that ICG itself may be prone to
considerable error and it was therefore not used as a reference
standard in this work [31], [32].
4
Compute SQI Remove Outliers
PC2
PC1
PC3
Fig. 3. Outlier identification and removal for the SCG data from Pig 1. Points highlighted in red represent the bottom 2% of SCG signals as per the SQI.
Data is visualized in the first three PCA dimensions.
C. Notation
The matrix XiRM×Ndenotes the row-wise matrix
of MSCG signals of length Nfor Pig i, such that Xi=
{x1,x2, ..., xM}. The vector piRMcontains the catheter-
derived PEP values for each signal in Xi. In general, the
subscript iindicates that the matrix or vector belongs to Pig
i. The matrix X¯
idenotes the row-wise matrix of SCG signals
for all animal subjects excluding Pig i;p¯
itherefore contains
the PEP values for each signal in X¯
i. The notation xjXi
denotes the jth row (or, signal segment) in Xi.
D. Signal Quality Indexing
Once segmented SCG signals and corresponding AO refer-
ence values for each heartbeat were obtained, the final step of
pre-processing was to remove low-quality signals. To do so,
the SQI previously developed in [33] was used. As described,
the SQI of each SCG signal segment xRNwas defined
based on its distance from a template tRNvia
SQI (x,t) = exp λD(x,t)
L(x,t)(1)
where λis a decay factor, D(·)is a distance function and
L(·)is the length of the signals after distance calculation. In
this manner, smaller values of distance resulted in an SQI near
1, and large values resulted in an SQI near 0. λwas set to 25
in this study as suggested in [33]; note that while this changes
the numerical range of SQI values, it does not change the
rank-ordering of signal quality, and thus changing this value
to another positive-valued real number would not affect the
results of this work. The distance metric used in this work
was the dynamic time warping (DTW) algorithm, a ubiquitous
method of estimating the distance between signals which
computes the minimum Euclidian distance after stretching
and compressing them in the time-domain [34]. Though [33]
imposed additional constraints on the DTW algorithm, this
work imposed only the fundamental constraints, as will be
detailed below. Therefore, the function D(·)in Equation 1
returned the distance between the warped signals, and L(·)
returned the length of the signals after warping.
The following processing was then performed separately for
each animal. The first 100 SCG signal segments during the
pre-hypovolemic baseline period were averaged elementwise
to form a template tifor the ith animal. Subsequently, the SQI
was calculated for each SCG segment xjXivia Equation
1, and the signals were ranked in order based on their SQI
scores. A percentile threshold was then set on the scores,
and the signals which fell below the threshold were removed
from subsequent processing. An example is shown in Figure
3, in which the bottom 2% of SCG signals are highlighted
and removed for the data from Pig 1 (X1). For visualization
purposes, principal component analysis (PCA) was performed
on the matrix X1, and the first three principal components
(PCs) were plotted.
E. Nonlinear Dimensionality Reduction
Formally, manifolds are topological spaces which are lo-
cally Euclidian, or approximately flat on small regions of
their surface [35]. When the intrinsic dimensionality of a
dataset — or, the number of latent or hidden variables —
is lower than the number of dimensions in the observed
feature space, a common result is that the data forms a lower-
dimensional manifold embedded in the higher-dimensional
feature space. Less formally, the data may be constrained to a
low-dimensional subspace of the original feature space, though
the subspace may be curved and nonlinear. In these cases,
it is desirable to re-embed the manifold in a feature space
closer to its intrinsic dimensionality to enable more robust
processing. Ideally, the dimensions of the new feature space
may correspond to latent variables in the data, though this
is not always a straightforward task. When the relationship
between the latent and observed variables is approximately
linear, linear dimensionality reduction techniques such as PCA
are commonly used to identify a suitable subspace; otherwise,
nonlinear methods may be more suitable for identifying these
more complex, curved subspaces.
