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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

Abstract—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 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 Xi∈RM×Ndenotes the row-wise matrix

of MSCG signals of length Nfor Pig i, such that Xi=

{x1,x2, ..., xM}. The vector pi∈RMcontains 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 xj∈Xi

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 x∈RNwas deﬁned

based on its distance from a template t∈RNvia

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 xj∈Xivia 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,gk∈Giis 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×N→Yfrom 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

Y−djk

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)

i∈RL, 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)

i−y(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 Xi∈RM×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=pi−pi(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

k∆p¯

i−∆y¯

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

PC1

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(b) (c)

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-20 020 40

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(f)

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

0.9

0.8

0.7

R2

ISOMAP Manifold Approx.

5

4

3

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0

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100-50 0 50

30

25

20

15

10

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Δy

(b)

30

25

20

15

10

5

0

-5

ΔPEP

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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