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# Modeling Consistent Dynamics of Cardiogenic Vibrations in Low-Dimensional Subspace

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The seismocardiogram (SCG) measures the movement of the chest wall in response to underlying cardiovascular events. Though this signal contains clinically-relevant information, its morphology is both patient-specific and highly transient. In light of recent work suggesting the existence of population-level patterns in SCG signals, the objective of this study is to develop a method which harnesses these patterns to enable robust signal processing despite morphological variability. Specifically, we introduce seismocardiogram generative factor encoding (SGFE), which models the SCG waveform as a stochastic sample from a low-dimensional subspace defined by a unified set of generative factors. We then demonstrate that during dynamic processes such as exercise-recovery, learned factors correlate strongly with known generative factors including aortic opening (AO) and closing (AC), following consistent trajectories in subspace despite morphological differences. Furthermore, we found that changes in sensor location affect the perceived underlying dynamic process in predictable ways, thereby enabling algorithmic compensation for sensor misplacement during generative factor inference. Mapping these trajectories to AO and AC yielded ${R^{2}}$ values from 0.81—0.90 for AO and 0.72—0.83 for AC respectively across five sensor positions. Identification of consistent behavior of SCG signals in low dimensions corroborates the existence of population-level patterns in these signals; SGFE may also serve as a harbinger for processing methods that are abstracted from the time domain, which may ultimately improve the feasibility of SCG utilization in ambulatory and outpatient settings.
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FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 1
Modeling Consistent Dynamics of Cardiogenic
Vibrations in Low-Dimensional Subspace
Jonathan Zia, Student Member, IEEE, Jacob Kimball, Student Member, IEEE,
Sinan Hersek, and Omer T. Inan, Senior Member, IEEE
Abstract—The seismocardiogram (SCG) measures the move-
ment of the chest wall in response to underlying cardiovascular
events. Though this signal contains clinically-relevant informa-
tion, its morphology is both patient-speciﬁc and highly transient.
In light of recent work suggesting the existence of population-level
patterns in SCG signals, the objective of this study is to develop
a method which harnesses these patterns to enable robust signal
processing despite morphological variability. Speciﬁcally, we
introduce seismocardiogram generative factor encoding (SGFE),
which models the SCG waveform as a stochastic sample from a
low-dimensional subspace deﬁned by a uniﬁed set of generative
factors. We then demonstrate that during dynamic processes
such as exercise-recovery, learned factors correlate strongly
with known generative factors including aortic opening (AO)
and closing (AC), following consistent trajectories in subspace
despite morphological differences. Furthermore, we found that
changes in sensor location affect the perceived underlying dy-
namic process in predictable ways, thereby enabling algorithmic
compensation for sensor misplacement during generative factor
inference. Mapping these trajectories to AO and AC yielded R2
values from 0.81–0.90 for AO and 0.72–0.83 for AC respectively
across ﬁve sensor positions. Identiﬁcation of consistent behavior
of SCG signals in low dimensions corroborates the existence of
population-level patterns in these signals; SGFE may also serve
as a harbinger for processing methods that are abstracted from
the time domain, which may ultimately improve the feasibility
of SCG utilization in ambulatory and outpatient settings.
Index Terms—seismocardiogram, dimensionality reduction,
autoencoder, cardiac monitoring, generative modeling
I. INTRODUCTION
ADVANCES in wearable sensing for outpatient monitoring
are revolutionizing both healthcare delivery and our
understanding and treatment of disease. In particular, there are
now myriad ways to monitor heart health outside the clinic
using wearable sensors. Among these, the seismocardiogram
(SCG) holds promise, particularly in monitoring diseases or
conditions affecting the mechanical aspects of cardiovascular
health and performance. The SCG measures the movement
of the chest wall in response to underlying cardiovascular
events [1]. Most notably, valvular events such as aortic opening
(AO) and closing (AC) have been shown to occur concurrently
with SCG features, with high correlations established between
cardiac timing intervals measured with the SCG compared
This material is based on work supported by the National Institutes of
Health under Grant 1R01HL130619-A1 and the National Center for Advanc-
ing Translational Sciences of the National Institutes of Health under Award
Number UL1TR002378.
J. Zia, J. Kimball, S. Hersek, and O. T. Inan are with the School of Electrical
and Computer Engineering at the Georgia Institute of Technology, Atlanta,
GA 30332 USA (email: zia@gatech.edu).
to reference standards [2], [3]. These correlations enable
inference of key indicators of cardiomechanical function which
derive from AO and AC such as pre-ejection period (PEP), left-
ventricular ejection time (LVET), and pulse transit time (PTT)
[4], [5]. Notably, the role of such indicators in the diagnosis
and management of cardiovascular diseases including hyper-
tention [6], heart failure [7], [8], and coronary artery disease
[9] has been well-studied.
Typically captured using a tri-axial accelerometer mounted
to the chest wall with concurrent ECG [10], [11], the appli-
cation of SCG in ambulatory and at-home environments has
been limited. By its nature, the morphology of the waveform is
highly transient in the time domain, inﬂuenced by the coupling
of the vascular system with the chest wall, the chest wall with
the sensing system, and by the patient’s physiological state.
Consequently, morphological variability poses a signiﬁcant
challenge in SCG processing [12]. Furthermore, prior literature
has shown that SCG morphology varies with sensor position as
well, requiring the sensor to be placed properly to accurately
estimate cardiomechanical indicators [12], [13].
The ultimate goal of this work is to develop a method of
SCG processing which adapts to the patient’s anatomy and
physiology as well as the position of the sensor for accurate
assessment of cardiomechanical indicators, namely rAO and
rAC — or the duration between the ECG R-peak and AO
and AC respectively. Doing so would not only improve the
robustness of SCG processing algorithms, but usability as well
by not requiring the user to move the sensor. Toward this goal,
this work proposes a new method of modeling SCG signals
which is summarized in Figure 1.
To develop this approach, we begin with the perspective
that the cardiovascular system — governed by closed-loop
autonomic feedback — follows simple dynamic processes in
response to individual stimuli [14]. A dynamic process is one
that is governed by a set of rules, such that future states of
the system may be predicted from past states and the system’s
inputs [15]. Consider a patient undergoing an exercise stress
test; after beginning in a baseline resting state, the patient tran-
sitions to a new equilibrium state upon the onset of exercise.
When the test is complete, the patient returns to their baseline
state. Figure 1(a) illustrates this process in a state space deﬁned
by rAO and rAC, which both decrease during exercise and
increase during recovery [16]. While the particular trajectory
in this state space in response to exercise may be patient-
speciﬁc, the dynamic behavior is largely preserved.
In this work, we model SCG signals as a stochastic sample
from an underlying dynamic process. Consider the process
This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.
The final version of record is available at https://doi.org/10.1109/JBHI.2020.2980979
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FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 2
Infer
Eq. 14
Exercise, Injury,
Illness, etc.
AC
AO
State 0 (Baseline)
Hemodynamic State Changes
Stress
Recovery
State 1
Anatomy
Physiology
Sensor Position
Hemodynamics
Static
Generative Factors
Seismocardiogram Signals
Localize Sensor
f2
f1
f3
Location-Specific
Regression
Misplaced Sensor
P1
P2
P3
P4
P4
P3
P2
P1
Model Low-Dim.
SCG Dynamics
Prior Work
Eq. 2
Eq. 1
Eq. 3
Diagnosis
Treatment
Management
Clinical
Outcomes
User-Specific
Subspace Mapping
SGFE (Eq. 4)
Compress Signals
(a)
(b)
(e)
(c)
(d)
(f)
(g)
Fig. 1. (a) Illustration of the consistent dynamics of the rAO and rAC interval during an exercise stress test. (b) Hemodynamic factors such as rAO and rAC
are among the generative factors of SCG signals. Other factors reﬂect the particular anatomy and physiology of the patient and sensor position, which are static
factors and do not change over time. (c) The SCG may be modeled as a stochastic sample from these underlying generative factors. (d) The proposed SGFE
maps SCG signals to a low-dimensional subspace by modeling them in this manner. (e) SCG signals exhibit consistent dynamics in this learned subspace,
however observed dynamics are dependent on sensor position. (f) Prior work has demonstrated that SCG sensor position on the chest wall may be localized.
