# Assessment of Breathing Parameters Using an Inertial Measurement Unit (IMU)-Based System

^{1}

^{2}

^{*}

## Abstract

**:**

_{B}) is an important vital sign that—if appropriately monitored—may help to predict clinical adverse events. Inertial sensors open the door to the development of low-cost, wearable, and easy-to-use breathing-monitoring systems. The present paper proposes a new posture-independent processing algorithm for breath-by-breath extraction of breathing temporal parameters from chest-wall inclination change signals measured using inertial measurement units. An important step of the processing algorithm is dimension reduction (DR) that allows the extraction of a single respiratory signal starting from 4-component quaternion data. Three different DR methods are proposed and compared in terms of accuracy of breathing temporal parameter estimation, in a group of healthy subjects, considering different breathing patterns and different postures; optoelectronic plethysmography was used as reference system. In this study, we found that the method based on PCA-fusion of the four quaternion components provided the best f

_{B}estimation performance in terms of mean absolute errors (<2 breaths/min), correlation (r > 0.963) and Bland–Altman Analysis, outperforming the other two methods, based on the selection of a single quaternion component, identified on the basis of spectral analysis; particularly, in supine position, results provided by PCA-based method were even better than those obtained with the ideal quaternion component, determined a posteriori as the one providing the minimum estimation error. The proposed algorithm and system were able to successfully reconstruct the respiration-induced movement, and to accurately determine the respiratory rate in an automatic, position-independent manner.

## 1. Introduction

_{B}), inspiratory time (T

_{I}) and expiratory time (T

_{E}) could foster early diagnosis of a wide range of respiratory disorders and help to track a patient’s condition, discriminating between stable and at-risk patients [1,2]. Conditions of interest could be sleep breathing disorders, sudden infant death syndrome, chronic obstructive pulmonary disease (COPD) and neuromuscular disorders. The current gold standard for measuring f

_{B}is to count the number of breaths in one minute, through auscultation or observation [3,4]. Other methods for breathing function assessment currently used in clinical practice are spirometry or pneumotachograph based on airflow measurement by using mouthpiece or facemask. In overnight polysomnography, breathing activity is assessed both by measuring respiratory flow, through pressure transducer or thermistors near the nostrils, and respiratory efforts (breathing-derived chest-wall movements), by strain-gauge belts. Also, exhaled carbon dioxide sensors, transthoracic inductance and impedance plethysmography and ECG—or PPG—derived f

_{B}have been used to measure breathing signal. Despite their accuracy, these methods are uncomfortable and intrusive, and are not suitable for continuous monitoring in the clinical environment and at home. An emerging area of interest is to use motion sensors to detect the small breathing-derived movements/orientation changes of the chest wall. This method is particularly suitable for long-term breathing monitoring because it is unobtrusive, tolerable, and low-cost. The principle was first presented with a single-axis accelerometer in animal model (dog) using a pressure transducer in the trachea as reference [5]. Starting from this point, a variety of studies demonstrated the feasibility of using one accelerometer placed on the chest wall to derive respiratory signal and/or breathing frequency in different positions [6,7,8,9,10,11,12,13,14]. Morillo et al. [8] combined a piezoelectric single-axis accelerometer and a polarized capacitive microphone placed on the suprasternal notch to collect information of the cardiac, respiratory, and snoring activities for the screening of patients affected by Sleep Apnea-Hypopnea Syndrome. Measurements were limited to the supine position, that was selected to increase the sensitivity of the single-axis accelerometer, limiting the generality of the findings. The analysis method was based on the estimation of breathing frequency through the identification of the peak of the spectrum or autocorrelation; the main limitation of this approach is that, when the breathing is irregular, a main peak may not exist, and individual breaths must be identified and counted. Hung et al. [7] moved from single-axis to biaxial accelerometers. The aim of their study was to evaluate the reliability of the device in terms of detection of the onsets of expiration and expiration, and to assess the feasibility of differentiating between different breathing patterns (normal breathing, apnea, deep breathing). The signals from both axes (anteroposterior and longitudinal) of the accelerometer were summed, limiting the analysis to the sagittal plane, in sitting and lying positions. An adaptive band-pass filter was applied with a variable passband centered at the detected dominant breathing frequency.

## 2. Materials and Methods

#### 2.1. Device Architecture and Hardware Description

#### 2.2. Quaternion-Based Orientation Estimation and Fusion Algorithm

_{0}q

_{1}q

_{2}q

_{3}]), since they require less computing time and avoid the singularity problems (i.e., “gimbal lock”) typical of other orientation descriptors, e.g., Euler angles. The fusion of the data collected from the sensors is done by using the sensor fusion algorithm proposed by Madgwick et al. [29], based on an analytically derived and optimized gradient descent algorithm enabling levels of accuracy exceeding that of the Kalman-based algorithm, with low computational (277 scalar arithmetic operations each filter update) load and low sampling rates (e.g., 10 Hz); this orientation filter also provides an online magnetic distortion compensation algorithm and gyroscope bias drift compensation. The sensors data were collected at 40 Hz and the fusion algorithm was updated with the same rate, but due to limited buffer of the BLE module and to the stricter timings used for the Bluetooth communication, just one quaternion out of 4 computed is considered (10 Hz); nevertheless, the final sampling rate was considered appropriate given the relative low frequency of the respiratory signal [0.1 ÷ 1 Hz]. Thus, the microprocessor of each unit, receives data from accelerometer, gyroscope and magnetometer that are on board and implements Madgwick fusion filter [29] to compute a quaternion representing the change of orientation of each unit relative to the earth frame $({}_{Earth}{}^{Th}\widehat{\mathit{q}},{}_{Earth}{}^{Ab}\widehat{\mathit{q}},{}_{Earth}{}^{Ref}\widehat{\mathit{q}}$), or more correctly the change of orientation of the earth relative to each unit frame [29]. In fact, in quaternion form, an arbitrary orientation of a coordinate frame B relative to coordinate frame A, achieved through a rotation of angle θ around an axis

^{A}

**r**(r

_{x}, r

_{y}, r

_{z}) defined in frame A, is univocally represented through the normalized quaternion ${}_{B}{}^{A}\widehat{\mathit{q}}$ defined by Equation (1):

#### 2.3. Quaternion-Derived Breathing Frequency

**Pre-processing**block includes the preliminary steps that leads to chest-wall respiratory-related orientation change signals. The orientations changes of thoracic and abdominal units were referred to the reference unit frame (that in turn represents orientation changes of trunk) applying Equations (2) and (3) respectively:

**Dimension-reduction**block takes the quaternions obtained from Equations (2) and (3), that are composed by 4 components each, and provides as output 2 single-component signals (1 for the abdomen and 1 for the thorax) representing chest-wall respiratory-related orientation change signals. These two signals represent the input of the power spectrum block and of the processing block. To reduce dimension from 4 components to 1, two possibilities were investigated as shown in Figure 2:

- (i).
- Best quaternion component selection
- (ii).
- PCA-based fusion of the quaternion components

**X**(m × n), where m was the number of observations of the time series and n the number of variables (quaternion components). Then, the univariate means were subtracted from the n columns, to center the data. Singular Value Decomposition (SVD) was used to compute the eigenvectors (

**V**= [v

_{1}, v

_{2}, v

_{3}, v

_{4}]) and corresponding eigenvalues (λ

_{1}, λ

_{2}, λ

_{3}, λ

_{4}). Original data were finally projected in the new coordinate system (

**Y**=

**XV**) and the first principal component, accounting for the largest possible variance, was selected and passed to other blocks [30,31].

