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Continuous signal quality estimation for robust heart rate extraction from photoplethysmographic signals

Continuous signal quality estimation for robust heart rate extraction from photoplethysmographic... DE GRUYTER Current Directions in Biomedical Engineering 2020;6(3): 20203131 Jonas Massmann*, Timo Tigges, and Reinhold Orglmeister Continuous signal quality estimation for robust heart rate extraction from photoplethysmographic signals https://doi.org/10.1515/cdbme-2020-3131 parameters has been rising for several years [1]. Due to the mobile application, however, it is highly susceptible to motion Abstract: This study presents a novel method for estimat- artifacts that make the signal unusable. ing the signal quality of photoplethysmographic (PPG) sig- Therefore, an important aspect is the detection and inter- nals. For this purpose a robust classifier is implemented and pretation of interferences in the signal. In the literature, nu- evaluated by using finger- and inear-PPG. A new procedure is merous publications have appeared in recent decades on the proposed, which uses feature reduction to determine the Ma- detection of artifacts, which already detect disturbances with halanobis distance of the PPG-pulses to a statistical reference adequate accuracy. Nevertheless, motion artifacts in the PPG model and thus facilitates a robust heart rate extraction. The are still a major challenge and no gold standard for detection evaluation of the algorithm is based on a classical binary clas- has yet been established. sification using a manually annotated gold standard. For the It is noticeable that nearly all the analyzed publications finger-PPG a sensitivity of 86 ± 15 % and a specificity of are based on a hand-annotated gold standard. There is no uni- 94 ± 13 % was achieved. Additionally, a novel classification form annotation of the pulses and the assessment of the sig- method which is based on a continuous signal quality index is nal quality is very individual. It is not clearly defined when used. Pulse rate estimation errors greater than 5 BPM can be the quality of the measurement is no longer sufficient and the detected with a sensitivity of 91 ± 13 % and a specificity of pulse is not suitable for further analysis. For example, in [1] 91 ± 15 %. Also, a functional correlation between the signal two independent annotators for the quality assessment of pulse quality index and the standard deviation of the pulse rate error waves could only achieve an average agreement of 66.04 % of is shown. The proposed classifier can be used for improving all observations (kappa coefficient of 𝜅 = 0.48). the heart rate extration in pulse rate variability analysis or in In this paper the following three questions are analyzed the area of mobile monitoring for battery saving. and discussed: Keywords: signal quality index, artifacts, pulse oximetry, – How can motion artifacts in the PPG be better detected photoplethysmography, heart rate using a beat-to-beat algorithm? – Which morphological features are suitable as a continu- ous signal quality index (SQI) for the quality assessment 1 Introduction of pulse waves? – Can morphological features be used to determine a cer- Pulse oximetry is an inexpensive, optical measuring method, tainty for an estimated pulse rate? which has already become established as a standard procedure for non-invasive measurement of arterial oxygen saturation in 1987 [5]. Besides, other vital parameters such as blood pres- sure, pulse rate or respiration rate can be continuously deter- 2 Methods mined with photoplethysmography (PPG). With its portable and cost-effective application, pulse oximetry is an important 2.1 Algorithm component in monitoring of critically ill patients. Also, the general interest in portable monitoring systems for the vital To estimate the pulse wave quality a robust classifier is imple- mented and evaluated. A new procedure is proposed, which uses feature reduction to determine the Mahalanobis distance *Corresponding author: Jonas Massmann, Chair of Electronics and Medical Signal Processing, Faculty of Electrical Engineering, (MD) of the PPG-pulses to a statistical reference model. Technical University Berlin, Einsteinufer 17, Berlin, Germany, Prior to the actual pulse analysis, the raw signal 𝑦 (𝑛) 𝑟𝑎𝑤 e-mail: jonas.s.massmann@campus.berlin-tu.de is preprocessed and the individual pulses must be segmented. Timo Tigges, Reinhold Orglmeister, Chair of Electronics and In the preprocessing a 4th order Butterworth lowpass filter Medical Signal Processing, Technische Universitat Berlin, Berlin, with a cut-off frequency of 20 Hz and second filter stage Germany Open Access. © 2020 Jonas Massmann et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License. 