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`EXHIBIT 2005
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`Estimating Respiratory and Heart Rates from the
`Correntropy Spectral Density of the
`Photoplethysmogram
`
`Ainara Garde1,2*, Walter Karlen1,2, J. Mark Ansermino1,2, Guy A. Dumont1,2
`
`1 Electrical and Computer Engineering in Medicine Group, The University of British Columbia and BC Childrens Hospital, Vancouver, British Columbia, Canada,
`2 Anesthesiology, Pharmacology and Therapeutics, The University of British Columbia and BC Childrens Hospital, Vancouver, British Columbia, Canada
`
`Abstract
`
`The photoplethysmogram (PPG) obtained from pulse oximetry measures local variations of blood volume in tissues,
`reflecting the peripheral pulse modulated by heart activity, respiration and other physiological effects. We propose an
`algorithm based on the correntropy spectral density (CSD) as a novel way to estimate respiratory rate (RR) and heart rate
`(HR) from the PPG. Time-varying CSD, a technique particularly well-suited for modulated signal patterns, is applied to the
`PPG. The respiratory and cardiac frequency peaks detected at extended respiratory (8 to 60 breaths/min) and cardiac (30 to
`180 beats/min) frequency bands provide RR and HR estimations. The CSD-based algorithm was tested against the
`Capnobase benchmark dataset, a dataset from 42 subjects containing PPG and capnometric signals and expert labeled
`reference RR and HR. The RR and HR estimation accuracy was assessed using the unnormalized root mean square (RMS)
`error. We investigated two window sizes (60 and 120 s) on the Capnobase calibration dataset to explore the time resolution
`of the CSD-based algorithm. A longer window decreases the RR error, for 120-s windows, the median RMS error (quartiles)
`obtained for RR was 0.95 (0.27, 6.20) breaths/min and for HR was 0.76 (0.34, 1.45) beats/min. Our experiments show that in
`addition to a high degree of accuracy and robustness, the CSD facilitates simultaneous and efficient estimation of RR and
`HR. Providing RR every minute, expands the functionality of pulse oximeters and provides additional diagnostic power to
`this non-invasive monitoring tool.
`
`Citation: Garde A, Karlen W, Ansermino JM, Dumont GA (2014) Estimating Respiratory and Heart Rates from the Correntropy Spectral Density of the
`Photoplethysmogram. PLoS ONE 9(1): e86427. doi:10.1371/journal.pone.0086427
`
`Editor: Derek Abbott, University of Adelaide, Australia
`
`Received June 17, 2013; Accepted December 10, 2013; Published January 22, 2014
`Copyright: ß 2014 Garde et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
`unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
`
`Funding: This work was supported in part by The Natural Sciences and Engineering Research Council of Canada (NSERC), and the Canadian Institutes of Health
`Research (CIHR) through Collaborative Health Research Projects Program. The funders had no role in study design, data collection and analysis, decision to
`publish, or preparation of the manuscript.
`
`Competing Interests: The authors have declared that no competing interests exist.
`
`* E-mail: ainara.garde@cw.bc.ca
`
`Introduction
`
`The ability to track multiple vital signs from a simple, low cost,
`and easy to use non-invasive sensor is desirable to facilitate
`physiological tele-monitoring. There is a clear need for reliable
`and simple methods for tracking cardio-respiratory activity over
`time to monitor patients in the intensive care environment or
`patients at home with long-term disease with associated instability
`in respiratory or cardiovascular function. Therefore, the remote
`and automated monitoring of heart rate (HR) and respiratory rate
`(RR) is an important field of research [1].
`An abnormal RR is often an early sign of critical illness. For
`example, an essential criterion integrated in guidelines for the
`diagnosis of pneumonia in children (age 1–5 years)
`is
`the
`assessment of an elevated RR (.40 breaths/min) [2]. However,
`clinical measurement of RR has been shown to have poor
`reliability and repeatability [3]. A reliable estimate of RR assessed
`in an automated way is therefore crucial in the application of
`remote tele-monitoring, where persons with no specialized training
`are conducting the assessment. This would enable early support
`for timely recognition and management of physiological deterio-
`ration of high-risk patient groups [4].
