Noninvasive estimation of the electrohysterographic action-potential conduction velocity.

Abstract

Electrophysiological monitoring of the fetal-heart and the uterine-muscle activity, referred to as an electrohysterogram, is essential to permit timely treatment during pregnancy. While remarkable progress is reported for fetal-cardiac-activity monitoring, the electrohysterographic (EHG) measurement and interpretation remain challenging. In particular, little attention has been paid to the analysis of the EHG propagation, whose characteristics might be predictive of the preterm delivery. Therefore, this paper focuses, for the first time, on the noninvasive estimation of the conduction velocity of the EHG-action potentials. To this end, multichannel EHG recording and surface high-density electrodes are used. A maximum-likelihood method is employed for analyzing the EHG-action-potential propagation in two dimensions. The use of different weighting strategies of the derived cost function is introduced to deal with the poor signal similarity between different channels. The presented methods were evaluated by specific simulations proving the best weighting strategy to lead to an accuracy improvement of 56.7%. EHG measurements on ten women with uterine contractions confirmed the feasibility of the method by leading to conduction velocity values within the expected physiological range.

Full text

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2178 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 9, SEPTEMBER 2010
Noninvasive Estimation of the Electrohysterographic
Action-Potential Conduction Velocity
Chiara Rabotti∗, Massimo Mischi, S. Guid Oei, and Jan W. M. Bergmans, Senior Member, IEEE
Abstract—Electrophysiologicalmonitoringofthefetal-heartand
the uterine-muscle activity, referred to as an electrohysterogram,
is essential to permit timely treatment during pregnancy. While
remarkable progress is reported for fetal-cardiac-activity moni-
toring, the electrohysterographic (EHG) measurement and inter-
pretationremainchallenging.Inparticular,littleattentionhasbeen
paid to the analysis of the EHG propagation, whose characteris-
tics might be predictive of the preterm delivery. Therefore, this
paper focuses, for the first time, on the noninvasive estimation of
the conduction velocity of the EHG-action potentials. To this end,
multichannel EHG recording and surface high-density electrodes
are used. A maximum-likelihood method is employed for analyz-
ing the EHG-action-potential propagation in two dimensions. The
use of different weighting strategies of the derived cost function
is introduced to deal with the poor signal similarity between dif-
ferent channels. The presented methods were evaluated by specific
simulations proving the best weighting strategy to lead to an ac-
curacy improvement of 56.7%. EHG measurements on ten women
with uterine contractions confirmed the feasibility of the method
by leading to conduction velocity values within the expected phys-
iological range.
IndexTerms—Actionpotentials(APs),conductionvelocity(CV),
electrohysterography (EHG), electromyography, high density elec-
trodes, maximum likelihood (ML) estimation.
I. INTRODUCTION
T
public health and medical interventions to reduce the incidence
of preterm birth have been introduced. The preterm birth rate
has, however, risen in most industrialized countries and it still
accounts for 75% of perinatal mortality and more than 50%
of long-term morbidity [1], with an associated annual-societal-
economic cost that, in the United States alone, was estimated to
an amount of 26.2 billion in 2005 [2]. It is well established that
HE UNDERSTANDING of risk factors and mechanisms
related to preterm labor has been advancing and many
ManuscriptreceivedNovember20,2009;revisedFebruary5,2010andApril
13, 2010; accepted April 14, 2010. Date of publication May 10, 2010; date of
current version August 18, 2010. This work was supported by the Dutch Tech-
nology Foundation, STW. Asterisk indicates corresponding author.
∗C. Rabotti is with the Department of Electrical Engineering, Eindhoven
University of Technology, Eindhoven 5600MB, The Netherlands (e-mail:
c.rabotti@tue.nl).
M. Mischi and J. W. M. Bergmans are with the Department of Electrical
Engineering, Eindhoven University of Technology, Eindhoven 5600MB, The
Netherlands (e-mail: m.mischi@tue.nl; j.w.m.bergmans@tue.nl).
S. G. Oei is with the Department of Obstetrics and Gynecology, M´ axima
Medical Center, Veldhoven 5500 MB, The Netherlands, and is also with the
Department of Electrical Engineering, Eindhoven University of Technology,
Eindhoven, The Netherlands (e-mail: g.oei@mmc.nl).
Digital Object Identifier 10.1109/TBME.2010.2049111
pregnancy-monitoring techniques are essential to assess the key
risk factors and permit timely medical intervention; however,
accurate prediction of the delivery time, which can be the key
parameter for timely treatment of premature labor, still remains
a major challenge [3].
Next to fetal-heart-rate monitoring, detection and evaluation
of the uterine contractions are of major importance. Typical
techniques adopted in clinical practice involve the use of either
an external tocodynamometer, which provides a noninvasive in-
dication of contraction onset timing based on external strain
gauges, or an internal catheter, which measures the intrauterine-
amniotic pressure [3]. Only the latter technique provides quan-
titative information, but it is invasive and applicable only during
labor [3].