A classic technique for learning and re-embedding man-
ifolds is the ISOMAP algorithm, the steps of which are
illustrated in Figure 4(a)–(c) for the data in Figure 3. This
algorithm is composed of three parts [20]:
1) Graph Creation: A graph is constructed from a sub-
sampling of points Gi={g1,g2, ..., gL}from the
5
30
20
10
0
-10
-20
-30
-30 -20 -10 0 10 20 30 40
PC1
PC2
(-)
(+)
Initial Point
PC3
PC1
PC2
20
0
-20
-40
-20
0
20
40 -40
-20
0
20
40
Manifold Approximation ISOMAP
010 20 30 40
-10
-20 010 20 30 40
-10
-20
40
20
0
-20
-40
40
20
0
-20
-40
-20
-10
0
10
20
PC3
PC1
PC2
-20
-10
0
10
20
0
20
40
60
-20
-40
-60
-60 -40 -20 0 20 40 60 80
𝒚(")
𝒚$
(a) (b) (c)
(d) (e)
Δ𝜃 > 0
Δ𝜃 < 0
Fig. 4. (a) Data from Pig 1 over the entire protocol after removing outliers with an SQI cutoff of 10%. (b) Illustration of the graph creation step of ISOMAP.
(c) The manifold in (b) mapped to a two-dimensional subspace using classical MDS. (d) Data from all animal subjects after removing outliers with an SQI
cutoff of 10% and applying the same PCA transformation to all subjects. Colors correspond to the different animals (Pig 1 = blue; Pig 2 = green; Pig 3 =
orange; Pig 4 = purple; Pig 5 = red; Pig 6 = gold). (e) Manifold approximation process overlaid on data from (d). The initial datapoint in the experiment (blue)
for each animal was mapped to a point on the reference circle (orange). Each subsequent point was then mapped to the circle, with its angular displacement
relative to the initial point (positive = green; negative = red) recorded. Note that a unit circle was used in this study, though a large circle is shown here.
overall dataset Xi={x1,x2, ..., xM}, which form the
nodes of the graph. A connection between nodes gjand
gkare formed if and only if there exists a point x`in
the original dataset whose nearest neighbors are gjand
gkas per the Euclidian distance.
2) Geodesic Distance Estimation: The geodesic distance
between each pair of nodes gj,gkGiis estimated by
computing the shortest path between each pair of nodes
that traverses the graph’s connections. In this work, this
is performed with the Floyd-Warshall algorithm [36].
3) Manifold Re-Embedding: The goal of this step is to
learn a mapping f:RL×NYfrom the observation
space of Gito a lower-dimensional space Y=RL×D
which preserves the geodesic distances between pairs of
points in the graph. In this work, we employ “classical”
multidimensional scaling (MDS) to learn this mapping
[37]. Specifically, MDS minimizes the loss function
L(f, Gi) =
Pj,k djk
Ydjk
G2
Pj,k djk
Y2
1/2
,(2)
where djk
Y=kf(gj)f(gk)k2is the Euclidian distance
(or the `2-norm) between f(gj)and f(gk)in the output
space Yand djk
Gis the estimated Euclidian distance
between the feature vectors gjand gk[37].
To obtain an accurate embedding of SCG manifolds the SQI
was first applied to the data from each animal to remove out-
liers. The cutoff was increased in increments of 5% from 0%
to 20% to observe the effects of the SQI on the performance of
this method. 10% of the remaining signals were then randomly
selected to form the set Gias in [20]. The above algorithm
was then performed to compute the geodesic distance between
each pair of nodes, and MDS was used to map each point in
Gito a two-dimensional subspace Y=RL×2. This resulted
in obtaining the vectors y(1)
iand y(2)
iRL, corresponding
to the mapping of each point in Gito the two dimensions
of Yrespectively. In this work, y(1)
iwas defined as the
dimension which contained the larger variance, as shown
in Figure 4(c). Two dimensions were chosen based on the
observation that the SCG manifolds were two-dimensional for
all subjects, as will be shown subsequently in Figure 5. Figure
4 provides an overview of this process for Pig 1. As the
final step of processing, the latent variable ywas obtained
for each animal by computing the offset of each element in
y(1)
ifrom the initial element in the vector y(1)
i(0), such that
yi=y(1)
iy(1)
i(0). This was done in order to obtain the
displacement of each point on the manifold rather than the
absolute position. As will be detailed later, this latent variable
was then used to estimate the change in PEP (PEP) via linear
6
regression.
Figure 4(a) shows the data from Pig 1 after a 10% cutoff was
applied using the SQI. Note that while the data is plotted in the
first three PCA dimensions, PCA was used for visualization
purposes only with regards to ISOMAP. Figure 4(b) shows the
result of graph creation, and Figure 4(c) shows the resulting
mapping of the nodes of G1to the two-dimensional subspace
Y. This process was repeated independently for all animals
in the protocol.