2 Massmann et al., SQI estimation for PPG-Signals mental statistical reference is formed during the initialization rawsignal pulse wave phase and updated during the further process. For the valida- tion of the pulse quality, the distance 𝐷 between the parameter preprocessing normalization vector 𝑃 and the reference distribution 𝑀 is calculated with 𝐷 = ||𝑀 − 𝑃 ||. This can be solved using the MD with √︁ segmentation feature reduction 𝑇 −1 𝐷(𝑃 ,𝜇 ,𝛴 ) = (𝑃 − 𝜇 ) 𝛴 (𝑃 − 𝜇 ), 𝑖 𝑖 𝑀,𝑖 𝑀,𝑖 𝑖 𝑀 𝑀 (1) distance SQI inititalization whereby 𝜇 is the empirical mean and 𝛴 is the covari- 𝑀,𝑖 𝑀,𝑖 ance matrix of 𝑀 during analysis of the 𝑖-th pulse wave. The No D<v pulse analysis MD has the major advantage that it is scale-invariant, unitless Yes and takes the correlation of the parameters into account. model update To achieve an adaptive classification which can adapt to SQI signal changes and is patient independent, artifact-free pulse Fig. 1: Superordinate signal path. The schematic procedure of the waves are learned during the process. If the MD of a new pulse beat-to-beat pulse analysis is highlighted in grey. is less than or equal to a learning threshold 𝐷 ≤ 𝑣, its param- eter vector 𝑃 is added to the basic statistical truth 𝑀 . Due to performance reasons only the updated mean value and the co- with a 4th order Butterworth high pass filter and a cut-off fre- variance matrix is saved. Apart from the initialization phase, quency of 0.5 Hz is used. To adjust the sampling frequencies these can be calculated iteratively, which makes real-time im- of the PPG to the ECG, a spline interpolation is used, which is plementation easier. Based on an initialization value, the 𝑖-th aligned with the sampling points of the ECG signal. The algo- arithmetic mean value can be calculated elementwise with rithm presented by Zong et. al. was used to detect the diastoles 𝑃 (𝑘)− 𝜇 (𝑘) 𝑖 𝑀,𝑖−1 in finger- and inear-PPG [9], which were used for the pulse 𝜇 (𝑘) = 𝜇 (𝑘) [8]. (2) 𝑀,𝑖 𝑀,𝑖−1 segmentation. After an initialization phase, quality estimation The iterative estimation of the covariance matrix results in is performed beat-to-beat for each separated pulse. The signal ∑︁ flow is shown in figure 1 on the left side. 𝛴 = (𝑃 − 𝜇 )(𝑃 − 𝜇 ) [3]. (3) 𝑀 𝑖 𝑀 𝑖 𝑀 In pulse analysis, each pulse is normalized, modeled and 𝑁 − 1 𝑛=1 evaluated separately. This beat-to-beat pulse analysis is shown The MD results in the SQI. To achieve a bounded mea- in the flowchart in figure 1 on the right side. For normaliza- sure, the calculated distances D are considered in the space of tion, the DC signal component is removed, by setting the value the cumulated 𝜒 -distribution function 𝐹 given by of the first diastole to zero. Since start and end value are not (︀ )︀ SQI = 100· 1− 𝐹 (𝐷(𝑃 ,𝜇 ,𝛴 ) | 𝑀) . (4) necessarily the same, a linear correction is applied. Further- 𝑖 𝑀,𝑖 𝑀,𝑖 more, the pulse waves are normalized to the systolic point 2 1− 𝐹 indicates the complement of the cumulative 𝜒 distri- and thus have a uniform height of one. Finally, the length of bution function. The degree of freedom is given by the number each pulse is normalized, using the method for compression of modeling parameters 𝑀 , according to the feature vector 𝑃 of ECG signals by Wei et al. [2], which is also suitable for length. Consequently, the SQI ranges over a limited range of PPG-signals [4]. A fixed length of 512 samples showed the values between 0 and 1, which simplifies later interpretation. best results. In the feature reduction, each normalized pulse is reduced to a set of parameters 𝑃 , which are representing the signal 2.2 Data foundation morphology as accurately as possible. In the present study, three different types of signal modeling techniques are tested. The data of a transmissive finger- and a reflective inear-PPG The first analysed model is based on various morphological measurement of 30 healthy patients are used, resulting in an parameters. The second tested model is based on the system analysis of 160175 pulse waves. Due to the slightly different response, and the last model is using a curve-fitting procedure morphological properties, the finger- and inear-PPG signal are to remodel the pulse wave. All modeling functions are return- evaluated separately to see where the algorithm performs best. ing the vector 𝑃 , which is used for determining the quality For validation, an additional ECG-signal was