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Accelerometer-based estimation of respiratory rate
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PAPER
Accelerometer-based estimation of respiratory rate using principal
component analysis and autocorrelation
Mads C F Hostrup1, Anne Sofie Nielsen1, Freja E Sørensen1, Jesper O Kragballe1,
Morten U Østergaard1, Emil Korsgaard2, Samuel E Schmidt2and Dan S Karbing3,∗
1Department of Health Science and Technology, Aalborg University, Aalborg, Denmark
2CardioTech Group, Department of Health Science and Technology, Aalborg University, Aalborg, Denmark
3Respiratory and Critical Care Group, Department of Health Science and Technology, Aalborg University, Aalborg, Denmark
∗Author to whom any correspondence should be addressed.
E-mail: dank@hst.aau.dk
Keywords: respiratory rate, accelerometer, respiratory measurement, principal component analysis, autocorrelation
Abstract
Objective. Respiratory rate (RR) is an important vital sign but is often neglected. Multiple
technologies exist for RR monitoring but are either expensive or impractical. Tri-axial
accelerometry represents a minimally intrusive solution for continuous RR monitoring, however,
the method has not been validated in a wide RR range. Therefore, the aim of this study was to
investigate the agreement between RR estimation from a tri-axial accelerometer and a reference
method in a wide RR range. Approach. Twenty-five healthy participants were recruited. For
accelerometer RR estimation, the accelerometer was placed on the abdomen for optimal breathing
movement detection. The acquired accelerometry data were processed using a lowpass filter,
principal component analysis (PCA), and autocorrelation. The subjects were instructed to breathe
at slow, normal, and fast paces in segments of 60s. A flow meter was used as reference.
Furthermore, the PCA-autocorrelation method was compared with a similar single axis method.
Main results. The PCA-autocorrelation method resulted in a bias of 0.0 breaths per minute (bpm)
and limits of agreement (LOA) =[−1.9; 1.9 bpm] compared to the reference. Overall, 99% of the
RRs estimated by the PCA-autocorrelation method were within ±2 bpm of the reference. A Pearson
correlation indicated a very strong correlation with r=0.99 (p<0.001). The single axis method
resulted in a bias of 3.7 bpm, LOA =[−14.9; 22.3 bpm], and r=0.44 (p<0.001). Significance. The
results indicate a strong agreement between the PCA-autocorrelation method and the reference.
Furthermore, the PCA-autocorrelation method outperformed the single axis method.
1. Introduction
Respiratory rate (RR), which is the number of breaths per minute (bpm), can be used as a predictor for
serious clinical events such as cardiac arrest and admission to the intensive care unit, up to 24 h prior to the
event (Liu et al 2019). Furthermore, relative variations in RR are larger than the variation in blood pressure
and heart rate (HR), which makes RR a more sensitive marker of clinically relevant changes in a patient’s
condition (Subbe et al 2003, Elliott and Coventry 2012).
Subtle changes outside the normal RR range can indicate exacerbations in a patient’s condition (Liu et al
2019), while the normal RR range varies with gender, weight, age, and overall health (Ambekar and Prabhu
2015). Clinical conditions can also cause an RR range outside the normal RR within the range of 12–20 bpm
for adults (Fekr et al 2014, Doheny et al 2020). Therefore, it is important to be able to track subtle changes in
RR across a wide range of RR.
To the best of the authors’ knowledge, there are no official clinical guidelines for acceptable error margin
for RR monitoring devices. However, Breteler et al (2020) concluded that ±3 bpm or within ±10% of the
reference standard, is acceptable for clinical purposes.
© 2025 The Author(s). Published on behalf of Institute of Physics and Engineering in Medicine by IOP Publishing Ltd
Physiol. Meas. 46 (2025) 035005 M C F Hostrup et al
In general wards, the measurement of RR is often neglected due to busy time schedules of nurses, lack of
awareness regarding the importance of monitoring RR, and nurses subjectively assessing patients as stable
(Elliott and Coventry 2012, Singh et al 2020). However, when RR is estimated it is usually performed by
manual counting by nurses (Liu et al 2019), which provides only a momentary insight of the patient’s
condition. Thus, RR is not measured continuously, which may result in undetected deterioration of a
patient’s condition (Singh et al 2020). Furthermore, manual counting has shown to provide inaccurate
estimates of RR (Liu et al 2019).
Several methods have been developed for continuous RR monitoring to improve patient outcomes
(Elliott and Coventry 2012, Liu et al 2019). Current methods for RR monitoring are capnometry,
modulation of photoplethysmography (PPG) signals, and respiratory belts (Liu et al 2019). Capnometry is
often used as the gold standard, however, it requires expensive equipment, can be uncomfortable for the
patient, and can interfere with the natural breathing of subjects (Liu et al 2019). Hence, it is impractical for
continuous RR monitoring in general wards.