In the past few years, a noninvasive alternative technique has
been proposed that promises reliable assessment of the uterine
activity without the use of intrauterine catheterization. Quan-
titative information on the myometrium (uterine muscle) is in
fact derived from the analysis of its electrical activity, referred
to as an electrohysterogram. Several techniques have been pro-
posed for the analysis of the electrohysterographic (EHG) sig-
nal. Some authors have developed methods for the noninvasive
estimation of the intrauterine pressure [4]–[6], while other au-
thors could distinguish between two different EHG frequency
components [7] or observe a shift in the frequency content of
the EHG signal as delivery approaches [8], [9], possibly be-
ing able to predict the course of pregnancy. The ultimate goal
and main challenge remain the prediction of preterm delivery.
While the reported techniques are mostly based on single chan-
nel measurements [9], we believe that important information
for monitoring and predicting the progress of pregnancy resides
in the EHG signal propagation characteristics as also suggested
in [10] and [11].
Different from skeletal muscles, which are striated and
present an anatomical direction of propagation parallel to the
fiber orientation, the myometrium is a smooth muscle; as a
result, the direction of propagation of the myometrium intra-
cellular action potential (AP), i.e., the electrical activation of
the myometrial cells, is a priori unknown [7]. The propagation
of electrical activity in the myometrium mainly depends, in
fact, on the specific pattern of gap–junction connections which
are dynamically formed between cells during each contrac-
tion[12],[13].Possibleadditionalparametersthatmayinfluence
the propagation of uterine APs are calcium waves [14] and the
possible bundle arrangement of the myometrium fibers [15].
APs usually occur in bursts. Each burst usually corresponds
to a contraction event [16]. The burst frequency and duration as
well as the AP frequency within a burst are highly dependent on
0018-9294/$26.00 © 2010 IEEE

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RABOTTI et al.: NONINVASIVE ESTIMATION OF THE ELECTROHYSTEROGRAPHIC ACTION-POTENTIAL CONDUCTION VELOCITY 2179
the subject and the parturition stage. In human, the bursts’ dura-
tion can be more than 1 min [16], with a burst frequency around
0.1 Hz [7]. The AP frequency within a burst has been reported
to range between 0.1 and 10 Hz [7], with the majority of studies
focusing on the frequency range 0.1–3 Hz [17], [18] and 0.3–
1 Hz [8], [11], [16], [19]. Most of the previous literature was
dedicated to the analysis of the entire burst and only few stud-
ies were dedicated to the analysis of single surface APs [13],
[19], [20]. However, in vitro studies have demonstrated that,
in association with the increase of the gap–junction number,
individual APs propagate for longer distance and with higher
conductionvelocity(CV)atparturitionthanatpreterm[13].Fur-
thermore,asdifferentAPshavedifferentpropagation properties
evenwithinthesameburst,analysisofsingleAPCVcanleadto
moredetailedinformationcomparedtothewholeburstanalysis.
In this paper, we focus, for the first time, on a method for
the estimation of the CV of single surface APs, which are ex-
tracted from EHG signals recorded noninvasively on women
in labor. By surface AP, we refer to a spike extracted from a
single-channel EHG burst that, being recorded noninvasively,
is the weighted average of the electrical activity of all the un-
derlying excited cells [21], [22]. An additional novelty of this
paper resides in the EHG signal recording methodology, which
comprises the use of a high-density (HD) electrode grid. The
grid, in fact, integrates a larger number of electrodes (64) with a
reduced surfaceandsmallerinterelectrodedistancewithrespect
to the previous literature [5], [6], [10], [18], [23]. Furthermore,
due to a priori unknown AP direction of propagation, the bi-
dimensional arrangement of the electrodes on the grid (8×8)
permits to estimate all the possible CV directions along the
abdominal plane parallel to the abdominal surface.
Several methods are available from the electromyography
literature for the measurement of the surface AP CV. Due to
the signal source (skeletal muscles), these methods use mono-
dimensional information, as the direction of propagation can
be derived from the muscle-fiber orientation. These methods
can be divided in four major categories [24]: cross-correlation
function maximization [25], phase difference [26], maximum
likelihood (ML) [27], and the detection of spectral dips [28]. A
four-electrodeimplementationofthismethod(multidip)leading
to an analytical solution, has been presented in [29], where
Farina and Negro mention the possibility of further increase of
the number of electrodes. One of the main issues related to the
use of the spectral dips is the large variance in their detection,
which is due to the variance of the estimated power spectrum
[24]. Furthermore, more extensive validation is required before
adapting the method to EHG measurement. In particular, due to
the varying direction of propagation of the AP, the extension of
the spectral multidip method to two dimensions is neither trivial
nor practical.