(g) By applying position-speciﬁc regression to the learned subspace, the hemodynamic factors rAO and rAC may be inferred independently from the other
factors. Purple boxes indicate an unsupervised model while orange boxes indicate a supervised mdoel. Equation numbers correspond to those in the text.
above; if rAO and rAC were the only factors inﬂuencing the
SCG, this waveform could be losslessly-encoded by the two-
dimensional subspace of Figure 1(a). In reality, the subspace
which deﬁnes SCG is likely dependent upon a variety of
other cardiogenic factors, requiring additional dimensions to
achieve lossless encoding [1], [12]. Furthermore, observed
signals sampled from this subspace may also be affected by
other factors such as the patient’s anatomy and physiology
and sensor location on the chest wall [17]. As shown in Figure
1(b), the factors which inﬂuence the generation of SCG signals
are known as generative factors [18], [19].
Though SCG morphology is highly variable, its hemo-
dynamic generative factors, such as rAO and rAC, follow
consistent dynamics; these observed signals may therefore
exhibit consistent behavior in subspaces deﬁned by these
factors [16] as in Figure 1(a). Mapping signals into these
subspaces may thereby enable analysis methods that are robust
to morphological variability. To do so, this work introduces the
seismocardiogram generative factor encoder (SGFE), which
maps SCG signals into a learned low-dimensional subspace
(latent space) as illustrated in Figure 1(c)-(e). As will be
shown, SCG signals exhibit consistent behavior in this sub-
space despite morphological variability, though they follow
trajectories that are dependent on sensor position. It is then
shown that if sensor position is known, a position-speciﬁc
linear regression model can be applied to the learned subspace
of Figure 1(e) to accurately estimate the known generative
factors rAO and rAC. With this approach, one may estimate the
hemodynamics underlying the SCG signal independently from
the other generative factors which affect SCG morphology.
To enable this work, prior literature has demonstrated that
sensor location on the chest wall may be inferred from SCG
signals without user-calibration [20]; therefore, in this work
it is assumed that sensor position is known. Regarding SCG
modeling, previous studies have proposed principal compo-
nent analysis (PCA), independent component analysis (ICA),
and eigenvector decomposition as possible subspace mapping
methods for SCG processing [21]–[23]. Similar methods have
also been employed for other cardiovascular signals including
ECG and PPG for the purposes of noise reduction and feature
extraction [24], [25]. Notably, though, such methods do not
incorporate the dynamic behavior of these signals.
The purpose of this work is to formulate the SGFE and
analyze its ability to encode the known hemodynamic gen-
erative factors rAO and rAC. In the following section, we
introduce the SGFE, ﬁrst illustrating that SCG signals yield
consistent trajectories in the low-dimensional latent space of
this model despite morphological variability. Subsequently, we
will analyze whether this subspace encodes useful information
by characterizing its ability to estimate changes in the rAO and
rAC intervals. Finally, we will show that consistent changes in
subspace behavior due to sensor placement enables algorithmic
compensation when inferring AO and AC event timing using
this subspace. The contributions of this work include:
1) Introducing the SGFE as a method of inferring seismo-
cardiogram generative factors
2) Demonstrating that SCG waveforms follow consistent
patterns in low-dimensional subspace
3) Demonstrating algorithmic correction for sensor mis-
placement for generative factor inference.
FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 3
II. ME TH OD S
A. Notation
For brevity in the following sections, shorthand will be
used when describing matrices and vectors. Matrices in this
work are collections of row-wise vectors containing data from
subsequent observations in the time interval T:= [1, T ].
Consider an example T-by-Mmatrix of real numbers U
RT×M. It can be assumed that, U:= [u>
1...u>
T]>where
utRMtT. In other words, Uis composed of T
vectors of length M, where each vector utis an observation
at time t. Since this notation is used frequently, the shorthand
U:={u(M)}Tis used. In any such matrix, u(i,j)refers to
the element of Uin the ith row and jth column while u(i)
t
refers to the ith element in vector ut.
Tuples, which are ordered sequences of objects, are in-
dicated by lists of variables enclosed by parentheses. For
example, the notation V:= (U,w)is used to deﬁne the
variable Vas a tuple of the matrix Uand vector w.
B. Mathematical Framework
Since the SCG derives from the chest wall’s response to
underlying events, we can abstract this signal as
FRΦ(F|P)XP(1)
where F:={f(D)}Trepresents the hemodynamic generative
factors of the signal, Ris a response function that generates
the waveform, and XP:={x(M)}Tis the set of observed
SCG vectors from position P. The response function Ris
parameterized by Φ, which represents the static generative
factors related to the patient’s anatomy and physiology (Figure
1(b)), and is conditioned on the sensor position P. Under
the assumption that hemodynamic factors vary dynamically
according to the state of the cardiovascular system, the factors
at each timestep may be described as
(s0,)G(s0,)F(2)
where s0RKis an initial state vector, :={δ(L)}T
represents changes in state at each point in the time period
T, and Gis a generator function that produces hemodynamic
generative factors using this state information. Though the
dimensionality of Fand the state variables s0and are
in reality unknown, acceptable values for D,K, and Lin a
computational model may be inferred, as will be subsequently
described. The implications of modeling the SCG in this
manner is that there may exist an encoder function Esuch
that
XPEΦ(XP|P)(s0,).(3)
Now consider that, given a set of observations XPgenerated
with Equation 1, we wish to approximate the factors Fthat
yielded these signals. Using Equations 2 and 3, this may be
accomplished via
XPEΦ(XP|P)(s0,)G(s0,)F.(4)
While the functions Eand Gare unknown, learning functions
experimentally that approximate this behavior may allow in-
ference of hemodynamic generative factors.
C. Model Architecture
This formulation naturally parallels the architecture of a
sequence-to-sequence VAE [26]. The proposed model for this
study is shown in Figure 2(a). The input to the model is a se-
quence X:={x(M)}Tof Tconsecutive heartbeat-separated
SCG signals with length M. Note that, for simplicity, the
effect of sensor position is omitted for the time being and
will subsequently be re-introduced.
To compress the signals, each signal xiXis processed
with the multi-layer convolutional network shown in Figure
2(b). This network is composed of N= 6 convolution
blocks in series, which convolve the signal with each of kn
ﬁlters (kernels) of length nin the nth block with unit step.
Convolutional networks are commonly used in cardiovascular
signal processing due to the temporal dependence of time-
series data [27]. The outputs of each convolution layer are
normalized before application of an exponential linear unit
(ELU) activation function [28], [29]. As was performed in
[30], dropout regularization with a rate of 0.2is imposed
on the output of the activation function [31]. Dimensionality
reduction is induced by gradually decreasing the number of
ﬁlters (kn= [64,64,32,32,16,16]) and max pooling, which
down-samples each signal by a factor of two. To accommodate
for shorter signals, the kernel length is also decreased (n=
[7,5,5,3,3,2]). These parameters were derived heuristically
from [30], which explored dimensionality reduction of SCG
signals with convolutional networks. Like most of the model,
the layers in this network are time-distributed, meaning the
same operation is performed for each signal xiX.
Before modeling the dynamics present in X, the outputs
of the compression network are ﬂattened and passed through
a dense “read-in” layer with 64 input units, 2×(K+L)
output units, and rectiﬁed linear unit (ReLU) activation with
out layers — also called projection layers — exist because
generative factors may present differently as signal features
across patients. Thus, though the subspace deﬁned by the
generative factors may be conserved, mapping into and out
of this subspace may require compensation for signal het-
erogeneity by ﬁtting these layers on a session-speciﬁc basis.
In other words, the projection layers capture anatomical and
physiological differences — represented by Φin Equations 1,
3, and 4 — so that the dynamic model can focus on inferring
factors that are common to the population.