`
`Pulse oximetry is widely used in health facilities to monitor
`physiological vital
`signs.
`It
`is based on the principle of
`photoplethysmography (PPG), an optical technique to measure
`local variations of blood volume in tissues. Two light-emitting
`diodes (LEDs) illuminate the tissue and a photo detector detects
`the light reflected by the tissue. The intensity of the light detected
`varies with each heart beat as the blood volume changes over time
`[5]. Blood oxygen saturation (SpO2) is calculated by measuring
`the difference in absorption of oxygenated and deoxygenated
`hemoglobin at two distinct wavelengths, red (660 nm) and infrared
`(940 nm). Oxygenated blood preferably absorbs infrared light and
`transmits red light and deoxygenated blood has the inverted
`absorption characteristics [4].
`The PPG is a complex signal composed of different but related
`components. The most recognized PPG waveform component is
`the peripheral pulse synchronized to each heart beat
`(AC
`component). This AC component is superimposed and modulated
`by a quasi DC component that varies slowly due to respiration,
`vasomotor activity and vasoconstrictor waves [4]. In addition, an
`autonomic response to respiration causes a variation of HR
`synchronized with RR, referred to as respiratory sinus arrhythmia.
`The PPG signal is also influenced by other mechanisms that are
`not completely understood. However, it is generally accepted that
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`

`Respiratory & Heart Rate from PPG with Correntropy
`
`Vc(m):e{jvm,
`
`ð1Þ
`
`XN
`
`{1
`
`Pv(v)~
`
`m~{(N{1)
`
`where Vc(m) is the centered correntropy function, in which the
`mean of the transformed data is subtracted so as to reduce the
`effect of output DC bias. It is estimated by Vc(m)~V (m){ VV
`where Vc(m) is the correntropy function and VV the correntropy
`mean, defined as:
`
`ð2Þ
`
`ð3Þ
`
`k(x(n){x(n{m)),
`
`XN
`
`V (m)~
`
`1
`N{mz1
`
`n~m
`
`XN
`XN
`
`k(x(n){x(n{m)):
`
`m~1
`
`n~m
`
`1 N
`
`2
`
`V ~
`
`The sigmoidal, Gaussian, polynomial, and spline kernels are the
`most commonly used symmetric positive definite kernels, applied
`to machine learning, function approximation, density estimation,
`and support vector machine classification [22], [23]. The Gaussian
`kernel function, applied in the present study, is given by
`
`h
`
`i
`
`k(x(n){x(n{m))~
`
`1ffiffiffiffiffiffi
`p
`
`
`2ps
`
`{(x(n){x(n{m))2
`2s2
`
`e
`
`,
`
`ð4Þ
`
`where s is the kernel parameter, here set using Silverman’s rule of
`density estimation [19].
`is a
`[19],
`Correntropy,
`introduced by Santamaria et al.
`similarity measure defined in terms of inner products of vectors
`in a kernel parameter space. It provides information on both the
`time structure and the statistical distribution. In addition, the use
`of kernel methods makes the correntropy computationally efficient
`since it can be computed directly from the data.
`Autoregressive (AR) spectral analysis based on the Yule-Walker
`method was applied to improve spectral resolution compared to
`conventional techniques [18]. The autoregressive coefficients were
`estimated from the correntropy function, using the YuleWalker
`equations [24]. The selection of model order is a trade-off between
`the frequency resolution and the spurious peaks. The optimal
`model order between 5 and 15 was selected using the minimal
`description length criteria defined by Rissanen [25].
`HR and RR estimation. The CSD over time shows both
`respiratory and cardiac frequency peaks reflecting the RR and HR
`respectively (Figure 2). These peaks can be tracked in the region of
`the respiratory and cardiac frequency bands. Reference HR and
`RR ranges were extracted from a review of observational studies
`that used HR data from 143,346 children and RR data from 3,881
`children (from 6 months to 18 years old) [26]. Based on 99th and
`1st centiles for children and young adults, the HR could range
`from 30 to 180 beats/min (0.5 to 3 Hz, respectively) and RR from
`8 to 60 breaths/min (0.14 to 1 Hz, respectively [26]. The range in
`adults is much more restricted but would be included in this range.