Among the remaining three methods, the phase difference
and the ML method, unlike the cross-correlation method, are
bothimplementedinthefrequency domainandpermitCVmea-
surements that are not limited by the time-sampling rate [24].
Given the EHG frequency content, usually lower than 1 Hz [4],
this characteristic is highly desirable, permitting low sampling
rates and, therefore, reducing the complexity of the signal anal-
Fig. 1.Scheme of the measurement setup.
ysis. The ML method [30], compared to the phase-difference
method, permits a complete exploitation of our multichannel
measurements because it allows using all the available acqui-
sition channels, leading to an increased robustness to a low
SNR. Furthermore, different from the spectral multidip, the ML
method can be easily extended to two dimensions.
The ML method has been, therefore, chosen for the EHG
analysis.DuetothemodelsassumedfortheAPpropagationand
for the noise, the ML estimation is equivalent to a mean-square-
error minimization. We improved the ML method described
in [30] by weighting the derived cost function. A set of weights
is automatically determined based on SNR estimates at each
channel. Two different weighting approaches are here presented
and compared. The method in [30] has been further extended to
two dimensions, permitting to estimate amplitude and direction
of the CV.
II. METHODOLOGY
In this section, more detailed information is provided on the
proposed CV-estimation methods. These methods are based on
the characteristics of the measured signals, depending on the
measurement system, presented in Section II-A, as well as on
the implemented preprocessing steps, presented in Section II-B.
The implemented ML method and the proposed improvements
are then presented in Section II-C and II-D, respectively.
A. Measurement
After approval of the medical committee of the hospital, ten
measurements were performed at the M´ axima Medical Center
in Veldhoven, The Netherlands, on ten women in labor who
signed an informed written consent. The sensors were placed
as described in Fig. 1, after skin preparation with an abrasive
paste for contact impedance reduction. The EHG signal was
recorded by a Refa system (TMS International, Enschede, The
Netherlands) comprising a multichannel amplifier for electro-
physiological signals and a grid of 64 (8×8) HD electrodes (1
mm diameter, 4 mm interelectrode distance, respectively). The
HD electrode grid, whose characteristics are more extensively
described in [19], was placed on the midline of the abdomen be-
low the umbilicus; the ground (GRD) electrode was positioned

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2180 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 9, SEPTEMBER 2010
Fig. 2.
tion matrix after filtering and downsampling.
Example of EHG surface APs recorded by one column of the acquisi-
on the right hip. In order to obtain an efficient rejection of elec-
tromagneticinterference,anactiveGRDelectrodewasusedand
allcableswereactivelyshielded[31].Anexternaltocogramwas
employed to support the assessment of the contraction period.
B. Data Preprocessing
Given the narrow-band nature of the EHG signal, similar to
the previous studies [8], [11], [16], [19], the acquired signals
were band-pass filtered by a sixth-order Butterworth filter with
low and high cut-off frequencies at 0.1 and 0.8 Hz, respectively.
This permitted to suppress most of the noise introduced by the
respiration, the maternal electrocardiogram (ECG), and the ab-
dominal electromyogram [19], [32]. The filtered signals could,
therefore, be downsampled from 1024 to 16 Hz without intro-
ducing aliasing and reducing significantly the computational
complexity of the following analysis. This is particularly con-
venient when dealing with 64 parallel channels. Fig. 2 shows an
EHGsurfaceAPsequenceregisteredbyonecolumn(eightchan-
nels) of the acquisition matrix after filtering and downsampling.
In line with the results shown in [20], the example indicates that
within the same burst the direction and speed of propagation
can vary from one surface AP to the next one. This peculiarity
of single-surface APs suggests that their analysis, relative to the
whole EHG burst analysis, provides additional and different in-
formation that may be of clinical relevance. The expected shape
of the EHG surface AP can be derived by the previous studies
on the EHG surface AP, where propagating action potentials
were directly recorded from the uterus surface [20], and where
the EHG surface AP has been measured and modeled [19].
C. Maximum-Likelihood Method
Following the schematic representation of Fig. 3, we assume
the EHG to propagate with velocity v and with incidence angle
θ (θ ∈ [−π,π]) with respect to the vertical axis of the electrode
grid. Due to the size of the electrode grid, which is of the order
of the signal wavelength [19], we can assume the EHG surface
AP to be a planar wave. The signal is detected by Nrrows and
Nccolumns of electrodes. Assuming that the same signal shape
s(n) is measured at each channel, the adopted ML method is
developed under the hypothesis that the signal xrc measured
Fig. 3.Schematic description of the system model.
at the channel (r,c) in the rth row (r ∈ [1,2,...,Nr]) and cth
column(c ∈ [1,2,...,Nc])oftheelectrodegridcanbemodeled
as
xrc(n) = s(n − (r − 1)τr− (c − 1)τc) + wrc(n)
where n indicates the time sample (n ∈ [1,2,...,N]) and
wrc(n)iswhiteGaussiannoisewithvarianceσ2
at channel (r,c). The choice of the noise model is supported by
the narrow band nature of the signal of interest. As from (1), in
each channel (r,c) the reference signal shape s(n) is delayed
by τrand τctime samples with respect to the preceding row and
column, respectively.