Since respiration induces changes in the peripheral circulation, it is possible to estimate RR from a PPG
signal (Allen 2007, Liu et al 2019). This is a cost-effective method of RR estimation as it does not require any
additional equipment (Liu et al 2019). However, Addison et al (2015) showed that the error of estimating RR
from a PPG signal had a bias of −0.48 bpm and limits of agreement (LOA) =[−3.9; 3 bpm], calculated from
the provided 1 standard deviation (SD) of 1.77 bpm, which exceeds the acceptable error margin proposed by
Breteler et al (2020).
Respiratory belts can be used to measure RR by either strain gauge or impedance principles (Bates et al
2010). For short-term use, respiratory belts are popular, however, they are constrictive and uncomfortable,
making them impractical for continuous RR monitoring (Bates et al 2010, Liu et al 2019).
A low-cost and minimally intrusive solution could leverage accelerometry and be applied across a broad
range of settings, such as continuous monitoring in general wards (Doheny et al 2020). This method of RR
estimation is performed by placing the accelerometer on the chest or abdomen to measure the accelerations
affiliated with breathing, using data from either a single axis or multiple axes (Bates et al 2010, Fekr et al
2014, Hung 2017, Preejith et al 2017, Doheny et al 2020, Jacobs et al 2021, Schipper et al 2021, Romano et al
2022). Performance of RR estimation using accelerometers varies. Schipper et al (2021) reported an
agreement interval, defined as the difference between the 97.5th and 2.5th percentiles of the distribution of
differences in RR estimates between the accelerometer and respiratory impedance plethysmography. In a
supine position, they reported an agreement interval of 0.67 bpm with 1 SD of 0.33 bpm across all subjects.
Additionally, Schipper et al (2021) used a fusion of three axes with a novel form of principal component
analysis (PCA). Romano et al (2022) reported LOA =[−4.7; 4.7 bpm] for participants in a standing position
and using a single axis. However, participants in Schipper et al (2021) were instructed to breathe normally
and in Romano et al (2022) the participants were instructed to breathe quietly. The RRs measured by
Schipper et al (2021) and Romano et al (2022) were approximately 9–25bpm derived by visual inspection of
their Bland-Altman figures. Hereby, previous articles did not widely cover abnormal RR ranges, which are
essential for detecting exacerbation in patient conditions.
Consequently, it is unknown whether the proposed algorithms are capable of estimating abnormal RRs
outside the range 9–25 bpm. Fekr et al (2014) estimated RRs in a broad range of RRs (7–66 bpm) with an
r=0.99, however, no LOA or average error were reported. Thus, there is a potential in using an
accelerometer in RR estimation, however, the use of the method in a broad range of RRs is still limited.
Additionally, breathing patterns (Benchetrit 2000) and breathing movements (Tobin et al 1983a,1983b)
vary between individuals, and hereby, the axis with the most prominent respiratory signal might also vary.
Furthermore, changes in patient position might cause the axis of interest to change (Bates et al 2010). It has
recently been shown that there is an interaction between posture and breathing pattern on abdominal muscle
activation which may affect respiratory motion (Kawabata and Shima 2023). Consequently, a fusion of all
three axes from the accelerometer may address the problem of the most prominent axis not being consistent.
Therefore, the aim of this study is to investigate the agreement between RR estimation, using a tri-axial
accelerometer, and a reference method across a clinically relevant RR range.
2. Methods and materials
2.1. Criteria for participating in the study
Healthy participants above 18 years without any previous or currently known pulmonary or cardiac diseases
were included. All participants were students recruited on campus, covered by an educational agreement
with the scientific ethical committee of Northern Jutland. All participants gave written informed consent
before participating. The research was conducted in accordance with the principles embodied in the
2
Physiol. Meas. 46 (2025) 035005 M C F Hostrup et al
Figure 1. The experimental setup. 1: Camera. 2: NI-DAQ. 3: Accelerometer. 4: Flow meter. 5: iWorx Recorder. The participant was
lying in a supine position on an examination couch with a 30◦incline. A noseclip covered the participant’s nose to ensure
breathing occurred through the flow meter.
Declaration of Helsinki and in accordance with local statutory requirements. Pregnant women were excluded
from the study.
2.2. Data collection
A tri-axial accelerometer (SDI 1521, Silicon Designs Inc. Kirkland, USA) was placed on the abdomen 3 cm
above the umbilicus. The x-axis was in the superior–inferior (head-to-feet) direction, the y-axis was in the
lateral-medial (left-to-right) direction, and the z-axis was in the dorsal–ventral (back-to-front) direction.
