Linear and nonlinear analysis of airflow recordings to help in sleep apnoea-hypopnoea syndrome diagnosis.

Abstract

This paper focuses on the analysis of single-channel airflow (AF) signal to help in sleep apnoea-hypopnoea syndrome (SAHS) diagnosis. The respiratory rate variability (RRV) series is derived from AF by measuring time between consecutive breathings. A set of statistical, spectral and nonlinear features are extracted from both signals. Then, the forward stepwise logistic regression (FSLR) procedure is used in order to perform feature selection and classification. Three logistic regression (LR) models are obtained by applying FSLR to features from AF, RRV and both signals simultaneously. The diagnostic performance of single features and LR models is assessed and compared in terms of sensitivity, specificity, accuracy and area under the receiver-operating characteristics curve (AROC). The highest accuracy (82.43%) and AROC (0.903) are reached by the LR model derived from the combination of AF and RRV features. This result suggests that AF and RRV provide useful information to detect SAHS.

Full text

Page 1

Linear and nonlinear analysis of airflow recordings to help in sleep apnoea–hypopnoea
syndrome diagnosis
This article has been downloaded from IOPscience. Please scroll down to see the full text article.
2012 Physiol. Meas. 33 1261
(http://iopscience.iop.org/0967-3334/33/7/1261)
Download details:
IP Address: 157.88.129.82
The article was downloaded on 27/06/2012 at 13:07
Please note that terms and conditions apply.
View the table of contents for this issue, or go to the journal homepage for more
HomeSearchCollectionsJournalsAboutContact usMy IOPscience

Page 2

IOP PUBLISHING
PHYSIOLOGICAL MEASUREMENT
Physiol. Meas. 33 (2012) 1261–1275
doi:10.1088/0967-3334/33/7/1261
Linear and nonlinear analysis of airflow recordings to
help in sleep apnoea–hypopnoea syndrome diagnosis
G C Guti´ errez-Tobal1, R Hornero1, D´Alvarez1, J V Marcos1
and F del Campo2
1Biomedical Engineering Group, ETSI de Telecomunicaci´ on, University of Valladolid,
Paseo Bel´ en 15, 47011, Valladolid, Spain
2Hospital Universitario R´ ıo Hortega, Servicio de Neumolog´ ıa, c/Dulzaina 2, 47012, Valladolid,
Spain
E-mail: gguttob@ribera.tel.uva.es, robhor@tel.uva.es, dalvgon@ribera.tel.uva.es,
jvmarcos@gmail.com and fsas@telefonica.net
Received 16 February 2012, accepted for publication 6 June 2012
Published 27 June 2012
Online at stacks.iop.org/PM/33/1261
Abstract
This paper focuses on the analysis of single-channel airflow (AF) signal
to help in sleep apnoea–hypopnoea syndrome (SAHS) diagnosis. The
respiratory rate variability (RRV) series is derived from AF by measuring time
between consecutive breathings. A set of statistical, spectral and nonlinear
features are extracted from both signals. Then, the forward stepwise logistic
regression (FSLR) procedure is used in order to perform feature selection
and classification. Three logistic regression (LR) models are obtained by
applying FSLR to features from AF, RRV and both signals simultaneously.
The diagnostic performance of single features and LR models is assessed
and compared in terms of sensitivity, specificity, accuracy and area under
the receiver-operating characteristics curve (AROC). The highest accuracy
(82.43%) and AROC (0.903) are reached by the LR model derived from the
combination of AF and RRV features. This result suggests that AF and RRV
provide useful information to detect SAHS.
Keywords: sleep apnoea–hypopnoea syndrome, airflow, respiratory rate
variability, feature extraction, feature selection
1. Introduction
Thesleepapnoea–hypopnoeasyndrome(SAHS)ischaracterizedbyrepetitiveeventsofapnoea
(completecessationofbreathing)andhypopnoea(significantbreathingreduction)duringsleep
(Flemons et al 2003). SAHS has been associated with other diseases such as hypertension,
atrial fibrillation, stroke, cardiac failure, aortic dissection and sudden cardiac death (L´ opez-
Jim´ enez et al 2008). Furthermore, daytime sleepiness caused by SAHS is a risk factor for
occupational accidents and motor-vehicle collisions (Lindberg et al 2001, Sassani et al 2004).
0967-3334/12/071261+15$33.00© 2012 Institute of Physics and Engineering in MedicinePrinted in the UK & the USA1261