The CV calculation requires the estimation of (τr,τc), which
canbeobtainedbythemaximizationofp((τr,τc)|xrc(n),s(n)).
Using Bayesian inference and assuming p(τr,τc) uniform, the
maximization of p((τr,τc)|xrc(n),s(n)) corresponds to the
maximization of the probability p(xrc(n)|(τr,τc),s(n)) of
the samples of the signal xrc(n), given the row and column
sample delays τrand τcand the reference shape s(n), i.e.,
(1)
rcthatispresent
p(xrc(n)|(τr,τc),s(n)) =
?N
Furthermore, the ML estimation of (τr,τc) corresponds to
the maximization of ln(p(xrc(n)|(τr,τc),s(n))) [33], where
1
(2π)
N
2 σN
rc
· e
−
n = 1[xr c(n )−s (n −(r −1)τr−(c −1)τc)]2
2σ2
r c
.
(2)
ln(p(xrc(n)|(τr,τc),s(n))) = ln
?N
The expression in (3) can be extended to the entire matrix in-
cluding all rows r and columns c. The estimation of (τr,τc)
reduces, therefore, to the minimization of the cost function
?
1
(2π)
N
2 σN
rc
?
+
−
n=1[xrc(n) − s(n − (r − 1)τr− (c − 1)τc)]2
2σ2
rc
. (3)
ε2(τr,τc) =
Nr
?
r=1
Nc
?
c=1
N
?
n=1
[xrc(n)+
−s(n − (r − 1)τr− (c − 1)τc)]2.
Since the signals xrc(n) are only available for discrete values
of τrand τc, minimization of (4) results in a discrete estimate of
(4)

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RABOTTI et al.: NONINVASIVE ESTIMATION OF THE ELECTROHYSTEROGRAPHIC ACTION-POTENTIAL CONDUCTION VELOCITY2181
theoptimum(τr,τc),whichdependsonthesamplingrate.Byus-
ing Parseval’s equality, (4) can be transformed in the frequency
domain, where τrand τcbecome continuous multiplicative fac-
tors of the phase and can be estimated without resolution limits.
Indicated by Xrc(f) and S(f), the Fourier transform of the
signal recorded at the channel (r,c) and of the reference shape,
respectively, the resulting cost function is
E2(τr,τc) =
2
N
Nr
?
r=1
Nc
?
c=1
N/2
?
f=1
?
Xrc(f)+
−S(f)e−j2πf[(r−1)τr+(c−1)τc]?2.
From the description in Fig. 3, for an interelectrode distance
equal to d and a temporal-sampling frequency fs, it follows that
τr and τc are related to the conduction velocity v and to the
incidence angle θ by
(5)
τr= fsd cos(θ)
v
τc= fsd sin(θ)
v
.
(6)
The shape function S(f) can be estimated as the average of
all the channels Xrc(f) after alignment, i.e., in the temporal
frequency domain
?S (f) =
The resulting estimated cost function?E2(τr,τc) is then
?E2(τr,τc) =
1
NrNc
m=1
p=1
1
NcNr
Nr
?
r=1
Nc
?
c=1
Xrc(f)ej2πf[(r−1)τr+(c−1)τc].
(7)
2
N
Nr
?
Nc
?
r=1
Nc
?
Xmp(f)ej2πf[(m−r)τr+(p−c)τc]?2. (8)
c=1
N/2
?
f=1
?
Xrc(f)+
−
Nr
?
D. Channel Weighting
The model in (1) is based on the assumption that the signals
recorded at different channels are delayed versions of the same
reference shape s(n). This assumption, already weak for skele-
tal muscles [27], is even weaker for the myometrium, where
differences in the volume conductor and cell-to-cell conduction
pathunderneaththeelectrodesmaycauseshapevariationsofthe
propagating APs [7].In(1),suchshape variations areaccounted
for by the noise term wrc(n). In order to increase the robustness
of the CV estimation to surface AP shape variations due to the
presenceofnoise,themethodisimprovedbyintroducingproper
weights, arc∈ R+, in the cost function. The resulting weighted
cost function?E2
a(τr,τc) is defined as
?E2
a(τr,τc) =
2
N
Nr
?
r=1
Nc
?
c=1
N/2
?
f=1
?
arc
?