Modeling dynamics requires estimation of the initial state
s0and change in state at each timestep . As shown in Figure
2(c), the former is computed with a bi-directional long short-
term memory (LSTM) network EZ, where the output is the
average between the ﬁnal outputs of the forward and backward
layers [32]. Shown in Figure 2(d), the latter is also computed
with a bi-directional LSTM network E, where an output δt
is produced at each timestep as the average output between
the forward and backward cells. However, since this is a VAE
instantiation, these values are not evaluated explicitly; rather,
they are drawn from a Gaussian distribution, the parameters
of which are explicitly evaluated. Thus, the output of EZis
a tuple (µ0,σ0),µ0,σ0RK. The output of Eat each
FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 4
a)
n = 1…N
1-D Convolution (kn, ℓn)
+ Batch Normalization
ELU Activation
+ Dropout
1-D Max Pooling
Batch Normalization +
Flatten
X
EΔ
EZ
μδ
σδ
μZ
σZ
G
X
~
Compression
Decompression
Factors
Signal Encoding Signal Dynamics Signal Decoding
Dropout + Dense
Bi-directional LSTM
Bi-directional LSTM
b1
bT-1
f2
f1fT
f2
f1fT
x2
x1xT
μδσδ
μZσZ
n = N…1
Sample
μZσZμδσδ
f2
f1fT
LSTM
bTbT-1 b1
bT
x2
x1xT
Generative Factors
1-D Convolution (kn, ℓn)
+ Batch Normalization
ELU Activation
+ Dropout
1-D Upsampling
Dropout + Dense
1-D Convolution (k*, ℓ*)
+ Normalize
Compression Network
Repeat Block
Time Distributed Layer
Initial State Encoder
Dynamic State Encoder
Generator Network
Decompression Network
f Forward LSTM Cell
b Backward LSTM Cell
Time-Distributed Output
b)
c) d)
Sample
e)
f)
s0
δt
~~~
Fig. 2. (a) Proposed seismocardiogram generative factor encoder (SGFE). Detailed descriptions are provided in the text. (b) The input Xis ﬁrst processed
by a compression network, which uses a series of Ntime-distributed convolution blocks to compress the input vector. Each 1-D convolution layer nhas
knkernels with length n. A read-in layer encodes the resultant vector as inputs to the dynamic model. Two bi-directional LSTM networks encode (c) the
initial state of the system s0and (d) the change in state with each timestep δt. (e) The generator network is an LSTM network that outputs estimates of the
generative factors at each timestep. The factors are passed through a read-out layer, which is used to construct the estimate ˜
Xof the original input. (f) This
is achieved with a decompression network, a mirror-image of the compression network. 1-D = one-dimensional.
timestep tTis a tuple (µδ,t,σδ,t),µδ,t ,σδ,t RL. The
ith element of the initial state vector s0is then sampled from
s(i)
0∼ N µ(i)
0, σ(i)
0i[1, K].(5)
where N(µ, σ)is a Gaussian distribution with mean µand
standard deviation σ. Similarly, at each timestep t, the jth
element of the state change vector δtis sampled from
δ(j)
t∼ N µ(j)
δ,t , σ(j)
δ,t j[1, L], t T.(6)
Note that each element in s0and δtis drawn independently.
The probabilistic nature of the VAE yields a structured latent
space, as nearby points will produce inherently similar outputs.
As shown in Figure 2(e), the generator network estimates
the generative factors at each timestep based on the system
state. The generator is a uni-directional LSTM network, out-
putting a vector of factors ftRDat each step t. As before,
these factors are passed through a read-out dense layer with
Dinputs and 64 outputs, which maps the generative factors
to corresponding signal features. Like the read-in layer, this
mapping is learned on a session-speciﬁc basis to account for
changes in factor manifestation as signal features.
Finally, the translated factors are used to construct the output
signals ˜
X:={˜x(M)}Twith the decompression network
shown in Figure 2(f). This is a mirror-image of the com-
pression network of Figure 2(b), with the number and length
FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 5
of kernels applied in the reverse order and up-sampling by
a factor of two rather than max pooling. The output of the
decompression network is a convolution layer with a single
ﬁlter (k?= 1) with length ?=1such that the output is a
single vector at each timestep.
D. Human-Subject Experimental Protocol
Experimental data used in this study was collected under
two protocols approved by the Georgia Institute of Technology
Institutional Review Board (IRB). In the ﬁrst protocol, SCG
data was collected from different locations on the chest wall
during exercise-recovery. In the second, SCG sensors were lo-
cated on the mid-sternum only, however the protocol featured
a large cohort of subjects. The latter was therefore used to
train the dynamic model and tune hyperparameters while the
former was used to test model performance.
1) Protocol 1: This protocol, explained in detail in [17],
included 10 healthy subjects (5 male, 5 female; age 24.7 ±
2.3 years; weight 70 ±10.5 kg; height 170 ±11.6 cm) and
was performed on two consecutive days. During the sessions,
electrocardiogram (ECG), impedance cardiogram (ICG), and
SCG signals were collected concurrently. On the ﬁrst day,
individual accelerometers for SCG data collection were placed
on the mid-sternum, 7.5 cm to the right, and 7.5 cm to the
left. On the second day, SCG sensors were placed on the mid-
sternum, 5 cm above, and 5 cm below. For each session, the
subject stood motionless for a 60 second rest period, followed
by a stepping exercise for 60 seconds, and concluding with
a ﬁve-minute recovery period during which the subject stood
upright and motionless. For consistency in this study, only data
from the ﬁrst of the two sessions was used for SCG data from
the central sensor location. Furthermore, this study uses the
notation C, L, R, T, B to refer to the center, left, right, top,
and bottom sensor locations respectively.
2) Protocol 2: This protocol, explained in detail in [33],
included 36 healthy subjects (21 male, 15 female; age 24.7
±3.4 years; weight 68.5 ±13.6 kg; height 170.9 ±9.5
cm). SCG was recorded with an accelerometer on the mid-
sternum along with reference ECG and ICG signals. As
with the previous protocol, the subjects began by standing
upright and motionless for a ﬁve-minute rest period; they
then performed three minutes of walking at 4.83 km/h on
a treadmill followed by 90 seconds of a squatting exercise;
the protocol then concluded with the subject again standing
upright and motionless for a ﬁve-minute recovery period.
E. Signal Pre-Processing
1) Noise Reduction: All signals were ﬁltered with a band-
pass ﬁnite impulse response (FIR) ﬁlter with Kaiser window.
Cutoff frequencies were 0.5-40 Hz for the ECG, 1-30 Hz
for ICG, and 1-40 Hz for SCG [33]. During data collection,
these signals were sampled at 2000 Hz. For the SCG signals,
only the dorsoventral axis (z-axis) acceleration was used
to minimize network complexity, as this is considered the
most useful axis for SCG processing [4]. The signals were
heartbeat-separated using the R-peaks of the concurrent ECG
signal as a reference. It should be noted that the results in this
in this ﬁeld has explored ECG-free SCG segmentation [34].
All signal segments were then abbreviated to a length of 800
samples (400 ms) before being down-sampled to M= 256
samples using linear interpolation with an anti-aliasing ﬁlter.
Note that a signal length of 400 ms was sufﬁcient to capture
AC for this dataset due to its focus on exercise recovery, during
which LVET is low; this may not hold true for other datasets,
and signal length should be adjusted accordingly. For each
protocol and for each subject, the dataset was windowed using
a sliding window of 50 signal segments with 50% overlap
such that T= 50. All signal segments were then normalized
to have zero mean and unit variance. As the ﬁnal step of
processing, ICG and SCG signal segments were smoothed
using a rolling-window ensemble average of ﬁve heartbeats
to remove aberrant noise.
2) AO and AC Estimation: Reference values for AO and
AC were obtained from ICG B- and X-points respectively.
The B-point was computed as the point of maximum sec-
ond derivative occurring before the global maximum of the
waveform; the X-point was computed as the lowest signal
minimum following the global maximum [35]. While ICG is
commonly used for this purpose, the gold-standard for AO
and AC estimation is the echocardiogram; for this reason, the
reference values obtained from ICG are intended for use in
this study as AO and AC correlates rather than ground-truth
measurements [36]. All timing intervals were computed in
reference to the respective ECG R-peak for each heartbeat.