**Spectrum Analysis**block include a set of steps needed to optimize the subsequent processing phase. The two signals representing chest-wall (abdominal and thoracic) respiratory-related orientation obtained downstream of the dimension-reduction block underwent the following steps (Figure 1):

- (i).
- A low-frequency threshold (f
_{LOW}) was determined based on a first estimate of the breathing frequency (f_{B}). The rough estimate of f_{B}was done by identifying maxima points of the signal and computing the f_{B}, breath by breath, as reciprocal of the temporal distance between consecutive maxima points. Then, the mean (f_{B_Rough}) and the standard deviation (f_{B_Rough_SD}) of the f_{B}over the entire trial were computed. To facilitate maxima points identification, signals were at first band-bass filtered using a first-order infinite impulse response (IIR) Butterworth filter [0.05 Hz–2 Hz] and smoothed with a third-order Savitzky–Golay [32] finite impulse response (FIR) filter (fixed window length = 31 samples). Low thresholds f_{LOW}Ab and f_{LOW}Th were determined for the abdominal and thoracic signals respectively as difference f_{B_Rough}− f_{B_Rough_SD}. Then the minimum value between f_{LOW}Ab and f_{LOW}Th was chosen as final low-frequency threshold, named f_{LOW}, and it was used in the next step. - (ii).
- PSD estimate (Welch’s method, Hamming window size: 300 samples, overlapping: 50 samples) was computed and the spectrum frequency corresponding to the breathing rate was identified, both for the thorax (f
_{peak_T}) and the abdomen (f_{peak_A}), by looking for the local peak of the PSD within the window [f_{LOW}÷ 2 Hz]. The use of a low threshold, based on a rough estimate of the breathing frequency, supports the selection of the PSD peak linked to breathing rate and avoid selecting wrong peaks, often related to low-frequency oscillation artifacts. - (iii).
- The breathing frequency derived by the spectrum was used to set an adaptive band-pass filter, as proposed in a previous study [7], centered on f
_{peak}frequency. For the abdomen, upper (f_{U}) and lower (f_{L}) cut-off frequency points for the band-pass filter were defined, by applying Equations (4) and (5) respectively [7]:

_{U_A}= f

_{peak_A}+ 0.04,

_{L_A}= max (0.05, (f

_{peak_A}− 0.04)),

_{U_T}= f

_{peak_T}+ 0.04,

_{L_T}= max (0.05, (f

_{peak_T}− 0.04)),

_{peak}, a set of parameters was selected to optimize subsequent smoothing and minima/maxima detection phases of the processing block.

**Processing**block includes all the steps needed to extract breathing frequency and temporal parameters from the signals obtained downstream of the dimension-reduction block. Chest-wall respiratory-related orientation change signals (abdominal and thoracic) underwent the following steps:

- (i).
- Adaptive band-pass filter. The signals were band-pass filtered (first-order IIR Butterworth filter), with f
_{U}and f_{L}cut-off frequency points determined within the spectrum analysis block. - (ii).
- Smoothing. Filtered signals were furtherly smoothed (third-order Savitzky–Golay FIR filter) to simplify subsequent identification of maxima and minima points. The level of smoothing (window length) was automatically selected based on f
_{peak}, i.e., increasing window length for decreasing f_{peak}. Relation between optimal window length values and f_{peak}values has been determined empirically. - (iii).
- Minima and maxima points detection. A set of optimized parameters (i.e., minimum peak distance (MPD) and minimum prominence threshold (MPT)) was automatically selected based on f
_{peak}to optimize recognition of minima and maxima points of the smoothed signals. Optimal MPD and MPT values depending on f_{peak}were experimentally determined. - (iv).
- Breathing frequency extraction. Breath by breath, inspiratory time (T
_{I}) was computed as the temporal distance between a minimum point (m_{i}) and the consecutive maximum point (M_{i}); Expiratory time (T_{E}) was computed as the temporal distance between the maximum point (M_{i}) and the consecutive minimum point (m_{i}+ 1); total time (T_{TOT}) was computed as ${\mathrm{T}}_{\mathrm{TOT}}={\mathrm{T}}_{\mathrm{I}}+{\mathrm{T}}_{\mathrm{E}}$ [s], duty cycle (DC) was computed as $\frac{{\mathrm{T}}_{\mathrm{I}}}{{\mathrm{T}}_{\mathrm{TOT}}}\times 100$ [%] and breathing frequency was computed as $\frac{60}{\left({\mathrm{T}}_{\mathrm{TOT}}\right)}$ [breaths/minute]. A mean value for each of the above-mentioned parameter was computed for each trial (~3 min).

#### 2.4. Experimental Setup

_{B}but same tidal volume of QB (↑f

_{B}, V

_{T}=), (III) increasing f

_{B}and reducing tidal volume (↑f

_{B}, V

_{T}↓), (IV) decreasing f

_{B}with the same tidal volume of QB (↓f

_{B}, V

_{T}=), (V) decreasing f

_{B}increasing tidal volume of QB (↓f

_{B}, V

_{T}↑). QB trial was repeated two times, thus, each subject performed 6 trials of the duration of 3 min each. The SVC maneuver was used to align OEP signal and device signals during data analysis, since it is generally recognizable with respect to QB. In fact, SVC requires a maximal inspiration followed by a complete expiration without forced or rapid effort.

_{B}, V

_{T}=, ↑f

_{B}, V

_{T}↓, ↓f

_{B}, V

_{T}=, ↓f

_{B}, V

_{T}↑) until the end of the trial; in case of fatigue they were asked to perform a second SVC before returning to QB. This procedure was repeated in seated position and in supine position.

#### 2.5. Statistical Analysis

_{B}, T

_{I}, T

_{E}and DC were extracted from the best quaternion components identified online by using “Area” and “Peak” methods, and from the signal obtained with the PCA-based fusion method, both for the thoracic and abdominal tracings. Moreover, to evaluate the performance of the selection methods (“Area” and “Peak”) and their ability to select the best component, the same parameters were obtained for all the quaternion components (q

_{0}, q

_{1}, q

_{2}, q

_{3}) and compared with those obtained by OEP, on the abdominal and thoracic compartment, respectively. The “Ideal” quaternion component was identified a posteriori, trial by trial, as the one providing the minimum estimation error of the breathing frequency. Obviously, the “Ideal” component cannot be identified during online analysis, or when a reference method is not present. Thus, for each trial, 5 sets of parameters were available:

- f
_{B_OEP}, T_{I_OEP}, T_{E_OEP}and DC_{_OEP} - f
_{B_Peak}, T_{I_Peak}, T_{E_Peak}and DC_{_Peak} - f
_{B_Area}, T_{I_Area}, T_{E_Area}and DC_{_Area} - f
_{B_PCA}, T_{I_PCA}, T_{E_PCA}and DC_{_PCA} - f
_{B_}_{Ideal}, T_{I_}_{Ideal}, T_{E_}_{Ideal}and DC_{_}_{Ideal}

_{B_OEP}< 6 breaths/minute or f

_{B_OEP}> 60 breaths/minute were discarded. Then, the absolute (Equation (8)) and relative (Equation (9)) errors of estimation in static conditions (supine and seated position) were computed for each parameter:

_{B}and DC estimation, non-parametric alternative to the one-way Analysis of variance (ANOVA) with repeated measures (Friedman test) was performed to assess if significant differences between methods (“Area”, “Peak”, “PCA”) and “Ideal” component occurred, “Ideal”); post-hoc analysis was done performing Wilcoxon signed-rank tests on the different combinations of related methods, applying the correction for multiple comparisons using false discovery rate (FDR) method [38,39].