Page 3

1262G C Guti´ errez-Tobal et al
TheprevalenceofSAHShasbeenestimatedat1%–5%ofadultmenand2%womeninwestern
countries. However, studies reported up to 5% of adult population remaining undiagnosed
(Young et al 2002).
The gold standard for SAHS diagnosis is polysomnography (PSG) (Flemons et al 2003).
PSG is an overnight test in which many physiological signals are monitored. The apnoea–
hypopnoea index (AHI) from PSG is used to characterize its severity (Patil et al 2007).
Despite its effectiveness, PSG is an expensive and complex test, since it needs the supervision
of specialists and a visual inspection of signals to compute AHI. This results in longer waiting
lists and increased delay time for a final diagnosis (Flemons et al 2004). Therefore, there
is a demand of new helping methods of diagnosis capable of overcoming PSG drawbacks
(Penzel et al 2002). Many studies have focused on analysing a reduced set of signals from
overnight PSG. Typically, the diagnostic ability of electrocardiogram (Penzel et al 2002),
electroencephalogram (Poyares et al 2002), airflow (AF) (Nakano et al 2007, Han et al 2008),
and blood oxygen saturation (SpO2) (´Alvarez et al 2010) has been evaluated.
The AF waveform is directly affected by the occurrence of respiratory events (Flemons
et al 2003). Apnoeas are reflected by near-zero values, whereas hypopnoeas cause amplitude
reduction. In contrast, clear oscillations are observed for normal breathing periods. Therefore,
an intensive analysis of the information from the single-channel AF signal is proposed to help
in SAHS detection. In addition to the AF signal, the respiratory rate variability (RRV) series
is also analysed. RRV is computed by measuring the time between consecutive breathings in
AF, similar to the well-known heart rate variability series (Cysarz et al 2008). The normal
pattern for RRV also reflects alterations in the presence of SAHS, since sleep apnoea modifies
the respiratory oscillation (Cysarz et al 2008).
The main purpose of the current study is to evaluate the diagnostic usefulness of AF and
RRV series in SAHS detection. In order to characterize SAHS, the extraction of statistical,
spectral and nonlinear features from AF and RRV is proposed. Common parameters such
as statistical moments have shown to be useful in SAHS detection (Roche et al 1999, de
Chazal et al 2003). Furthermore, frequency analysis has been successfully applied to study
different diseases (Casolo et al 1991, Penzel et al 2002, Poza et al 2007). Moreover, nonlinear
methods have recently proved high capability to help in SAHS diagnosis (´Alvarez et al 2006,
Hornero et al 2007, Morillo et al 2009). After feature extraction, a feature selection stage
is implemeted. It is carry out by means of the forward stepwise logistic regression (FSLR)
methodology(HosmerandLemeshow1999),whichhasbeensuccessfullyusedinpriorstudies
ofSAHS(´Alvarezetal2010).Thelogisticregression(LR)modelsobtainedthroughtheFSLR
procedure combine the non-redundant information from the features extracted (Hosmer and
Lemeshow 1999). Finally, the diagnostic performance of the single features and the LR
models are assessed and compared in terms of sensitivity, specificity, accuracy and area under
the receiver-operating characteristic curve (AROC).
2. Subjects and signals
2.1. Subjects under study
In this study, 148 subjects suspected of suffering from SAHS were involved (79% males
and 21% females). The recordings were obtained in the sleep unit of Hospital Universitario
R´ ıo Hortega in Valladolid, Spain. All subjects presented common symptoms such as daytime
hypersomnolence,loudsnoring,nocturnalchokingandawakeningsorreferredapnoeicevents.
The subjects were free from any medication which could influence the respiratory centre.
Neither patients suffering from hypothyroidism (two out of the total subjects) nor those

Page 4

Linear and nonlinear analysis of airflow recordings to help in SAHS diagnosis 1263
Table 1. Demographic and clinical data of the population under study. Data are presented as
mean ± SD or n (%). SAHS-positive: subjects with sleep apnoea–hypopnoea syndrome; SAHS-
negative: subjects without sleep apnoea–hypopnoea syndrome; BMI: body mass index; time:
recording time; AHI: apnoea–hypopnoea index.
All subjects SAHS-positiveSAHS-negative
Subjects (n)
Age (years)
Males (n)
BMI (kg m−2)
Time (h)
AHI (events/h)
148
50.87 ± 11.68
117 (79.0%)
29.1 ± 4.6
7.24±0.38
–
100 (67.6%)
51.89 ± 11.41
85 (85.0%)
29.9 ± 4.7
7.23 ± 0.36
32.9 ± 24.3
48 (32.4%)
48.75 ± 12.07
32 (66.7%)
27.6 ± 4.9
7.27 ± 0.43
4.0 ± 2.4
suffering from chronic obstructive pulmonary disease (COPD) (six out of the total subjects)
were excluded. Physicians considered 100 subjects affected (positive) and 48 not affected
(negative) by SAHS. The AHI threshold for a positive diagnosis was 10 events/h at least.
Apnoea was defined as the cessation of AF for 10 s or more. Hypopnoea was defined as a
minimum of 30% of amplitude reduction for at least 10 s accompanied by a 4% or more
decrease in the saturation of haemoglobin. The Review Board on Human Studies accepted the
protocol, and all subjects gave their informed consent to participate in the study. Demographic
and clinical data of the participants are summarized in table 1.
2.2. AF and RRV signals
The AF recordings were obtained from overnight PSG (Alice 5, Respironics, Philips
Healthcare, the Netherlands). The sensor used to register AF was a thermistor (Pro-Tech,
Respironics, Philips Healthcare, the Netherlands) and the sampled rate was 10 Hz. Previous
to the automatic analysis, a visual inspection of the signals was carried out to assess their
quality. Four recordings were excluded due to prolonged malfunction of the thermistor. Thus,
the remaining 148 AF recordings were entirely analysed.
A peak detection algorithm was implemented to locate inspiratory onsets in AF signal
(Korten and Haddad 1989). Then, RRV was computed by measuring the time between
consecutive locations (Cysarz et al 2008).
Figure 1(a) shows an example of the AF signal and figure 1(b) shows the corresponding
RRV signal. The first 34 s of the AF signal corresponds to a normal breathing pattern.
Consequently, the time between breathings remains around 4.2 s in the RRV signal. Then,
a hypopnoea is shown in the AF signal which is reflected by a decrease in the RRV signal
amplitude. Finally, since the AF normal breathing pattern is recovered, the time between
breathings begins to increase.
3. Methods
The proposed methodology started with a spectral analysis of AF and RRV recordings to
determine those frequency bands associated with SAHS. Afterwards, spectral, nonlinear and
statistical features were extracted from AF and RRV. Then several LR models were obtained
by means of the FSLR method. Finally, diagnostic performance of single features and LR
models was assessed.