`An extreme range may occur in critical illness, such as an elevated
`HR in the presence of an arrhythmia or an elevated RR (w 40
`breaths/min in children with pneumonia [2]) as an early indicator
`of critical illness. However, those pathological or abnormal RR
`and HR values will also be included in this extended HR and RR
`ranges extracted from the review. Therefore, the maximum value
`
`it has potential to provide clinically useful information about the
`cardio-vascular and respiratory system [6] and its SpO2 pattern
`characterization has successfully applied to detect sleep apnea [7].
`Well-established methods have been described for the estima-
`tion of SpO2 and HR from the PPG [8], [9]. In addition, several
`methods based on characterization of the PPG cycles morphology
`in the time domain, using time-frequency analysis [10], [11], [12],
`[13], [14], [15], [16] digital filtering [5], [17] and smart fusion [6]
`have been proposed to estimate RR. However, this estimation of
`RR in pulse oximetry is not yet commercially established. The
`simultaneous estimation of HR and RR from the PPG signal
`would provide a low processing overhead that is desirable for
`simple and low cost physiological monitor. This would reduce vital
`sign monitoring hardware to one peripheral sensor and one signal-
`processing step.
`Correntropy-based spectral density (CSD) has been found to be
`particularly well suited for the characterization of modulated
`signals. This method provides an improved spectral resolution
`compared to conventional techniques like power spectral density
`(PSD)and shows promise in the detection of modulated patterns
`[18]. Correntropy is a generalized correlation function that
`provides information on higher-order statistics. It is able to detect
`nonlinearities that conventional techniques (based on second-order
`statistics), may be unable to detect. Another attractive property of
`the correntropy function is its robustness against impulsive noise
`[19], [20].
`In this paper we propose a novel algorithm based on CSD to
`estimate both RR and HR simultaneously from the PPG signal
`obtained from pulse oximetry. The initial application will be to
`develop an easy-to-use portable device that measures multiple vital
`signs. This algorithm is ideally suited to be implemented on the
`Phone OximeterH, a mobile device that integrates a commercially
`available and federal drug administration (FDA) approved pulse
`oximeter (Xpod) with a mobile phone. The Phone OximeterH enables
`the analysis of vital signs and intuitive display of information to
`health care providers [21]. In addition, Phone Oximeter’s SpO2
`characterization has been successfully applied to detect sleep
`apnea [7].
`This paper is organized as follows; the Materials and Methods
`section describes the dataset used for the development and testing
`of the newly developed algorithm to estimate RR and HR based
`on CSD, and explains the algorithm with brief description of CSD
`and PSD methods. The accuracy of the CSD-based algorithm is
`presented in the Results
`section, which is
`followed by the
`Discussion, Limitations and Conclusion sections.
`
`Materials and Methods
`
`CSD-based Algorithm
`Conventional spectral analysis assumes a stationary signal and is
`therefore unable to identify HR and RR changes over time. An
`approach to account for such changes is to implement a time-
`varying spectral analysis. Firstly, a sliding time window of 60 s or
`120 s with 50% overlap is used to segment PPG signal
`into
`segments assumed to be stationary and suitable for spectral
`analysis. Secondly, the CSD is applied to the signal segments.
`Thirdly, the HR is estimated by detecting the maximum frequency
`peak within the cardiac frequency band and filtered from the
`signal, and lastly the RR is estimated by detecting the maximum
`frequency peak within the respiratory frequency band (see
`Figure 1).
`Correntropy spectral density. The CSD is a generalization
`of the conventional power spectral density. It is based on the
`Fourier transform of the centered correntropy function [18],
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`January 2014 | Volume 9 |
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`

`Respiratory & Heart Rate from PPG with Correntropy
`
`order between 5 and 15 was selected using the minimal description
`length criteria defined by Rissanen [25].