_{B}, T

_{I}, T

_{E}, linear regression analysis and correlation analysis (Pearson’s product-moment correlation r

_{P}, or Spearman’s rank-order correlation r

_{S}, if data were not normally distributed) were performed between measurements obtained with the device and measurements obtained with the OEP, for the supine and seated position, respectively.

## 3. Results

#### 3.1. Breathing Patterns

_{1}e QB

_{2}, ↑f

_{B}, V

_{T}=, ↑f

_{B}, V

_{T}↓, ↓f

_{B}, VT=, ↓f

_{B}, V

_{T}↑) estimated with OEP and device, using “PCA”, “Area”, and “Peak” methods and the “Ideal” component, for all subjects, in supine and seated position. Sample size (n) of each condition is reported in Table 1 for the breathing pattern ↑f

_{B}, V

_{T}↓, just one thoracic tracing was available for seated position (n = 1). It can be noticed that each subject demonstrated a different breathing frequency for each breathing pattern and SD in the forced breathing patterns is higher than those obtained for QB, meaning that subjects interpreted the required speed differently.

#### 3.2. Accuracy Errors

_{B}and DC are presented in Figure 4. For what concerns f

_{B}estimation in supine position, relative errors obtained using PCA were similar or even better than those provided by the “Ideal” component; on the contrary, both component-selection methods, namely “Area” and “Peak”, provided errors higher than 10%, both for the abdominal and the thoracic compartments. Errors obtained with PCA resulted significantly lower than those obtained with the “Area” method, both for the abdominal (Wilcoxon post-hoc test FDR-adjusted, p = 0.038) and thoracic compartment (Wilcoxon post-hoc test FDR-adjusted, p = 0.015); also, PCA was significantly better than “Peak” method considering abdominal compartment (Wilcoxon post-hoc test FDR-adjusted, p = 0.038). Errors obtained with “Ideal” component resulted significantly lower than those obtained with the component-selection methods both for the abdominal (Wilcoxon post-hoc test FDR-adjusted, Ideal vs. Area p = 0.038, Ideal vs. Peak p = 0.038) and thoracic (Wilcoxon post-hoc test FDR-adjusted, Ideal vs. Area p = 0.000, Ideal vs. Peak p = 0.020) compartments.

_{B}estimation errors obtained with component-selection methods were lower on average than those obtained in supine position, while PCA performances declined. This led to a sort of equalization effect, confirmed also by the statistical analysis: significant differences remained only for comparisons “Ideal” vs. “Area” method (Wilcoxon post-hoc test FDR-adjusted, AB: p = 0.102, TH: p = 0.015) and “Ideal” vs. “Peak” method (Wilcoxon post-hoc test FDR-adjusted, AB: p = 0.006, TH: p = 0.015).

_{B}, T

_{I}and T

_{E}obtained with the device using different methods (Area, Peak, Ideal, PCA) relative to OEP are reported in Table 2.

#### 3.3. Linear Regression and Correlation Analysis

_{B}(Figure 5), T

_{I}(Figure 6) and T

_{E}(Figure 7). For each scatter plot the regression line is computed, both for thorax and abdomen, and the relative equations are reported.

_{B}, results obtained with correlation analysis confirmed what emerged from estimation error analysis: in supine position, PCA exhibited the best performances in terms of correlation with OEP measurements both in terms of regression line and correlation coefficient. In seated position, “Ideal” component was the one with the highest correlation with OEP measurements, followed by PCA.

_{I}estimation in supine position, “Ideal” component provided the best performances, followed by PCA method; “Peak” and “Area” methods provided comparable, poor performances. In seated position, measurements of T

_{I}provided by component-selection methods were on average more correlated with OEP measurements than measurements obtained using PCA-fusion method. The “Ideal” component presented the best results, followed by “Area” and “Peak” methods; PCA provided the worst performance considering the abdominal compartment, while correlation between measurements obtained with the thoracic unit and OEP measurements was good.

_{E}was on average more problematic. In terms of regression lines in fact, slope values were far from the unity for all the considered methods, highlighting a proportional error leading to an overestimation for low values of expiratory time and an underestimation at high expiratory times, as shown in Figure 7. For what concerns supine position, correlation coefficients were good both for “Ideal” component and PCA-fusion method; on the contrary, correlation coefficients were low both for “Area” and “Peak” methods. Also, in seated position correlation coefficients provided by “Ideal” and PCA-fusion method were higher than those provided by “Area” and “Peak” methods, especially with respect to the thoracic compartment.

#### 3.4. Bland–Altman Analysis

_{B}(Figure 8), T

_{I}(Figure 9) and T

_{E}(Figure 10). In Bland–Altman plots, the difference of the two paired measurements (device–OEP) is plotted against the mean of the two measurements (device+OEP)⁄2. Results of agreement analysis, including evaluation of heteroscedasticity (Kendall’s τ correlation and relative p-value) are reported in Table 4. As shown there, for homoscedastic data, the mean of the differences representing the fixed bias, and LOAs were computed. On the other hand, for heteroscedastic data, OLS line of best fit representing the proportional bias and upper and lower 95% V-shape confidence limits (UCL and LCL) are reported.

_{B}), agreement between OEP and the device is very strong when the “Ideal” component or the PCA-fusion are used, both in supine and seated position. In relation to time estimation, the agreement decreases for all the methods considered. In particular, for what concerns inspiratory times, a significant relationship between errors and mean value emerged, with a general increase of the difference (device–OEP) at higher time values (overestimation of the device), both in supine and seated position. Also, for expiratory times absolute errors increased with increasing time values, but in this case the device underestimated at high time values (negative slope of the OLS).

#### 3.5. Quaternion Component Selection

_{0}was never selected by “Area” and “Peak” methods, while the “Ideal” component was q

_{0}in 14.86 % of cases (n = 74) in supine position and 6.76% of cases (n = 74) in seated position. In seated position, the component q

_{1}was selected more frequently as best component both by using “Area” (44.59) and “Peak” (39.19%) methods. In contrast, in supine position, the components q

_{2}(“Area” 51.35%, “Peak”: 41.89) and q

_{3}(“Area”: 39.19% and “Peak”: 40.54%) were selected more frequently.

_{0}component, that was clearly less selected, the other quaternion components were almost equally selected as “Ideal” component considering all the trials, both in supine position (q

_{0}: 14.86%, q

_{1}: 22.97%, q

_{2}: 32.43%, q

_{3}: 29.73%), and seated position (q

_{0}: 6.76%, q

_{1}: 33.78, q

_{2}: 22.97%, q

_{3}: 36.49%).

_{B}estimation error, in supine position, the “Area” method was able to identify the “Ideal” component in 45.94% of the cases (relative frequency for the event “the component selected by “Area” method and the “Ideal” component corresponded”), the “Peak” method identified the “Ideal” component in 52.70% of the cases, while for the 45.94% of the cases neither the “Area” method nor the “Peak” method were able to identify the “Ideal” component. In 44.59% of cases, “Area” method and “Peak” method selected the same quaternion component, that was also identified as “Ideal” component.

## 4. Discussion

_{I}, T

_{E}and duty cycle), “Ideal” component provided the best results, while PCA-fusion method gave results comparable to the best component-selection methods. Thus, a quaternion component providing the best performance exists, the problem lies in its a priori identification. In fact, both “Area” and “Peak” methods failed to identify it on the basis of spectral analysis (in 45.94% of the cases neither the “Area” method nor the “Peak” method were able to identify the “Ideal” component), and no quaternion component emerged as the most selected as “Ideal” component (supine q

_{0}:14.86%, q

_{1}: 22.97%, q

_{2}: 32.43%, q

_{3}: 29.73%; seated q

_{0}: 6.76%, q

_{1}: 33.78, q

_{2}: 22.97%, q

_{3}: 36.49%).