Thus, rAO (PEP) and rAC refer to the time in milliseconds
between the ECG R-peak and AO and AC respectively.
F. Loss Function and Training Protocol
The goal of training was to minimize the loss function
L=αMSE X,˜
X+βD0+1
T
T
X
t=1
Dt.(7)
The MSE operator computes the mean square error between
Xand ˜
X, speciﬁcally
MSE X,˜
X=1
MT
M
X
m=1
T
X
t=1
(x(t,m)˜x(t,m))2.(8)
When calculating the reconstruction error, each target vector
xiXand output vector ˜xj˜
Xwas normalized as will
be described below. The variables D0and Dtin Equation 7
represent the Kullback-Leibler (KL) divergence, which is a
measure of similarity between two probability distributions.
For distributions Pand Q, The KL divergence is given by
D(PkQ) = X
x
P(x) log Q(x)
P(x).(9)
In Equation 7, the variable D0is given by
D0=
K
X
k=1
DN(0,1)kN µ(k)
0, σ(k)
0 (10)
FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 6
and the variable Dtis similarly given by
Dt=
L
X
=1
DN(0,1)kN µ()
δ,t , σ()
δ,t .(11)
While the MSE term represents the reconstruction error, the
divergence terms impose a penalty on the distributions from
which s0and are sampled. This has two beneﬁts for the
model. First, the size of the state space deﬁned by s0and is
limited, as divergence from a zero-centered distribution with
unity variance will increase the KL divergence; this increases
the continuity of the latent space, as it is disadvantageous for
inputs from different sessions to cluster in different locations
of the state space. Second, this serves to disentangle the
dimensions of the state space, since redundancy in information
encoded by each variable may increase the KL divergence as
well [37]. Increases in KL divergence are tolerated only if they
lead to a sufﬁcient decrease in reconstruction error.
The variables αand βin Equation 7 are scalars computed
during the ﬁrst training step which normalize the value of each
term to 0.5. This serves to equalize the contribution of both
terms and express the loss at each epoch as a percentage of
initial error with random network weights.
Since the AO-related features in the ﬁrst half of the signal
generally have a higher SNR than the AC-related features in
the second half, the ﬁrst and second halves of each signal
vector were normalized separately with zero mean and unit
variance. If this normalization was not performed, the decrease
in MSE resulting from modeling AC-related features did not
surpass the increase in KL divergence penalty for doing so.
Though this method produced a discontinuity in the middle
of each signal, it has the beneﬁt of not increasing the number
of hyperparameters parameters of the model as would be the
case with other solutions such as using a true β-variational
scheme [37] or weighing the MSE differently at each sample
point. Furthermore, normalizing the amplitude features has
the beneﬁt of preventing the model from encoding amplitude
features, which are not of interest in this model [30].
The model was implemented in Keras with Tensorﬂow
backend. The hardware setup was based on a 3.6GHz Intel
Core i7 7820X processor with a GeForce GTX 1080 Ti GPU.
Training was performed using mini-batch stochastic gradient
descent [38]. At the beginning of each epoch — which repre-
sents a group of training steps in which all training samples
are incorporated — the training samples were randomized and
split into batches of 32 samples for each gradient computation.
with initial learning rate 0.001, β1= 0.9,β2= 0.999, and
= 1.0×107, which are the standard hyperparameters
for this optimizer [39]. The learning rate was decayed by
a factor of 0.5 after each set of 10 consecutive epochs
without achieving a new minimum validation loss. Training
was terminated after 30 such consecutive epochs. This model
required 95 minutes to train using 9.3×106training samples.
During training, a simplifying assumption was made
whereby a single pair of projection layers was trained for
all sessions in the training set. Thus, data from all sessions
was mixed together at the beginning of each epoch. Subse-
quently, during testing, session-speciﬁc projection layers were
learned by freezing all network weights besides those in the
projection layers and repeating the same training protocol
separately for each session in the testing set. Learning session-
speciﬁc projection layers for the training set greatly increased
computational complexity and did not yield corresponding im-
provements in model performance, so this was only performed
during testing.
G. Dimensionality Estimation
Before modeling SCG dynamics, proper dimensionality for
the state variables s0and was estimated. The model in
Figure 2 was ﬁtted with recovery-period data from the 36
subjects of Protocol 2, training on 16 subjects, validating on
10, and testing on 10. The value of βin Equation 7 was set to
zero such that the latent space was not arbitrarily regularized.
As a starting point, the values of Kand Lwere both set to
10, and Dwas set to 20. In this study, Dwas always set to
K+Lsuch that the generator network did not additionally
perform dimensionality reduction or expansion.
After training, the vector s0and matrix were computed
for each sample in the testing set. Concatenating the former
across testing samples yielded a matrix S0RN×Kwhere N
is the number of testing samples. The dimensionality of the
initial state was estimated by performing PCA on the matrix
S0and returning the variance explained by each resultant PCA
dimension, of which there were K[40].
Note that returns a vector at δteach timestep tT,
and thus RT×Lfor each testing sample. Therefore, for
each timestep t, the vector δtwas concatenated across testing
samples to yield Tmatrices tRN×L. PCA was performed
on each matrix tand the variance explained by each PCA
dimension was calculated. For each dimension, the variance
explained was averaged across each timestep to compute
the mean variance explained across time. To determine the
dimensionality of s0and used in this study, a cutoff of
10% variance explained was used, as additional dimensions
would increase the complexity of the model without yielding
signiﬁcant increases in explained variance.
H. Training and Testing Dynamic Model
The model in Figure 2 was trained using the exercise-
recovery period data from each of the 36 subjects in Protocol
2. To focus the modeling on dynamic processes, resting period
data was not used. A total of 10 subjects in the training set
were selected at random for validation and thereby removed
from the training set. Based on results from the previous
section, the dimensionality parameters Kand Lwere set to 4
and the parameter Dwas therefore set to 8.
After training, all network weights save for those in the
projection layer were frozen. The model was then trained
separately on data from each subject and sensor position in
the testing set. This consisted of data from the 10 subjects in
Protocol 1 with ﬁve position-speciﬁc sessions each, leading
to 50 session-speciﬁc pairs of projection layers with uni-
versal compression, dynamic, and decompression networks.
Therefore, though the subspace deﬁned by generative factors
FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 7
remained constant, projection into and out of this subspace was
learned on a session-speciﬁc basis. For each testing sample,
data collected included s0,,F, and ˜
X.
Held-out validation was not used for learning session-
speciﬁc projection layers in the testing set. This is because
the SGFE is a fully-unsupervised model, meaning that for
practical implementation, it is a reasonable assumption that
data collected from the patient may be used to update the
model and infer generative factors concurrently. Furthermore,
since the projection layers accounted for approximately 1% of
network parameters (1096 of 103169 total), this enabled rapid
training of the session-speciﬁc projections, supporting that this
approach is reasonable for quasi-real-time feedback systems.
I. Visualizing Behavior of Subspace Projections
For visual analysis of subspace behavior, the goal of the
following method was to identify the pair of dimensions in
the learned subspace Fthat encoded the most consistent
linear trajectories. Linear trajectories were expected to arise
in the latent space because, as will be illustrated, AO and AC
were found experimentally to follow linear trends in exercise-
recovery when plotted against one another.
To do so, for each session in the test set deﬁned by the
subject S[1,10] and sensor position P∈ {C,L,R,T,B},
the subspace projection FRT×Dfor each of NS,P samples
in the session was concatenated to form the matrix FS,P
RT NS,P ×D. In this manner, each matrix FS,P contained the
subspace encoding of all data for one of the 50 sessions in
the test set. These matrices were further concatenated row-
wise across all subjects to form the matrix FPfor each sensor
position. Thus, FPcontained the subspace encoding of all data
from sessions from a particular sensor position.