`
`Simulation Database
`To show certain performance properties of the algorithm a
`simulated PPG signal was first produced. Respiration has three
`different effects on the PPG waveform. The first and more
`predominant effect is a shift in the baseline during each breath.
`The second is a change of the amplitude of the pulse beats with
`each breath which implies that the PPG signal
`is subject to
`amplitude modulation (AM) [15]. The third effect is a variation of
`HR due to an autonomic response to respiration and usually
`decreases with age. Based on the first 2 effects for sake of
`simplicity, the PPG signal was simulated using AM and a baseline
`shift as follows:
`
`½
`x(n)~ (1zm cos (vrn)) cos (vcn)
`
`Šzb(n),
`
`ð7Þ
`
`where fc~vc=2p is the cardiac frequency, fr~vr=2p is the
`respiratory frequency, m [½0,1Š is the modulation index and b(n) is
`the baseline shift synchronized with fr. One hundred outliers with
`values between mean + 5 standard deviation of x(n) were
`randomly added to the signal to simulate noise.
`
`Capnobase Database
`Ethics statement. All subjects were studied according to a
`protocol approved by the University of British Columbia and
`Children’s and Women’s Health Centre of British Columbia
`Research Ethics Board. Informed and written consent to be part of
`the research database was obtained for all subjects. For subjects
`under 16 years of age, parental/guardian written consent was
`obtained. Written assent was obtained for all subjects over the age
`of 11 years.
`Database. Capnobase is an on-line database that contains
`physiological
`signals collected during simultaneously elective
`surgery and routine anesthesia for the purpose of development
`of improved monitoring algorithms in adults and children [27].
`The signals were recorded from 59 children (median age: 8.7,
`range 0.8–16.5 years) and 35 adults (median age: 52.4, range
`26.2–75.6 years) receiving general anesthesia at
`the British
`Columbia Children’s Hospital and St. Paul’s Hospital, Vancouver
`BC, respectively. The recordings included ECG with a sampling
`frequency of 300 Hz, capnometry with a sampling frequency of 25
`Hz, and PPG with a sample frequency of 100 Hz. All signals were
`recorded with S/5 Collect software (Datex-Ohmeda, Finland)
`using a sampling frequency of 300 Hz (PPG and capnometry with
`lower sampling rates were automatically up-sampled).
`Capnobase contains a benchmark dataset with forty-two 8-min
`segments from 29 pediatric and 13 adults cases containing reliable
`recordings of spontaneous or controlled breathing. The capno-
`metric waveform was used as
`the reference gold standard
`recording for RR. A research assistant manually labeled each
`breath in the capnogram and pulse peak in the PPG and validated
`the derived instantaneous reference RR and HR. The beginning
`and end of all artifacts in the PPG waveforms were also manually
`labeled and almost 50% of the cases contained artifacts due to
`movements or similar noise. Capnobase also contains a calibration
`dataset with one hundred twenty-four 2-min segments randomly
`selected from the remaining 52 cases. This dataset is particularly
`challenging because it includes other disturbances such as cardiac
`oscillations etc., which influence the respiratory induced param-
`eters and it also contains substantially more movement artifacts
`than the benchmark dataset. Signals with significant apnea have
`
`Figure 1. Overview of the CSD-based algorithm. Initially the PPG
`signal is segmented into windows (60 s or 120 s) with 50% of overlap. In
`the subsequent step the CSD is applied to calculate the spectrum of the
`windowed signals. The HR is estimated by detecting the maximum
`frequency peak within the cardiac frequency band. The signal is then
`low pass filtered and the RR is estimated by detecting the maximum
`frequency peak within the respiratory frequency band.
`doi:10.1371/journal.pone.0086427.g001
`
`peak frequencies in the cardiac frequency band (0.5 to 3 Hz) and
`in the respiratory frequency band (0.14 to 1 Hz) were automat-
`ically extracted, reflecting HR and RR, respectively.