_{B}estimation performance in terms of mean absolute errors (<2 breaths/minute), correlation (r > 0.963) and agreement (see Table 4) with the reference method. Comparing our results in terms of accuracy errors with those obtained by previous studies is difficult because in most cases only relative errors were reported, but these errors depend on the breathing frequency adopted. Liu et al. [14] reported a mean absolute error of 15.45 breaths/minute (thus about 7 times higher than the error obtained in this study) during quiet sitting. Bates et al. [13] obtained an RMS error of 0.38 breaths/minute and a peak error of 3 breaths/minute in a postoperative patient during sleep. Considering comparable conditions (abdominal compartment in supine position) we obtained an RMS error of 1.51 breaths/minute, using PCA-fusion method, but in our study different, forced, breathing patterns were included, leading to higher mean error.

_{B}measurements obtained with the proposed method and OEP, our results are comparable to those obtained by Bates et al. [13] that reported a correlation coefficient equal to 0.985 between measurements of f

_{B}obtained with the accelerometer and nasal cannula. Mann et al. [11] obtained a correlation coefficient of 0.97 between measurements of f

_{B}obtained with a tri-axial accelerometer and with a system based on oxygen consumption measurement (Oxycon Mobile). In both cases [11,13], breath-by-breath analysis was not possible. Liu et al. [14] reported correlation coefficients lower than 0.6 between f

_{B}computed with a 3-axis accelerometer and with the reference (Airflow CO

_{2}analysis).

_{B}in supine position, we built Bland–Altman plot with proportional bias (OLS: y = 0.008x + 0.130, thus going from 0.18 (at x = 6 breaths/minute) to 0.61 (at x = 60 breaths/minute) breaths/minute) and V-shaped limits (LCL: y = −0.038x − 2.039 thus the lower limit goes from −2.26 (at x = 6 breaths/minute) to −4.32 (at x = 60 breaths/minute) breath/minute; UCL: y = 0.054x + 2.299; thus the upper limit goes form 2.62 (at x = 6 breaths/minute) to 5.539 (at x = 60 breaths/minute) breaths/minute) ). Thus, considering comparable breathing frequency ranges our results are closer to those obtained by Morillo et al. [8] and Lapi et al. [17]. On the contrary, Dehkrodi et al. [9] obtained better results; unfortunately, the steps to obtain the acceleration derived respiratory (ADR) signal are not described in detail.