used, which was index. recorded simultaneously. The ECG was recorded with a sam- In the multivariate distribution 𝑀 the parameter values 𝑃 pling frequency of 500 Hz, whereas the PPG signals with a of 𝑁 artifact-free pulses are stored. This constitutes the funda- sampling frequency of 250 Hz. For further information about mental truth with which further pulses are rated. The funda- the data acquisition please refer to [7, 6]. Massmann et al., SQI estimation for PPG-Signals 3 not pursued. By observing the SQI with respect to the abso- lute pulse error, an exponential correlation can be presumed. Therefore, the moving standard deviation of the standard er- ror is calculated using a bootstrapping method. The averaged values of the standard deviations per window interval are then fitted using an exponential function. This is used for pulse rate correction, with respect to a fixed pulse rate error threshold. The estimated standard deviation is used to set this threshold. Errorbound inBPM 1-specificity Fig. 2: Exemplary represen- Fig. 3: Exemplary extract of tation of AUC through a set of ROC-curves over different pulse 3 Results error bounds ℰ . rate error bounds ℰ . The red 𝜃 𝜃 dots mark the optimal Youden For the binary classification based on hand-annotated pulses index. the polynomial model with an order of v fi e showed the best re- sults. This leads to a sensitivity of 86± 15 % and a specificity of 94± 13 % for the dataset of the finger-PPG. The results of the 2.3 Evaluation methods inear-PPG fall slightly below the finger-PPG with a sensitivity of 77± 15 % and a specificity of 76± 20 %. By removing the The evaluation of the algorithm is conducted in three steps. negative classified pulses in the finger-PPG the pulse error rate First of all, a binary classification for the identification of can be improved from 1.24± 7.87 BPM to 0.71± 5.49 BPM. strong artifacts in the PPG is conducted, which is evaluated The same holds true for the inear-PPG, with an improvement using a manually annotated gold standard. The binary classifi- from 3.56± 16.41 BPM to 2.93± 15.46 BPM. cation is rated by sensitivity and specificity. The optimization For the binary classification based on a variable pulse rate is based on the receiver operating characteristic curve and the error threshold, the feature-based model using a combination area under the curve is used to determine the optimal thresh- of the first derivative, the pulse length and the skewness, per- old. In the first place, the different models are analyzed sepa- forms the best. A fixed threshold for error bounds is found. rately and the optimal model parameters are determined. Sec- The classification results for both measurements are shown in ondly, the optimal threshold for each model is searched by figure 4. Thereby pulse rate errors in the finger-PPG greater using the Youden index. With having the optimal threshold than 5 BPM can be detected with a sensitivity of 91 ± 13 % for each model, a comparison of the three models is done in and a specificity of 91 ± 15 %. Pulse rate errors less than the last step. This evaluation is performed separately for the 4 BPM are almost undetectable. The data set of the inear-PPG finger-PPG and the inear-PPG. results in slightly better classification rates with a sensitivity In the second step of the evaluation the classification is of 91 ± 5 % and a specificity of 93 ± 16 % for pulse error based on a continuous signal quality index and is optimized rates above 6 BPM. In the last evaluation, which is based on and evaluated with respect to the estimation error of the pulse rate. The classification problem is reduced to a binary prob- lem, using a variable error bound. Therefore, a ROC-analysis Sensitivity Specificity is done with multiple error bounds ℰ , shown in figure 3. This 1 1 leads to a set of Area Under Curve (AUC) values (see figure 0.8 0.8 2), which can be summed up to a performance value and used 0.6 0.6 as an optimization parameter. The actual optimization process 0.4 0.4 is equivalent to the binary classification with a manually an- 0.2 0.2 notated gold standard, comprising a parameter finding of each 0 0 0 5 10 0 5 10 model with an AUC optimization, a threshold optimization for Absolute error limit in BPM Absolute error limit in BPM every single model and a model comparison. (a) Finger-PPG (b) Inear-PPG Finally, the classification is evaluated using a continuous SQI. For this purpose, the MD is considered as quantiles in Fig. 4: Sensitivity SE and specificity SP of the classification, cal- the space of the 𝜒 -distribution function. It is assumed that