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Enhancing the Robustness of Smartphone Photoplethysmography: A Signal Quality Index Approach

Identifieur interne : 000822 ( Pmc/Corpus ); précédent : 000821; suivant : 000823

Enhancing the Robustness of Smartphone Photoplethysmography: A Signal Quality Index Approach

Auteurs : Ivan Liu ; Shiguang Ni ; Kaiping Peng

Source :

RBID : PMC:7181214

Abstract

Heart rate variability (HRV) provides essential health information such as the risks of heart attacks and mental disorders. However, inconvenience related to the accurate detection of HRV limits its potential applications. The ubiquitous use of smartphones makes them an excellent choice for regular and portable health monitoring. Following this trend, smartphone photoplethysmography (PPG) has recently garnered prominence; however, the lack of robustness has prevented both researchers and practitioners from embracing this technology. This study aimed to bridge the gap in the literature by developing a novel smartphone PPG quality index (SPQI) that can filter corrupted data. A total of 226 participants joined the study, and results from 1343 samples were used to validate the proposed sinusoidal function-based model. In both the correlation coefficient and Bland–Altman analyses, the agreement between HRV measurements generated by both the smartphone PPG and the reference electrocardiogram improved when data were filtered through the SPQI. Our results support not only the proposed approach but also the general value of using smartphone PPG in HRV analysis.


Url:
DOI: 10.3390/s20071923
PubMed: 32235543
PubMed Central: 7181214

Links to Exploration step

PMC:7181214

Le document en format XML

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<p>Heart rate variability (HRV) provides essential health information such as the risks of heart attacks and mental disorders. However, inconvenience related to the accurate detection of HRV limits its potential applications. The ubiquitous use of smartphones makes them an excellent choice for regular and portable health monitoring. Following this trend, smartphone photoplethysmography (PPG) has recently garnered prominence; however, the lack of robustness has prevented both researchers and practitioners from embracing this technology. This study aimed to bridge the gap in the literature by developing a novel smartphone PPG quality index (SPQI) that can filter corrupted data. A total of 226 participants joined the study, and results from 1343 samples were used to validate the proposed sinusoidal function-based model. In both the correlation coefficient and Bland–Altman analyses, the agreement between HRV measurements generated by both the smartphone PPG and the reference electrocardiogram improved when data were filtered through the SPQI. Our results support not only the proposed approach but also the general value of using smartphone PPG in HRV analysis.</p>
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<pmc article-type="research-article">
<pmc-dir>properties open_access</pmc-dir>
<front>
<journal-meta>
<journal-id journal-id-type="nlm-ta">Sensors (Basel)</journal-id>
<journal-id journal-id-type="iso-abbrev">Sensors (Basel)</journal-id>
<journal-id journal-id-type="publisher-id">sensors</journal-id>
<journal-title-group>
<journal-title>Sensors (Basel, Switzerland)</journal-title>
</journal-title-group>
<issn pub-type="epub">1424-8220</issn>
<publisher>
<publisher-name>MDPI</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="pmid">32235543</article-id>
<article-id pub-id-type="pmc">7181214</article-id>
<article-id pub-id-type="doi">10.3390/s20071923</article-id>
<article-id pub-id-type="publisher-id">sensors-20-01923</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Enhancing the Robustness of Smartphone Photoplethysmography: A Signal Quality Index Approach</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0001-8171-9356</contrib-id>
<name>
<surname>Liu</surname>
<given-names>Ivan</given-names>
</name>
<xref ref-type="aff" rid="af1-sensors-20-01923">1</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Ni</surname>
<given-names>Shiguang</given-names>
</name>
<xref ref-type="aff" rid="af2-sensors-20-01923">2</xref>
<xref rid="c1-sensors-20-01923" ref-type="corresp">*</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Peng</surname>
<given-names>Kaiping</given-names>
</name>
<xref ref-type="aff" rid="af1-sensors-20-01923">1</xref>
<xref ref-type="aff" rid="af3-sensors-20-01923">3</xref>
</contrib>
</contrib-group>
<aff id="af1-sensors-20-01923">
<label>1</label>
Data Science and Information Technology Research Center, Tsinghua-Berkeley Shenzhen Institute, Tsinghua University, Shenzhen 518055, China;
<email>liusq15@mails.tsinghua.edu.cn</email>
(I.L.);
<email>pengkp@tsinghua.edu.cn</email>
(K.P.)</aff>
<aff id="af2-sensors-20-01923">
<label>2</label>
Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, China</aff>
<aff id="af3-sensors-20-01923">
<label>3</label>
Department of Psychology, Tsinghua University, Beijing 100084, China</aff>
<author-notes>
<corresp id="c1-sensors-20-01923">
<label>*</label>
Correspondence:
<email>ni.shiguang@sz.tsinghua.edu.cn</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>30</day>
<month>3</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="collection">
<month>4</month>
<year>2020</year>
</pub-date>
<volume>20</volume>
<issue>7</issue>
<elocation-id>1923</elocation-id>
<history>
<date date-type="received">
<day>05</day>
<month>3</month>
<year>2020</year>
</date>
<date date-type="accepted">
<day>28</day>
<month>3</month>
<year>2020</year>
</date>
</history>
<permissions>
<copyright-statement>© 2020 by the authors.</copyright-statement>
<copyright-year>2020</copyright-year>
<license license-type="open-access">
<license-p>Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (
<ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">http://creativecommons.org/licenses/by/4.0/</ext-link>
).</license-p>
</license>
</permissions>
<abstract>
<p>Heart rate variability (HRV) provides essential health information such as the risks of heart attacks and mental disorders. However, inconvenience related to the accurate detection of HRV limits its potential applications. The ubiquitous use of smartphones makes them an excellent choice for regular and portable health monitoring. Following this trend, smartphone photoplethysmography (PPG) has recently garnered prominence; however, the lack of robustness has prevented both researchers and practitioners from embracing this technology. This study aimed to bridge the gap in the literature by developing a novel smartphone PPG quality index (SPQI) that can filter corrupted data. A total of 226 participants joined the study, and results from 1343 samples were used to validate the proposed sinusoidal function-based model. In both the correlation coefficient and Bland–Altman analyses, the agreement between HRV measurements generated by both the smartphone PPG and the reference electrocardiogram improved when data were filtered through the SPQI. Our results support not only the proposed approach but also the general value of using smartphone PPG in HRV analysis.</p>
</abstract>
<kwd-group>
<kwd>smartphone photoplethysmography</kwd>
<kwd>heart rate variability</kwd>
<kwd>signal quality index</kwd>
<kwd>pulse waveform</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="sec1-sensors-20-01923">
<title>1. Introduction</title>
<p>Heart rate (HR) is an indicator of the balance of multiple physiological systems such as the cerebral cortex, autonomic nervous system, endocrine system, and baroreflex [
<xref rid="B1-sensors-20-01923" ref-type="bibr">1</xref>
,
<xref rid="B2-sensors-20-01923" ref-type="bibr">2</xref>
]. Even while at rest, HR continuously adapts to physiological adjustments such as changes in arterial pressure caused by breathing [
<xref rid="B3-sensors-20-01923" ref-type="bibr">3</xref>
]. By observing HR variability (HRV), researchers can assess our physical capability to adapt to internal physiological requests or changes in our surroundings. </p>
<p>Studies have linked HRV to several health-related variables such as gender [
<xref rid="B4-sensors-20-01923" ref-type="bibr">4</xref>
], body mass index [
<xref rid="B5-sensors-20-01923" ref-type="bibr">5</xref>
], exercise habits [
<xref rid="B6-sensors-20-01923" ref-type="bibr">6</xref>
], quality of sleep [
<xref rid="B7-sensors-20-01923" ref-type="bibr">7</xref>
,
<xref rid="B8-sensors-20-01923" ref-type="bibr">8</xref>
], insulin resistance [
<xref rid="B9-sensors-20-01923" ref-type="bibr">9</xref>
], and inflammation [
<xref rid="B10-sensors-20-01923" ref-type="bibr">10</xref>