`For improved resolution around the respiratory frequency peak,
`the HR was filtered using a zero-phase 5th order low pass filter
`with a cutoff frequency of 0.1 Hz below the cardiac frequency. In
`addition,
`frequency peaks close to the secondary harmonics
`around HR were excluded when an elevated RR (w 45 breaths/
`min) were detected. An example of the RR and HR extracted
`from the time varying CSD (Figure 2) is illustrated in Figure 3.
`Power spectral density. Following the same concept a PSD-
`based algorithm was implemented. For a parametric PSD, the
`signal x(n) was modeled through an AR model by
`
`a½kŠx(n{k)ze(n),
`
`ð5Þ
`
`Xp
`
`x(n)~{
`
`k~1
`
`e , a½kŠ
`where e(n) denotes zero-mean white noise with variance s2
`the AR coefficients and p the model order. Once the autore-
`gressive coefficients and the variance s2
`e have been estimated, the
`PSD of an autoregressive process is computed by means of
`
`ð6Þ
`
`

`
`2 ,
`
`s2
`e
`~1 a½kŠ:e{j:vkT
`
`P
`
`p k
`
`1z
`
`

`
`Px(v)~
`
`being T the sampling period. As for the CSD, the optimal model
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`

`Respiratory & Heart Rate from PPG with Correntropy
`
`Figure 2. Time-varying CSD of 8-min PPG signal. Both respiratory and cardiac frequency peaks reflect RR and HR, respectively. Respiratory
`frequency peak is around 0.3 Hz (18 breaths/min) and cardiac frequency peak around 1.25 Hz (75 beats/min).
`doi:10.1371/journal.pone.0086427.g002
`
`been excluded from the analysis. Datasets can be downloaded
`from the on-line database, CapnoBase.org [27]. CSD-based
`algorithm was optimized using the calibration dataset and then
`validated using the benchmark dataset. Both, the calibration and
`benchmark datasets with reference RR and HR have been
`previously used to test RR estimation from PPG [6].
`
`Algorithm Evaluation
`The accuracy of the CSD-based algorithm was evaluated and
`compared to other methods, using the un-normalized root mean
`square (RMS) error. The RMS error was calculated for each
`subject, considering all estimations over time:
`
`s
`
`Xn
`
`ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
`i xest
`(xref
`
`,
`
`ð8Þ
`
`)2
`
`i~1
`
`i
`
`1 n
`
`RMS error~
`
`Validation. The calibrated algorithm was then validated
`using the Capnobase benchmark dataset. All subjects and all signal
`segments with mechanical or spontaneous breathing,
`including
`those with artifacts, were analyzed. The median error and 1st and
`3rd quartiles were calculated to account for a non-normal RMS
`distribution. A Bland-Altman plot was also performed to compare
`the estimated HR and RR to the reference rates.
`In addition, the performance of our algorithm was compared to
`previously proposed methods based on PPG cycles morphology
`[6], time-frequency analysis [15], [7] and digital filtering [17],
`using the Capnobase benchmark dataset. These methods have
`been implemented according to the description included on these
`papers.
`related samples using
`for
`A Wilcoxon signed-rank test
`Bonferroni correction for multiple comparisons was also applied
`to evaluate the statistical significance of our algorithm’s improve-
`ment. The normality of all distributions was tested using One-
`Sample Kolmogorov-Smirnov test.
`
`Results
`
`CSD Output
`The median RR error obtained with the CSD-based algorithm
`applied to the calibration dataset was 4.2 breaths/min when using
`60-s windows and 1.9 breaths/min when using 120-s windows.
`The RMS error significantly (pv 0.05) decreased with longer
`(10sSilverman) reduced the spurious
`windows. A kernel size of
`harmonics and provided more accurate RR estimates (see Figure 4)
`[19]. Therefore, a 10sSilverman was applied to the Capnobase
`Benchmark dataset.