## 5. Conclusions

## 6. Patents

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Subbe, C.; Davies, R.; Williams, E.; Rutherford, P.; Gemmell, L. Effect of Introducing the Modified Early Warning Score on Clinical Outcomes, cardio-pulmonary Arrests and Intensive Care Utilisation in Acute Medical Admissions. Anaesthesia
**2003**, 58, 797–802. [Google Scholar] [CrossRef] [PubMed] - Cretikos, M.A.; Bellomo, R.; Hillman, K.; Chen, J.; Finfer, S.; Flabouris, A. Respiratory Rate: The Neglected Vital Sign. Med. J. Aust.
**2008**, 188, 657. [Google Scholar] - World Health Organization. Acute Respiratory Infections in Children: Case Management in Small Hospitals in Developing Countries, a Manual for Doctors and Other Senior Health Workers; World Health Organization: Geneva, Switzerland, 1990. [Google Scholar]
- Karlen, W.; Gan, H.; Chiu, M.; Dunsmuir, D.; Zhou, G.; Dumont, G.A.; Ansermino, J.M. Improving the Accuracy and Efficiency of Respiratory Rate Measurements in Children using Mobile Devices. PLoS ONE
**2014**, 9, e99266. [Google Scholar] [CrossRef] [PubMed] - Torres, A.; Fiz, J.; Galdiz, B.; Gea, J.; Morera, J.; Jané, R. Assessment of Respiratory Muscle Effort Studying Diaphragm Movement Registered with Surface Sensors. Animal Model (Dogs). In Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEMBS’04), San Francisco, CA, USA, 1–4 September 2004; pp. 3917–3920. [Google Scholar]
- Reinvuo, T.; Hannula, M.; Sorvoja, H.; Alasaarela, E.; Myllyla, R. Measurement of Respiratory Rate with High-Resolution Accelerometer and EMFit Pressure Sensor. In Proceedings of the 2006 IEEE Sensors Applications Symposium, Houston, TX, USA, 7–9 February 2006; pp. 192–195. [Google Scholar]
- Hung, P.; Bonnet, S.; Guillemaud, R.; Castelli, E.; Yen, P.T.N. Estimation of Respiratory Waveform using an Accelerometer. In Proceedings of the 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI 2008), Paris, France, 14–17 May 2008; pp. 1493–1496. [Google Scholar]
- Morillo, D.S.; Ojeda, J.L.R.; Foix, L.F.C.; Jiménez, A.L. An Accelerometer-Based Device for Sleep Apnea Screening. IEEE Trans. Inf. Technol. Biomed.
**2010**, 14, 491–499. [Google Scholar] [CrossRef] [PubMed] - Dehkordi, P.K.; Marzencki, M.; Tavakolian, K.; Kaminska, M.; Kaminska, B. Validation of Respiratory Signal Derived from Suprasternal Notch Acceleration for Sleep Apnea Detection. In Proceedings of the 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Boston, MA, USA, 30 August–3 September 2011; pp. 3824–3827. [Google Scholar]
- Fekr, A.R.; Janidarmian, M.; Radecka, K.; Zilic, Z. A Medical Cloud-Based Platform for Respiration Rate Measurement and Hierarchical Classification of Breath Disorders. Sensors
**2014**, 14, 11204–11224. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mann, J.; Rabinovich, R.; Bates, A.; Giavedoni, S.; MacNee, W.; Arvind, D. Simultaneous Activity and Respiratory Monitoring using an Accelerometer. In Proceedings of the 2011 International Conference Body Sensor Networks (BSN), Dallas, TX, USA, 23–25 May 2011; pp. 139–143. [Google Scholar]
- Jin, A.; Yin, B.; Morren, G.; Duric, H.; Aarts, R.M. Performance Evaluation of a Tri-Axial Accelerometry-Based Respiration Monitoring for Ambient Assisted Living. In Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2009), Minneapolis, MN, USA, 2–6 September 2009; pp. 5677–5680. [Google Scholar]
- Bates, A.; Ling, M.J.; Mann, J.; Arvind, D. Respiratory Rate and Flow Waveform Estimation from Tri-Axial Accelerometer Data. In Proceedings of the 2010 International Conference on Body Sensor Networks (BSN), Singapore, 7–9 June 2010; pp. 144–150. [Google Scholar]
- Liu, G.; Guo, Y.; Zhu, Q.; Huang, B.; Wang, L. Estimation of Respiration Rate from Three-Dimensional Acceleration Data Based on Body Sensor Network. Telemed. e-Health
**2011**, 17, 705–711. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Yoon, J.; Noh, Y.; Kwon, Y.; Kim, W.; Yoon, H. Improvement of Dynamic Respiration Monitoring through Sensor Fusion of Accelerometer and Gyro-Sensor. J. Electr. Eng. Technol.
**2014**, 9, 334–343. [Google Scholar] [CrossRef] - Gollee, H.; Chen, W. Real-Time Detection of Respiratory Activity using an Inertial Measurement Unit. In Proceedings of the 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS 2007), Lyon, France, 23–26 August 2007; pp. 2230–2233. [Google Scholar]
- Lapi, S.; Lavorini, F.; Borgioli, G.; Calzolai, M.; Masotti, L.; Pistolesi, M.; Fontana, G.A. Respiratory Rate Assessments using a Dual-Accelerometer Device. Respir. Physiol. Neurobiol.
**2014**, 191, 60–66. [Google Scholar] [CrossRef] - Gaidhani, A.; Moon, K.S.; Ozturk, Y.; Lee, S.Q.; Youm, W. Extraction and Analysis of Respiratory Motion using Wearable Inertial Sensor System during Trunk Motion. Sensors
**2017**, 17, 2932. [Google Scholar] [CrossRef] - Cesareo, A.; Gandolfi, S.; Pini, I.; Biffi, E.; Reni, G.; Aliverti, A. A Novel, Low Cost, Wearable Contact-Based Device for Breathing Frequency Monitoring. In Proceedings of the 2017 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Seogwipo, Korea, 11–15 July 2017; pp. 2402–2405. [Google Scholar]
- Romei, M.; Mauro, A.L.; D’angelo, M.; Turconi, A.; Bresolin, N.; Pedotti, A.; Aliverti, A. Effects of Gender and Posture on Thoraco-Abdominal Kinematics during Quiet Breathing in Healthy Adults. Respir. Physiol. Neurobiol.
**2010**, 172, 184–191. [Google Scholar] [CrossRef] - Aliverti, A.; Pedotti, A. Opto-electronic plethysmography. In Mechanics of Breathing; Springer: Milano, Italy, 2002; pp. 47–59. [Google Scholar]
- Aliverti, A.; Dellacà, R.; Pelosi, P.; Chiumello, D.; Gattinoni, L.; Pedotti, A. Compartmental Analysis of Breathing in the Supine and Prone Positions by Optoelectronic Plethysmography. Ann. Biomed. Eng.
**2001**, 29, 60–70. [Google Scholar] [CrossRef] [PubMed] - Aliverti, A.; Dellaca, R.; Pelosi, P.; Chiumello, D.; Pedotti, A.; Gattinoni, L. Optoelectronic Plethysmography in Intensive Care Patients. Am. J. Respir. Crit. Care Med.
**2000**, 161, 1546–1552. [Google Scholar] [CrossRef] [PubMed] - Cala, S.; Kenyon, C.; Ferrigno, G.; Carnevali, P.; Aliverti, A.; Pedotti, A.; Macklem, P.; Rochester, D. Chest Wall and Lung Volume Estimation by Optical Reflectance Motion Analysis. J. Appl. Physiol.
**1996**, 81, 2680–2689. [Google Scholar] [CrossRef] [PubMed] - Ferrigno, G.; Carnevali, P.; Aliverti, A.; Molteni, F.; Beulcke, G.; Pedotti, A. Three-Dimensional Optical Analysis of Chest Wall Motion. J. Appl. Physiol.
**1994**, 77, 1224–1231. [Google Scholar] [CrossRef] [PubMed] - Konno, K.; Mead, J. Measurement of the separate volume changes of rib cage and abdomen during breathing. J. Appl. Physiol.
**1967**, 22, 407–422. [Google Scholar] [CrossRef] [PubMed] - Hamilton, W.R. XI. On Quaternions; Or on a New System of Imaginaries in Algebra. Lond. Edinb. Dublin Philos. Mag. J. Sci.
**1848**, 33, 58–60. [Google Scholar] [CrossRef] - Rosenfeld, B. The History of Non-Euclidean Geometry: Evolution of the Concept of a Geometrical Space; Springer-Verlag: Berlin, Germany, 1988. [Google Scholar]
- Madgwick, S.O.; Harrison, A.J.; Vaidyanathan, R. Estimation of IMU and MARG Orientation using a Gradient Descent Algorithm. In Proceedings of the 2011 IEEE International Conference on Rehabilitation Robotics (ICORR), Zurich, Switzerland, 29 June–1 July 2011; pp. 1–7. [Google Scholar]
- Pearson, K. LIII. On Lines and Planes of Closest Fit to Systems of Points in Space. Lond. Edinb. Dublin Philos. Mag. J. Sci.
**1901**, 2, 559–572. [Google Scholar] [CrossRef] - Hotelling, H. Analysis of a Complex of Statistical Variables into Principal Components. J. Educ. Psychol.
**1933**, 24, 417. [Google Scholar] [CrossRef] - Savitzky, A.; Golay, M.J. Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Anal. Chem.
**1964**, 36, 1627–1639. [Google Scholar] [CrossRef] - Kenyon, C.M.; Cala, S.J.; Yan, S.; Aliverti, A.; Scano, G.; Duranti, R.; Pedotti, A.; Macklem, P.T. Rib cage mechanics during quiet breathing and exercise in humans. J. Appl. Physiol.
**1997**, 83, 1242–1255. [Google Scholar] [CrossRef] - Layton, A.M.; Moran, S.L.; Garber, C.E.; Armstrong, H.F.; Basner, R.C.; Thomashow, B.M.; Bartels, M.N. Optoelectronic plethysmography compared to spirometry during maximal exercise. Respir. Physiol. Neurobiol.
**2013**, 185, 362–368. [Google Scholar] [CrossRef] [PubMed] - LoMauro, A.; Cesareo, A.; Agosti, F.; Tringali, G.; Salvadego, D.; Grassi, B.; Sartorio, A.; Aliverti, A. Effects of a Multidisciplinary Body Weight Reduction Program on Static and Dynamic Thoraco-Abdominal Volumes in Obese Adolescents. Appl. Physiol. Nutr. Metab.
**2016**, 41, 649–658. [Google Scholar] [CrossRef] [PubMed] - Lo Mauro, A.; D’Angelo, M.G.; Romei, M.; Motta, F.; Colombo, D.; Comi, G.P.; Pedotti, A.; Marchi, E.; Turconi, A.C.; Bresolin, N.; et al. Abdominal Volume Contribution to Tidal Volume as an Early Indicator of Respiratory Impairment in Duchenne Muscular Dystrophy. Eur. Respir. J.
**2010**, 35, 1118–1125. [Google Scholar] [CrossRef] [PubMed] - Cesareo, A.; LoMauro, A.; Santi, M.; Biffi, E.; D’Angelo, M.G.; Aliverti, A. Acute Effects of Mechanical Insufflation-Exsufflation on the Breathing Pattern in Stable Subjects with Duchenne Muscular Dystrophy. Respir. Care
**2018**. [Google Scholar] [CrossRef] [PubMed] - Benjamini, Y.; Hochberg, Y. Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. J. R. Stat. Soc. Ser. B Methodol.
**1995**, 57, 289–300. [Google Scholar] [CrossRef] - Benjamini, Y.; Yekutieli, D. The Control of the False Discovery Rate in Multiple Testing Under Dependency. Ann. Stat.
**2001**, 1165–1188. [Google Scholar] - Altman, D.G.; Bland, J.M. Measurement in Medicine: The Analysis of Method Comparison Studies. Statistician
**1983**, 307–317. [Google Scholar] [CrossRef] - Bland, J.M.; Altman, D. Statistical Methods for Assessing Agreement between Two Methods of Clinical Measurement. Lancet
**1986**, 327, 307–310. [Google Scholar] [CrossRef] - Bland, J.M.; Altman, D.G. Measuring Agreement in Method Comparison Studies. Stat. Methods Med. Res.
**1999**, 8, 135–160. [Google Scholar] [CrossRef] - BREHM, M.; Scholtes, V.A.; Dallmeijer, A.J.; Twisk, J.W.; Harlaar, J. The Importance of Addressing Heteroscedasticity in the Reliability Analysis of ratio-scaled Variables: An Example Based on Walking energy-cost Measurements. Dev. Med. Child Neurol.
**2012**, 54, 267–273. [Google Scholar] [CrossRef] - Bland, J. How Do I Estimate Limits of Agreement When the Mean or SD of Differences Is Not Constant? Available online: https://www-users.york.ac.uk/~mb55/meas/glucose.htm (accessed on 4 October 2018).
- Ludbrook, J. Confidence in Altman–Bland Plots: A Critical Review of the Method of Differences. Clin. Exp. Pharmacol. Physiol.
**2010**, 37, 143–149. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Block Diagram of the Analysis algorithm that allows derivation of breathing temporal parameters (f

_{B}. T

_{I}, T

_{E}) from quaternion-based orientation change signals recorded on Thorax, Abdomen and Reference point.