Page 5

1264G C Guti´ errez-Tobal et al
(a)
(b)
Figure 1. Normal breathing pattern followed by hypopnoea event in (a) AF signal and
(b) corresponding RRV signal.
3.1. Definition of spectral bands of interest
The bands of interest were defined as the frequency regions of power spectral density
(PSD) in which the highest statistical differences between SAHS-positive and SAHS-negative
populations were found. PSD of recordings was estimated by means of a non-parametric
Welch method (Welch 1967). This method divides the signals into M overlapping segments of
length L. Then, a smooth time window w[n] is applied, and the modified periodogram of each
windowed segment vL[n] is computed by means of the discrete Fourier transform (DFT) V[f]
(Welch 1967):
ˆP[f] =|V[f]|2
where fsis the sample rate:
N−1
?
and
1
M
n=0
Finally, the average of all DFTs is calculated to obtain the PSD function. A 2048-sample
Hamming window, with 50% overlap and 4096-point DFTs, was used to compute the PSD of
AF and RRV recordings. A cubic spline interpolation (resampling at 10 Hz) was applied to
RRV series before the computation of the PSDs.
The representations of the joint PSDs of each SAHS-positive and SAHS-negative
populations were obtained. The median of the PSD values at each frequency component
fsLU,
(1)
V[f] =
n=0
vL[n]e−j(2πk/N)n,
(2)
U =
M−1
?
|w(n)|2.
(3)

Page 6

Linear and nonlinear analysis of airflow recordings to help in SAHS diagnosis 1265
(a)
(b)
(c)
(d)
Figure 2. Spectral bands of interest of AF and RRV. AF (a) and RRV (b) median-based
representations of PSDs from SAHS-positive (black line) and SAHS-negative (grey line)
populations. AF (c) and RRV (d) whole spectrum p-value versus frequency representations (solid
line).
was applied due to its robustness to outliers. Figures 2(a) and (b) show this median-based
representation for AF and RRV, respectively. The p-value from the Kruskal–Wallis test was
usedtofindstatisticallysignificantdifferencesalongfrequencies(p-value<0.01).Figures2(c)
and (d) display the p-value versus frequency representations for AF and RRV, respectively.
Figure 2(c) only shows significant differences in the very low frequency band (0.002–
0.151 Hz). This agrees with figure 2(a), which displays the greatest qualitative differences
in the same band of the spectrums of AF signals. The spectral band of interest was that with
the highest statistically significant differences, i.e. 0.022–0.059 Hz. Moreover, the plot in
figure 2(d) indicates significant differences in most of the frequency components of the RRV
spectrum. However, the highest differences were also found at the very low band. This is also
consistent with the corresponding median-based representation of the PSD (figure 2(b)). The
spectral band of interest was 0.095–0.132 Hz.
3.2. Feature extraction
3.2.1.
differ from SAHS-positive and SAHS-negative populations. In order to typify the statistical
behaviourofthesedistributions,thefirst-to-fourthstatisticalmoments(Mt1–Mt4)wereobtained
from time series. The arithmetic mean (Mt1), standard deviation (SD) (Mt2), skewness (Mt3)
and kurtosis (Mt4) quantify the central tendency, dispersion, asymmetry and peakedness of
data, respectively.
Statistical moments.
The distributions of AF and RRV values are expected to

Page 7

1266G C Guti´ errez-Tobal et al
3.2.2. Spectral features.
means of spectral analysis. Seven spectral features were extracted from the frequency bands
of interest and the same features were obtained from the full PSDs.
Peak amplitude (PA) is the maximum of PSD in a given frequency interval. Band power
(BP) represents the spectral power of a region. Both of them are conventional parameters and
can be computed as follows:
The reccurrent nature of apnoeic events can be characterized by
PA = max
PSD{PSD(f)},
f(Hz) ∈ [fi,fN],
i = 1,2,...,N,
(4)
BP =
fN
?
fi=f1
PSD(fi),
i = 1,2,...,N,
(5)
where N is the number of points in the band and fiare the frequency components of the
spectrum. Figures 2(a) and (b) indicate that higher PA and BP values are expected for the
SAHS-positive population.
The Wootters distance (WD) is a disequilibrium measurement (Wootters 1981). This
parameter requires the PSD to be normalized (PSDn) in order to consider it as a probability
density function (pdf). It is possible to measure the distance between the pdf and the uniform
distribution (Wootters 1981):
?
fi=f1
with f1and f2being the limits of the frequency range where WD is applied and N is the
number of the corresponding PSDnpoints. If PSDnis equal to a uniform distribution along
frequencies (as in white noise), then WD will be equal to zero. Moreover, if the normalized
spectrum is condensed into a narrow frequency band (as in a sum of sinusoids), WD reaches
the highest values. According to figures 2(a) and (b), differences between WD values from
both populations are expected.
Finally, first-to-fourth statistical moments (Mf1–Mf4) of the amplitude values of PSDs
were also obtained. Differences between the distributions of PSD values are reflected by these
parameters.
WD = arccos
f2
?
?PSDn(f) ·
?1/N
?
,
(6)
3.2.3. Nonlinearfeatures.
subjects modifies the corresponding AF and RRV waveforms. Since central tendency measure
(CTM), Lempel–Ziv complexity (LZC) and approximate entropy (ApEn) are applied in time
domain, it is expected that these parameters can reflect the differences in the variability,
complexity and irregularity of time series from populations.
The CTM quantifies the degree of variability or chaos in a time series (Cohen et al 1996).
CTM is based on the plots of the first-order differences representing x[n+2]−x[n+1] versus
x[n+1]−x[n], where x[n] are the time serie values (Ab´ asolo et al 2006). It is calculated by
counting the points that fall within a circle of radius ρ around the origin and dividing it by the
total number of points (Cohen et al 1996):
ThehighrecurrenceofapnoeasandhypopnoeasinSAHS-positive
CTM =
1
N − 2
n−2
?
n=1
δ(n),
(7)
where
δ(n) =
?1 if {(x[n + 2] − x[n + 1])2+ (x[n + 1] − x[n])2}1/2< ρ
otherwise,
0
(8)