The following was then performed for all P. For each pair
of column vectors (fi,fj)FP, i 6=j, linear regression was
used to ﬁnd the optimal linear ﬁt between fiand fj. The
pair i, j in which the coefﬁcient of determination (R2) of the
linear ﬁt averaged across all Pwas maximal was selected
as the optimal axis pair for further analysis [41]. Subspace
trajectories were visualized by plotting the resultant vectors
f1and f2against one another.
Though this method is useful in identifying hyperplanes in
the learned subspace in which trajectories are consistent, this
does not necessarily mean that the information encoded in the
hyperplane is useful and that the two dimensions simply co-
vary despite attempts at disentanglement. Therefore, a second
qualitative analysis was performed to determine whether the
identiﬁed dimensions may contain useful information about
the known generative factors AO and AC. For ﬁve of the 10
subjects in the testing set chosen at random, the ICG-derived
rAO interval was plotted against the rAC interval on a scatter
plot for the ﬁrst of the two recording sessions. Best-ﬁt lines
were then overlaid on data from each subject to better visualize
the trajectories of these intervals. For the same subjects, the
subspace projections f1and f2from the same session for the
central sensor location were plotted on a scatter plot. Best-
ﬁt lines were again overlaid on the subspace encoding for
each patient in order to observe whether changes in rAO/rAC
trajectories may be reﬂected by the identiﬁed dimensions.
J. Visualizing Sensor Location Effect on Observed Dynamics
Though the hyperplane deﬁned by f1and f2may be a
suitable subspace in which to observe the consistent dynamics
of SCG signals, it may be sub-optimal for visualizing the
effects of changing sensor state on observed dynamics. To
do so more effectively, PCA was used to ﬁnd an informative
three-dimensional representation of the the subspace F, and
the average trajectory for each of the ﬁve sensor positions was
then plotted in these PCA dimensions for visualization.
To do so, the matrix FPwas concatenated across positions
to form Ftot RT Ntot×Dwhere Ntot is the total number of
samples in the testing set. The matrix Ftot thus contained
the subspace projections for all samples in the testing set.
PCA was then perfomed on Ftot to obtain the transformation
ARD×Dmapping dimensions of Ftot into the orthogonal
subspace deﬁned by PCA dimensions.
The following was then performed for each matrix FS,P ,
which contained the subspace encoding for the session with
subject Sand position P. Each of the 10 matrices FS,P ,
S[1,10] was averaged elementwise to obtain a session-
averaged matrix ¯
FP.¯
FPthereby contained the subspace
encoding for position Paveraged across all subjects. Sub-
sequently, this matrix was transformed using the matrix Ato
obtain AP=¯
FPA, the projection of ¯
FPin the PCA subspace.
Finally, for each position, the ﬁrst three dimensions of AP
were then plotted on a scatter plot for visualization.
K. Evaluating Generative Factor Inference
Based on the results of qualitative analysis, quantitative
analysis was performed to determine the extent to which
the learned subspace Fencodes known generative factors
derived from the ICG reference. Since VAE models are fully-
unsupervised, generative factors may not necessarily corre-
spond to the dimensions of the latent space in a one-to-one
manner; rather, such factors may be encoded by combinations
of dimensions. Because of this, we instead apply transforma-
tions to the latent space to better estimate generative factors.
In this work, linear regression was used to infer ICG-
derived AO and AC event timing using the learned subspace
dimensions. As shown in Figure 1(g), this method identiﬁed a
linear mapping from the dimensions of Fto known generative
factors. To begin with, a separate linear mapping was learned
for each sensor position Pand with each of the 10 subjects
in the testing set held-out. To do so, least-squares regression
was used to solve
XP, ¯
S= argmin
X
kYP, ¯
SFP, ¯
SXk2
2(12)
where FP, ¯
Sis the matrix FPwith the subject Sheld-out and
YP, ¯
Sis a matrix where each column is a vector of known
generative factor values corresponding to each row of FP, ¯
S.
The columns of YP, ¯
Sthus contained the ICG-derived rAO
and rAC intervals respectively. This process was performed
for each of the ﬁve sensor positions and with each of the 10
subjects held-out. Once the mapping XP, ¯
Swas learned for
each held-out subject, it was used to obtain predictions from
the held-out subject such that
˜
YP,S =FP,S XP, ¯
S(13)
FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 8
Fig. 3. Percent variance explained by each PCA dimension for model trained
using K= 10,L= 10 with β= 0. Results are shown for initial state vector
s0(blue), and state change matrix (red) using logarithmic axis.
where ˜
YP,S is a vector of predicted generative factors for
subject Swith sensor position P. The R2and root-mean-
square error (RMSE) were obtained for the predicted factors
˜
YP,S versus the known generative factors YP,S after each
session, and the performance results were plotted for each
sensor position [40].
L. Quantifying Sensor Location Effect on Subspace Encoding
If alterations in sensor state have predictable effects on
observed dynamics, this would mean that the mapping from
the latent space Fto the generative factors would perform
strongly for signals from a single position, but sub-optimally
for others. Consequently, if sensor placement was known, this
would allow algorithmic compensation for sensor placement
when inferring generative factors. To observe this effect, the
following was calculated for each pair of positions Pi, PjP
and subject S:
˜
Y(i,j),S =FPi,S XPj,¯
S(14)
where Piis the position being tested and the mapping was
trained using data from Pj. For each session — corresponding
to subject Sand sensor location Pi— the R2was obtained
between ˜
Y(i,j),S and YPi,S for both the rAO and rAC intervals,
where the former is the model’s estimate and the latter is the
ICG-derived reference values. The result was then averaged
across subjects to yield the matrices ˜
YAO,˜
YAC R5×5, where
each element ˜y(i,j )was the average R2across subjects for
sensor data from position Piwith a mapping trained using data
from position Pj. The performance matrices ˜
YAO and ˜
YAC
were then plotted as confusion matrices to visualize changes in
performance when using different position-speciﬁc mappings
for testing data from each position.
III. RES ULTS A ND DISCUSSION
A. Dimensionality Estimation
Figure 3 shows the variance explained by PCA dimensions
for s0and . Notably, after the ﬁrst four PCA dimensions, the
variance explained by additional dimensions of s0or does
not exceed 10%. Therefore, by limiting the dimensionality
of these vectors to 4, the complexity of the network is
reduced without sacriﬁcing the ability to encode information
that substantially impacts signal reconstruction.
Dimensionality selection presents an essential trade-off in
autoencoder architectures. Low dimensionality of the latent
layers both reduces network complexity — limiting the num-
ber of parameters that must be learned while increasing
generalizability — and compels each dimension to encode
more useful attributes, in terms of variance explained. On the
other hand, limiting dimensionality too severely may inhibit
the network from adequately reconstructing the signal, and
thus small variations that may nevertheless be important in
encoding factors such as sensor state may not be represented
in the latent space [42]. For this reason, the selected dimen-
sionality may not generalize to applications in which encoding
of more minute changes in SCG morphology is required.
Along these lines, while the chosen dimensionality was
adequate for sensor state encoding, the results in Figure 3
do not necessarily indicate that the process underlying SCG
generation is inherently low-dimensional. During the dynamic
process of exercise-recovery explored in this work, variance
in the SCG waveform is likely driven by key factors such as
valvular event timing, which may lead the contribution of other
factors to be understated. In other applications and during other
processes, the dimensionality of the latent space for effective
computational modeling may increase or decrease.
B. Visualizing Behavior of Subspace Projections
Subspace projections of SCG signals for two subjects during
exercise-recovery are shown in Figure 4. From the ﬁrst and last
columns of the ﬁgure, it is apparent that signal morphology
between the subjects — and even at different sensor loca-
tions for the same subject — often varies substantially. This
time-domain variability is juxtaposed with trajectories in the
learned subspace which are largely conserved. Speciﬁcally, the
subspace projection of the signal during this period follows an
approximately linear trajectory in the reference frame deﬁned
by the selected subspace dimensions f1and f2.