`CSD shows two clear frequency peaks at HR and RR locations,
`for both simulated and in-vivo signals (Figure 5 and 6). As reported
`in our previous work [18], the AM effect is reflected in CSD
`through a frequency peak at its true position. In comparison, the
`AM in PSD is manifested as secondary harmonics surrounding the
`cardiac frequency peak. Further, CSD is more robust to impulsive
`
`and xest
`where n is the number of observations and xref
`are the
`i
`i
`reference and the estimated values, respectively. The median of
`the instantaneous reference RR and HR were compared to the
`estimations for each time window.
`Calibration. The spectral resolution increases with longer
`time-windows with a concomitant reduction in real-time perfor-
`mance (clinicians are required to wait longer for each estimation).
`To investigate the trade-off in window size, the accuracy of the
`algorithm was evaluated with the calibration dataset, using time
`windows of 60 s and 120 s with an overlap of 50%. The statistical
`significance of the error with the different windows was evaluated
`using Wilcoxon signed-rank test to compare related samples.
`The choice of the kernel parameter (s) is trade-off between the
`power of the respiratory peak and the spurious peaks. The power
`of the respiratory peak and spurious harmonics decreases as s
`increases [18]. The CSD-based algorithm’s sensitivity to s was
`evaluated using the calibration dataset. The s calculated according
`to Silverman’s rule (sSilverman) was used as a reference.
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`Respiratory & Heart Rate from PPG with Correntropy
`
`Figure 3. Time-varying estimated and manually labeled reference RR and HR. Estimated (solid blue with * markers) and manually labeled
`(dotted red with+markers) reference RR in (A) and HR in (B). For this subject the RMS errors estimating RR and HR are 0.25 breaths/min and 0.35
`beats/min, respectively.
`doi:10.1371/journal.pone.0086427.g003
`
`noise (see Figure 5.D and Figure 5.F, respectively) compared to the
`PSD approach. This is because the Gaussian kernel makes
`k(x(n){x(n{m))&0 when either x(n) or x(n{m) is an artifact.
`Although the baseline shift is present in both PSD and CSD,
`CSD provides a more robust respiratory modulation frequency
`peak compared to the PSD (see Figure 5.C and Figure 5.E,
`respectively). The enhanced modulation peak is also observed in
`the in-vivo signals (Figure 6.F and Figure 6.G, respectively) where
`the CSD analysis provides a clearer respiratory frequency peak
`compared to the PSD.
`
`Benchmark Accuracy Measurements
`The CSD-based algorithm provided a significantly lower RR
`error compared to the PSD-based algorithm (Table 1). Expanding
`the permitted cardiac and respiratory frequency bands, increased
`the total range of the errors (Figure 7). RR or HR misdetections
`increased the RMS error considerably.
`The median RR error significantly decreased (pv 0.05) with
`longer time windows for using CSD (from 1.77 to 0.95 breaths/
`min) and PSD (from 7.82 to 3.18 breaths/min) approaches.
`However,
`the median error was not statistically different
`in
`estimating HR with longer time windows.
`A Bland-Altman plot (Figure 8) showed good agreement with a
`HR bias of 0.18 and limits of agreement of 21.52 to 1.91, and a
`RR bias of 21.1 and limits of agreement of 26.52 to 4.32.
`The accuracy of the algorithm per subject is illustrated in
`Figure 9, where the estimated RR and HR using a 60-s sliding
`
`window and reference values for each subject are represented.
`When analyzing the estimation for each time-window (Figure 10),
`it can be observed that most of RR errors are accumulated at low
`frequencies (v 15 breaths/min). However, there are some errors
`located out of the normal range because of artifacts and the use of
`extended respiratory and cardiac frequency bands. The number of
`erroneous estimates was reduced when increasing the window
`length, which is reflected by a lower error range when using 120-s
`windows.
`Table 1 illustrates the performance of a number of methods
`using the Capnobase benchmark dataset. CSD-based method
`provided the lowest RR error when using 120-s windows. A
`Wilcoxon signed-rank test for related samples with Bonferroni
`correction for multiple comparisons has shown the significant
`improvement (pv0.05) of our algorithm when compared to PSD
`and the methods proposed by [7] and [17].