Xrc(f)
−?S(f)e−j2πf[(r−1)τr+(c−1)τc]??2.
standard deviation of the channel noise σrc[34], i.e.,
(9)
The weights are chosen to be inversely proportional to the
arc=A
σrc
=
A
2
N
??N/2
f=1|Wrc(f)|2
(10)
whereAindicatesaproperscalingfactortonormalizetheweight
sum to 1. For the expression of arcin the frequency domain,
last term of (10), Parseval’s equality is used, where |Wrc(f)|2
is the noise power spectrum in the considered channel (r,c).
In order to obtain an estimate of the noise power for the
generic channel (r,c), the model in (1) is expressed in the tem-
poral frequency domain f as
Xrc(f) = S(f)e−j2πf[(r−1)τr+(c−1)τc]+ Wrc(f).
(11)
By assuming the reference shape S(f) and the noise Wrc(f)
to be uncorrelated, the noise can be estimated from
N/2
?
f=1
Xrc(f)X∗
rc(f) =
N/2
?
f=1
S(f)S∗(f) +
N/2
?
f=1
|Wrc(f)|2
(12)
where (·)∗is the conjugate operator. The noise power derived
by (12) can then be substituted in (10) to provide the weights
arc=
A
2
N
??N/2
f=1(Xrc(f)X∗
rc(f) − S(f)S∗(f))
.
(13)
The shape?S(f) defined in (7) as the average of the aligned
?S(f) in (9), can be employed in (13).
in (13) can be calculated as the weighted average of the signals
Xrc(f), i.e.,
signals Xrc, which is used as an estimate of the reference signal
Alternatively,theestimate?Sw(f)ofthereferenceshapeS(f)
?Sw(f) =
Using?Sw(f) as an estimate of S(f) in (13), the alternative
aw
2
N
Nr
?
r=1
Nc
?
c=1
aw
rcXrc(f)ej2πf[(r−1)τr+(c−1)τc].
(14)
channel weights aw
rcare defined as
rc=
A
??N/2
f=1Xrc(f)X∗
rc(f) −?Sw(f)?S∗
w(f)
(15)
and using (14) for?Sw(f) and?S∗
w(f), (15) can be expressed as,
(16), shown at the bottom of the page.
aw
rc=
A
2
N
??N/2
f=1Xrc(f)X∗
rc(f) −?Nr
r=1
?Nc
c=1(aw
rc)2Xrc(f)X∗
rc(f)
.
(16)

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2182 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 9, SEPTEMBER 2010
TABLE I
COST FUNCTIONS AND WEIGHTING STRATEGIES
Fig. 4. SNR distribution of 40 APs randomly selected from ten patients.
The NrNc equations are of the same form as (16), which
holds for each channel (r,c), and the condition on the weight
sum
Nr
?
r=1
Nc
?
c=1
aw
rc= 1
(17)
lead to a system of (NrNc) + 1 linearly independent equations,
where the NrNcunknown weights and the scaling factor A can
be univocally derived. Using the same weights aw
function and the reference shape in (13) leads to the following
expressionoftheestimatedalternativecostfunction?E2
?E2
−?Sw(f)e−j2πf[(r−1)τr+(c−1)τc]??2
where differently from the cost function E2(τr,τc) in (9), the
weightsaw
the signals Xrc(f) as an estimate of the reference shape S(f).
Forvalidation,thethreecostfunctionsE2(τr,τc),E2
and?E2
study [35], the use of clustering in combination with weighting
was successfully proposed, for the first time, to select a subset
of electrodes for the CV estimation in one direction and to
improve the estimate accuracy. In the present study, we tested
the combined use of clustering and weighting by defining the
cluster distance as the reciprocal of the weights aw
For the minimization of the cost functions, the Nelder–Mead
Simplex search method was used [36]. The values of τr and
τc are initialized according to the average values reported in
the literature for the uterine AP CV in the circumferential di-
rection (2.8 cm/s) and in the longitudinal direction (6.8 cm/s),
respectively [20]. The proposed methods were implemented in
MATLAB (Mathworks). For each surface AP, with the algo-
rithm running on an Intel Core2 Duo Processor with 1.97 GB
RAM, the CV estimate was obtained in about 1 min.
rcfor the cost
aw (τr,τc)
aw (τr,τc) =
2
N
Nr
?
r=1
Nc
?
c=1
N/2
?
f=1
?
aw
rc
?
Xrc(f)+
(18)
rcarecalculatedusingtheweightedaverage?Sw(f)of
aw (τr,τc), whose definitions are summarized in Table I,
were compared on simulated and real signals. In our previous
a(τr,τc),
rc.