**Figure 2.**Dimension-reduction block in detail. Starting from the 4 components [q

_{0}, q

_{1}, q

_{2}, q

_{3}] of each quaternion (Abdominal: Ab and Thoracic: Th), three methods are applied to obtain a single-component signal: two methods based on best quaternion component selection (“Area” and “Peak”) and one method based on the fusion of the 4 components through Principal Component Analysis (PCA). “Area” method selects the quaternion component with the larger area under the Power Spectral Density (PSD) estimate, while “Peak” method selects the quaternion component with the highest PSD’s peak. PCA-fusion method selects the first principal component (PC_1) that accounts for the largest variance in the data.

**Figure 3.**Experimental setup. Retroreflective-marker configuration for optoelectronic plethysmography (OEP) and IMU-unit (Ab: Abdomen, Th: Thorax, Ref: Reference) placement in supine (A and B panels) and seated (C and D panels) positions. Panel E shows the experimental setup and the OEP Lab; Infrared cameras of the motion capture system are also noticeable.

**Figure 4.**Relative errors (E%) of estimation of breathing frequency (

**a**,

**b**) and Duty Cycle (

**c**,

**d**) in supine (

**a**,

**c**) and seated (

**b**,

**d**) positions, computed for each method (Peak, Area and PCA) and for the “Ideal” component with respect to the reference (OEP). Errors are computed both for the Thoracic and abdominal compartments. Horizontal blue lines indicate statistical significance of difference (post-hoc analysis, Wilcoxon test FDR corrected).

**Figure 5.**Comparisons of breathing frequency (f

_{B}expressed as breaths/minuteute) measurements by using the proposed device and by using Optoelectronic plethysmography (OEP) presented as regression analysis, in supine (top panels) and seated (bottom panels) positions. For what concerns f

_{B}measurements obtained with the IMU-device, three dimension-reduction methods were considered: Area, Peak and PCA-fusion. The performance obtained by using these three methods is benchmarked against that obtained with the Ideal quaternion component determined a posteriori based on the minimum estimation error. The regression line between measurements done by OEP and the proposed device is plotted, and the relative equation presented, both for the thorax and the abdomen.

**Figure 6.**Comparisons of inspiratory time (T

_{I}expressed as seconds) measurements by using the proposed device and by using Optoelectronic plethysmography (OEP) presented as regression analysis, in supine (top panels) and seated (bottom panels) positions. For what concerns T

_{I}measurements obtained with the IMU-device, three dimension-reduction methods were considered: Area, Peak and PCA-fusion. The performance obtained by using these three methods is benchmarked against that obtained with the Ideal quaternion component determined a posteriori based on the minimum estimation error. The regression line between measurements done by OEP and the proposed device is plotted, and the relative equation presented, both for the thorax and the abdomen.

**Figure 7.**Comparisons of expiratory time (T

_{E}, expressed as seconds) measurements by using the proposed device and by using Optoelectronic plethysmography (OEP) presented as regression analysis, in supine (top panels) and seated (bottom panels) positions. Regarding T

_{E}measurements obtained with the IMU-device, three dimension-reduction methods were considered. Area, Peak and PCA-fusion. The performance obtained by using these three methods is benchmarked against that obtained with the Ideal quaternion component determined a posteriori based on the minimum estimation error. The regression line between measurements done by OEP and the proposed device is plotted, and the relative equation presented, both for the thorax and the abdomen.

**Figure 8.**Agreement analysis between OEP and the IMU-based device for breathing frequency (f

_{B}, expressed as breaths/minuteute) measurements, in supine (top panels) and seated (bottom panels) position. In each Bland–Altman plot the differences between measurements of f

_{B}obtained by using the IMU-based device and by using OEP are plotted against the mean of the two measurements. For homoscedastic data, the mean of the differences (bias: —) and limits of agreement (black dotted line) from mean − 1.96 s to mean + 1.96 s are represented by lines parallel to the X axis. For heteroscedastic data, the proportional bias (—) is represented by the ordinary least squares (OLS) line of best fit for the difference on mean values; V-shaped upper and lower 95% confidence limits (- - -) are calculated according to Bland [44].

**Figure 9.**Agreement analysis between OEP and the IMU-based device for inspiratory time (T

_{I}, [s]) measurements, in supine (top panels) and seated (bottom panels) position. In each Bland–Altman plot the differences between measurements of T

_{I}obtained by using the IMU-based device and by using OEP are plotted against the mean of the two measurements. For homoscedastic data, the mean of the differences (bias: —) and limits of agreement (- - -) from mean − 1.96 s to mean + 1.96 s are represented by lines parallel to the X axis. For heteroscedastic data, the proportional bias (—) is represented by the OLS line of best fit for differences on mean values; V-shaped upper and lower 95% confidence limits (- - -) are calculated according to Bland [44].

**Figure 10.**Agreement analysis between OEP and the IMU-based device for expiratory time (T

_{E}, [s]) measurements, in supine (top panels) and seated (bottom panels) position. In each Bland–Altman plot the differences between measurements of T

_{E}obtained by using the IMU-based device and by using OEP are plotted against the mean of the two measurements. For homoscedastic data, the mean of the differences (bias: —) and limits of agreement (- - -) from mean − 1.96 s to mean + 1.96 s are represented by lines parallel to the X axis. For heteroscedastic data, the proportional bias (—) is represented by the OLS line of best fit for differences on mean values; V-shaped upper and lower 95% confidence limits (- - -) are calculated according to Bland [44].

**Figure 11.**Relative frequencies of quaternion component (q

_{0}, q

_{1}, q

_{2}, q

_{3}) selection using Area and Peak methods and of quaternion component selection as Ideal component, in supine and seated position. Each portion of the rings represents the ratio between the number of times that each quaternion component has been selected (by Area and Peak methods or as Ideal component respectively) and the total number of trials (n = 74).