Page 8

Linear and nonlinear analysis of airflow recordings to help in SAHS diagnosis1267
with N being the points of the time series. CTM achieves values between 0 and 1, reaching
values closer to1when agiven series islessvariable (values moreconcentrated around centre)
and closer to 0 when it has more variability. Radius ρ has to be selected experimentally,
depending on the character of signals (Cohen et al 1996). A method based on p-value was
usedtoselectρ (Horneroetal1999).First,CTMoftimeserieswascomputedbyfixingseveral
radii. Then a statistical significance test was applied to select the ρ which ensured the most
significant differences between populations, i.e. the lowest p-value. In this study, two radii
were used: ρ1= 31 for the AF signal and ρ2= 6.61 for the RRV signal.
The complexity of finite sequences can be estimated by means of LZC (Lempel and Ziv
1976). Larger values of the parameter correspond to higher complexity in these sequences
(Zhang et al 2001). The first step in LZC estimation is to convert the time series into finite
sequences of simbols, s(i) (Zhang et al 2001, Ab´ asolo et al 2006). Binary sequences have
been commonly proposed. Due to its robustness to outliers, we assumed the median value as
the threshold to assign a simbol to each value of time series. Once the sequence is obtained,
it is scanned from left to right, and a complexity counter c(n) is increased every time a new
subsequence of consecutive characters is encountered (Zhang et al 2001). Finally, c(n) is
normalized to make the method independent of the length of sequences:
LZC =c(n)
where
n
logα(n),
and α = 2 since the sequence is binary.
ApEn is an irregularity measure in time series which was originally developed to be
applied over short and noisy data sets (Pincus 1991). ApEn can assess both dominant and
subordinates patterns in data for which other methods cannot make the feature recognition
easy (Pincus 2001). ApEn has two user-specified parameters: a length m and a tolerance
window r. Theoretically, the ApEn is defined as
b(n),
(9)
b(n) =
(10)
ApEn(m,r) = lim
N→∞[φm(r) − φm+1(r)],
(11)
where N is the total number of points of the original time series and φm(r) is the average of the
logarithmic likelihood patterns of length m that are repeated along the original sequence. The
tolerance parameter r is used to determine the similarity between patterns. Since N is finite,
the ApEn is commonly applied as the statistic (Pincus 1991):
ApEn(m,r,N) = φm(r) − φm+1(r).
Larger values of ApEn correspond to more irregularity in the data (Pincus 2001). Despite
their influence in the ApEn outcome, there are no guidelines to optimize the m and r values
(Hornero et al 2005). Thus, m = 1, m = 2 and r = 0.1, 0.15, 0.2, 0.25 times the SD of the
original data sequence have been proposed as input parameters. These values produce good
statistical reproducibility of ApEn for time series of length N ? 60 (Pincus 2001). In order to
choose between these values, the p-value-based methodology previously described was used,
and m = 1 and r = 0.25 SD were selected for both AF and RRV signals.
(12)
3.3. Feature selection
The features described in the previous subsections measure different properties of AF and
RRV.Theinformationcontainedintheseparametersmaybecomplementary.Forsimultaneous
analysisofthesefeatures,severalLRmodelswereobtained.Themethodusedtoautomatically

Page 9

1268G C Guti´ errez-Tobal et al
select the features was FSLR which was proposed by Hosmer and Lemeshow (1999). This
procedure was applied to the features from AF, RRV and both signals (AF-RRV).
3.3.1. Forward stepwise logistic regression (FSLR).
describetherelationshipbetweenaresponsevariable(outcome)andtheexplanatoryvariables.
In this study, the response is a dichotomous variable codifying the diagnosis of a subject
(‘0’ non-affected, and ‘1’ affected by SAHS), and the explanatory variables are the features
explainedpreviously.Forthisoutcomevariable,theLRmodelhasbecomethestandardmethod
of analysis:
eβ0+βTx
1 + eβ0+βTx,
where π(x) values range between 0 and 1, and can be interpreted as the probability of
membership to the SAHS-positive population. β0is a constant for each model and β is a
vector with coefficients for each component of x. Both β0and β are estimated according to
the maximum-likelihood criterion (Hosmer and Lemeshow 1999).
The more variables included in a LR model (higher dimensionality), the more dependent
the model becomes on the observed data due to overfitting. Thus, feature selection was used in
order to obtain models with higher capability of generalization. The FSLR procedure has been
proposed for this purpose. It checks the relevance of features, including or excluding them
according to a fixed decision rule. In this work, the decision rule chosen has been the p-value
of the likelihood ratio (Hosmer and Lemeshow 1999). FSLR is characterized by a forward
selection followed by the backward elimination of variables at each step.
A regression-based method was used to
π(x) =
(13)
3.4. Statistical analysis
Thenon-parametricKruskal–WallistestwasusedtoassessthedifferencesbetweentheSAHS-
positive and the SAHS-negative populations, with a p-value < 0.01 considered as significant.
To ensure statistical validity of results, a leave-one-out cross-validation approach was
applied. Sensitivity (percentage of SAHS-positive subjects correctly diagnosed), specificity
(percentage of SAHS-negative subjects correctly diagnosed) and accuracy (proportion of total
subjects under study correctly classified) were computed by averaging all results from the
cross-validation process. Additionally, the AROC was computed to quantify the diagnostic
performance of a given method (Zweig and Campbell 1993).
4. Results
4.1. Diagnostic performance of single features
A total of 21 features were extracted from each of the two series. Table 2 summarizes the
measurements (mean ± SD) obtained for each feature in SAHS-positive and SAHS-negative
populations. The p-value from the non-parametric Kruskal–Wallis significance test is also
shown.
In the case of the AF signal, six out of seven spectral features obtained from the band
of interest showed statistically significant differences between populations (p-value < 0.01).
Only one out of seven (Mf3) spectral features computed from the full PSD also showed
p-value < 0.01. Neither the statistical moments in time domain nor the nonlinear features
achieved statistically significant differences. In contrast, two statistical moments (Mt2and
Mt3) and two nonlinear features (CTM and LZC) obtained from RRV showed p-value < 0.01.