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RABOTTI et al.: NONINVASIVE ESTIMATION OF THE ELECTROHYSTEROGRAPHIC ACTION-POTENTIAL CONDUCTION VELOCITY2183
TABLE II
STANDARD DEVIATION OF THE DELAY ESTIMATES FOR DIFFERENT VELOCITIES AND ANGLES OF INCIDENCE
Fig. 5.
selected surface AP is also shown in the top of the figure by magnifying a time
segment of the burst at the contraction peak.
Example of EHG bursts and corresponding tocogram. An example of
III. RESULTS
A. Simulated Signals
ThepresentedCV-estimationmethodsareevaluatedbymeans
of simulations based on real signals. A time interval of 10 s
including a complete EHG surface AP was extracted from real
EHG recording to obtain the reference shape s(n). This signal
was then artificially delayed to simulate the measurement of
the same surface AP by the other electrodes on the grid. Two
arbitrary velocities of 4 and 10 cm/s and four different angles
of incidence, equal to 0, π/12, π/6, and π/4, were considered.
Fig. 6.Mean and standard deviations of the CV amplitude for all patients.
After downsampling at 16 Hz, the delays corresponded to a
fraction of the sampling frequency.
White Gaussian noise was then added to the reference shape
signal to simulate the remaining 63 channels. In order to deter-
mine a realistic SNR, 40 APs (four per subject) were selected
from the available recorded signals. The SNR was estimated by
(12) in each channel. The distribution of the SNR expressed in
dB over the forty 64-channel recordings, (see Fig. 4), resulted
wellrepresentedbyaGaussianprobabilitydensityfunction(cor-
relation coefficient R = 0.97 with the Gaussian fit), with mean
and standard deviations equal to 5.88 and 7.41 dB, respectively.
Therefore, for each simulated velocity and angle of incidence,
1000 different noise sequences were generated and added to
each channel; the SNR was randomly distributed among the
channels according to a Gaussian probability density function
with the same mean and standard deviation estimated from the
real signals.
The 64-channel simulations were then used to evaluate the
different methods for the CV estimation. The CV estimates
were calculated by the ML method alone, and after the use
of the two different weighting strategies in Table I. The stan-
dard deviations of the error for the row delay τr (SDr) and
the column delay τc (SDc) are reported in Table II for each
simulated angle of incidence and for the different used cost
functions. The maximum mean error was lower than 5% of the
referencevalueofdelay.Onaverage,weightingthecostfunction
reduced thestandard deviation oftheerrorby44.06% ± 8.03%.

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2184 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 9, SEPTEMBER 2010
Fig. 7.
of the surface AP is proportional to the gray level of the map. The reported maps, from (a) to (b), were recorded every 100 ms.
Temporal sequence of surface AP propagation maps as recorded by the whole 64-channel electrode grid after spatial interpolation. The local amplitude
Weighting both the cost function and the reference shape pro-
vided an average improvement of 56.70% ± 2.25%.
B. Real Signals
The measurement feasibility was also tested on ten women
between the 38th and the 41st weeks of gestation with uterine
contractions. Nine women were classified to be in labor (dilata-
tion>3cm)anddeliveredwithin13hfromtheEHGrecording.
During contractions, time segments were visually inspected and
two surface APs were determined per each woman around the
contraction peak. InFig.5,anexample recording ofEHGbursts
after preprocessing and the associated tocographic signal are
shown. The figure shows that the amplitude during the quies-
cent period is significantly lower than during the activity burst.
The magnified time segment in Fig. 5 shows that the surface AP
propagates along the recording electrodes with a velocity of few
centimeterpersecond.Thissuggeststhattheselectedwaveform
originatesfromuterineactivityandnotfromartifactsduetomo-
tion, which typically do not propagate, or to the ECG, which
is not expected to show propagation along electrodes placed on
the abdomen. The longer duration of surface APs relative to
the internal measurements reported in the literature [20] can be
explained by the effect of the volume conductor [19] and by
the fact that the signal recorded by each surface electrode is the
weighted average of the electrical activity of all the underlying
excited cells [21], [22].
The surface AP visual selection aimed at excluding possible
circulating excitations and re-entries [37]. Surface APs origi-
nating in the middle of the electrode grid and then propagating
in two different directions or not propagating through the entire
electrode were also excluded. Only those surface APs origi-
nating outside or on the border of the electrode grid and then
propagating through the entire electrode grid were selected.
Themethod comprisingtheminimizationof thecostfunction
?E2
reported in Fig. 6 for all patients. On average, we found vertical
and horizontal components of the velocity amplitude equal to
3.68±3.24and3.76±3.21cm/s,respectively.Theseestimates
are within the expected physiological range [7]. Concerning
the wave-incidence angle, as was earlier demonstrated by in-
vitro studies, a preferred direction of propagation of single AP
could not be highlighted and, even within the same contraction,
different incidence angles were detected for different APs.