This consistency is essential because it suggests that this
subspace encodes features that are common to SCG signals de-
spite apparent morphological differences. As aforementioned,
this is made possible by the session-speciﬁc projection layers,
which encode the translation between estimated generative fac-
tors and time-domain signal features. In this manner, anatomi-
cal heterogeneity is captured by the projection into and out of
this subspace, and not by the subspace itself. Such a result
suggests that constructing models which incorporate rather
than eschew patient-speciﬁc heterogeneity may consistently
model underlying patterns.
With regards to practically implementing such a system, it
is important to note that this subspace projection was learned
in a fully-unsupervised manner. Therefore, it is reasonable
to assume that such patient-speciﬁc tuning of the model for
optimal performance will be feasible in practical systems: the
projection may be learned passively without any labeled train-
ing data. Furthermore, approximately 1% of model parameters
FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 9
Center
LeftRightTop
Bottom
Subject 1 SCG Subject 2 SCGSubspace Trajectory
Time (ms)
Amplitude (A.U.)
f1
f2
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4
-0.3 0
0.4
-0.8
0 400
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-4
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-4
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-0.3 0
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-0.8
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0.4
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f1
f2
Time (ms)
Amplitude (A.U.)
Time (ms)
Amplitude (A.U.)
f1
f2
f1
f2
Time (ms)
Amplitude (A.U.)
Fig. 4. Subspace projections of recovery-period SCG data for two subjects. The rows of the ﬁgure represent each of the ﬁve different sensor positions. The
left and right columns show a subset of the amplitude-normalized SCG data from Subjects 1 and 2 respectively, with the second and third columns showing
the corresponding subspace trajectories in green and blue respectively. The axes represent learned subspace dimensions f1and f2; gray points in the ﬁgure
represent subspace projections with the same sensor position from the remaining patients in the testing set. Trajectory directions are overlaid (black, dotted).
A.U. = arbitrary units.
were contained by the projection layers, which may enable
rapid training in quasi-real-time systems. While training the
full model required approximately ﬁve hours with this dataset
and hardware setup, ﬁtting session-speciﬁc projection layers
was typically achieved in less than three minutes.
An example of the relationship between ICG-derived rAO
and rAC and the learned subspace dimensions f1and f2
is shown in Figures 5(a) and (b). Figure 5(a) shows the
trajectories in the subspace deﬁned by rAO and rAC for each
subject, while Figure 5(b) shows the corresponding trajectories
FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 10
0.4
-0.3
f2
f1
-0.8 0
0.3
0
Normalized AO
Normalized AC
0.4 0.9
(b)(a)
0
0.5
-0.5
0.1 -0.1 -0.3 0.4
PC 1
PC 2
PC 3
-0.5 -0.7
-0.6
-0.4
-0.2
0
0.2
(c)
C
L
R
T
B
Fig. 5. (a) ICG-derived AO and AC points during exercise-recovery for ﬁve subjects in the test set, with each subject assigned a different color. AO and
AC are shown as scatter points; best-ﬁt lines for the scatter points are overlaid as dashed lines. (b) Subspace trajectories in dimensions f1and f2from
centrally-placed sensors for the same subjects with the same color-coding as in (a). Subspace projections are shown as scatter points with best-ﬁt lines overlaid
as dashed lines. (c) Trajectories in PCA dimensions of Ffor SCG signals from each of the ﬁve sensor positions averaged across all subjects. From lightest
to darkest shading, the positions include center, left, right, top, and bottom. The trajectories are also indicated with black dashed lines.
in the subspace deﬁned by f1and f2. In Figure 5(a), the
linear dynamics are apparent; while the trajectories are similar
for most patients, one of the patients in this set — shown
in purple — has a trajectory which differs visibly from the
others. This difference is reﬂected in Figure 5(b), which shows
a corresponding change in trajectory in the learned subspace.
The qualitative results shown in Figures 4 and 5(a)-(b) serve
to visually demonstrate what will be shown quantitatively
in the following sections. To enable robust generative factor
inference, subspace trajectories for similar processes must be
consistent, and changes in underlying generative factors must
be reﬂected in the learned subspace.
C. Visualizing Sensor Location Effect on Observed Dynamics
While the dimensions f1and f2demonstrate consistent
trajectories for all positions, they may not best illustrate
changes in observed dynamics associated with sensor location.
Figure 5(c) shows the session-averaged trajectories for each
of the ﬁve sensor positions in the ﬁrst three PCA dimensions
of F. The ﬁgure illustrates that each of the sensor positions
has a characteristic, distinguishable trajectory in the subspace.
Changing the position of the SCG sensor is akin to altering
the reference frame from which the underlying hemodynamic
process is observed. This is reﬂected in Figure 5(c): though the
trajectories observed at each position are consistently linear,
their direction varies with the change in reference frame. As
will be shown, predictable changes in these trajectories allow
for correcting the altered reference frame algorithmically when
inferring generative factors, mitigating the effect of sensor
position on observed dynamics.
D. Evaluating Generative Factor Inference
The performance of position-speciﬁc linear mappings for
rAO and rAC inference from the learned subspace Fis shown
in Figures 6(a) and (b). Figure 6(a) shows that these mappings
produced values that correlated strongly with ICG-derived
intervals. Additionally, Figure 6(b) shows the RMSE between
estimated and reference values for the generative factors.
Notably, while the R2values for rAO only slightly exceed
those for rAC, the RMSE of the estimated rAO is signiﬁcantly
lower than that of rAC. This indicates that while the learned
subspace Feffectively encoded changes in rAO and rAC,
the precise value of rAC had a larger offset versus the ICG
reference. This is unsurprising, since the signal features cor-
responding to AC generally have lower energy, often causing
ambiguity for precise AC identiﬁcation. Beyond demonstrating
accurate asseessment of rAO and rAC, Figures 6(a) and (b)
demonstrate that the latent space of the SGFE model contains
information on measurable physical phenomena.
The RMSE for rAO estimation shown in Figure 6(b) is
within acceptable limits for all sensor positions, which in
prior work typically falls between 11–18ms compared to ICG-
derived reference values [33]. For instance, [13] used XGBoost
regression on an ad hoc feature set to estimate rAO using
SCG sensors in four different sensor locations, achieving
RMSE values from 11.6(±0.4)ms to 17.1(±0.6)ms using z-
axis acceleration. Recently, [33] used a similar method to
achieve an RMSE of 11.46(±0.32)ms from centrally-placed
sensors fusing multiple accelerometer and gyroscope axes. As
shown in Figure 6(b), the RMSE for this task ranged from
7.23(±1.54)ms to 10.53(±1.11)ms in this work. Regarding
rAC estimation, the RMSE was larger than for rAO when
expressed in miliseconds; however, since the rAC interval is
much longer than rAO, the error in rAC estimation relative to
its magnitude was comparable to that of rAO. This is reﬂected
in Figure 6(a), which shows a more comparable R2between
estimated and true rAO and rAC, with values in the range
0.81–0.90 for rAO and 0.72–0.83 for rAC.
Though the results in Figures 6(a) and (b) show that some
sensor locations achieved somewhat higher performance than
others, it is important to note that the optimal sensor location
for rAO and rAC estimation is likely an idiosyncracy depen-
dent upon the processing method or perhaps even the dataset
being used. For instance, Figure 6(b) suggests that the lower-
sternum sensor placement is optimal for rAO estimation while
[13] achieved highest performance under the left clavicle.
Finally, it is important to note that ICG is not the gold-standard
FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 11
Estimated AO (ms)
Estimated AC (ms)
Training Set
Testing Set
C
L
R
T
B
C L R TB0
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60
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90
60 70 80 90
ICG-Derived AO (ms)
400
650
600
550
500
450
ICG-Derived AC (ms)
440 560
460 480 500 520 540
Testing Set
C
L
R
T
B
Training Set
C L R TB
Position
C L RTB
0
0.2
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0.8
1.0
R2
0
5
10
15
20
25
RMSE (ms)
Position
C L RTB
R2
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 6. (a) R2and (b) RMSE between ICG-derived rAO (blue) and rAC (red) and estimations from the learned subspace Fusing position-speciﬁc linear
mappings (x-axis) on held-out subjects. (c) Scatter plot of ICG-derived vs. estimated rAO for one subject with sensors placed in the center (black), left (blue),
and right (green) locations using the linear mapping trained on centrally-placed SCG data. 1:1 correspondence line is overlaid (black, dashed). (d) Confusion
matrix of average R2for rAO estimation for all held-out subjects for a speciﬁc sensor position (y-axis) derived using linear mappings trained on a speciﬁc
position (x-axis). Analogous results for rAC estimation are shown in (e) and (f).
reference for AO and AC event timing; therefore, the results
in Figure 6(b) do not necessarily reﬂect the true error of the
estimated generative factors.