Page 10

Linear and nonlinear analysis of airflow recordings to help in SAHS diagnosis
1269
Table 2. Average values (mean ± SD) for the features extracted from AF and RRV signals in the SAHS-positive and the SAHS-negative populations. M1–M4: statistical moments of
recordings in time domain; CTM: central tendency measure; LZC: Lempel—Ziv complexity; ApEn: approximate entropy; Mf1–Mf4: statistical moments obtained from full PSDs; PA:
maximum of the full PSDs; BP: total spectral power; WD: Wootters distance; Mf1b–Mf4b: statistical moments obtained from the spectral band of interest (AF: 0.022–0.059 Hz, RRV:
0.095–0.132 Hz.); PAb: maximum of PSD at the spectral band of interest; BPb: spectral power at the band of interest; WDb: Wootters distance at the spectral band of interest.
AF signal RRV signal
Feature SAHS-positiveSAHS-negative
p-value SAHS-positiveSAHS-negative
p-value
Mt1
Mt2
Mt3
Mt4
CTM
LZC
ApEn
Mf1
Mf2
Mf3
Mf4
PA
BP
WD
Mf1b
Mf2b
Mf3b
Mf4b
PAb
BPb
WDb
0.06 ± 0.21
190.38 ± 80.30
0.28 ± 0.24
8.25 ± 15.83
0.635 ± 0.184
0.279 ± 0.029
0.412 ± 0.073
8.4 × 103± 8.0 × 103
4.7 × 104± 5.1 × 104
8.02 ± 1.77
80.09 ± 35.18
59.9 × 104± 68.2 × 104
1.71 × 107± 1.64 × 107
0.798 ± 0.022
9.9 × 104± 12.9 × 104
39.6 × 103± 10.5 × 103
0.042 ± 0.689
2.402 ± 0.905
16.8 × 104± 30.7 × 104
1.1 × 105± 20.4 × 105
0.109 ± 0.0608
0.04 ± 0.11
179.87 ± 91.42
0.28 ± 0.31
11.74±21.40
0.628 ± 0.185
0.283 ± 0.027
0.435 ± 0.074
7.9 × 103± 9.4 × 103
4.9 × 104± 6.4104
8.94 ± 2.19
96.98 ± 46.25
68.5 × 104± 96.7 × 104
1.63 × 107± 1.93 × 107
0.808 ± 0.018
3.4 × 104± 2.3 × 104
7.1 × 103± 0.8 × 103
−0.451 ± 0.634
2.675 ± 1.026
4.4 × 104± 3.7104
5.3 × 105± 3.5 × 105
0.063 ± 0.0372
p > 0.01
p > 0.01
p > 0.01
p > 0.01
p > 0.01
p > 0.01
p > 0.01
p > 0.01
p > 0.01
p < 0.01
p > 0.01
p > 0.01
p > 0.01
p > 0.01
p < 0.01
p < 0.01
p < 0.01
p > 0.01
p < 0.01
p < 0.01
p < 0.01
3.66 ± 0.51
1.04 ± 0.33
0.81 ± 1.39
12.9 ± 12.7
0.989 ± 0.017
0.992 ± 0.035
1.46 ± 0.072
0.22 ± 0.14
1.69 ± 1.03
12.58 ± 4.28
232.60 ± 158.77
37.55 ± 23.52
451.15 ± 285.91
0.904 ± 0.009
2.96 ± 2.53
0.98 ± 0.86
0.16 ± 0.39
2.0 ± 0.43
4.61 ± 3.72
49.1 ± 41.6
0.14 ± 0.07
3.64 ± 0.50
0.85 ± 0.28
0.03 ± 1.11
9.9 ± 8.0
0.998 ± 0.002
0.975 ± 0.037
1.44 ± 0.075
0.15 ± 0.10
1.40 ± 1.04
17.51 ± 4.51
418.02 ± 184.65
39.60 ± 32.36
307.2 ± 205.49
0.908 ± 0.008
1.39 ± 0.91
0.56 ± 0.42
0.23 ± 0.38
1.99 ± 0.40
2.34 ± 1.48
23.3 ± 15.1
0.16 ± 0.08
p > 0.01
p < 0.01
p < 0.01
p > 0.01
p < 0.01
p < 0.01
p > 0.01
p < 0.01
p > 0.01
p < 0.01
p < 0.01
p > 0.01
p < 0.01
p < 0.01
p < 0.01
p < 0.01
p > 0.01
p > 0.01
p < 0.01
p < 0.01
p > 0.01