An example of surface AP propagation is shown in Fig. 7, by
means of a temporal sequence of spatial maps, representing the
electrode grid; the local amplitude of the recorded surface AP
is proportional to the gray level of the map. Therefore, the dark
region represents the depolarization phase of the surface AP.
In the first four maps, the repolarization phase of the preceding
surfaceAP(lightregion)isalsovisible.Thereportedmapsrefer
to 8 different instants, 1 every 100 ms, of the surface AP prop-
agation. In the presented example, the surface AP propagates
with an incidence angle of about 6◦and a velocity of 4 cm/s, as
detected by the proposed method.
aw (τr,τc) was applied on the entire 8 × 8 electrode matrix.
Theaverageandstandarddeviationofthevelocityamplitudeare
IV. DISCUSSION AND CONCLUSION
There are only few studies dedicated to the EHG signal prop-
agation properties by multichannel recordings [10], [11]. These
studies investigated the propagation on a large scale by ana-
lyzing the EHG bursts on the whole uterine muscle. A simi-
lar approach has also been attempted by multichannel tocog-
raphy [38]. On the contrary, this paper focuses on the CV

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RABOTTI et al.: NONINVASIVE ESTIMATION OF THE ELECTROHYSTEROGRAPHIC ACTION-POTENTIAL CONDUCTION VELOCITY2185
estimation of single APs. The surface AP CV is an additional
parameter of potential clinical relevance. As on a large scale
this parameter cannot be accurately derived [11], the propaga-
tion analysis is here carried out on a small scale using an HD-
electrode grid. This small-scale analysis provides local propa-
gation parameters that can fundamentally contribute, possibly
in combination to the global parameters derived by large-scale
analysis, to the development of diagnostic and prognostic tools
for uterine contraction monitoring and labor prediction.
The measurement of the EHG surface AP CV is here pro-
posed for the first time. The use of an electrode matrix permits
estimating the CV vector in two dimensions. This is an impor-
tant aspect in EHG measurements because, different from the
electromyographic CV measurements, the EHG CV direction
is not known a priori. For the signal analysis, we propose an
MLmethod, which isimplemented intwodimensions and com-
prises the use of weights in the cost function. The weight values
depend on the estimated SNR.
Results,onthesimulatedsignals,showthattheestimateaccu-
racy is significantly improved by the use of weights. Among the
two different weighting strategies that were proposed, the use
of the same weights for estimating the reference signal shape
and for the cost function results in more accurate estimates. As
compared to the ML method alone, on average, the error vari-
ance diminished by 56.70%, becoming up to less than 3% of the
measured value.
In our previous study [35], the use of clustering in combi-
nation with weighting was successfully proposed, for the first
time,toselectasubsetofelectrodesfortheCVestimationinone
direction and to improve the estimate accuracy. In the present
study, we tested the combined use of clustering and weighting
by defining the cluster distance as the reciprocal of the weights
aw
and weighting led to an estimate accuracy comparable to that
of the best weighting strategy (i.e., the use of the cost function
?E2
therefore, not explicitly reported.
The method feasibility was confirmed by measurements on
ten women at term with uterine contractions. Calculation of the
CV amplitude led to values that are within the expected phys-
iological range [7], [13], [20]. As for the incidence angle of
propagating surface AP, different from what is reported for the
propagationofthewholeelectricalburst[11],wecouldnothigh-
light a most frequent direction of the surface AP propagation
patternevenwithinthesamecontraction.Thesamevariabilityin
both origin and direction of the surface AP propagation pattern
has been previously observed in in-vivo and in-vitro studies on
theuterus,and,atleastduringlabor[20],itseemsphysiological.
For practical reasons, the real-signal analysis was conducted
on APs that were previously selected around the contraction
peak in order to exclude waves originating within the electrode
area and then propagating in two different directions below
the electrode grid. Noteworthy, the proposed method for the CV
estimationisnotlimitedbythisassumption.Infact,ifthesurface
APoriginateswithintheregioncoveredbytheelectrodegridand
then propagates in two different directions [20], an additional
rc. On our simulated signals, the combined use of clustering
aw (τr,τc)) alone. As the clustering can be viewed as a form
of binary weighting, these results could be expected and are,
step is required for detecting the pacemaker electrode (i.e., the
first electrode recording the burst). The CV can be estimated
for the two directions of propagation by applying the proposed
method separately on the two subsets of electrodes in which the
grid can be divided by the pacemaker electrode.
AdditionalexclusioncriteriaforthesurfaceAPselectionwere
circulating excitation, re-entries, and partial propagation along
the electrode grid. These phenomena have been previously ob-
servedforthemyometriumactivityinanimalstudies.Inparticu-
lar, in rats circulating excitation had an occurrence of 22% [37].