E. Quantifying Sensor Location Effect on Subspace Encoding
Figures 6(c)-(f) show the effect of sensor position on the
encoding of known generative factors in the learned subspace.
Figures 6(c) and (e) show that rAO and rAC estimates correlate
more consistently with the ICG-derived values when the
proper position-speciﬁc mapping is used. Figures 6(d) and
(f) illustrate this effect for all subjects in the testing set and
with all sensor position and linear mapping combinations. This
result corroborates Figure 5(c) in suggesting that subspace
trajectories from a particular position are more similar to those
from the same position than to others; therefore, if the position
is known, the proper linear mapping XPcan be applied to
the subspace Fto obtain estimates of the generative factors.
In effect, modeling sensor position as a generative factor as
shown in Figure 1(b) enables adaptation to sensor placement
by removing the bias in observed dynamics introduced by the
sensor’s position.
Notably, mismatching the linear model to the true sensor
position in Figures 6(c) and (e) still yielded generative factor
estimates that followed the same general trend, though the
variance of these trends was higher. This may be because the
linear mapping is primarily driven by dimensions in which
dynamics are consistent such as f1and f2in Figure 4 while the
remaining dimensions are used for ﬁne-tuning these estimates.
The above results demonstrate the ﬁnal step for algorithmic
correction of sensor misplacement for rAO and rAC inference.
After reducing the dimensionality of SCG signals with SGFE,
selecting a position-speciﬁc regression model between the
latent space and rAO and rAC enables improved estimation
of these parameters, as shown in Figures 6(d) and (e). These
results also highlight the clinical application of this work: by
inferring these indicators in a manner that is robust to changes
in SCG morphology and sensor position, the practicality of
using SCG in healthcare settings may be improved.
F. Limitations and Future Work
To achieve the potential clinical applications of this work,
future studies should ﬁrst explore how to optimize this model
for rAO and rAC estimation; as optimization of deep learning
models is a complex process and largely dependent on the
nature of the dataset, this procedure and discussion should
be explored at length in future studies. As the focus of this
work was model formulation rather than optimization, these
hyperparameters were derived heuristically from the results
in [30]. Future work should also compare the performance of
SGFE-based models to existing methods of rAO and rAC esti-
mation in outpatient and clinical environments and, if possible,
employ echocardiography as a gold-standard reference in lieu
of ICG. While the sample size of this study was designed for
validation of the model, comparisons against other methods
will require both optimization of the model and a larger cohort
of subjects. More broadly, a key avenue of future work is
exploring the role of SCG generative factor modeling in the
diagnosis and assessment of disease states. In particular, the
underlying dynamics of SCG signals may vary in heart failure
patients compared to healthy controls. Elucidating differences
FINAL MANUSCRIPT: LAST EDITED TUESDAY MARCH 11, 2020 12
in these dynamics may yield a deeper understanding of the
effect of heart failure on SCG signals [7], [8].
IV. CONCLUSION
In seeking to improve the usability of SCG signals in
clinical and outpatient environments, this work presented a
new method of modeling SCG signals using dynamic and
generative modeling. It was shown that SCG signals exhibit
consistent behavior in low dimensions despite morphological
variability. Harnessing this result enabled the inference of key
cardiomechanical indicators while adapting to inter-subject
variability and sensor misplacement. Ultimately, developing
SCG processing methods which are robust to these factors may
better enable the noninvasive assessment of cardiomechanical
function for the diagnosis and management of cardiovascular
disease.
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... The proposed seismocardiogram model in [21] represents blood flow through large vessels in the upper part of the body. The written mathematical model explains the systolic and diastolic phases and forces [34]. This mathematical model is helpful and suited to explaining heart work from a mechanical perspective. ...
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Nonclinical measurements of a seismocardiogram (SCG) can diagnose cardiovascular disease (CVD) at an early stage, when a critical condition has not been reached, and prevents unplanned hospitalization. However, researchers are restricted when it comes to investigating the benefits of SCG signals for moving patients, because the public database does not contain such SCG signals. The analysis of a mathematical model of the seismocardiogram allows the simulation of the heart with cardiovascular disease. Additionally, the developed mathematical model of SCG does not totally replace the real cardio mechanical vibration of the heart. As a result, a seismocardiogram signal of 60 beats per min (bpm) was generated based on the main values of the main artefacts, their duration and acceleration. The resulting signal was processed by finite impulse response (FIR), infinitive impulse response (IRR), and four adaptive filters to obtain optimal signal processing settings. Meanwhile, the optimal filter settings were used to manage the real SCG signals of slowly moving or resting. Therefore, it is possible to validate measured SCG signals and perform advanced scientific research of seismocardiogram. Furthermore, the proposed mathematical model could enable electronic systems to measure the seismocardiogram with more accurate and reliable signal processing, allowing the extraction of more useful artefacts from the SCG signal during any activity.
... The timings of the SCG markers allow estimating time intervals that give important insights into cardiac mechanics, such as pre-ejection period (PEP), left ventricular ejection time, rapid diastolic filling time, isovolumic contraction and relaxation times [11][12][13][14][15][16]. In particular, the PEP, which is commonly defined as the time interval between the onset of the QRS complex (i.e., the Q-wave) in the Electrocardiogram (ECG) signal and the subsequent AO event in the SCG, has been the subject of numerous studies because of its key role in determining the health status of patients with heart failure [17][18][19][20]. ...
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Forcecardiography (FCG) is a novel technique that measures the local forces induced on the chest wall by the mechanical activity of the heart. Specific piezoresistive or piezoelectric force sensors are placed on subjects’ thorax to measure these very small forces. The FCG signal can be divided into three components: low-frequency FCG, high-frequency FCG (HF-FCG) and heart sound FCG. HF-FCG has been shown to share a high similarity with the Seismocardiogram (SCG), which is commonly acquired via small accelerometers and is mainly used to locate specific fiducial markers corresponding to essential events of the cardiac cycle (e.g., heart valves opening and closure, peaks of blood flow). However, HF-FCG has not yet been demonstrated to provide the timings of these markers with reasonable accuracy. This study addresses the detection of the aortic valve opening (AO) marker in FCG signals. To this aim, simultaneous recordings from FCG and SCG sensors were acquired, together with Electrocardiogram (ECG) recordings, from a few healthy subjects at rest, both during quiet breathing and apnea. The AO markers were located in both SCG and FCG signals to obtain pre-ejection periods (PEP) estimates, which were compared via statistical analyses. The PEPs estimated from FCG and SCG showed a strong linear relationship (r > 0.95) with a practically unit slope, and 95% of their differences were found to be distributed within ± 4.6 ms around small biases of approximately 1 ms, corresponding to percentage differences lower than 5% of the mean measured PEP. These preliminary results suggest that FCG can provide accurate AO timings and PEP estimates.
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Cardiovascular disease is a major cause of death worldwide. New diagnostic tools are needed to provide early detection and intervention to reduce mortality and increase both the duration and quality of life for patients with heart disease. Seismocardiography (SCG) is a technique for noninvasive evaluation of cardiac activity. However, the complexity of SCG signals introduced challenges in SCG studies. Renewed interest in investigating the utility of SCG accelerated in recent years and benefited from new advances in low-cost lightweight sensors, and signal processing and machine learning methods. Recent studies demonstrated the potential clinical utility of SCG signals for the detection and monitoring of certain cardiovascular conditions. While some studies focused on investigating the genesis of SCG signals and their clinical applications, others focused on developing proper signal processing algorithms for noise reduction, and SCG signal feature extraction and classification. This paper reviews the recent advances in the field of SCG.