`
`Discussion
`
`In this study we have presented a novel methodology to estimate
`both RR and HR simultaneously from pulse oximetry based on
`CSD. The performance of
`the algorithm has been validated
`against a benchmark dataset using RMS error, comparing all
`estimations with reference RR and HR rates manually labeled by
`a research assistant. The algorithm has shown high accuracy and
`robustness estimating RR and HR simultaneously from PPG, even
`when the search is extended to account for pathological and/or
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`Respiratory & Heart Rate from PPG with Correntropy
`
`Figure 4. CSD sensitivity to the kernel parameter. CSD-based algorithm’s perfomance estimating RR is illustrated for the kernel values:
`sSilverman, 10sSilverman, 100sSilverman and 1000sSilverman. The sSilverman is calculated by Silverman’s rule.
`doi:10.1371/journal.pone.0086427.g004
`
`Figure 5. CSD applied to a simulated signal. (A) Simulated signal with 0.2 Hz modulation respiratory frequency (12 breaths/min), 1 Hz cardiac
`frequency (60 beats/min), and m~1, (B) same simulated signal with some outliers randomly added, (C) and (D) the CSD of the simulated signal with
`and without outliers, and (E) and (F) the PSD of the simulated signal with and without outliers, respectively. CSD analysis provides a clearer and more
`robust against outliers respiratory frequency peak than conventional PSD.
`doi:10.1371/journal.pone.0086427.g005
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`Respiratory & Heart Rate from PPG with Correntropy
`
`Figure 6. CSD applied to an in-vivo signal. CSD and PSD performance applied to an in-vivo signal (1 min) of one infant subject: (A) reference HR
`(dotted red line with . markers) and mean HR represented by a dotted grey line, (B) reference RR (dotted red line with . markers) and mean RR
`represented by a dotted grey line, (C) ECG signal, (D) capnometry, (E) PPG signal, (F) CSD and (G) PSD applied to the PPG signal. In addition, the
`average CSD and PSD spectrum of the database’s population is illustrated in the background on (F) and (G) respectively, where the cardiac
`component is represented in dark grey and the filtered signal that corresponds to respiration in light grey.
`doi:10.1371/journal.pone.0086427.g006
`
`abnormal rates to 8 to 60 breaths/min and 30 to 180 beats/min.
`In addition to its accuracy and robustness,
`the RR error
`significantly decreased when longer time windows were used.
`Moreover to generalize our findings broad ranges of subjects
`including children and adults, under controlled ventilation or
`spontaneously breathing over a wide RR ranges were studied.
`
`Using CSD for frequency estimation is preferable to conventional
`PSD functions as it accounts for higher-order moments and is more
`robust to outliers [20]. CSD is particularly useful in signals with
`amplitude modulation like the PPG signal that was analyzed in this
`study. CSD provides the modulation frequency at its actual location
`along the frequency axis [18],
`instead of at
`locations of
`the
`secondary harmonics surrounding the carrier frequency peak. The
`
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`January 2014 | Volume 9 |
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`Issue 1 | e86427
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`Respiratory & Heart Rate from PPG with Correntropy
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`Figure 7. Boxplot of RMS error. Boxplot of the (A) RR and (B) HR RMS error estimated using time windows of 60 s and 120 s and tracked around
`extended RR (from 8 to 60 breaths/min) and HR (from 30 to 180 beats/min). 1st quartile, median, and 3rd quartile values are displayed as bottom,
`middle and top horizontal line of the boxes. Whiskers are used to represent the most extreme values within 3 times the interquartile range from the
`quartile. Outliers (data with values beyond the ends of the whiskers) were displayed as crosses.
`doi:10.1371/journal.pone.0086427.g007
`
`respiratory effect on the PPG respiration is usually present as a
`baseline shift and an AM synchronized with each breath [15]. CSD
`represents both baseline shift and respiratory AM component at the
`same position, whereas a direct PSD of the signal provides only the
`RR derived from the baseline shift at its real position (see Figures 5
`and 6). Thus, in signals with a dominant AM component, CSD will
`provide a more robust respiratory frequency peak.