Page 11

1270G C Guti´ errez-Tobal et al
Table 3. Results from the diagnostic assessment of single features extracted from AF and RRV
recordings, derived from the leave-one-out cross-validation procedure. Sen.: sensitivity; Spe.:
specificity; Acc.: accuracy; AROC: area under receiver-operating characteristics curve. AROCs >
0.800 are in bold.
AF signal RRV signal
FeatureSen.(%)Spe.(%)Acc.(%)AROC Sen.(%)Spe.(%) Acc.(%) AROC
Mt1
Mt2
Mt3
Mt4
CTM
LZC
ApEn
Mf1
Mf2
Mf3
Mf4
PA
BP
WD
Mf1b
Mf2b
Mf3b
Mf4b
PAb
BPb
WDb
49.00
53.00
59.00
60.00
54.00
57.00
61.00
58.00
50.00
68.00
63.00
48.00
58.00
69.00
71.00
74.00
58.00
63.00
74.00
71.00
65.00
58.33
50.00
37.50
50.00
47.92
58.33
56.25
50.00
47.92
56.25
56.25
56.25
50.00
54.47
83.33
87.50
68.75
56.25
83.33
83.33
70.83
52.03
52.03
52.03
56.76
52.03
57.43
59.49
55.41
49.32
64.19
60.81
50.68
55.41
64.19
75.00
78.38
61.49
60.81
77.03
75.00
66.89
0.520
0.555
0.543
0.537
0.510
0.553
0.585
0.554
0.502
0.634
0.612
0.513
0.561
0.631
0.826
0.851
0.676
0.581
0.840
0.838
0.797
48.00
65.00
60.00
73.00
68.00
62.00
52.00
65.00
61.00
77.00
79.00
56.00
65.00
64.00
61.00
61.00
50.00
47.00
59.00
62.00
61.00
52.08
62.5
77.08
47.92
75.00
56.25
50.00
62.50
52.08
68.75
70.83
41.67
62.50
56.25
79.17
62.50
52.08
52.08
66.67
79.17
47.92
49.39
64.19
65.54
64.86
70.27
60.14
51.35
64.19
58.11
74.32
76.35
51.35
64.19
61.49
66.89
61.49
50.68
48.65
61.49
67.57
56.76
0.538
0.669
0.704
0.595
0.800
0.654
0.577
0.676
0.618
0.809
0.807
0.528
0.676
0.633
0.745
0.702
0.559
0.508
0.745
0.756
0.567
Table 4. Results from the diagnostic assessment of the LR models, derived from the leave-one-
out cross-validation procedure. Sen.: sensitivity; Spe.: specificity; Acc.: accuracy; AROC: area
under receiver-operating characteristics curve. The number of features introduced as independent
variables at each model are in parentheses. AROCs>0.800 are in bold.
ModelSelected featuresSen.(%)Spe.(%)Acc.(%)AROC
AF (21)
RRV (21)
AF-RRV (42)
WDb, BPb, PA, Mf2b
Mf3, CTM
Mf3RRV, PAAF, BPbAF
84.00
84.00
88.00
70.83
58.33
70.83
79.73
75.68
82.42
0.889
0.850
0.903
Furthermore, nine out of 14 RRV spectral features obtained from the full PSD and the band
of interest presented statistically significant differences.
The results of the individual diagnostic assessment of the features are shown in table 3.
Consistent with the statistical significance test analysis, those features with p-value < 0.01
improved the diagnostic performance of the others. For the AF signal, the highest accuracy
(78.38%) and AROC (0.851) were reached by Mf2b. In the case of RRV, the highest accuracy
(76.35%) was obtained by Mf4, whereas Mf3achieved the highest AROC (0.809).
4.2. Performance of the FSLR procedure
Table 4 shows the diagnostic results provided by the LR models. The features automatically
selected are also specified. The order of appearance of the selected features in the table is the
same as the order obtained from the FSLR method.

Page 12

Linear and nonlinear analysis of airflow recordings to help in SAHS diagnosis1271
Figure 3. Bland–Altman plot comparing the AHI from MLRAF_RRVwith the AHI from PSG.
Table 5. Linear correlation analysis between features selected to the models and BMI/Age. ρ:
Pearson’s correlation coefficient.
Feature
ρ (BMI)
ρ (Age)
WDbAF
BPbAF
PAAF
Mf2bAF
Mf3RRV
CTMRRV
0.222
0.314
0.156
0.269
−0.054
−0.225
0.115
0.021
−0.071
−0.003
−0.051
−0.262
Four parameters (WDb, BPb, Mf2band PA) were automatically selected by the FSLR
procedure when all 21 AF features were introduced as independent variables. The AF model
reached 79.73% accuracy and 0.889 AROC. Mf3and CTM were automatically selected in
the case of the RRV model, obtaining 75.68% accuracy and 0.850 AROC. Finally, the
highestsensibility(88.00%),specificity(70.83%),accuracy(82.43%)andAROC(0.903)were
achieved bytheAF-RRVmodel.Threeparameterswereautomaticallyselected:Mf3fromRRV
and PA and BPbfrom AF. These features were used to obtain a multivariate linear regression
model (MLRAF_RRV). The output of MLRAF_RRV(estimated AHI) was compared to the AHI
from PSG. The Bland–Altman plot shown in figure 3 was used for this purpose. It displays an
overestimation tendency for lower AHI values whereas an underestimation tendency is shown
when the AHI becomes higher. Finally, table 5 shows the assessment of linear correlation
between all the features automatically selected and the BMI and age. None of the features
obtained high values of Pearson’s correlation coefficient with BMI or age.