culated over all error borders using a fixed threshold. The classifi- the previously determined model of binary classification with cation result of the finger PPG and the inner ear PPG is shown in red. In grey the respective 95 % confidence intervals. a variable error bound is also best suited for the determination of a continuous SQI. Another optimization process is therefore AUC( ) sensitivity SE, SP SE, SP 4 Massmann et al., SQI estimation for PPG-Signals a continuous SQI, a direct functional correlation between the Complete data set Compensated data set SQI and the standard deviation of the pulse rate error is shown. By using the moving standard deviation with a window size of 100 100 10 %, the bootstrap method reaches a 95 % confidence inter- val of ± 1.91 BPM. The exponential fitting takes place with a 50 50 quadratic mean deviation of 0.94 BPM with an adjusted co- efficient of determination of 0.94. The estimated standard de- 0 0 20 60 100 140 20 60 100 140 viation 𝜎^ is shown in figure 5. The SQI thus shows a direct ECG heart rate in BPM ECG heart rate in BPM correlation with the standard deviation of the pulse rate error. Complete data set Compensated data set 100 100 60 60 50 50 20 20 0 0 20 60 100 140 20 60 100 140 0 20 40 60 80100 0 20 40 60 80100 ECG heart rate in BPM ECG heart rate in BPM SQIin% SQI in% Fig. 6: Correction of the heart rate detection based on the pulse (a) Finger-PPG (b) Inear-PPG error barrier. Marked in black, the error bound ℰ = 5 BPM. The Fig. 5: Curve fitting of the MD in 𝜒 -space with respect to the color mapping is based on the estimated standard deviation in standard deviation. figure 5. decomposition. IEEE Transactions on Information Technology This can be used for a correction of the pulse rate estima- in Biomedicine, 5(4):290–299, Dec 2001. tion, based on a variable error bound. In figure 6, a correction [3] Philippe Pierre Pebay. Formulas for robust, one-pass paral- of pulse rate errors less then 5 BPM is done. This leads to a re- lel computation of covariances and arbitrary-order statistical duction of the pulse rate estimation error from 1.24± 7.87 BPM moments. Technical report, Sandia National Laboratories, 9 to 0.44± 1.39 BPM for the finger-PPG and 3.56± 16.41 BPM [4] Maik Pflugradt, Benjamin Moeller, and Reinhold Orglmeis- to 0.46± 2.09 BPM for the inear-PPG. ter. OPRA: A fast on-line signal quality estimator for pulsatile signals. IFAC-PapersOnLine, 48(20):459–464, 2015. [5] Allan B Shang, Raymond T Kozikowski, Andrew W Winslow, and Sandy Weininger. Development of a standardized method 4 Conclusion & Outlook for motion testing in pulse oximeters. Anesthesia & Analgesia, 105(6):S66–S77, 2007. The presented algorithm enables a robust detection of signal [6] T. Tigges, L. Bajrami, A. Pielmus, M. Klum, R. Orglmeister, artifacts in PPG-signals with very good results. Compared to L. Wiegand, and A. Feldheiser. Heart rate variability analy- other algorithms, the novel algorithm shows particularly good sis during lower body negative pressure test induced central hypovolemia. Current Directions in Biomedical Engineering, classification results. The SQI can improve autonomous PPG 5:65–68, 09 2019. analysis without ECG. Especially in the area of pulse rate vari- [7] T. Tigges, A. Feldheiser, A. Pielmus ¸, M. Klum, L. Wiegank, ability analysis it can be a great benefit to have a signal qual- and R. Orglmeister. Evaluation of pulse arrival times during ity information. Additionally, it can be used for battery saving lower body negative pressure test for the non-invasive de- methods in the area of mobile monitoring. tection of hypovolemia. In 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pages 3770–3774, 2019. [8] B. P. Welford. Note on a method for calculating corrected References sums of squares and products. Technometrics, 4(3):419–420, [9] W. Zong, T. Heldt, GB. Moody, and RG. Mark. An open-source [1] Mohamed Elgendi. Optimal signal quality index for photo- algorithm to detect onset of arterial blood pressure pulses. In plethysmogram signals. Bioengineering, 3(4), 2016. Computers in Cardiology, 2003, pages 259–262. IEEE, 2003. [2] Jyh-Jong Wei, Chuang-Jan Chang, Nai-Kuan Chou, and Gwo- Jen Jan. Ecg data compression using truncated singular value inBPM inBPM Finger-PPG pulse rate in BPM Finger-PPG pulse rate in BPM Inear-PPG pulse rate in BPM Inear-PPG pulse rate in BPM http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Current Directions in Biomedical Engineering de Gruyter

Continuous signal quality estimation for robust heart rate extraction from photoplethysmographic signals