]. A low HRV has been used to predict several health problems including heart attacks [
<xref rid="B11-sensors-20-01923" ref-type="bibr">11</xref>
], headaches [
<xref rid="B12-sensors-20-01923" ref-type="bibr">12</xref>
], and renal impairment [
<xref rid="B13-sensors-20-01923" ref-type="bibr">13</xref>
]. Given that mental states influence the activation of the sympathetic nervous system (SNS) and the parasympathetic nervous system (PNS) [
<xref rid="B14-sensors-20-01923" ref-type="bibr">14</xref>
,
<xref rid="B15-sensors-20-01923" ref-type="bibr">15</xref>
], and that HR is modulated by the SNS and PNS, researchers have associated HRV with mental characteristics such as attention span [
<xref rid="B14-sensors-20-01923" ref-type="bibr">14</xref>
,
<xref rid="B16-sensors-20-01923" ref-type="bibr">16</xref>
], decision making [
<xref rid="B17-sensors-20-01923" ref-type="bibr">17</xref>
], social behavior [
<xref rid="B18-sensors-20-01923" ref-type="bibr">18</xref>
,
<xref rid="B19-sensors-20-01923" ref-type="bibr">19</xref>
], and emotional modulation [
<xref rid="B20-sensors-20-01923" ref-type="bibr">20</xref>
]. </p>
<p>Despite the importance of HRV in clinical diagnoses and preventative medical applications, the cost and immobility of traditional electrocardiogram (ECG) equipment limits its potential for continuous health monitoring. The advances in information technology have introduced several new approaches to make health information more accessible than before. Among these approaches, smartphone photoplethysmography (PPG) has gained prominence [
<xref rid="B21-sensors-20-01923" ref-type="bibr">21</xref>
,
<xref rid="B22-sensors-20-01923" ref-type="bibr">22</xref>
]; it is an optical method that uses sensors to monitor the microvascular blood volume changes in body tissues [
<xref rid="B23-sensors-20-01923" ref-type="bibr">23</xref>
]. As hemoglobin absorbs more light than the surrounding tissue, an increase (systole) or decrease (diastole) in the amount of blood can be assessed by employing the differences in the intensities of the lights and the converted waveforms. Smartphone PPG detects heartbeats by recording videos of fingertips using the in-built camera [
<xref rid="B24-sensors-20-01923" ref-type="bibr">24</xref>
,
<xref rid="B25-sensors-20-01923" ref-type="bibr">25</xref>
]. </p>
<p>The primary motivation for using smartphone PPG, compared to other wearable devices, is that it requires minimal equipment. Given that smartphones with in-built cameras have become a part of modern life, using them to access health information is an ideal alternative when ECGs or similar medical devices are not available [
<xref rid="B26-sensors-20-01923" ref-type="bibr">26</xref>
]. In addition, there have been several reported techniques for increasing the accuracy of smartphone PPG, such as point-of-interest selection [
<xref rid="B27-sensors-20-01923" ref-type="bibr">27</xref>
], bandpass filtering [
<xref rid="B28-sensors-20-01923" ref-type="bibr">28</xref>
], adaptive signal thresholding [
<xref rid="B29-sensors-20-01923" ref-type="bibr">29</xref>
], motion detection techniques [
<xref rid="B30-sensors-20-01923" ref-type="bibr">30</xref>
,
<xref rid="B31-sensors-20-01923" ref-type="bibr">31</xref>
,
<xref rid="B32-sensors-20-01923" ref-type="bibr">32</xref>
], interpolation techniques [
<xref rid="B33-sensors-20-01923" ref-type="bibr">33</xref>
], and signal decomposition methods [
<xref rid="B34-sensors-20-01923" ref-type="bibr">34</xref>
,
<xref rid="B35-sensors-20-01923" ref-type="bibr">35</xref>
,
<xref rid="B36-sensors-20-01923" ref-type="bibr">36</xref>
]. Bioengineering studies indicate that the average HR [
<xref rid="B37-sensors-20-01923" ref-type="bibr">37</xref>
] and HRV measured using smartphone PPG are comparable with those measured using gold standard ECGs [
<xref rid="B21-sensors-20-01923" ref-type="bibr">21</xref>
,
<xref rid="B28-sensors-20-01923" ref-type="bibr">28</xref>
,
<xref rid="B38-sensors-20-01923" ref-type="bibr">38</xref>
,
<xref rid="B39-sensors-20-01923" ref-type="bibr">39</xref>
,
<xref rid="B40-sensors-20-01923" ref-type="bibr">40</xref>
].</p>
<p>Although it is a promising solution for practical data collection and has an accuracy that has been well proved in several experiments, using smartphone PPG to measure HRV has received limited research attention in applied disciplines such as medicine or psychology [
<xref rid="B41-sensors-20-01923" ref-type="bibr">41</xref>
]; a possible explanation is the lack of robustness in practical scenarios. When smartphone users measure their heartbeats outside a laboratory environment, slight hand movements or ambient light changes can corrupt the PPG signals. Software designed to process the camera signals have limited control over the underlying operating system and hardware. Further, camera settings—especially exposure and white balance—differ between smartphone models and may change automatically when the environment changes. The low frame (sampling) rate of smartphone cameras is another source of randomness [
<xref rid="B42-sensors-20-01923" ref-type="bibr">42</xref>
,
<xref rid="B43-sensors-20-01923" ref-type="bibr">43</xref>
]. The sampling rate can be as high as 1000 Hz for medical equipment [
<xref rid="B44-sensors-20-01923" ref-type="bibr">44</xref>
]; however, for most smartphone cameras, it is less than 30 Hz [
<xref rid="B40-sensors-20-01923" ref-type="bibr">40</xref>
], and this can result in the fiducial point detection technique (FPDT) easily missing the actual point. Frame rate instability—as a design to prevent the CPU from overloading or overheating—further degrades the acquisition performance [
<xref rid="B26-sensors-20-01923" ref-type="bibr">26</xref>
,
<xref rid="B45-sensors-20-01923" ref-type="bibr">45</xref>
].</p>
<p>While it is difficult to ensure the robustness of using smartphone PPG in assessing HRV against a less controlled environment, other strategies can be employed to make smartphone PPG practically workable. Users today are familiar with various consumer-grade healthcare devices such as home blood pressure monitors or ECG chest straps. Several of these devices, while validated in laboratories, also have limited mechanisms to deal with randomness found in real-life scenarios. A common strategy to overcome such limitations is to provide measurement quality information so that users can discard corrupted data and reperform the measurement. However, only a few smartphone PPG studies have considered this potential solution [
<xref rid="B46-sensors-20-01923" ref-type="bibr">46</xref>
]. </p>
<p>This study aimed to bridge the gap in the literature by providing a smartphone PPG quality index (SPQI) that can filter out low-quality data and perform HRV measurements that are comparable to the results from ECGs. We propose a novel approach to fit collected data points to a pre-defined model and calculate the success rate as an index of signal quality. Based on the physiological studies of the radial pulse waveform [
<xref rid="B47-sensors-20-01923" ref-type="bibr">47</xref>
], the current study designed a sinusoidal function-based regression model that can fit the right-skewed pulse signal and determine the quality of data using the success rate of the convergence in the optimization. Further, we conducted an empirical experiment to validate the proposed approach. The potential uses and limitations are also discussed before concluding this paper.</p>
</sec>
<sec id="sec2-sensors-20-01923">
<title>2. Materials and Methods </title>
<sec id="sec2dot1-sensors-20-01923">
<title>2.1. Signal Pre-Processing</title>
<p>The current study employed three steps to convert film frames of the fingertip to pulse waveforms for further analysis.</p>
<sec id="sec2dot1dot1-sensors-20-01923">
<title>2.1.1. Signal Extraction and Conversion</title>
<p>For each data collection session, a self-developed app first activated the in-built flashlight and recorded 120 × 160 pixel videos with approximately 30 frames per second (the actual frame rate was determined by the underlying operating system) (see
<xref ref-type="fig" rid="sensors-20-01923-f001">Figure 1</xref>
a). Raw YUV-format picture frames retrieved from the preview function were then converted into the RGB format. Then, the input signals
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</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:mover accent="true">
<mml:mi>G</mml:mi>
<mml:mo>¯</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>σ</mml:mi>
<mml:mi>G</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
<mml:mtext> </mml:mtext>
<mml:mi>i</mml:mi>
<mml:mo></mml:mo>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo></mml:mo>