Page 13

1272G C Guti´ errez-Tobal et al
5. Discussion and conclusions
The utility of AF signals in SAHS detection was assessed. The information from RRV series,
which was derived from AF, was also evaluated. Statistical, spectral and nonlinear features
were used to characterize the behaviour of AF and RRV recordings in SAHS-positive and
SAHS-negative populations. AF and RRV frequency bands of interest within the very low
frequency region were proposed for SAHS detection. Regarding the AF signal, since the
normal breathing rate at rest is set close to 15 breaths per minute, i.e. 0.25 Hz. (Farr´ e et al
1998), the spectral components at very low frequencies of AF correspond to an abnormal
respiratory behaviour. Moreover, the selected spectral band of interest was located below
0.1 Hz. (0.022–0.059 Hz.). Since apnoea and hypopnoea events last 10 s or more (Flemons
et al 2003), the band is consistent with pathophysiology. However, further analysis is required
in order to assess the cause-motivating differences in frequencies higher than 0.1 Hz. The
occurrence of larger number of short-time respiratory events in SAHS-positive subjects is
proposed as a cause for this behaviour. In the case of RRV spectrum, significant differences
were found in most of the spectral components, indicating major changes in time between
breathings caused by SAHS. Most of the AF features that achieved significant differences
between populations were extracted from the spectral band of interest. In contrast, p-value
<0.01 was achieved by statistical, spectral and nonlinear features from RRV. This suggested
that RRV signal contains useful information about SAHS in time and frequency domains. The
diagnostic performance of the features reinforced the ideas exposed above: several spectral
features from the AF band of interest reached higher values of AROC (0.825–0.851) than any
other single feature. This confirmed the usefulness of the spectral information contained in
AF signals to help in SAHS diagnosis.
None of the features selected for the AF, RRV and AF-RRV models presented high
linear correlation with BMI or age of subjects under study. The AF-RRV model achieved
the highest diagnostic performance (82.42% accuracy and 0.903 AROC). Mf3RRV, PAAFand
BPbAFwere automatically selected, containing information from both AF and RRV signals.
One out of the two hypothyroidism patients (false positive) and none of the COPD patients
were misclassified. These results showed that the FSLR procedure improved the diagnostic
performance of single features and suggested that information contained in AF and RRV
signals could be complementary.
The AF signals obtained from thermistor have been recently analysed to help in SAHS
diagnosis. Two hundred and eighty eight subjects participated in a multi-centre study to
evaluate a screening device based on the detection of respiratory events (Shochat et al 2002).
Thus, 86% sensitivity, 57% specificity and 0.81 AROC were achieved in the classification
of subjects. The same methodology was applied to a different population, comparing the
screening performance of the device to the performance of nocturnal pulsioximetry (Gergely
et al 2009). The results of the study achieved 71.9% sensitivity and 73.1% specificity using
AHI = 15 as a cut-off threshold. The AF-RRV model obtained in this work improved the
diagnostic performance of both studies.
ThereexistsanextensiveliteraturefocusedontheanalysisofAFfromnasalpressure(NP)
sensor. Most of them aimed to locate respiratory events in AF. Subsequently, a respiratory
disturbanceindex(RDI)iscomputedinordertoassessitsdiagnosticperformance(DeAlmeida
et al 2006, Erman et al 2007, Nakano et al 2007, Grover and Pittman 2008, Wong et al 2008,
Tonelli et al 2009, Chen et al 2009, Rofail et al 2010). Populations involved in these studies
rangedfrom25to200subjects(83.5 ± 64.6,mean ± SD).Sensitivity,specificityandAROC
reached ranged 82%–97%, 62%–90% and 0.84–0.98, respectively. The best results achieved
in this study are included in these intervals.

Page 14

Linear and nonlinear analysis of airflow recordings to help in SAHS diagnosis1273
Some limitations have to be taken into account. The population under study could be
larger, with a more balanced proportion of SAHS-positive and SAHS-negative subjects.
Furthermore, all subjects were suspected of having SAHS before PSG test. A control
group (subjects without any symptoms) should be analysed in order to assess the universal
application of the methodology. It would provide additional information to complete this
study. The use of a thermistor to acquire the AF signal, instead of a NP sensor, is al.so
a limitation. Measurements from thermistor are only indirectly related to the AF, resulting
in the underdetection of hypopnoeas (Farr´ e et al 1998). The NP sensor has shown a better
performance for detecting obstructive respiratory events (Bahammam 2004). However, it
has a roughly quadratic relationship with the flow, causing AF changes to be exaggerated
and, consequently, resulting in an overestimation of apnoea events (Bahammam 2004). The
American Academy of Sleep Medicine recommends the use of both types of sensors due
to these disadvantages (Iber et al 2007). The comparison of features extracted from the
signals acquired with the two sensors and the joint analysis of the information extracted from
them are future goals. Another limitation has to be considered. The variability of AHI from
PSG in successive nights is well known (Carlile and Carlile 2008, Levendowski et al 2009).
However,night-to-nightvariabilityisnotoftenassessedduetoeconomics andtimelimitations
(Levendowski et al 2009). Repeated sleep studies in successive nights would be necessary
to complete the assessment of this methodology. Finally, the use of an AHI threshold = 10
events/h to discriminate SAHS is also a limitation since subjects in the range 5–10 events/h
could benefit from the continuous positive airway pressure (CPAP) treatment. CPAP is the
most widely used treatment for severe SAHS (Lindberg et al 2006, Marshall et al 2006).
Further work is needed to assess the accuracy of the methodology for screening those patients
who would benefit from CPAP.
In summary, AF and RRV signals were analysed. A spectral band of interest was located
in a region of the AF spectrum corresponding to anomalous respiration. The statistical
significance test and the diagnostic performance assessment of the features confirmed the
usefulness of the information contained in AF and RRV. Results from the FSLR procedure
suggested that data extracted from them can complement each other. Moreover, the AF-RRV
modelimprovedthediagnosticperformanceofallthesinglefeatures.Thebestresultsobtained
from this study improved the results from those studies which involved thermistor and are
comparable to those involving NP. Therefore, the proposed methodology could be useful to
help in SAHS diagnosis.
Acknowledgments
This work has been partially supported by the project VA111A11-2 from Consejer´ ıa
de Educaci´ on de la Junta de Castilla y Le´ on, by the Proyectos Cero on Ageing from
Fundaci´ on General CSIC, by Consejer´ ıa de Educaci´ on de la Junta de Castilla y Le´ on (Orden
EDU/1204/2010) and by the European Social Found.
References
Ab´ asolo D, Hornero R, G´ omez C, Garc´ ıa M and L´ opez M 2006 Analysis of background activity in Alzehimer’s
disease patients with Lempel–Ziv complexity and central tendency measure Med. Eng. Phys. 28 315–22
´Alvarez D, Hornero R, Ab´ asolo D, del Campo F and Zamarr´ on C 2006 Nonlinear characteristics of blood oxygen
saturation from nocturnal oximetry for obstructive sleep apnoea detection Physiol. Meas. 27 399–412
´AlvarezD,HorneroR,MarcosJ VanddelCampoF2010Multivariateanalysisofbloodoxygensaturationrecordings
in obstructive sleep apnea diagnosis IEEE Trans. Biomed. Eng. 57 2816–24