`
`the CSD is an appropriate
`The results demonstrate that
`technique to provide simultaneous and efficient estimation of
`RR and HR, and will permit to monitor of HR and RR non-
`invasively using only a peripheral sensor. The relevance of this
`algorithm from the clinical perspective is that it facilitates an
`accurate identification of abnormal or pathological rates. Thus,
`this promising algorithm will expand the functionality and
`diagnostic power of pulse oximeters. A number of algorithms
`
`Table 1. RMS error estimating RR and HR with different methods.
`
`Methods
`
`CSD120 s
`
`PSD120 s
`
`Karlen et al. [6]
`
`Garde et al. [7]
`
`Shelley et al. [15]
`
`Nakajima et al. [17]
`
`Median (1st and 3rd quartile)
`
`RR-RMS error (breaths/min)
`
`HR-RMS error (beats/min)
`
`0.95 (0.27, 6.20)
`
`3.18 (1.20, 11.3)*
`
`1.56 (0.60, 3.15)
`
`3.5 (1.1, 11)*
`
`1.91 (0.41, 7.01)
`
`7.47 (0.59, 10.6)*
`
`0.76 (0.34, 1.45)
`
`0.58 (0.21, 1.17)
`
`0.48 (0.37, 0.77)
`
`0.35 (0.2, 0.59)
`
`n/a
`
`n/a
`
`RMS error median (quartiles) estimating RR and HR using different methods. The statistical significant difference (pv0.05) of the RMS error obtained with the CSD-based
`algorithm in comparison to other methods is indicated (asterisk *).
`doi:10.1371/journal.pone.0086427.t001
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`Respiratory & Heart Rate from PPG with Correntropy
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`Figure 8. Bland-Altman for HR and RR estimation. Bland-Altman plots for comparison of (A) HR and (B) RR to the reference HR and RR manually
`labeled by the research assistant. The bias and 95% of limits of agreement are ploted in solid lines. It showed a bias of 0.18 and limits of agreement of
`21.52 to 1.91 beats/min for the estimated HR versus reference HR and a bias of 21.1 and limits of agreement of 26.52 to 4.32 breaths/min for the
`estimated RR versus reference RR.
`doi:10.1371/journal.pone.0086427.g008
`
`based on the PPG signal morphology [13], [28] time-frequency or
`spectral analysis [11], [12], [14], [15], [17] digital filtering [5],
`[17], and complex demodulation [10] have been proposed to
`detect RR from PPG. Most of these methods are restricted to
`healthy ranges only and many are computationally expensive.
`Moreover, most of
`these methods have been tested only in
`controlled environments (research laboratories), and their robust-
`ness to artifacts and other influences that are very common in the
`ambulatory environment have not typically been demonstrated.
`Therefore, some of these methods have been implemented and
`
`applied to the same Capnobase benchmark dataset. CSD-based
`algorithm has provided lower RR error (0.95 breaths/min) using
`120-s windows. The main limitation of the methods proposed by
`Shelley et al. [15] and Nakajima et al. [17] is that they restrict
`their estimations to RR v 40 breaths/min.
`The Smart Fusion method proposed by Karlen et al [6] is
`computationally efficient and was evaluated in an ambulatory
`environment. It combines the three respiratory induced variations
`(frequency, intensity, and amplitude) using a mean calculation. This
`method improved the robustness of the RR estimation, with a
`
`Figure 9. Scatter plot, error per subject. Scatter plot showing the median value of estimated and reference values of (A) RR and (B) HR for each
`subject using 60-s time window. The respiratory and cardiac frequency peaks are detected around the extended RR and HR range. Observations with
`artifacts are included. The dotted line represents the optimal performance.
`doi:10.1371/journal.pone.0086427.g009
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`January 2014 | Volume 9 |
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`Issue 1 | e86427
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`Respiratory & Heart Rate from PPG with Correntropy
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`Figure 10. Scatter plot, er