<mml:mo>,</mml:mo>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
where
<inline-formula>
<mml:math id="mm5">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
is the amount of data collected in each data collection session. Because standard deviation can represent the relative strength of each channel, the signals were combined with the standard deviation-weighted average as follows:
<disp-formula id="FD2-sensors-20-01923">
<label>(2)</label>
<mml:math id="mm6">
<mml:mrow>
<mml:mrow>
<mml:mtext> </mml:mtext>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:msub>
<mml:mo></mml:mo>
<mml:mi>G</mml:mi>
</mml:msub>
<mml:mo>×</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>G</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo></mml:mo>
<mml:mi>σ</mml:mi>
<mml:msub>
<mml:mo></mml:mo>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mo>×</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo></mml:mo>
<mml:mi>σ</mml:mi>
<mml:msub>
<mml:mo></mml:mo>
<mml:mi>R</mml:mi>
</mml:msub>
<mml:mo>×</mml:mo>
<mml:msub>
<mml:mi>n</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>σ</mml:mi>
<mml:msub>
<mml:mo></mml:mo>
<mml:mi>R</mml:mi>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:mi>σ</mml:mi>
<mml:msub>
<mml:mo></mml:mo>
<mml:mi>G</mml:mi>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:mi>σ</mml:mi>
<mml:msub>
<mml:mo></mml:mo>
<mml:mi>B</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
where
<disp-formula>
<mml:math id="mm7">
<mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>σ</mml:mi>
<mml:mi>C</mml:mi>
<mml:mo></mml:mo>
</mml:msubsup>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>σ</mml:mi>
<mml:mi>C</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mrow>
<mml:mi>if</mml:mi>
<mml:mtext> </mml:mtext>
</mml:mrow>
<mml:msub>
<mml:mi>σ</mml:mi>
<mml:mi>C</mml:mi>
</mml:msub>
<mml:mo>></mml:mo>
<mml:mn>0.5</mml:mn>
<mml:mo>,</mml:mo>
<mml:mtext> </mml:mtext>
<mml:mn>3</mml:mn>
<mml:mo><</mml:mo>
<mml:mover accent="true">
<mml:mi>C</mml:mi>
<mml:mo>¯</mml:mo>
</mml:mover>
<mml:mo><</mml:mo>
<mml:mn>252</mml:mn>
<mml:mtext> </mml:mtext>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:mrow>
<mml:mi>otherwise</mml:mi>
<mml:mtext> </mml:mtext>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
<mml:mo>,</mml:mo>
<mml:mtext> </mml:mtext>
<mml:mi>C</mml:mi>
<mml:mo></mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>B</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>G</mml:mi>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
and
<inline-formula>
<mml:math id="mm8">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:mi mathvariant="bold-italic">T</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>|</mml:mo>
<mml:mi>i</mml:mi>
<mml:mo></mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>.</mml:mo>
<mml:mo>.</mml:mo>
<mml:mo>,</mml:mo>
<mml:mi>k</mml:mi>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
denotes the time at which the i
<sup>th</sup>
data point was collected. A color channel was removed from the weighted average
<inline-formula>
<mml:math id="mm9">
<mml:mrow>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
when the average of the input (
<inline-formula>
<mml:math id="mm10">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>C</mml:mi>
<mml:mo>¯</mml:mo>
</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula>
) was either too small or too close to the upper limit of 255, or when the standard deviation (
<inline-formula>
<mml:math id="mm11">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>σ</mml:mi>
<mml:mi>C</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
) was too small (
<inline-formula>
<mml:math id="mm12">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>σ</mml:mi>
<mml:mi>C</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:mn>0.5</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
). In addition, the signs of the red and blue channel were reversed to denote the inverse relationship between the green channel and the other two channels.</p>
</sec>
<sec id="sec2dot1dot2-sensors-20-01923">
<title>2.1.2. Beat-to-Beat Interval (BBI) Segmentation</title>
<p>After converting the signals to a waveform input, we divided the “continuous” waveform dataset
<inline-formula>
<mml:math id="mm13">
<mml:mrow>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
into segments representing each beat-to-beat interval (BBI). Given that the radial pulse waveform follows a right-skewed bell shape, distinct plateaus can be observed on the first derivatives during each heartbeat (see
<xref ref-type="fig" rid="sensors-20-01923-f001">Figure 1</xref>
b). Although the exact position of the maximum of the waveform is susceptible to noise, the detection of the plateau is relatively robust. Therefore, this study used a set of local maxima (
<inline-formula>
<mml:math id="mm14">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">M</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
)—above the 70th percentile (
<inline-formula>
<mml:math id="mm15">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>70</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
) of the first derivatives
<inline-formula>
<mml:math id="mm16">
<mml:mrow>
<mml:mrow>
<mml:msup>
<mml:mi>f</mml:mi>
<mml:mo></mml:mo>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
—to identify potential BBIs for further analysis.
<disp-formula id="FD3-sensors-20-01923">
<label>(3)</label>
<mml:math id="mm17">
<mml:mrow>
<mml:mrow>
<mml:mi mathvariant="bold-italic">M</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">M</mml:mi>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">M</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo></mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">M</mml:mi>
<mml:mi mathvariant="bold-italic">u</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>|</mml:mo>
<mml:mi>max</mml:mi>
<mml:msup>
<mml:mi>f</mml:mi>
<mml:mo></mml:mo>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>></mml:mo>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>70</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mtext> </mml:mtext>
<mml:msup>
<mml:mi>f</mml:mi>
<mml:mo></mml:mo>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo><</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mtext> </mml:mtext>
<mml:mfrac>
<mml:mrow>
<mml:mn>60</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo><</mml:mo>
<mml:mn>150</mml:mn>
<mml:mtext> </mml:mtext>
<mml:mo></mml:mo>
<mml:mi>j</mml:mi>
<mml:mo></mml:mo>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mtext> </mml:mtext>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:mi mathvariant="bold-italic">T</mml:mi>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>The distances between two successive data points in
<inline-formula>
<mml:math id="mm18">
<mml:mrow>
<mml:mi mathvariant="bold-italic">M</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
were converted into HRs to filter out points with HRs over 150. All first and second derivatives were calculated using first- and second-order central difference approximations. The set of maximum points (
<inline-formula>
<mml:math id="mm19">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
) of the waveform between two data points in
<inline-formula>
<mml:math id="mm20">
<mml:mrow>
<mml:mi mathvariant="bold-italic">M</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
is defined as
<inline-formula>
<mml:math id="mm21">
<mml:mrow>
<mml:mi mathvariant="bold-italic">P</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
:
<disp-formula id="FD4-sensors-20-01923">
<label>(4)</label>
<mml:math id="mm22">
<mml:mrow>
<mml:mrow>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo></mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mi mathvariant="bold-italic">q</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:mo>|</mml:mo>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:mo><</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:mo><</mml:mo>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>+</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mtext> </mml:mtext>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mi>max</mml:mi>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>|</mml:mo>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo><</mml:mo>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>+</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>The intervals segmented by the data points in
<inline-formula>
<mml:math id="mm23">
<mml:mrow>
<mml:mi mathvariant="bold-italic">P</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
are then defined as the set of BBIs (
<inline-formula>
<mml:math id="mm24">
<mml:mrow>
<mml:mi mathvariant="bold-italic">B</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