Page 15

1274G C Guti´ errez-Tobal et al
BaHammam A 2004 Comparison of nasal prong pressure and thermistor measurements for detecting respiratory
events during sleep Respiration 71 385–90
Carlile J and Carlile N 2008 Repeat study of 149 patients suspected of having sleep apnea but with an AHI<5 Sleep
31 A153
Casolo G, Balli E, Fazi A, Gori C, Freni A and Gensini G 1991 Twenty-four-hour spectral analysis of heart rate
variability in congestive heart failure secondary to coronary artery disease Am. J. Cardiol. 67 1154–8
de Chazal P, Heneghan H, Sheridan E, Reilly R, Nolan P and O’Malley
single-lead electrocardiogram for the detection of obstructive sleep apnoea IEEE Trans. Biomed. Eng.
50 686–96
Chen H, Lowe A A, Bai Y, Hamilton P, Fleetham J A and Almeida F R 2009 Evaluation of a portable recording
device (ApneaLinkTM) for case selection of obstructive sleep apnea Sleep Breath 13 213–9
Cohen M E, Hudson D L and Deedwania P C 1996 Applying continuous chaotic modelling to cardiac signal analysis
IEEE Eng. Med. Biol. Mag. 15 97–102
Cysarz D, Zerm R, Bettermann H, Fr¨ uhwirth M, Moser M and Kr¨ oz M 2008 Comparison of respiratory
rates derived from heart rate variability, ECG amplitude, and nasal/oral airflow Ann. Biomed. Eng. 36 2085–94
De Almeida F R, Ayas N T, Ueda H, Hamilton P, Ryan F C and Lowe A A 2006 Nasal pressure recordings to detect
obstructive sleep apnea Sleep Breath 10 62–69
Erman M K, Stewart D, Einhorn D, Gordon N and Casal E 2007 Validation of the ApneaLinkTMfor the screening of
sleep apnea: a novel and simple single-channel recording device J. Clin. Sleep Med. 3 387–92
Farr´ e R, Montserrat J M, Rotger M, Ballester E and Navajas D 1998 Accuracy of thermistors and thermocouples as
flow-measuring devices for detecting hypopnoeas Eur. Respir. J. 11 179–82
Flemons W W, Douglas N J, Kuna S T, Rodenstein D O and Wheatley J 2004 Access to diagnosis and treatment of
patients with suspected sleep apnea Am. J. Respir. Crit. Care Med. 169 668–72
Flemons W W, Littner M R, Rowley J A, Gay P, Anderson W M, Hudgel D W, McEvoy D and Loube D I 2003
Home diagnosis of sleep apnea: a systematic review of the literature Chest 124 1543–79
Gergely V, Pallos H, Mashima K, Miyazaki S, Tanaka T, Okawa M and Yamada N 2009 Evaluation of the usefulness
of the SleepStrip for screening obstructive sleep apnea–hypopnea syndrome in Japan Sleep Biol.
Rhythms 7 43–51
GroverS SandPittmanS D2008Automateddetectionofsleepdisorderedbreathingusinganasalpressuremonitoring
device Sleep Breath 12 339–45
Han J, Shin H B, Jeong D U and Park K S 2008 Detection of apnoeic events from single channel nasal airflow using
2nd derivative method Comput. Methods Programs Biomed. 98 199–207
Hornero R, Aboy M, McNames J and Goldstein B 2005 Interpretation of approximate entropy. Case studies
in the analysis of intracranial pressure during elevations in traumatic brain injury IEEE Trans. Biomed.
Eng. 53 1671–80
Hornero R, Alonso A, Jimeno N, Jimeno A and L´ opez M 1999 Nonlinear analysis of time series generated by
schizophrenic patients IEEE Eng. Med. Biol. Mag. 3 84–90
Hornero R,´Alvarez D, Ab´ asolo D, del Campo F and Zamarr´ on C 2007 Utility of approximate entropy from
overnight pulse oximetry data in the diagnosis of the obstructive sleep apnea syndrome IEEE Trans. Biomed.
Eng. 54 107–13
Hosmer D W and Lemeshow S 1999 Applied Logistic Regression (New York: Wiley)
Iber C, Ancoli-Israel S, Chesson A and Quan S F 2007 The AASM Manual for the Scoring of Sleep and Associated
Events: Rules, Terminology and Technical Specifications (Westchester, IL: American Academy of Sleep
Medicine)
Korten J B and Haddad G G 1989 Respiratory waveform pattern recognition using digital techniques Comput. Biol.
Med. 19 207–17
Lempel A and Ziv J 1976 On the complexity of finite sequences IEEE Trans. Inf. Theory 24 530–6
Levendowski D, Steward D, Woodson B T, Olmstead R, Popovic D and Westbrook P 2009 The impact of obstructive
sleep apnea variability measured in-lab versus in-home on sample size calculations Int. Arch. Med. 2 1–8
Lindberg E, Berne C, Elmasry A, Hedner J and Janson C 2006 CPAP treatment of a population-based sample—What
are the benefits and the treatment compliance? Sleep Med. 7 553–60
LindbergE,CarterN,GislasonTandJansonC2001Roleofsnoringanddaytimesleepinessinoccupationalaccidents
Am. J. Respir. Crit. Care Med. 164 2031–5
L´ opez-Jim´ enez F, Kuniyoshi F H S, Gami A and Somers V K 2008 Obstructive sleep apnea: implications for cardiac
and vascular disease Chest 133 793–804
Marshall N S, Barnes M, Travier N, Campbell A J, Pierce R J, McEvoy R D, Neill A M and Gander P H 2006
Continuous positive airway pressure reduces daytime sleepiness in mild to moderate sleep apnoea: a meta-
analysis Thorax 61 430–4
2003 Automated processing of