F. Manifold Approximation
There are several drawbacks to using ISOMAP for manifold
mapping. Estimating geodesic distance between each pair of
points is a computationally-intensive process; for instance,
the Floyd-Warshall algorithm has O(N3)complexity, though
there exist slightly more efficient algorithms. Furthermore,
ISOMAP is highly-sensitive to outliers, as these may create
skip-junctions across the manifold during graph creation,
invalidating the calculated geodesic distance.
For practical application in wearable systems, we propose
a simple manifold approximation algorithm for comparison to
ISOMAP, illustrated in Figure 4(d) and (e). Figure 4(d) shows
the data from all six animals, each with a different color, after
applying the SQI with a cutoff of 10%. The data from all
animals was combined to learn a single PCA transformation
for plotting all the data on the same axes.
Since data from all animals exhibited consistent rotational
dynamics, a simple manifold approximation could be per-
formed, as illustrated in Figure 4(e). For each animal, a
separate PCA transformation was learned from the data from
the remaining five animals (X¯
i) and applied to the data from
the held-out animal (Xi). The initial sample from the Pig iwas
then mapped to the nearest point on a unit circle in the plane
of PC1 and PC2, centered at the origin. Each subsequent point
was then also mapped to the nearest point on the unit circle,
and the angular offset between the new point and the initial
point was recorded. This resulted in a vector θicontaining
the angular offset for each SCG signal in Xi. This process is
illustrated in Figure 4(e), and was also repeated with an SQI
cutoff increasing from 0% to 20% in increments of 5%.
As will be detailed, the latent variable θwas then used to
estimate PEP in an analogous manner to yfrom ISOMAP.
Unlike the ISOMAP algorithm, the manifold approximation
algorithm has O(N), and is thereby much more rapid; this
enabled performing the analysis on all available datapoints
rather than a sub-sampling. The total computation time of
the ISOMAP algorithm for all subjects was 16 minutes on
a 3.6GHz Intel Core i7 7820X processor despite sampling
10% of the available SCG signal segments; the corresponding
time was 33 seconds for the manifold approximation algorithm
despite sampling all available segments.
G. Estimating Changes in Pre-Ejection Period
To determine whether there existed a relationship between
SCG manifolds and PEP, we began by visualizing trends in
the data. For each animal, the SCG data was combined to
form a matrix XiRM×Nafter removing outliers with an
SQI cutoff of 10%. The data was visualized by performing
PCA on the matrix Xi, and datapoints were shaded based on
the PEP magnitude. Gradations in shading corresponding to
a particular axis of the resulting manifold would suggest a
relationship between the latent variables of the manifold and
PEP which may be estimated with manifold mapping.
Following this step, we would like to determine the extent
to which changes in the latent variables obtained from man-
ifold mapping correlate with changes in PEP. Regarding the
ISOMAP method, the latent variable of interest is y, which
was obtained for each subject upon performing MDS on the
graph nodes. Regarding the proposed manifold approximation,
the variable of interest is the offset θ. For each animal, the
vector pidenoting PEP was first computed by subtracting
each element of the vector of ground-truth PEP values pi
from the initial value pi(0), namely pi=pipi(0). The
coefficient of determination (R2) was determined between
ytot and θtot — or, the vectors yiand θiconcatenated
across all animals — and the corresponding changes in PEP
ptot after again applying an SQI cutoff of 10% [38].
To yield more insight on the accuracy of these meth-
ods, PEP was estimated using leave-one-subject-out cross
validation (LOSO-CV) for both the ISOMAP and manifold
approximation methods, and was performed separately for
each SQI cutoff. For ISOMAP, PEP was estimated from y;
for each animal, a vector y¯
iwas created which contained the
values of yfor the remaining five animals in the study. This
vector was regressed to the corresponding vector of PEP
values p¯
ifor each datapoint in y¯
iusing least squares
regression of the form
βi= argmin
ˆ
β
kp¯
iy¯
iˆ
βk2
2(3)
where βiis the learned parameterization. This linear regres-
sion was then applied to the values of yifor the held-out
animal, and the root-mean-square error (RMSE) between true
and estimated PEP was recorded for each animal [38]. This
process was repeated for the manifold approximation method,
however the regression was learned between θand p.