):
<disp-formula id="FD5-sensors-20-01923">
<label>(5)</label>
<mml:math id="mm25">
<mml:mrow>
<mml:mrow>
<mml:mi mathvariant="bold-italic">B</mml:mi>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>|</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo></mml:mo>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:mi>min</mml:mi>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:mi mathvariant="bold-italic">P</mml:mi>
<mml:mo> </mml:mo>
<mml:mo>|</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>></mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>60</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo><</mml:mo>
<mml:mn>150</mml:mn>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
</sec>
<sec id="sec2dot1dot3-sensors-20-01923">
<title>2.1.3. BBI Normalization</title>
<p>To reduce the problem caused by baseline drifting [
<xref rid="B40-sensors-20-01923" ref-type="bibr">40</xref>
], the amplitudes of data points in each BBI were normalized in proportion to the height difference of the two successive peaks as described below (see
<xref ref-type="fig" rid="sensors-20-01923-f001">Figure 1</xref>
c):
<disp-formula id="FD6-sensors-20-01923">
<label>(6)</label>
<mml:math id="mm26">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>normalized</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>×</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo></mml:mo>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mtext> </mml:mtext>
<mml:mo></mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:mtext> </mml:mtext>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mtext> </mml:mtext>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>t</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo></mml:mo>
<mml:mi mathvariant="bold-italic">B</mml:mi>
<mml:mtext> </mml:mtext>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>The normalized data points were used to fit the regression model and to determine heartbeat points with various FPDTs. The current study then applied the R package RHRV [
<xref rid="B48-sensors-20-01923" ref-type="bibr">48</xref>
] to convert the heartbeat points generated by the FPDTs to HRV measures for further analysis.</p>
</sec>
</sec>
<sec id="sec2dot2-sensors-20-01923">
<title>2.2. Sinusoidal Function-Based Photoplethysmography (PPG) Quality Index</title>
<p>Although the exact contour of the waveform is influenced by the characteristics of the individuals’ systemic circulation [
<xref rid="B49-sensors-20-01923" ref-type="bibr">49</xref>
], the general shapes are similar. For most healthy people, the contour is right skewed and bell shaped, with a dicrotic notch in the middle [
<xref rid="B50-sensors-20-01923" ref-type="bibr">50</xref>
]. Since the shapes of the pulse waveforms are similar, PPG studies use waveform morphology to differentiate acceptable signals from contaminated ones [
<xref rid="B51-sensors-20-01923" ref-type="bibr">51</xref>
]. </p>
<p>Two families of functions have been used to describe the pulse waveform: Gaussian (or modifications, such as the Rayleigh functions) [
<xref rid="B46-sensors-20-01923" ref-type="bibr">46</xref>
,
<xref rid="B52-sensors-20-01923" ref-type="bibr">52</xref>
,
<xref rid="B53-sensors-20-01923" ref-type="bibr">53</xref>
,
<xref rid="B54-sensors-20-01923" ref-type="bibr">54</xref>
] and sinusoidal functions. Since sinusoidal functions are more commonly used in hemodynamic studies (i.e., Fourier analysis) to predict health-related variables [
<xref rid="B55-sensors-20-01923" ref-type="bibr">55</xref>
], and are less computationally demanding, this study fit the pulse waveform with the sum of sinusoidal functions. </p>
<p>We define the model as:
<disp-formula id="FD7-sensors-20-01923">
<label>(7)</label>
<mml:math id="mm27">
<mml:mrow>
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi mathvariant="sans-serif">ω</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:munderover>
<mml:mstyle mathsize="140%" displaystyle="true">
<mml:mo></mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
<mml:msub>
<mml:mi>ω</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>×</mml:mo>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mtext>   The_SMF</mml:mtext>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
where
<inline-formula>
<mml:math id="mm28">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mi>sin</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>×</mml:mo>
<mml:mi>c</mml:mi>
<mml:mo>×</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo></mml:mo>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>×</mml:mo>
<mml:mi>π</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
is the i
<sup>th</sup>
sinusoidal function,
<inline-formula>
<mml:math id="mm29">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>ω</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo></mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
is the weighting of the i
<sup>th</sup>
sinusoidal function,
<inline-formula>
<mml:math id="mm30">
<mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo></mml:mo>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
is the scaling parameter,
<inline-formula>
<mml:math id="mm31">
<mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mo></mml:mo>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
is the displacement parameter, and
<inline-formula>
<mml:math id="mm32">
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
is the number of sinusoidal functions included in the model (
<xref ref-type="fig" rid="sensors-20-01923-f002">Figure 2</xref>
a,b). As an explorative study, the frequencies of the sinusoidal functions (
<inline-formula>
<mml:math id="mm33">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
<mml:mo>></mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
) were provided as multipliers of the base function
<inline-formula>
<mml:math id="mm34">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
to reduce model complexity. In addition, the weightings
<inline-formula>
<mml:math id="mm35">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="sans-serif">ω</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
were restricted to positive values and
<inline-formula>
<mml:math id="mm36">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo></mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>×</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo> </mml:mo>
<mml:mo></mml:mo>
<mml:mi>i</mml:mi>
<mml:mo>></mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
to keep the model (Equation (1)) right skewed and approximately bell shaped. Future studies may relax these constraints.</p>
<p>The model fit the input data points using nonlinear least-squares optimization with 10,000 iterations. Based on previous experience, we used a set of initial values:
<inline-formula>
<mml:math id="mm37">
<mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mn>4</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mi>c</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>h</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>7</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>7</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>3</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>0.1</mml:mn>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
. Since the sum of the squared errors in the regression did not change significantly when
<italic>n</italic>
was greater than four in our preliminary data analysis, we set
<italic>n</italic>
= 4 in the model. When the waveform of an interval was severely corrupted, or the section contained many artifacts, the model failed to converge before reaching the maximum number of iterations or had a large root mean square error (RMSE). The model fitting was considered to have failed when the RMSE was larger than 0.5. The maximum number of iterations and the threshold for the RMSE were determined based on experience; future studies may re-examine these constraints. Further, because the pulse waveform was relatively stable, for each BBI, we used the fitting results from previous BBIs to filter out parameters that were outliers. When either
<inline-formula>
<mml:math id="mm38">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>ω</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
and
<inline-formula>
<mml:math id="mm39">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>ω</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
were outside of the boundary determined by Tukey’s method, i.e., more than 1.5 times the interquartile range beyond the quartiles, the fitting was considered to have failed. We then defined the SPQI as the success rate of the model-fitting process.