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© 2020 by Walter de Gruyter Berlin/Boston
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DOI
10.1515/cdbme-2020-3131
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Abstract

DE GRUYTER Current Directions in Biomedical Engineering 2020;6(3): 20203131 Jonas Massmann*, Timo Tigges, and Reinhold Orglmeister Continuous signal quality estimation for robust heart rate extraction from photoplethysmographic signals https://doi.org/10.1515/cdbme-2020-3131 parameters has been rising for several years [1]. Due to the mobile application, however, it is highly susceptible to motion Abstract: This study presents a novel method for estimat- artifacts that make the signal unusable. ing the signal quality of photoplethysmographic (PPG) sig- Therefore, an important aspect is the detection and inter- nals. For this purpose a robust classifier is implemented and pretation of interferences in the signal. In the literature, nu- evaluated by using finger- and inear-PPG. A new procedure is merous publications have appeared in recent decades on the proposed, which uses feature reduction to determine the Ma- detection of artifacts, which already detect disturbances with halanobis distance of the PPG-pulses to a statistical reference adequate accuracy. Nevertheless, motion artifacts in the PPG model and thus facilitates a robust heart rate extraction. The are still a major challenge and no gold standard for detection evaluation of the algorithm is based on a classical binary clas- has yet been established. sification using a manually annotated gold standard. For the It is noticeable that nearly all the analyzed publications finger-PPG a sensitivity of 86 ± 15 % and a specificity of are based on a hand-annotated gold standard. There is no uni- 94 ± 13 % was achieved. Additionally, a novel classification form annotation of the pulses and the assessment of the sig- method which is based on a continuous signal quality index is nal quality is very individual. It is not clearly defined when used. Pulse rate estimation errors greater than 5 BPM can be the quality of the measurement is no longer sufficient and the detected with a sensitivity of 91 ± 13 % and a specificity of pulse is not suitable for further analysis. For example, in [1] 91 ± 15 %. Also, a functional correlation between the signal two independent annotators for the quality assessment of pulse quality index and the standard deviation of the pulse rate error waves could only achieve an average agreement of 66.04 % of is shown. The proposed classifier can be used for improving all observations (kappa coefficient of 𝜅 = 0.48). the heart rate extration in pulse rate variability analysis or in In this paper the following three questions are analyzed the area of mobile monitoring for battery saving. and discussed: Keywords: signal quality index, artifacts, pulse oximetry, – How can motion artifacts in the PPG be better detected photoplethysmography, heart rate using a beat-to-beat algorithm? – Which morphological features are suitable as a continu- ous signal quality index (SQI) for the quality assessment 1 Introduction of pulse waves? – Can morphological features be used to determine a cer- Pulse oximetry is an inexpensive, optical measuring method, tainty for an estimated pulse rate? which has already become established as a standard procedure for non-invasive measurement of arterial oxygen saturation in 1987 [5]. Besides, other vital parameters such as blood pres- sure, pulse rate or respiration rate can be continuously deter- 2 Methods mined with photoplethysmography (PPG). With its portable and cost-effective application, pulse oximetry is an important 2.1 Algorithm component in monitoring of critically ill patients. Also, the general interest in portable monitoring systems for the vital To estimate the pulse wave quality a robust classifier is imple- mented and evaluated. A new procedure is proposed, which uses feature reduction to determine the Mahalanobis distance *Corresponding author: Jonas Massmann, Chair of Electronics and Medical Signal Processing, Faculty of Electrical Engineering, (MD) of the PPG-pulses to a statistical reference model. Technical University Berlin, Einsteinufer 17, Berlin, Germany, Prior to the actual pulse analysis, the raw signal 𝑦 (𝑛) 𝑟𝑎𝑤 e-mail: jonas.s.massmann@campus.berlin-tu.de is preprocessed and the individual pulses must be segmented. Timo Tigges, Reinhold Orglmeister, Chair of Electronics and In the preprocessing a 4th order Butterworth lowpass filter Medical Signal Processing, Technische Universitat Berlin, Berlin, with a cut-off frequency of 20 Hz and second filter stage Germany Open Access. © 2020 Jonas Massmann et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License. 