Partial propagation of the surface AP along the electrode grid
are common events especially at the beginning or at the end of
a burst as highlighted in [39], where only in 25% of the bursts,
the mapped area was completely activated by the first AP. As
confirmed in the literature, the high probability of these events,
which we all excluded from the real-signal analysis, imposed a
limitation to the amount of analyzed signals.
The advantage of using an HD 2-D grid for the EHG signal
recordingishighlightedbythereportedsequenceofpropagation
maps. Furthermore, the example of surface AP in the maps
satisfies the planar-wave approximation that we assumed in our
propagation model.
In conclusion, our results show that the proposed ML method
is suitable for the 2-D estimation of the EHG surface AP con-
duction velocity. Moreover, the use of weights for both the
reference shape and the cost function leads to more accurate
estimates than the use of the ML alone and should, therefore,
be preferred. However, even if conceived for estimating the CV
of surface AP extracted from the EHG signal, the proposed
method can be employed for the analysis of other types of sig-
nal, in particular, when the direction of propagation is a priori
unknown.
For EHG surface AP analysis, the method, as currently pre-
sented, requires an accurate detection of the surface AP as pre-
requisite for the signal analysis. Future research will focus on
implementation and clinical evaluation aspects such as the pos-
sibility of automatically selecting surface APs. In general, this
work opens new possibilities for future clinical studies aimed at
assessing the CV-vector dynamics and its value for analysis of
the pregnancy course and, most importantly, for prediction of
preterm delivery.
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New York:
Chiara Rabotti was born in Florence, Italy, in 1977.
She received the M.Sc. degree in electrical engineer-
ing from the University of Florence, Florence, Italy,
in 2004, and the Ph.D. degree from the Eindhoven
University of Technology, Eindhoven, The Nether-
lands, in 2010.
Since 2010, she has been a Postdoctoral Fellow
at the Signal Processing Systems Group, Eindhoven
University of Technology. Her research interests in-
clude biomedical signal processing with specific fo-
cus on electrohysterography, electromyography, and
electrocardiography.
Dr. Rabotti is a member of the IEEE Engineering in Medicine and Biology
Society.
Massimo Mischi was born in Rome, Italy, in 1973.
He received the M.Sc. degree in electrical engineer-
ing from La Sapienza University, Rome, Italy, in
1999. In 2000, he joined as research Assistant at the
Eindhoven University of Technology, Eindhoven, the
Netherlands,wherein2002,hecompletedatwo-year
Post-Master program in technological design, infor-
mation and communication technology, and in 2004,
he received the Ph.D. degree.
Hisresearchfocusedonthedevelopmentofcardio-
vascular diagnostic methods by contrast ultrasonog-
raphy. Since 2007, he has been an Assistant Professor at the Eindhoven Univer-
sity of Technology. His current research interests include several topics in the
area of biomedical signal processing.
Dr. Mischi is currently the Secretary of the Benelux Chapter of the IEEE
Engineering in Medicine and Biology Society.

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RABOTTI et al.: NONINVASIVE ESTIMATION OF THE ELECTROHYSTEROGRAPHIC ACTION-POTENTIAL CONDUCTION VELOCITY2187
S. Guid Oei received the Ph.D. degree from the
LeidenUniversity,Leiden,TheNetherlands,in1996.
HesubspecializedinperinatologyatFlindersUniver-
sity, Adelaide, Australia.
He is currently a Gynaecologist-Perinatologist
in the Department of Obstetrics and Gynecology,
M´ axima Medical Center (MMC), Veldhoven, The
Netherlands, where he has been the Dean and the
Director of the Medical Simulation and Education
Centre. He is also a Professor in fundamental perina-
tology in the Department of Electrical Engineering,
Eindhoven University of Technology, Eindhoven, The Netherlands.
Jan W. M. Bergmans (SM’91) received the de-
gree of Elektrotechnisch Ingenieur (cum laude) in
1982, and the Ph.D. degree in 1987, both from
Eindhoven University of Technology, Eindhoven,
The Netherlands.
From 1982 to 1999, he was with Phillips Re-
search Laboratories, Eindhoven, where he was in-
volved in the signal-processing techniques and in-
tegrated circuit-architectures for digital transmission
and recording systems. In 1988 and 1989, he was
an Exchange Researcher at Hitachi Central Research
Laboratories,Tokyo,Japan.Since1999,hehasbeenaProfessorandaChairman
of the Signal Processing Systems Group, Eindhoven University of Technology,
and an Advisor at Phillips Research Laboratories. He is the author or coauthor
of various refereed journals and is the author of the book Digital Baseband
Transmission and Recording (Norwell, MA: Kluwer, 1996). He holds 40 U.S.
patents.