Supine | QB 1 | ↑f_{B}, V_{T}= | ↓f_{B}, V_{T}= | ↑f_{B}, V_{T}↓ | ↓f_{B}, V_{T}↑ | QB 2 | |||||||

AB (n = 8) | TH (n = 7) | AB (n = 8) | TH (n = 8) | AB (n = 6) | TH (n = 6) | AB (n = 3) | TH (n = 2) | AB (n = 5) | TH (n = 6) | AB (n = 8) | TH (n = 8) | ||

OEP | 17.13 ± 2.23 | 17.62 ± 2.21 | 39.49 ± 10.26 | 39.48 ± 10.25 | 11.17 ± 2.64 | 11.14 ± 2.63 | 48.11 ± 13.29 | 47.66 ± 13.95 | 8.38 ± 2.40 | 8.61 ± 2.24 | 15.29 ± 4.34 | 15.24 ± 4.48 | |

Device | Area | 17.20 ± 2.15 | 18.53 ± 3.96 | 39.19 ± 10.84 | 38.16 ± 14.67 | 15.52 ± 8.14 | 19.29 ± 9.42 | 34.47 ± 34.58 | 30.01 ± 25.52 | 10.11 ± 3.91 | 10.62 ± 4.44 | 21.28 ± 8.14 | 16.55 ± 3.62 |

Peak | 17.20 ± 2.15 | 16.63 ±2.29 | 38.92 ± 11.12 | 38.96 ± 13.01 | 15.52 ± 8.14 | 16.97 ± 9.59 | 34.47 ± 34.58 | 53.39 ± 7.55 | 10.11 ± 3.91 | 9.32 ± 2.12 | 21.25 ± 8.15 | 16.55 ± 3.62 | |

PCA | 17.23 ± 2.09 | 17.03 ± 1.98 | 40.06 ± 9.22 | 40.63 ± 8.45 | 11.51 ± 2.59 | 11.56 ± 3.04 | 48.61 ± 12.64 | 49.93 ± 11.94 | 8.61 ± 2.19 | 8.95 ± 2.06 | 15.11 ± 4.82 | 15.23 ± 3.79 | |

Ideal | 17.57 ± 2.52 | 16.34 ± 2.00 | 39.81 ± 10.50 | 40.94 ± 9.97 | 12.11 ± 1.99 | 13.60 ± 2.61 | 49.53 ± 12.31 | 48.12 ± 13.89 | 9.34 ± 3.33 | 8.83 ± 2.06 | 17.74 ± 4.70 | 15.37 ± 3.82 | |

Seated | QB 1 | ↑f_{B}, V_{T}= | ↓f_{B}, V_{T}= | ↑f_{B}, V_{T}↓ | ↓f_{B}, V_{T}↑ | QB 2 | |||||||

AB (n = 8) | TH (n = 8) | AB (n = 8) | TH (n = 7) | AB (n = 8) | TH (n = 8) | AB (n = 2) | TH (n = 1) | AB (n = 6) | TH (n = 5) | AB (n = 7) | TH (n = 6) | ||

OEP | 16.99 ± 2.65 | 16.94 ± 2.77 | 42.74 ± 10.97 | 46.49 ± 7.58 | 14.57 ± 13.40 | 14.49 ± 13.41 | 33.20 ± 16.01 | 22.01 | 10.04 ± 3.56 | 10.05 ± 3.81 | 18.47 ± 4.32 | 18.47 ± 4.49 | |

Device | Area | 17.15 ± 2.86 | 15.78 ± 3.62 | 43.06 ± 11.22 | 40.71 ± 13.59 | 15.71 ± 13.52 | 17.06 ± 13.05 | 32.63 ± 12.87 | 27.62 | 10.83 ± 2.93 | 12.58 ± 4.08 | 19.80 ± 5.15 | 17.04 ± 2.09 |

Peak | 16.48 ± 3.58 | 16.27 ± 3.76 | 43.06 ± 11.22 | 40.71 ± 13.59 | 16.53 ± 13.50 | 17.15 ± 12.99 | 32.63 ± 12.87 | 27.62 | 10.83 ± 2.93 | 12.58 ± 4.08 | 17.23 ± 2.19 | 16.54 ± 1.95 | |

PCA | 16.54 ± 3.01 | 16.58 ± 2.10 | 42.26 ± 11.38 | 45.31 ± 8.56 | 16.07 ± 13.07 | 14.91 ± 13.39 | 33.79 ± 14.50 | 27.27 | 10.76 ± 2.90 | 11.35 ± 3.73 | 16.59 ± 2.17 | 15.47 ± 1.69 | |

Ideal | 16.68 ± 2.59 | 16.61 ± 2.34 | 42.64 ± 11.21 | 45.42 ± 7.98 | 15.29 ± 13.33 | 11.07 ± 2.36 | 33.38 ± 13.92 | 24.53 | 10.40 ± 3.53 | 10.29 ± 3.66 | 19.06 ± 4.89 | 18.73 ± 5.04 |

_{B}, [breaths/minute]) measurements with OEP and the device, using best component-selection methods (“Area” and “Peak”), PCA-fusion method and “Ideal” component, for the requested patterns. Data are reported for the supine and seated positions, subdivided in abdominal and thoracic contributions.

**Table 2.**Absolute errors of breathing frequency (E_f

_{B}), Inspiratory time (E_T

_{I}) and expiratory time (E_T

_{E}) obtained for the device with respect to OEP, using best component-selection methods (“Area” and “Peak”), PCA-fusion method and “Ideal” component.

Area | Peak | PCA | Ideal | |||
---|---|---|---|---|---|---|

E_f_{B} [breaths/minute] | supine | AB | 3.64 ± 7.46 | 3.64 ± 7.46 | 1.00 ± 1.24 | 1.39 ± 2.76 |

TH | 5.46 ± 8.89 | 3.17 ± 4.92 | 1.55 ± 1.51 | 1.56 ± 1.96 | ||

seated | AB | 2.19 ± 2.49 | 2.12 ± 2.74 | 1.71 ± 2.25 | 1.04 ± 1.24 | |

TH | 3.35 ± 5.68 | 3.31 ± 5.69 | 1.79 ± 2.04 | 0.96 ± 0.22 | ||

E_T_{I} [s] | supine | AB | 0.48 ± 0.73 | 0.48 ± 0.73 | 0.33 ± 0.51 | 0.20 ± 0.38 |

TH | 0.43 ± 0.52 | 0.41 ± 0.49 | 0.47 ± 0.67 | 0.17 ± 0.25 | ||

seated | AB | 0.33 ± 0.58 | 0.36 ± 0.56 | 0.46 ± 0.71 | 0.16 ± 0.27 | |

TH | 0.43 ± 0.48 | 0.44 ± 0.49 | 0.42 ± 0.35 | 0.17 ± 0.25 | ||

E_T_{E} [s] | supine | AB | 0.58 ± 0.82 | 0.58 ± 0.82 | 0.43 ± 0.58 | 0.29 ± 0.52 |

TH | 0.79 ± 0.94 | 0.67 ± 0.92 | 0.46 ± 0.63 | 0.36 ± 0.71 | ||

seated | AB | 0.43 ± 0.56 | 0.43 ± 0.56 | 0.43 ± 0.55 | 0.22 ± 0.31 | |

TH | 0.56 ± 0.66 | 0.56 ± 0.66 | 0.39 ± 0.41 | 0.24 ± 0.36 |

**Table 3.**Correlation outcomes across subjects and breathing patterns. Coefficient of correlation (r) between measurements obtained using Device vs. OEP are reported for f

_{B}. T

_{I}. and T

_{E}using best component-selection methods (“Area” and “Peak”), PCA-fusion method and “Ideal” component, in supine (Thorax: n = 37. Abdomen: n = 37) and seated (Thorax: n = 35. Abdomen: n = 39) position.