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The ballistocardiography (BCG) signal is a measurement of the vibrations of the center of mass of the body due to the cardiac cycle and can be used for noninvasive hemodynamic monitoring. The seismocardiography (SCG) signals measure the local vibrations of the chest wall due to the cardiac cycle. While BCG is a more well known modality, it requires the use of a modified bathroom scale or a force plate and cannot be measured in a wearable setting, whereas SCG signals can be measured using wearable accelerometers placed on the sternum. In this work we explore the idea of finding a mapping between zero mean and unit $\ell_2$ -norm SCG and BCG signal segments such that, the BCG signal can be acquired using wearable accelerometers (without retaining amplitude information). We use neural networks to find such a mapping and make use of the recently introduced UNet architecture. We trained our models on 26 healthy subjects and tested them on 10 subjects. Our results show that we can estimate the aforementioned segments of the BCG signal with a median Pearson correlation coefficient of 0.71 and a median absolute deviation (MAD) of 0.17. Furthermore, our model can estimate the R-I, R-J and R-K timing intervals with median absolute errors (and MAD) of 10.00 (8.90), 6.00 (5.93) and 8.00 (5.93), respectively. We show that using all three axis of the SCG accelerometer produces the best results while the head-to-foot SCG signal produces the best results when a single SCG axis is used.
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Objective: Systolic time intervals, such as the pre-ejection period (PEP), are important parameters for assessing cardiac contractility that can be measured non-invasively using seismocardiography (SCG). Recent studies have shown that specific points on accelerometer- and gyroscope-based SCG signals can be used for PEP estimation. However, the complex morphology and inter-subject variation of the SCG signal can make this assumption very challenging and increase the root mean squared error (RMSE) when these techniques are used to develop a global model. Methods: In this study, we compared gyroscope- and accelerometer-based SCG signals, individually and in combination, for estimating PEP to show the efficacy of these sensors in capturing valuable information regarding cardiovascular health. We extracted general time-domain features from all the axes of these sensors and developed global models using various regression techniques. Results: In single-axis comparison of gyroscope and accelerometer, angular velocity signal around head to foot axis from the gyroscope provided the lowest RMSE of 12.63 ± 0.49 ms across all subjects. The best estimate of PEP, with a RMSE of 11.46 ± 0.32 ms across all subjects, was achieved by combining features from the gyroscope and accelerometer. Our global model showed 30% lower RMSE when compared to algorithms used in recent literature. Conclusion: Gyroscopes can provide better PEP estimation compared to accelerometers located on the mid-sternum. Global PEP estimation models can be improved by combining general time domain features from both sensors. Significance: This work can be used to develop a low-cost wearable heart-monitoring device and to generate a universal estimation model for systolic time intervals using a single- or multiple-sensor fusion.
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Early diagnosis and prediction of heart diseases are essential to reduce the cardiac risks. Change in heart cycle morphologies is a vital diagnostic feature for cardiac clinical systems. A seismocardiogram (SCG) signal provides more detailed information of different cardiac phases in a heart cycle compared to othercardiac signals. Hence, heart cycle extraction using SCG is very important to examine cardiac activities. In this manuscript, an orthogonal subspace projection based framework is proposed to extract heart cycles from a SCG signal. The heart cycle is estimated by calculating intervals between consecutive aortic valveopening (AO) instants, and post aortic valve closing (postAC) instants. Orthogonal subspace projection is applied to the SCG signal on ECG subspace for AO peak detection. The signal generated from projection gives the locations of AO peaks in the SCG signal. The postAC peaks are determined on intervals between consecutive AO peaks using segmentation, FIR based smoothing, Butterworth high pass filtering, and finding maxima point. The performance of the proposed method is evaluated using SCG signals fromCEBS database, publicly available at Physionet archive. The performance results show that the proposed method produces an acceptable detection rate with a minimal detection error. The evaluation results of the proposed method show its extendibility in heart rate variability analysis and hemodynamic parameter extraction.
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This work proposes a new framework for measuring sternal cardio-mechanical signals from moving subjects using multiple sensors. An array of inertial measurement units (IMUs) are attached to the chest wall of subjects to measure the seismo-cardiogram (SCG) from accelerometers and the gyro-cardiogram (GCG) from gyroscopes. A digital signal processing method based on constrained independent component analysis is applied to extract the desired cardio-mechanical signals from the mixture of vibration observations. Electrocardiogram (ECG) and photoplethysmography (PPG) modalities are evaluated as reference sources for the constrained independent component analysis algorithm. Experimental studies with fourteen young, healthy adult subjects demonstrate the feasibility of extracting seismo- and gyro-cardiogram signals from walking and jogging subjects, with speeds of 3.0 miles per hour and 4.6 miles per hour, respectively. Beat-to-beat and ensemble-averaged features are extracted from the outputs of the algorithm. The beat-to-beat cardiac interval results demonstrate average detection rates of 91.44% during walking and 86.06% during jogging from SCG, and 87.32% during walking and 76.30% during jogging from GCG. The ensemble-averaged pre-ejection period (PEP) calculation results attained overall squared correlation coefficients of 0.9048 from SCG and 0.8350 from GCG with reference PEP from impedance cardiogram (ICG). Our results indicate that the proposed framework can improve the motion tolerance of cardio-mechanical signals in moving subjects. The effective number of recordings during day time could be potentially increased by the proposed framework, which will push forward the implementation of cardio-mechanical monitoring devices in mobile healthcare.
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Background: Remote monitoring of patients with heart failure (HF) using wearable devices can allow patient-specific adjustments to treatments and thereby potentially reduce hospitalizations. We aimed to assess HF state using wearable measurements of electrical and mechanical aspects of cardiac function in the context of exercise. Methods and results: Patients with compensated (outpatient) and decompensated (hospitalized) HF were fitted with a wearable ECG and seismocardiogram sensing patch. Patients stood at rest for an initial recording, performed a 6-minute walk test, and then stood at rest for 5 minutes of recovery. The protocol was performed at the time of outpatient visit or at 2 time points (admission and discharge) during an HF hospitalization. To assess patient state, we devised a method based on comparing the similarity of the structure of seismocardiogram signals after exercise compared with rest using graph mining (graph similarity score). We found that graph similarity score can assess HF patient state and correlates to clinical improvement in 45 patients (13 decompensated, 32 compensated). A significant difference was found between the groups in the graph similarity score metric (44.4±4.9 [decompensated HF] versus 35.2±10.5 [compensated HF]; P<0.001). In the 6 decompensated patients with longitudinal data, we found a significant change in graph similarity score from admission (decompensated) to discharge (compensated; 44±4.1 [admitted] versus 35±3.9 [discharged]; P<0.05). Conclusions: Wearable technologies recording cardiac function and machine learning algorithms can assess compensated and decompensated HF states by analyzing cardiac response to submaximal exercise. These techniques can be tested in the future to track the clinical status of outpatients with HF and their response to pharmacological interventions.
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Seismocardiography (SCG), the measurement of local chest vibrations due to the heart and blood movement, is a non-invasive technique to assess cardiac contractility via systolic time intervals such as the pre-ejection period (PEP). Recent studies show that SCG signals measured before and after exercise can effectively classify compensated and decompensated heart failure (HF) patients through PEP estimation. However, the morphology of the SCG signal varies from person to person and sensor placement making it difficult to automatically estimate PEP from SCG and electrocardiogram signals using a global model. In this proof-of-concept study, we address this problem by extracting a set of timing features from SCG signals measured from multiple positions on the upper body. We then test global regression models that combine all the detected features to identify the most accurate model for PEP estimation obtained from the best performing regressor and the best sensor location or combination of locations. Our results show that ensemble regression using XGBoost with a combination of sensors placed on the sternum and below the left clavicle provide the best RMSE= 11.6 ±0.4 ms across all subjects. We also show that placing the sensor below the left or right clavicle rather than the conventional placement on the sternum results in more accurate PEP estimates. IEEE