2 Massmann et al., SQI estimation for PPG-Signals mental statistical reference is formed during the initialization rawsignal pulse wave phase and updated during the further process. For the valida- tion of the pulse quality, the distance 𝐷 between the parameter preprocessing normalization vector 𝑃 and the reference distribution 𝑀 is calculated with 𝐷 = ||𝑀 − 𝑃 ||. This can be solved using the MD with √︁ segmentation feature reduction 𝑇 −1 𝐷(𝑃 ,𝜇 ,𝛴 ) = (𝑃 − 𝜇 ) 𝛴 (𝑃 − 𝜇 ), 𝑖 𝑖 𝑀,𝑖 𝑀,𝑖 𝑖 𝑀 𝑀 (1) distance SQI inititalization whereby 𝜇 is the empirical mean and 𝛴 is the covari- 𝑀,𝑖 𝑀,𝑖 ance matrix of 𝑀 during analysis of the 𝑖-th pulse wave. The No D<v pulse analysis MD has the major advantage that it is scale-invariant, unitless Yes and takes the correlation of the parameters into account. model update To achieve an adaptive classification which can adapt to SQI signal changes and is patient independent, artifact-free pulse Fig. 1: Superordinate signal path. The schematic procedure of the waves are learned during the process. If the MD of a new pulse beat-to-beat pulse analysis is highlighted in grey. is less than or equal to a learning threshold 𝐷 ≤ 𝑣, its param- eter vector 𝑃 is added to the basic statistical truth 𝑀 . Due to performance reasons only the updated mean value and the co- with a 4th order Butterworth high pass filter and a cut-off fre- variance matrix is saved. Apart from the initialization phase, quency of 0.5 Hz is used. To adjust the sampling frequencies these can be calculated iteratively, which makes real-time im- of the PPG to the ECG, a spline interpolation is used, which is plementation easier. Based on an initialization value, the 𝑖-th aligned with the sampling points of the ECG signal. The algo- arithmetic mean value can be calculated elementwise with rithm presented by Zong et. al. was used to detect the diastoles 𝑃 (𝑘)− 𝜇 (𝑘) 𝑖 𝑀,𝑖−1 in finger- and inear-PPG [9], which were used for the pulse 𝜇 (𝑘) = 𝜇 (𝑘) [8]. (2) 𝑀,𝑖 𝑀,𝑖−1 segmentation. After an initialization phase, quality estimation The iterative estimation of the covariance matrix results in is performed beat-to-beat for each separated pulse. The signal ∑︁ flow is shown in figure 1 on the left side. 𝛴 = (𝑃 − 𝜇 )(𝑃 − 𝜇 ) [3]. (3) 𝑀 𝑖 𝑀 𝑖 𝑀 In pulse analysis, each pulse is normalized, modeled and 𝑁 − 1 𝑛=1 evaluated separately. This beat-to-beat pulse analysis is shown The MD results in the SQI. To achieve a bounded mea- in the flowchart in figure 1 on the right side. For normaliza- sure, the calculated distances D are considered in the space of tion, the DC signal component is removed, by setting the value the cumulated 𝜒 -distribution function 𝐹 given by of the first diastole to zero. Since start and end value are not (︀ )︀ SQI = 100· 1− 𝐹 (𝐷(𝑃 ,𝜇 ,𝛴 ) | 𝑀) . (4) necessarily the same, a linear correction is applied. Further- 𝑖 𝑀,𝑖 𝑀,𝑖 more, the pulse waves are normalized to the systolic point 2 1− 𝐹 indicates the complement of the cumulative 𝜒 distri- and thus have a uniform height of one. Finally, the length of bution function. The degree of freedom is given by the number each pulse is normalized, using the method for compression of modeling parameters 𝑀 , according to the feature vector 𝑃 of ECG signals by Wei et al. [2], which is also suitable for length. Consequently, the SQI ranges over a limited range of PPG-signals [4]. A fixed length of 512 samples showed the values between 0 and 1, which simplifies later interpretation. best results. In the feature reduction, each normalized pulse is reduced to a set of parameters 𝑃 , which are representing the signal 2.2 Data foundation morphology as accurately as possible. In the present study, three different types of signal modeling techniques are tested. The data of a transmissive finger- and a reflective inear-PPG The first analysed model is based on various morphological measurement of 30 healthy patients are used, resulting in an parameters. The second tested model is based on the system analysis of 160175 pulse waves. Due to the slightly different response, and the last model is using a curve-fitting procedure morphological properties, the finger- and inear-PPG signal are to remodel the pulse wave. All modeling functions are return- evaluated separately to see where the algorithm performs best. ing the vector 𝑃 , which is used for determining the quality For validation, an additional ECG-signal was used, which was