<disp-formula id="FD8-sensors-20-01923">
<label>(8)</label>
<mml:math id="mm40">
<mml:mrow>
<mml:mrow>
<mml:mi>SPQI</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mi>number</mml:mi>
<mml:mtext> </mml:mtext>
<mml:mi>of</mml:mi>
<mml:mtext> </mml:mtext>
<mml:mi>successful</mml:mi>
<mml:mtext> </mml:mtext>
<mml:mi>model</mml:mi>
<mml:mtext> </mml:mtext>
<mml:mi>fittings</mml:mi>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mi>number</mml:mi>
<mml:mtext> </mml:mtext>
<mml:mi>of</mml:mi>
<mml:mtext> </mml:mtext>
<mml:mi>BBIs</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mtext>   The_SMF</mml:mtext>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
</sec>
<sec id="sec2dot3-sensors-20-01923">
<title>2.3. HRV Measures</title>
<p>There are three types of HRV measures: (1) time-domain, (2) frequency-domain, and (3) nonlinear. The frequency-domain components of HRV consist of four frequency bands: high frequency (HF), low frequency (LF), very low frequency (VLF), and ultralow frequency (ULF) (
<xref rid="sensors-20-01923-t001" ref-type="table">Table 1</xref>
). Given that this study only recorded 5-min videos, the ULF and VLF bands did not apply [
<xref rid="B56-sensors-20-01923" ref-type="bibr">56</xref>
]. The HF and LF values were log-transformed because they are not distributed normally [
<xref rid="B43-sensors-20-01923" ref-type="bibr">43</xref>
,
<xref rid="B57-sensors-20-01923" ref-type="bibr">57</xref>
]. The time-domain indices of HRV quantify variability in the BBI. This study included three commonly used time-domain measures for comparison: rMSSD, pNN50, and SDNN. Nonlinear HRV measures are computationally complex and were accordingly excluded from this study.</p>
</sec>
<sec id="sec2dot4-sensors-20-01923">
<title>2.4. FPDT</title>
<p>The current study included five frequently used FPDTs to compare the agreement between smartphone PPG and the reference ECG [
<xref rid="B26-sensors-20-01923" ref-type="bibr">26</xref>
,
<xref rid="B29-sensors-20-01923" ref-type="bibr">29</xref>
,
<xref rid="B58-sensors-20-01923" ref-type="bibr">58</xref>
,
<xref rid="B59-sensors-20-01923" ref-type="bibr">59</xref>
,
<xref rid="B60-sensors-20-01923" ref-type="bibr">60</xref>
,
<xref rid="B61-sensors-20-01923" ref-type="bibr">61</xref>
,
<xref rid="B62-sensors-20-01923" ref-type="bibr">62</xref>
,
<xref rid="B63-sensors-20-01923" ref-type="bibr">63</xref>
,
<xref rid="B64-sensors-20-01923" ref-type="bibr">64</xref>
] (
<xref rid="sensors-20-01923-t002" ref-type="table">Table 2</xref>
and
<xref ref-type="fig" rid="sensors-20-01923-f002">Figure 2</xref>
c).</p>
</sec>
<sec id="sec2dot5-sensors-20-01923">
<title>2.5. Agreement Analysis</title>
<p>We used two methods to compare the agreement between the smartphone PPG and reference ECG. First, we examined the Pearson correlation coefficients of the data generated by the smartphone PPG to the reference ECG. The correlation coefficients (r) were assessed with the Student’s
<italic>t</italic>
-test where
<disp-formula id="FD9-sensors-20-01923">
<label>(9)</label>
<mml:math id="mm41">
<mml:mrow>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mrow>
<mml:mtext> </mml:mtext>
<mml:mi>value</mml:mi>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mi>r</mml:mi>
<mml:msqrt>
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo></mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo></mml:mo>
<mml:msup>
<mml:mi>r</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:msqrt>
<mml:mtext>   Combined_Signal</mml:mtext>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
Second, we compared the agreement with the Bland–Altman method [
<xref rid="B65-sensors-20-01923" ref-type="bibr">65</xref>
]. The Bland–Altman ratio (BAR) is defined as:
<disp-formula id="FD10-sensors-20-01923">
<label>(10)</label>
<mml:math id="mm42">
<mml:mrow>
<mml:mrow>
<mml:mi>BAR</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>0.5</mml:mn>
<mml:mo>×</mml:mo>
<mml:mrow>
<mml:mo>[</mml:mo>
<mml:mrow>
<mml:mi>max</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>LA</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo></mml:mo>
<mml:mi>min</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>LA</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
<mml:mtext> </mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mi>MPM</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mtext>   Combined_Signal</mml:mtext>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
where LA is the half range of agreement limits (± 1.96 × SD), and MPM denotes the mean of the pairwise mean. The two measurements are considered to have a good or acceptable agreement when the BAR is less than 10% or 20% [
<xref rid="B40-sensors-20-01923" ref-type="bibr">40</xref>
,
<xref rid="B66-sensors-20-01923" ref-type="bibr">66</xref>
].</p>
</sec>
<sec id="sec2dot6-sensors-20-01923" sec-type="subjects">
<title>2.6. Participants and Data Collection</title>
<p>The study protocol was approved by the Ethical Board of the Department of Psychology, Tsinghua University; 226 students and university employees in Shenzhen, China, joined the study. The average age was 23.4 years (σ = 3.36) with equal percentages of male and female participants. After a 5-min debriefing, participants were asked to remain seated for the entire data collection process. They were asked to wear an ECG chest strap (H10, Polar Electro Oy, Finland; sampling rate 1000 Hz [
<xref rid="B67-sensors-20-01923" ref-type="bibr">67</xref>
]) and hold a smartphone (Mi 8 SE, Xiaomi, China; sampling rate 30 Hz) in their left hand. A self-developed app was then used to record 5-min videos of their fingertip multiple times during the 1-h session. A total of 1343 valid datasets were collected. The accuracy of the ECG chest strap is well-established in the literature [
<xref rid="B21-sensors-20-01923" ref-type="bibr">21</xref>
], and studies employ the chest strap in detecting HRV for convenience when a 24-lead ECG is not available [
<xref rid="B68-sensors-20-01923" ref-type="bibr">68</xref>
,
<xref rid="B69-sensors-20-01923" ref-type="bibr">69</xref>
].</p>
</sec>
</sec>
<sec sec-type="results" id="sec3-sensors-20-01923">
<title>3. Results</title>
<sec id="sec3dot1-sensors-20-01923">
<title>3.1. Correlation Coefficient Analysis</title>
<p>Before starting data analysis, this study applied Tukey’s rule to remove outliers. All remaining HRV measurements using smartphone PPG were significantly correlated (p < 0.05) with the results detected using ECG (
<xref rid="sensors-20-01923-t003" ref-type="table">Table 3</xref>
). In general, smartphone PPG provided better estimations for log HF (across the FPDTs, average
<inline-formula>
<mml:math id="mm43">
<mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.72</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
), log LF (average
<inline-formula>
<mml:math id="mm44">
<mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.70</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
), and SDNN (average
<inline-formula>
<mml:math id="mm45">
<mml:mrow>
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>0.73</mml:mn>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
) than for rMSSD and pNN50. Among the FPDTs, Tangent produced the best results, followed by Valley and M1D; however, M2D had the poorest performance. When the data were filtered with the SPQI, the correlation coefficients increased significantly. On average, they increased by 13% (from 0.669 to 0.758) and 26% (from 0.669 to 0.843) when the data were filtered with SPQI thresholds above 0.8 and 0.95, respectively. The improvement was particularly prominent for M2D, as the average correlation coefficient improved by 51% (from 0.472 to 0.712).</p>
<p>The advantage of using the SPQI is also apparent from the scatter plots (
<xref ref-type="fig" rid="sensors-20-01923-f003">Figure 3</xref>
). When all data are included, a significant portion lies away from the straight line; when corrupted data are filtered out, a higher portion of the data lies along the straight line. In particular, there is an asymmetric bias for rMSSD and pNN50. Smartphone PPG tended to produce larger values for these measures when the signal quality was low, and therefore, their correlation coefficients were lower. Since rMSSD and pNN50 are more susceptible to the randomness of the samples, the benefits of using the SPQI were also more prominent for these two measures. When we filtered the data with an SPQI threshold level of 0.95, the correlation coefficients for rMSSD and pNN50 increased from 0.64 and 0.77 to 0.88 and 0.92, respectively.</p>
<p>However, when the data set was filtered with an SPQI > 0.95, the reduction in the number of samples was not negligible (see
<xref rid="sensors-20-01923-t004" ref-type="table">Table 4</xref>
). On average, the number of samples decreased by 14% (from 1263 to 1060) and 56% (from 1263 to 557) when the data were filtered out by thresholds above 0.8 and 0.95, respectively.</p>
</sec>
<sec id="sec3dot2-sensors-20-01923">
<title>3.2. Bland–Altman Ratio Analysis</title>
<p>The Bland–Altman analysis showed similar results to the correlation coefficient analysis. Among all FPDTs, Tangent generated the smallest BAR for SDNN, log HF, and log LF (see
<xref rid="sensors-20-01923-t005" ref-type="table">Table 5</xref>
). M1D, in contrast, performed the best for rMSSD, and Valley had the lowest BAR for pNN50. The agreement of log HF and log LF was “acceptable” (BAR < 0.2) before filtering with the SPQI. The agreement of log HF and log LF generated by all FPDTs became “good” or close to “good” when the data were filtered with an SPQI > 0.95.</p>
<p>The effect of the SPQI can also be observed from the Bland–Altman plot (
<xref ref-type="fig" rid="sensors-20-01923-f004">Figure 4</xref>
). Considering data generated by Tangent, the number of points that lie beyond the upper and lower agreement limits was significantly reduced when the data were filtered with the SPQI. The same pattern was observed for all HRV measures. Similar to the correlation coefficient analysis, rMSSD and pNN50 showed the least agreement among HRV measures. Although filtering with an SPQI > 0.95 could significantly reduce the BAR, these two measures were still above the “acceptable” level for all FPDTs.</p>
</sec>
</sec>
<sec sec-type="discussion" id="sec4-sensors-20-01923">
<title>4. Discussion</title>
<sec id="sec4dot1-sensors-20-01923">
<title>4.1. Principal Findings</title>
<p>The results from both the correlation coefficient and Bland–Altman analyses validated our proposed strategy: removing data that cannot fit a pre-defined model can significantly increase the accuracy of smartphone PPG. By choosing a relatively more robust FPDT, such as Valley or Tangent, and filtering data with the SPQI, the agreement between smartphone PPG and ECG can have a “good” agreement, and the correlation coefficient can be over 0.9.</p>
<p>Among the FPDTs, Tangent and M2D were generally the best performers [
<xref rid="B40-sensors-20-01923" ref-type="bibr">40</xref>
,
<xref rid="B62-sensors-20-01923" ref-type="bibr">62</xref>
]. Our data showed that Tangent had the best agreement with ECG for SDNN, log HF, and log LF, while M1D and Valley had the highest agreement for rMSSD and pNN50, respectively; M2D was the worst performer in our data. Given that M2D performed well in previous studies, our results suggest that M2D may be more sensitive to the randomness found in corrupted data (which was manually removed in previous studies).</p>
<p>Compared with rMSSD, pNN50, and HF, SDNN and LF generated by smartphone PPG generally have a higher agreement with the reference ECG [
<xref rid="B33-sensors-20-01923" ref-type="bibr">33</xref>
,
<xref rid="B40-sensors-20-01923" ref-type="bibr">40</xref>
]; our data demonstrated similar results. Neither rMSSD nor pNN50 reached an acceptable agreement between the smartphone PPG and the ECG, even with SPQI > 0.95 filters. Our data showed that these two measures were more susceptible to randomness and systematic bias. SDNN and log LF had an acceptable or good agreement when the data were generated by Valley, M1D, or Tangent. The same was true for log HF.</p>
</sec>
<sec id="sec4dot2-sensors-20-01923">
<title>4.2. Limitations</title>
<p>Our data support the proposed method; however, there are still some limitations, as listed below. </p>
<p>First, the underlying assumption of the SPQI is that most people share common cardiac waveform characteristics. Although this hypothesis is based on empirical studies [