III. RES ULTS A ND DISCUSSION
A. Estimating Changes in Pre-Ejection Period
The manifolds formed by SCG signals during the experi-
mental protocol are shown in Figure 5(a)–(f) for each of the
six animals respectively. In the PCA dimensions pictured, it is
apparent that a similar two-dimensional semicircular manifold
was preserved across all animals in the study. Furthermore,
color gradation is present across the major axis of the mani-
fold, which corresponds to the axis along which yand θ
were measuring displacement. Therefore, Figure 5 indicates
that changes in PEP were related to displacement along the
major axis of the manifold in this study.
The relationship between yand PEP is further explored
in Figure 6(a), which shows a strong positive correlation
resulting in an R2of 95.3% across all subjects. Corre-
spondingly, Figure 6(b) shows a strong positive correlation
between θand PEP, resulting in an R2of 92.5% across
7
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75 136
75 125
62 120 87 150
62 125 100 150
Fig. 5. (a) – (f) Data from Pigs 1–6 respectively plotted on first 3 PCA dimensions, with transformations computed separately for each animal. Shading
corresponds to PEP, with darker shading indicating larger PEP. Colorbars are shown for each animal, indicating PEP in milliseconds.
all subjects. Building on these results, Figure 6(c) reports
the RMSE for estimating PEP using the latent variables
derived from ISOMAP and manifold approximation respec-
tively using held-out cross validation. The median RMSE was
lower for ISOMAP at 1.38ms, though manifold approximation
still estimated PEP with a median RMSE of 2.45ms. Prior
literature in the field of PEP estimation from SCG has focused
on estimating the precise timing of PEP rather than relative
changes as was performed in this work. Placing the results
of Figure 6(c) into context, the RMSE for automated PEP
estimation in prior studies has typically fallen between 9–
12ms, depending upon the method and reference [39], [40].
On the one hand, estimation of PEP rather than PEP itself
is a limitation of a manifold mapping approach compared to
prior literature; however, this may in turn enable physiological
monitoring in a morphology-free manner. Consider Figure
4(d), which shows the SCG manifolds for all animal subjects
on the same axes. Though the orientation of each manifold var-
ied due to differences in morphology, the underlying dynamics
which generate the manifold were consistent across subjects.
This enabled consistent determination of displacement along
the manifold despite its morphology-dependent position, as
performed with both ISOMAP and manifold approximation.
In this manner, a shift in perspective from the time-domain to
signal dynamics may be the key to unlocking morphology-free
SCG analysis, enabling more robust processing.
These results have further implications which transcend
PEP estimation with SCG signals. Namely, the observation
of consistent low-dimensional manifold structure in SCG
signals suggests that (1) these signals have low intrinsic
dimensionality despite their observation in high-dimensional
vector spaces; and (2) that the latent variables describing
these intrinsic dimensions have consistent dynamics for the
same physiological stimulus, in this case changes in blood
volume due to exsanguination and fluid resuscitation. These
observations may represent a shift in how we understand SCG
signals: rather than focusing on time-domain features of these
signals, data with such properties may be better understood
in terms of their low-dimensional dynamics, which lack the
stochasticity of signal morphology.
The SCG data forming the manifolds in Figure 5 and the
results in Figure 6 were obtained during both exsanguination
and fluid resuscitation. During this time, changes in PEP were
encoded in the manifolds formed by the SCG signals, and
hemorrhage-induced changes in this aspect of cardiomechan-
ical function were thereby quantifiable via manifold mapping
approaches. For this reason, these results demonstrate the clin-
ical potential for reliable physiological estimation from SCG
signals during trauma-induced hemorrhage and subsequent
treatment. Namely, estimating indicators of cardiomechanical
function such as PEP noninvasively may enable new clinical
tools to allow healthcare providers to manage trauma injury,
serving as additional indicators of the severity of hemorrhage
and the patients’ response to fluid resuscitation. By estimating
changes in PEP in a morphology-independent manner, these
results represent an important step in addressing the major
limitations preventing the ubiquitous application of SCG in
clinical environments such as these.