index. recorded simultaneously. The ECG was recorded with a sam- In the multivariate distribution 𝑀 the parameter values 𝑃 pling frequency of 500 Hz, whereas the PPG signals with a of 𝑁 artifact-free pulses are stored. This constitutes the funda- sampling frequency of 250 Hz. For further information about mental truth with which further pulses are rated. The funda- the data acquisition please refer to [7, 6]. Massmann et al., SQI estimation for PPG-Signals 3 not pursued. By observing the SQI with respect to the abso- lute pulse error, an exponential correlation can be presumed. Therefore, the moving standard deviation of the standard er- ror is calculated using a bootstrapping method. The averaged values of the standard deviations per window interval are then fitted using an exponential function. This is used for pulse rate correction, with respect to a fixed pulse rate error threshold. The estimated standard deviation is used to set this threshold. Errorbound inBPM 1-specificity Fig. 2: Exemplary represen- Fig. 3: Exemplary extract of tation of AUC through a set of ROC-curves over different pulse 3 Results error bounds ℰ . rate error bounds ℰ . The red 𝜃 𝜃 dots mark the optimal Youden For the binary classification based on hand-annotated pulses index. the polynomial model with an order of v fi e showed the best re- sults. This leads to a sensitivity of 86± 15 % and a specificity of 94± 13 % for the dataset of the finger-PPG. The results of the 2.3 Evaluation methods inear-PPG fall slightly below the finger-PPG with a sensitivity of 77± 15 % and a specificity of 76± 20 %. By removing the The evaluation of the algorithm is conducted in three steps. negative classified pulses in the finger-PPG the pulse error rate First of all, a binary classification for the identification of can be improved from 1.24± 7.87 BPM to 0.71± 5.49 BPM. strong artifacts in the PPG is conducted, which is evaluated The same holds true for the inear-PPG, with an improvement using a manually annotated gold standard. The binary classifi- from 3.56± 16.41 BPM to 2.93± 15.46 BPM. cation is rated by sensitivity and specificity. The optimization For the binary classification based on a variable pulse rate is based on the receiver operating characteristic curve and the error threshold, the feature-based model using a combination area under the curve is used to determine the optimal thresh- of the first derivative, the pulse length and the skewness, per- old. In the first place, the different models are analyzed sepa- forms the best. A fixed threshold for error bounds is found. rately and the optimal model parameters are determined. Sec- The classification results for both measurements are shown in ondly, the optimal threshold for each model is searched by figure 4. Thereby pulse rate errors in the finger-PPG greater using the Youden index. With having the optimal threshold than 5 BPM can be detected with a sensitivity of 91 ± 13 % for each model, a comparison of the three models is done in and a specificity of 91 ± 15 %. Pulse rate errors less than the last step. This evaluation is performed separately for the 4 BPM are almost undetectable. The data set of the inear-PPG finger-PPG and the inear-PPG. results in slightly better classification rates with a sensitivity In the second step of the evaluation the classification is of 91 ± 5 % and a specificity of 93 ± 16 % for pulse error based on a continuous signal quality index and is optimized rates above 6 BPM. In the last evaluation, which is based on and evaluated with respect to the estimation error of the pulse rate. The classification problem is reduced to a binary prob- lem, using a variable error bound. Therefore, a ROC-analysis Sensitivity Specificity is done with multiple error bounds ℰ , shown in figure 3. This 1 1 leads to a set of Area Under Curve (AUC) values (see figure 0.8 0.8 2), which can be summed up to a performance value and used 0.6 0.6 as an optimization parameter. The actual optimization process 0.4 0.4 is equivalent to the binary classification with a manually an- 0.2 0.2 notated gold standard, comprising a parameter finding of each 0 0 0 5 10 0 5 10 model with an AUC optimization, a threshold optimization for Absolute error limit in BPM Absolute error limit in BPM every single model and a model comparison. (a) Finger-PPG (b) Inear-PPG Finally, the classification is evaluated using a continuous SQI. For this purpose, the MD is considered as quantiles in Fig. 4: Sensitivity SE and specificity SP of the classification, cal- the space of the 𝜒 -distribution function. It is assumed that culated over all