<xref rid="B47-sensors-20-01923" ref-type="bibr">47</xref>
], this premise limits the application of the SPQI to individuals with abnormal cardiac waveforms since the SPQI classifies samples that do not meet the preset pattern as poor quality. We expect future studies may pursue this research direction and try to differentiate corrupted data from valid but abnormal samples.</p>
<p>Second, the assumed application scenario of the proposed method is to determine the quality of a sample collected from a new participant based on the theoretical waveform pattern found by previous studies. We did not consider the possibility of using historical data for each individual to build a personalized quality index. Since cardiac waveforms have a larger between-group deviation (compared to other people) and smaller within-group differences (compared to one’s historical data), a personalized quality index may help increase the accuracy, and resolve the shortcoming that the SPQI is not suitable for individuals with abnormal waveforms.</p>
<p>Third, there are many methods for improving smartphone PPG accuracy [
<xref rid="B27-sensors-20-01923" ref-type="bibr">27</xref>
,
<xref rid="B29-sensors-20-01923" ref-type="bibr">29</xref>
,
<xref rid="B30-sensors-20-01923" ref-type="bibr">30</xref>
,
<xref rid="B31-sensors-20-01923" ref-type="bibr">31</xref>
,
<xref rid="B32-sensors-20-01923" ref-type="bibr">32</xref>
,
<xref rid="B33-sensors-20-01923" ref-type="bibr">33</xref>
]. For example, adding a suitable bandpass filter for signal processing [
<xref rid="B28-sensors-20-01923" ref-type="bibr">28</xref>
] or excluding data with RR intervals that differ more than a certain threshold [
<xref rid="B70-sensors-20-01923" ref-type="bibr">70</xref>
] are simple and effective approaches to reduce noise. In the current study, however, we did not use other proven noise reduction methods because we aimed to compare the relative accuracy of data filtered with the quality index rather than increase absolute accuracy. Whether the combination of the noise reduction methods and a quality index can further increase the accuracy and usability of smartphone PPG still warrants further analysis.</p>
<p>Fourth, the sampling rate has a significant influence on the accuracy of HRV measures. Although there have been many different suggestions for the minimum sampling rate (ranging from 25 Hz [
<xref rid="B42-sensors-20-01923" ref-type="bibr">42</xref>
] to 125 Hz [
<xref rid="B43-sensors-20-01923" ref-type="bibr">43</xref>
] in PPG studies and 50 Hz [
<xref rid="B71-sensors-20-01923" ref-type="bibr">71</xref>
] to 1000 Hz [
<xref rid="B72-sensors-20-01923" ref-type="bibr">72</xref>
] in ECG studies), most smartphone cameras sample at about 30 Hz, which is below the level of most suggestions. Therefore, the poor measuring quality caused by low frame rates is generally considered a potential challenge to the validity of using the smartphone PPG method. However, researchers have proposed various methods to improve the accuracy rate at low frame rates [
<xref rid="B33-sensors-20-01923" ref-type="bibr">33</xref>
], and empirical studies have also indicated that smartphone PPG results are comparable to those obtained using gold standard ECGs [
<xref rid="B21-sensors-20-01923" ref-type="bibr">21</xref>
,
<xref rid="B28-sensors-20-01923" ref-type="bibr">28</xref>
,
<xref rid="B37-sensors-20-01923" ref-type="bibr">37</xref>
,
<xref rid="B38-sensors-20-01923" ref-type="bibr">38</xref>
,
<xref rid="B39-sensors-20-01923" ref-type="bibr">39</xref>
,
<xref rid="B40-sensors-20-01923" ref-type="bibr">40</xref>
]. There seems to be conflicting suggestions and conclusions in the literature, and therefore, more empirical evidence is required to clarify this issue. Further, smartphone-based physiological assessment applications are usually considered low-cost, convenient tools for public health and personal use. Many smartphone PPG studies, including the current study, aim to validate this new technology as an acceptable alternative when more sophisticated devices are not available, rather than using it as a substitute for medical-grade equipment.</p>
<p>Fifth, several traditional PPG quality indicators have been proposed in the literature [
<xref rid="B51-sensors-20-01923" ref-type="bibr">51</xref>
,
<xref rid="B73-sensors-20-01923" ref-type="bibr">73</xref>
]. However, the design of the smartphone is different from traditional medical PPG devices, which usually have a higher sampling rate [
<xref rid="B74-sensors-20-01923" ref-type="bibr">74</xref>
], are designed to reduce motion artifacts, and use transmitted light sources rather than reflected light sources. Besides, most traditional PPG quality indicators were not validated with HRV measures [
<xref rid="B73-sensors-20-01923" ref-type="bibr">73</xref>
]. It is still unclear whether these traditional PPG quality indicators are applicable to smartphone PPG data and HRV assessment.</p>
<p>Sixth, in this exploratory study, we proposed only one model design and did not compare other possible alternatives such as using the Gaussian function family or changing optimization constraints. Future studies may consider conducting an optimal parameter search and finding better model designs for the SPQI. </p>
<p>Finally, the higher the threshold, the higher the accuracy, and the fewer the valid samples (
<xref ref-type="fig" rid="sensors-20-01923-f005">Figure 5</xref>
). The balance of the measurement quality and external validity of the research results is an essential requirement that should be considered carefully in future studies.</p>
</sec>
</sec>
<sec sec-type="conclusions" id="sec5-sensors-20-01923">
<title>5. Conclusions</title>
<p>Smartphone PPG provides an unprecedented opportunity for both researchers and practitioners in clinical diagnoses, telemedicine, preventative medicine, and public health. Research on smartphone PPG also provides a theoretical foundation for several new research directions such as remote photoplethysmography [
<xref rid="B75-sensors-20-01923" ref-type="bibr">75</xref>
] and PPG-based blood pressure estimation [
<xref rid="B76-sensors-20-01923" ref-type="bibr">76</xref>
]. Although it may not become a substitute for the gold standard ECG, smartphones are easily accessible and reasonably accurate alternatives when medical-grade devices are extremely costly or unavailable (e.g., when dealing with an unexpected large-scale public health crisis, such as the recent coronavirus outbreak [
<xref rid="B77-sensors-20-01923" ref-type="bibr">77</xref>
,
<xref rid="B78-sensors-20-01923" ref-type="bibr">78</xref>
]). It is, however, an unfortunate reality that only a few researchers and ordinary users have used this new technology. The proposed quality index enables users to assess the credibility of the gathered HRV measures, which is essential to win the trust of practitioners or researchers in applied disciplines.</p>
<p>The number of participants in this study (n = 226 participants and 1336 collected samples) was relatively large compared with several other smartphone PPG studies [
<xref rid="B21-sensors-20-01923" ref-type="bibr">21</xref>
,
<xref rid="B38-sensors-20-01923" ref-type="bibr">38</xref>
,
<xref rid="B39-sensors-20-01923" ref-type="bibr">39</xref>
,
<xref rid="B40-sensors-20-01923" ref-type="bibr">40</xref>
,
<xref rid="B79-sensors-20-01923" ref-type="bibr">79</xref>
]. Therefore, the results from this study provide support, not only for the validity of the proposed SPQI, but also for the general value and practicality of using smartphone PPG in HRV analysis.</p>
</sec>
</body>
<back>
<app-group>
<app id="app1-sensors-20-01923">
<title>Supplementary Materials</title>
<p>The following are available online at
<uri xlink:href="https://www.mdpi.com/1424-8220/20/7/1923/s1">https://www.mdpi.com/1424-8220/20/7/1923/s1</uri>
.</p>
<supplementary-material content-type="local-data" id="sensors-20-01923-s001">
<media xlink:href="sensors-20-01923-s001.zip">
<caption>
<p>Click here for additional data file.</p>
</caption>
</media>
</supplementary-material>
</app>
</app-group>
<notes>
<title>Author Contributions</title>
<p>Conceptualization and writing, I.L.; supervision and funding acquisition, S.N. and K.P. All authors have read and agreed to the published version of the manuscript.</p>
</notes>
<notes>
<title>Funding</title>
<p>This study was funded by the Humanities and Social Sciences Foundation of China’s Ministry of Education (18YJAZH065), the RD program of Shenzhen (JCYJ20170307153032483, JCYJ20170817161546744), Shenzhen Key Research Base of Humanities and Social Sciences, and the Interdisciplinary Research Project of the Graduate School of Shenzhen of Tsinghua University (JC2017005).</p>
</notes>
<notes notes-type="COI-statement">
<title>Conflicts of Interest</title>
<p>The authors declare no conflict of interest.</p>
</notes>
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<floats-group>
<fig id="sensors-20-01923-f001" orientation="portrait" position="float">
<label>Figure 1</label>
<caption>
<p>Steps taken to convert raw signals to segmented and normalized pulse waveform.</p>
</caption>
<graphic xlink:href="sensors-20-01923-g001"></graphic>
</fig>
<fig id="sensors-20-01923-f002" orientation="portrait" position="float">
<label>Figure 2</label>
<caption>
<p>(
<bold>a</bold>
) Illustration of two frames of the video of a left fingertip captured using a smartphone camera (Mi 8 SE, Xiaomi, China). The frame captured during the systole phase is darker and converted to a larger value by photoplethysmography (PPG); the frame captured during the diastole phase is lighter and converted to a smaller value by PPG. (
<bold>b</bold>
) Illustration of using the sum of the four sinusoidal functions to fit the collected samples from a 19-year-old female. (
<bold>c</bold>
) Illustration of five types of fiducial points (Peak, Valley, Tangent, maximum first derivative (M1D), and maximum secondary derivative (M2D)) determined with both raw data points (blue) and the fitted model (orange).</p>
</caption>
<graphic xlink:href="sensors-20-01923-g002"></graphic>
</fig>
<fig id="sensors-20-01923-f003" orientation="portrait" position="float">
<label>Figure 3</label>
<caption>
<p>Scatter plot and correlation coefficients of smartphone PPG (with Tangent) and the reference ECG for the HRV measurements.</p>
</caption>
<graphic xlink:href="sensors-20-01923-g003"></graphic>
</fig>
<fig id="sensors-20-01923-f004" orientation="portrait" position="float">
<label>Figure 4</label>
<caption>
<p>Bland–Altman plot and BAR smartphone PPG (with Tangent) and reference ECG data for each HRV measure.</p>
</caption>
<graphic xlink:href="sensors-20-01923-g004"></graphic>
</fig>
<fig id="sensors-20-01923-f005" orientation="portrait" position="float">
<label>Figure 5</label>
<caption>
<p>Trade-off between the number of valid samples and the agreement (BAR or correlation coefficient) of log HF between the smartphone PPG (Tangent) and reference ECG.</p>
</caption>
<graphic xlink:href="sensors-20-01923-g005"></graphic>
</fig>
<table-wrap id="sensors-20-01923-t001" orientation="portrait" position="float">
<object-id pub-id-type="pii">sensors-20-01923-t001_Table 1</object-id>
<label>Table 1</label>
<caption>
<p>Definitions of time-domain and frequency-domain heart rate variability (HRV) measurements.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">HRV Measures</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Definition</th>
</tr>
</thead>
<tbody>
<tr>
<td colspan="2" align="left" valign="middle" rowspan="1">
<bold>Time-Domain</bold>
</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="1" colspan="1">
<bold>SDNN</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">Standard deviation of the average normal-to-normal (NN) intervals</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="1" colspan="1">
<bold>pNN50</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">Percentage of successive NN intervals that differ by more than 50 ms</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="1" colspan="1">
<bold>rMSSD</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">Root mean square of successive NN interval differences</td>
</tr>
<tr>
<td colspan="2" align="left" valign="middle" rowspan="1">
<bold>Frequency-Domain</bold>
</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="1" colspan="1">
<bold>HF</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">Absolute power of the high-frequency band (0.15–0.4 Hz)</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="1" colspan="1">