B. Effect of the SQI on Manifold Mapping
The effect of increasing the SQI cutoff on manifold-derived
estimation of PEP is detailed in Figure 6(d). As illustrated,
8
1.0
(a) (c)
(d)
-0.4 -0.2 0 0.2 0.4 0.6 0.8
Δθ (radians x π) Percentile Threshold
0 5 10 15 20
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5
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20
15
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Δy
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10
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Fig. 6. (a) The latent variable yderived from ISOMAP plotted against
PEP. (b) The latent variable θderived from manifold approximation
plotted against PEP. (c) Error in estimating PEP using ISOMAP and
manifold approximation, respectively. Colors in (a)–(c) correspond to animal-
specific colors in Figures 4(d) and 5. (d) The effect of the SQI percentile
threshold on the R2between yand PEP (dark gray) as well as θand
PEP (light gray).
the performance of both ISOMAP and manifold approxima-
tion improved as the cutoff was increased, an effect which
diminished once a threshold of 10% had been reached. Figure
3 serves as a representative example of why this was the
case for ISOMAP: removing low-quality signals as defined
by the SQI resulted in the emergence of the two-dimensional
manifolds of Figure 4, which could in turn be embedded more
reliably in the two-dimensional output space Y. Regarding
the proposed manifold approximation, preserving points which
better reflected the underlying rotational dynamics of the
signal led to more accurate approximation of angular offsets.
Importantly, the low percentage threshold at which per-
formance of these manifold mapping algorithms leveled off
suggested only a minority of SCG points could not be de-
scribed by a low-dimensional manifold structure. The im-
plication of this observation is that the manifolds observed
in Figure 4 were not merely consequences of applying the
SQI to inherently high-dimensional data; rather, the data itself
was predominantly described by a low-dimensional manifold
to begin with, with a minority of signal segments forming
outliers. This supports the assertion that a low-dimensional
manifold structure is intrinsic to SCG signals and were not
merely a consequence induced by the SQI itself. Conversely,
this result highlights the importance applying signal quality
indexing before searching for such structure in the data; as
illustrated in Figure 3, the presence of outliers may obscure
the underlying manifold-level dynamics, possibly contributing
to the historical difficulty in characterizing this behavior.
C. Study Limitations and Future Work
The current study focused on PEP estimation during trauma
injury using an animal model, which limits the generalization
of these results to a diverse array of possible applications
in human subjects. Future studies should explore manifold
mapping approaches for other interventions and for human
subjects as well, though these studies should ensure that a
reliable reference for PEP is used. Future work should also
explore whether changes in other physiological indicators typ-
ically derived from SCG, such as LVET, may also be estimated
using the latent variables of low-dimensional SCG manifolds.
This would improve the utility of such methods for trauma
injury triage, among other applications. As this work focused
on PEP estimation during hemorrhage and resuscitation, future
studies should further explore the potential role of manifold
mapping in estimating the extent and severity of hemorrhage
for possible application to the triage of trauma injury. While
estimating the change in PEP may suffice for some methods,
others may require direct estimation of PEP, highlighting a key
limitation of the current work.
To optimize the accuracy of such methods, future work may
explore a wide array of available methods for nonlinear di-
mensionality reduction and manifold mapping, many of which
have lower complexity than ISOMAP. Such improvements
may serve to reduce inter-subject variability, which as shown
in Figure 6(c) was an important limitation when the manifolds
were rapidly approximated.
IV. CONCLUSION
The emergence of ubiquitous, wearable sensing technolo-
gies has the potential to revolutionize the treatment and
management of cardiovascular disease. By integrating SCG
sensors into such systems, one may assess mechanical aspects
of cardiac function to obtain a holistic electromechanical
view of heart health when paired with other sensors. This is
especially useful in the case of trauma injury, where assessing
cardiomechanical function may enable new clinical tools for
managing hemorrhage and preventing hypovolemic shock.
Toward this goal, this study examined how PEP may be
estimated in the context of hemorrhage and fluid-resuscitation
using SCG signals in a manner that is abstracted from the time-
domain, addressing a significant challenge in SCG processing.
Importantly, the observation that SCG signals exhibit a consis-
tent topological structure during hemorrhage and resuscitation
suggests that although these signals may exhibit morphological
heterogeneity, signal dynamics are preserved and may thereby
lead to robust, consistent methods of physiological inference.
Though this dynamics-based approach enables the estima-
tion of changes in PEP in lieu of PEP itself, elucidating the
manifold structure of these signals represents a significant ad-
vancement in the field of SCG processing. Ultimately, analysis
methods which harness the intrinsic, underlying behavior of
these signals may better bridge the gap between the laboratory
and clinical practice, enabling the development of robust
clinical tools in the fight against trauma injury and heart
disease.
9
V. AC KN OWLED GM EN TS
We would like to thank Dr. Christopher Rolfes of Transla-
tional Training and Testing Laboratories, Inc. (T3 Labs) for
his role in collecting the data used in this study.
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