error borders using a fixed threshold. The classifi- the previously determined model of binary classification with cation result of the finger PPG and the inner ear PPG is shown in red. In grey the respective 95 % confidence intervals. a variable error bound is also best suited for the determination of a continuous SQI. Another optimization process is therefore AUC( ) sensitivity SE, SP SE, SP 4 Massmann et al., SQI estimation for PPG-Signals a continuous SQI, a direct functional correlation between the Complete data set Compensated data set SQI and the standard deviation of the pulse rate error is shown. By using the moving standard deviation with a window size of 100 100 10 %, the bootstrap method reaches a 95 % confidence inter- val of ± 1.91 BPM. The exponential fitting takes place with a 50 50 quadratic mean deviation of 0.94 BPM with an adjusted co- efficient of determination of 0.94. The estimated standard de- 0 0 20 60 100 140 20 60 100 140 viation 𝜎^ is shown in figure 5. The SQI thus shows a direct ECG heart rate in BPM ECG heart rate in BPM correlation with the standard deviation of the pulse rate error. Complete data set Compensated data set 100 100 60 60 50 50 20 20 0 0 20 60 100 140 20 60 100 140 0 20 40 60 80100 0 20 40 60 80100 ECG heart rate in BPM ECG heart rate in BPM SQIin% SQI in% Fig. 6: Correction of the heart rate detection based on the pulse (a) Finger-PPG (b) Inear-PPG error barrier. Marked in black, the error bound ℰ = 5 BPM. The Fig. 5: Curve fitting of the MD in 𝜒 -space with respect to the color mapping is based on the estimated standard deviation in standard deviation. figure 5. decomposition. IEEE Transactions on Information Technology This can be used for a correction of the pulse rate estima- in Biomedicine, 5(4):290–299, Dec 2001. tion, based on a variable error bound. In figure 6, a correction [3] Philippe Pierre Pebay. Formulas for robust, one-pass paral- of pulse rate errors less then 5 BPM is done. This leads to a re- lel computation of covariances and arbitrary-order statistical duction of the pulse rate estimation error from 1.24± 7.87 BPM moments. Technical report, Sandia National Laboratories, 9 to 0.44± 1.39 BPM for the finger-PPG and 3.56± 16.41 BPM [4] Maik Pflugradt, Benjamin Moeller, and Reinhold Orglmeis- to 0.46± 2.09 BPM for the inear-PPG. ter. OPRA: A fast on-line signal quality estimator for pulsatile signals. IFAC-PapersOnLine, 48(20):459–464, 2015. [5] Allan B Shang, Raymond T Kozikowski, Andrew W Winslow, and Sandy Weininger. Development of a standardized method 4 Conclusion & Outlook for motion testing in pulse oximeters. Anesthesia & Analgesia, 105(6):S66–S77, 2007. The presented algorithm enables a robust detection of signal [6] T. Tigges, L. Bajrami, A. Pielmus, M. Klum, R. Orglmeister, artifacts in PPG-signals with very good results. Compared to L. Wiegand, and A. Feldheiser. Heart rate variability analy- other algorithms, the novel algorithm shows particularly good sis during lower body negative pressure test induced central hypovolemia. Current Directions in Biomedical Engineering, classification results. The SQI can improve autonomous PPG 5:65–68, 09 2019. analysis without ECG. Especially in the area of pulse rate vari- [7] T. Tigges, A. Feldheiser, A. Pielmus ¸, M. Klum, L. Wiegank, ability analysis it can be a great benefit to have a signal qual- and R. Orglmeister. Evaluation of pulse arrival times during ity information. Additionally, it can be used for battery saving lower body negative pressure test for the non-invasive de- methods in the area of mobile monitoring. tection of hypovolemia. In 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pages 3770–3774, 2019. [8] B. P. Welford. Note on a method for calculating corrected References sums of squares and products. Technometrics, 4(3):419–420, [9] W. Zong, T. Heldt, GB. Moody, and RG. Mark. An open-source [1] Mohamed Elgendi. Optimal signal quality index for photo- algorithm to detect onset of arterial blood pressure pulses. In plethysmogram signals. Bioengineering, 3(4), 2016. Computers in Cardiology, 2003, pages 259–262. IEEE, 2003. [2] Jyh-Jong Wei, Chuang-Jan Chang, Nai-Kuan Chou, and Gwo- Jen Jan. Ecg data compression using truncated singular value inBPM inBPM Finger-PPG pulse rate in BPM Finger-PPG pulse rate in BPM Inear-PPG pulse rate in BPM Inear-PPG pulse rate in BPM

Journal

Current Directions in Biomedical Engineering – de Gruyter

Published: Sep 1, 2020

Keywords: signal quality index; artifacts; pulse oximetry; photoplethysmography; heart rate

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