<bold>LF</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">Absolute power of the low-frequency band (0.04–0.15 Hz)</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="1" colspan="1">
<bold>VLF</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">Absolute power of the very-low frequency band (0.003–0.04 Hz)</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="1" colspan="1">
<bold>ULF</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">Absolute power of the ultra-low frequency band (≤0.003 Hz)</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="1" colspan="1">
<bold>log HF</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">Log-transformed HF</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="1" colspan="1">
<bold>log LF</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">Log-transformed LF</td>
</tr>
<tr>
<td align="left" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">
<bold>log LF/HF</bold>
</td>
<td align="left" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">Log-transformed ratio of LF to HF</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="sensors-20-01923-t002" orientation="portrait" position="float">
<object-id pub-id-type="pii">sensors-20-01923-t002_Table 2</object-id>
<label>Table 2</label>
<caption>
<p>Definitions of fiducial point detection techniques (FPDTs).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">FPDT</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Fiducial Point Definition</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>Peak</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">The maximum point in each BBI.</td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>Valley</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">The minimum point in each BBI.</td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>M1D</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">The maximum point of the first derivative in each BBI.</td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>M2D</bold>
</td>
<td align="left" valign="middle" rowspan="1" colspan="1">The maximum point of the second derivative in each BBI.</td>
</tr>
<tr>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">
<bold>Tangent</bold>
</td>
<td align="left" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">The point where the tangent line from the M1D intersects the horizontal line from the Valley. The first derivatives of a discrete data set are determined by the difference function approximation.</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="sensors-20-01923-t003" orientation="portrait" position="float">
<object-id pub-id-type="pii">sensors-20-01923-t003_Table 3</object-id>
<label>Table 3</label>
<caption>
<p>Correlation coefficients between the results generated by smartphone PPG and ECG.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Threshold</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">FPDT</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">rMSSD</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">pNN50</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">SDNN</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">log HF</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">log LF</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Avg. (FPDT)</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Avg. (SPQI)</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>SPQI > 0</bold>
</td>
<td align="center" valign="middle" rowspan="1" colspan="1">Peak</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.520</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.652</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.692</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.639</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.607</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.622</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.669</td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">Valley</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.608</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.731</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.791</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.758</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.741</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.726</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M1D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.596</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.675</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.823</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.790</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.807</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.738</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M2D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.290</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.559</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.489</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.549</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.475</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.472</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">Tangent</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.615</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.752</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.864</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.843</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.858</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.786</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>SPQI > 0.8</bold>
</td>
<td align="center" valign="middle" rowspan="1" colspan="1">Peak</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.604</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.715</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.786</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.699</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.678</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.696</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.758</td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">Valley</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.702</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.834</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.879</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.844</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.842</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.820</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M1D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.705</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.777</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.915</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.846</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.882</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.825</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M2D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.393</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.665</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.626</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.629</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.536</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.570</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">Tangent</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.756</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.848</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.947</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.900</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.936</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.877</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>SPQI > 0.95</bold>
</td>
<td align="center" valign="middle" rowspan="1" colspan="1">Peak</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.689</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.768</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.847</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.799</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.749</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.770</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.843</td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">Valley</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.898</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.911</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.967</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.914</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.934</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.925</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M1D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.795</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.851</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.943</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.881</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.892</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.872</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M2D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.565</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.800</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.802</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.762</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.632</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.712</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">Tangent</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.879</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.923</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.974</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.939</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.954</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.934</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td colspan="7" align="left" valign="middle" style="border-bottom:solid thin" rowspan="1">
<bold>All correlation coefficients in the table have
<italic>p</italic>
< 0.05</bold>
</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="sensors-20-01923-t004" orientation="portrait" position="float">
<object-id pub-id-type="pii">sensors-20-01923-t004_Table 4</object-id>
<label>Table 4</label>
<caption>
<p>Number of valid samples filtered by different smartphone PPG quality index (SPQI) levels.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Threshold</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">FPDT</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">rMSSD</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">pNN50</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">SDNN</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">log HF</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1"> log LF</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Avg. (FPDT)</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Avg. (SPQI)</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>SPQI > 0</bold>
</td>
<td align="center" valign="middle" rowspan="1" colspan="1">Peak</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1283</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1331</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1276</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1226</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1257</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1274.6</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1263</td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">Valley</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1258</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1329</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1269</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1245</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1255</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1271.2</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M1D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1233</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1330</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1276</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1250</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1262</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1270.2</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M2D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1227</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1321</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1204</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1189</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1223</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1232.8</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">Tangent</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1250</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1325</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1274</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1236</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1246</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1266.2</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>SPQI > 0.8</bold>