Supine | Seated | ||||
---|---|---|---|---|---|

Thorax | Abdomen | Thorax | Abdomen | ||

f_{B} | Area | 0.580 ^{$} | 0.706 ^{$} | 0.748 ^{$} | 0.915 ^{$} |

Peak | 0.833 ^{$} | 0.706 ^{$} | 0.759 ^{$} | 0.861 ^{$} | |

PCA | 0.963^{$} | 0.985^{$} | 0.953 ^{$} | 0.924 ^{$} | |

Ideal | 0.935 ^{$} | 0.931 ^{$} | 0.974^{$} | 0.977^{$} | |

T_{I} | Area | 0.727 ^{#} | 0.665 ^{$} | 0.812 ^{#} | 0.812 ^{#} |

Peak | 0.785 ^{#} | 0.659 ^{$} | 0.809 ^{#} | 0.824 ^{#} | |

PCA | 0.783 ^{#} | 0.874^{#} | 0.926 ^{#} | 0.731 ^{#} | |

Ideal | 0.943^{#} | 0.862 ^{$} | 0.951^{#} | 0.948^{#} | |

T_{E} | Area | 0.600 ^{$} | 0.713 ^{#} | 0.682 ^{#} | 0.818 ^{#} |

Peak | 0.687 ^{$} | 0.712 ^{#} | 0.723 ^{#} | 0.835 ^{#} | |

PCA | 0.891^{#} | 0.864 ^{#} | 0.888 ^{#} | 0.824 ^{#} | |

Ideal | 0.874 ^{#} | 0.966^{$} | 0.938^{#} | 0.951^{#} |

^{$}Spearman correlation coefficient;

^{#}Pearson correlation coefficient; Bold: best correlation result.

**Table 4.**Agreement analysis outcomes across subjects and different breathing patterns. Bland and Altman plot statistics for measurements of f

_{B}. T

_{I}. and T

_{E}using best component-selection methods (“Area” and “Peak”), PCA-fusion method and “Ideal” component and, in supine (n = 74) and seated (n = 74) position.

τ | p-Value | Heteroscedastic? | Fixed Bias ^{a}/OLS | LOA ^{c}/V-Shape Limits ^{d} | ||
---|---|---|---|---|---|---|

f_{B} supine | Area | 0.159 | 0.045 | Yes | y = −0.054x + 2.316 ^{b} | UCL: y = 0.085x + 10.907 ^{d}LCL: y = −0.192x − 6.275 |

Peak | 0.142 | 0.074 | No | 1.380 ^{a} | From −11.95 to 14.72 ^{c} | |

PCA | 0.211 | 0.008 | Yes | y = 0.008x + 0.130 ^{b} | UCL: y = 0.054x + 2.299 ^{d}LCL: y = −0.038x − 2.039 | |

Ideal | 0.038 | 0.631 | No | 0.884 ^{a} | From −4.171 to 5.940 ^{c} | |

f_{B} seated | Area | 0.142 | 0.074 | No | 0.084 ^{a} | From −9.635 to 9.803 ^{c} |

Peak | 0.132 | 0.096 | No | −0.121 ^{a} | From −9.931 to 9.688 ^{c} | |

PCA | 0.108 | 0.174 | No | −0.23 ^{a} | From −5.474 to 5.010 ^{c} | |

Ideal | 0.196 | 0.014 | Yes | y = −0.021x + 0.597 ^{b} | UCL: y = 0.028x + 2.057 ^{d}LCL: y = −0.071x − 0.864 | |

T_{I} supine | Area | 0.302 | 0.000 | Yes | y = 0.084x − 0.019 ^{b} | UCL: y = 0.618x + 0.095 ^{d}LCL: y = −0.450x − 0.132 |

Peak | 0.334 | 0.000 | Yes | y = 0.104x − 0.021 ^{b} | UCL: y = 0.638x + 0.093 ^{d}LCL: y = −0.430x − 0.135 | |

PCA | 0.375 | 0.001 | Yes | y = 0.283x − 0.175 ^{b} | UCL: y = 0.926x − 0.840 ^{d}LCL: y = −0.390x + 0.354 | |

Ideal | 0.292 | 0.000 | Yes | y = −0.090x + 0.121 ^{b} | UCL: y = 0.158x + 0.163 ^{d}LCL: y = −0.338x + 0.078 | |

T_{I} seated | Area | 0.430 | 0.000 | Yes | y = 0.1022x − 0.0141 ^{b} | UCL: y = 0.834x + 0.112 ^{d}LCL: y = −0.618x − 0.409 |

Peak | 0.422 | 0.000 | Yes | y = 0.220x − 0.075 ^{b} | UCL: y = 0.642x − 0.173 ^{d}LCL: y = −0.438x + 0.197 | |

PCA | 0.489 | 0.000 | Yes | y = 0.171x − 0.0332 ^{b} | UCL: y = 0.7182x − 0.226 ^{d}LCL: y = −0.377x + 0.160 | |

Ideal | 0.313 | 0.000 | Yes | y = −0.059x + 0.129 ^{b} | UCL: y = 0.211x + 0.069 ^{d}LCL: y = −0.329x + 0.189 | |

T_{E} supine | Area | 0.421 | 0.000 | Yes | y = −0.170x + 0.166 ^{b} | UCL: y = 0.508x + 0.358 ^{d}LCL: y = −0.847x − 0.026 |

Peak | 0.405 | 0.000 | Yes | y = −0.138x + 0.144 ^{b} | UCL: y = 0.496x + 0.306 ^{d}LCL: y = −0.771x − 0.017 | |

PCA | 0.522 | 0.000 | Yes | y = −0.209x + 0.328 ^{b} | UCL: y = 0.667x + 0.037 ^{d}LCL: y = −1.084x + 0.620 | |

Ideal | 0.484 | 0.000 | Yes | y = −0.153x + 0.148 ^{b} | UCL: y = 0.3987x − 0.185 ^{d}LCL: y = −0.705x + 0.481 | |

T_{E} seated | Area | 0.384 | 0.000 | Yes | y = −0.216x + 0.364 ^{b} | UCL: y = 0.303x + 0.532 ^{d}LCL: y = −0.735x + 0.197 |

Peak | 0.396 | 0.000 | Yes | y = −0.231x + 0.413 ^{b} | UCL: y = 0.226x + 0.666 ^{d}LCL: y = −0.657x + 0.101 | |

PCA | 0.422 | 0.000 | Yes | y = −0.127x + 0.320 ^{b} | UCL: y = 0.284x + 0.498 ^{d}LCL: y = −0.538x + 0.142 | |

Ideal | 0.316 | 0.000 | Yes | y = −0.058x + 0.054 ^{b} | UCL: y = 0.383x + 0.337 ^{d}LCL: y = −0.500x − 0.228 |

^{a}Fixed Bias. obtained as the mean of differences (device – OEP). for homoscedastic data.

^{b}OLS: ordinary least squares line of best fit (proportional bias) for heteroscedastic data.

^{c}LOA: limits of agreement. computed as mean difference ± 1.96SD (for homoscedastic data).

^{d}V-shape limits: UCL and LCL 95% confidence limits. calculated according to Bland [44].

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**MDPI and ACS Style**

Cesareo, A.; Previtali, Y.; Biffi, E.; Aliverti, A.
Assessment of Breathing Parameters Using an Inertial Measurement Unit (IMU)-Based System. *Sensors* **2019**, *19*, 88.
https://doi.org/10.3390/s19010088

**AMA Style**

Cesareo A, Previtali Y, Biffi E, Aliverti A.
Assessment of Breathing Parameters Using an Inertial Measurement Unit (IMU)-Based System. *Sensors*. 2019; 19(1):88.
https://doi.org/10.3390/s19010088

**Chicago/Turabian Style**

Cesareo, Ambra, Ylenia Previtali, Emilia Biffi, and Andrea Aliverti.
2019. "Assessment of Breathing Parameters Using an Inertial Measurement Unit (IMU)-Based System" *Sensors* 19, no. 1: 88.
https://doi.org/10.3390/s19010088