</td>
<td align="center" valign="middle" rowspan="1" colspan="1">Peak</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1067</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1087</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1075</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1049</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1071</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1069.8</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1060</td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">Valley</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1062</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1083</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1073</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1056</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1066</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1068.0</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M1D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1052</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1085</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1067</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1054</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1068</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1065.2</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M2D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1006</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1078</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1012</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1032</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1057</td>
<td align="center" valign="middle" rowspan="1" colspan="1">1037.0</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">Tangent</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1046</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1081</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1065</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1053</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1064</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">1061.8</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>SPQI > 0.95</bold>
</td>
<td align="center" valign="middle" rowspan="1" colspan="1">Peak</td>
<td align="center" valign="middle" rowspan="1" colspan="1">565</td>
<td align="center" valign="middle" rowspan="1" colspan="1">550</td>
<td align="center" valign="middle" rowspan="1" colspan="1">566</td>
<td align="center" valign="middle" rowspan="1" colspan="1">558</td>
<td align="center" valign="middle" rowspan="1" colspan="1">565</td>
<td align="center" valign="middle" rowspan="1" colspan="1">560.8</td>
<td align="center" valign="middle" rowspan="1" colspan="1">557</td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">Valley</td>
<td align="center" valign="middle" rowspan="1" colspan="1">563</td>
<td align="center" valign="middle" rowspan="1" colspan="1">548</td>
<td align="center" valign="middle" rowspan="1" colspan="1">567</td>
<td align="center" valign="middle" rowspan="1" colspan="1">562</td>
<td align="center" valign="middle" rowspan="1" colspan="1">562</td>
<td align="center" valign="middle" rowspan="1" colspan="1">560.4</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M1D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">561</td>
<td align="center" valign="middle" rowspan="1" colspan="1">545</td>
<td align="center" valign="middle" rowspan="1" colspan="1">564</td>
<td align="center" valign="middle" rowspan="1" colspan="1">555</td>
<td align="center" valign="middle" rowspan="1" colspan="1">560</td>
<td align="center" valign="middle" rowspan="1" colspan="1">557.0</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M2D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">542</td>
<td align="center" valign="middle" rowspan="1" colspan="1">546</td>
<td align="center" valign="middle" rowspan="1" colspan="1">553</td>
<td align="center" valign="middle" rowspan="1" colspan="1">548</td>
<td align="center" valign="middle" rowspan="1" colspan="1">560</td>
<td align="center" valign="middle" rowspan="1" colspan="1">549.8</td>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
</tr>
<tr>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">Tangent</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">562</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">548</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">564</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">557</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">563</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">558.8</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="sensors-20-01923-t005" orientation="portrait" position="float">
<object-id pub-id-type="pii">sensors-20-01923-t005_Table 5</object-id>
<label>Table 5</label>
<caption>
<p>Bland–Altman ratios between the results generated by smartphone PPG and ECG.</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Threshold</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">FPDT</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">rMSSD</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">pNN50</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">SDNN</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Log HF</th>
<th align="center" valign="middle" style="border-top:solid thin;border-bottom:solid thin" rowspan="1" colspan="1">Log LF</th>
</tr>
</thead>
<tbody>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>SPQI > 0</bold>
</td>
<td align="center" valign="middle" rowspan="1" colspan="1">Peak</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.694 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.888 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.443 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.232 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.268 </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">Valley</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.552 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.813 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.344 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.199 * </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.215 </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M1D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.539 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.833 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.312 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.186 * </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.181 * </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M2D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.848 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.940 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.621 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.256 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.315 </td>
</tr>
<tr>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">Tangent</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.677 </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.905 </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.287 </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.166 * </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.156 * </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>SPQI > 0.8</bold>
</td>
<td align="center" valign="middle" rowspan="1" colspan="1">Peak</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.581 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.798 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.351 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.214 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.241 </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">Valley</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.451 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.660 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.262 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.164 * </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.165 * </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M1D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.433 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.701 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.220 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.164 * </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.141 * </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M2D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.653 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.808 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.455 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.233 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.291 </td>
</tr>
<tr>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">Tangent</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.469 </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.708 </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.177 * </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.134 * </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.105 * </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1">
<bold>SPQI > 0.95</bold>
</td>
<td align="center" valign="middle" rowspan="1" colspan="1">Peak</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.514 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.737 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.283 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.180 * </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.217 </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">Valley</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.297 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.547 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.144 * </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.129 * </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.108 * </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M1D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.367 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.615 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.179 * </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.150 * </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.136 * </td>
</tr>
<tr>
<td align="center" valign="middle" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" rowspan="1" colspan="1">M2D</td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.504 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.672 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.308 </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.195 * </td>
<td align="center" valign="middle" rowspan="1" colspan="1">0.257 </td>
</tr>
<tr>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1"></td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">Tangent</td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.325 </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.529 </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.123 * </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.108 * </td>
<td align="center" valign="middle" style="border-bottom:solid thin" rowspan="1" colspan="1">0.092 * </td>
</tr>
<tr>
<td colspan="7" align="left" valign="middle" style="border-bottom:solid thin" rowspan="1">
<bold>* acceptable or good agreement</bold>
</td>
</tr>
</tbody>
</table>
</table-wrap>
</floats-group>
</pmc>
</record>

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