The accelerometer was connected to an iWorx Recorder (IX-RA-834, iWorx Systems Inc. Dover, USA), which
was connected to a PC with LabScribe (version 23.0901, iWorx System Inc. Dover, USA) installed. The
sample frequency in LabScribe was configured to 5000 Hz. A one-directional flow meter (SFM3020,
Sensirion, Stäfa, Switzerland) was used as the reference. The flow meter was connected to a mouthpiece with
a breathing filter. The mouthpiece was sterilized for each participant, and the breathing filter was replaced for
each participant. The flow meter was connected to a NI-DAQ ADC (USB-6009, Emerson, Missouri, USA) to
sample the flow signal at 5000 Hz. A camera was used to record the experiment to verify any unexpected
abnormalities in the collected data. The experimental setup is illustrated in figure 1.
During the recording session of 5 min, the participants were instructed to breathe in paces of slow,
normal, and fast breathing in segments lasting 60 s each. The participants determined what they considered
as slow, normal, and fast breathing paces. The participants were randomly and evenly divided into two
groups with two different orders of breathing paces to reduce order bias. Group 1 had to breathe in the
following order: normal, fast, normal, slow, normal. Group 2 had to breathe in the following order: normal,
slow, normal, fast, normal.
2.3. Signal processing
The signal processing steps for the accelerometer data are illustrated in figure 2. The signal processing chain
operates on a single 60 s data segment at a time. MATLAB (R2023a, Mathworks, Natick, USA) was used for
all signal processing steps.
The signal processing algorithm was developed and tested using a random split of the recorded data, with
20% allocated for development and the remaining 80% used for testing the algorithm’s performance.
3
Physiol. Meas. 46 (2025) 035005 M C F Hostrup et al
Figure 2. The signal processing steps for one participant. First, raw accelerometer data was recorded from the x,y, and zaxes.
Next, a lowpass filter was applied to all three axes. The filtered data was then fused using PCA by projecting it onto the first
principal component. Finally, finding peaks within the autocorrelation was used to estimate the RR.
Lowpass filter: fourth-order Butterworth lowpass filters with cutoff frequencies ranging from 0.5–1.5 Hz
with 0.1 Hz increments were evaluated on the development data. The evaluation resulted in a 0.8 Hz cutoff
frequency as the optimal cutoff frequency. Consequently, all accelerometer data segments with RR measured
from the flow meter above 48bpm were excluded, since all RRs above 48bpm would have been attenuated
due to the filter’s cutoff frequency. The lowpass filter was applied to all three axes of accelerometer data.
PCA: after lowpass filtering, a PCA was performed to fuse and make use of all three axes of the accelerometer
data. As the accelerometer data was three-dimensional, the PCA returned three principal components where
the first principal component was retained. The normalization step of the PCA was deliberately omitted.
Afterward, the accelerometer data was projected onto the first principal component, and this projected signal
served as the input for the RR estimation algorithm.
RR estimation algorithm: the autocorrelation of the projected signal was calculated. Autocorrelation
identifies repeating patterns within a signal by measuring its similarity with lagged versions of itself,
highlighting the primary periodic components (Shen et al 2018). For periodic signals, the autocorrelation
function produces a series of decaying peaks corresponding to repeating patterns (Shen et al 2018). When
multiple periodic components are present, such as respiratory- and heart-induced motion, two series of
decaying peaks will be present, where the largest peak is assumed to represent the dominant respiratory
motion. The lag of this peak can then be converted into an RR estimate. To detect peaks in the
autocorrelation, the ‘findpeaks()’ function from MATLAB was used. The amplitudes of the first two detected
peaks were compared, and the largest peak was selected, assuming that the respiratory-induced signal would
be the most prominent after low-pass filtering. The autocorrelations appeared smooth with minimal noise,
and manual visual inspection of the identified peaks confirmed that the ‘findpeaks()’ function reliably
detected the correct peaks. The number of lags from lag zero to the largest detected peak was then converted
to an RR estimate for each segment using the following equation:
RR =(SamplingFrequency
LagsToLargestPeak )·60.(1)
An upper limit on the maximum RR estimate was imposed by configuring the ‘findpeaks()’ function to
ignore any peaks detected within the first 6250 lags. This corresponds to ignoring RR estimates above
48 bpm, as any peak earlier than the first 6250 lags would most likely be due to signal noise.
Single z-axis: to evaluate the effectiveness of combining all three axes of accelerometer data, a simplified
signal processing method was also developed using only the z-axis from the accelerometer. This simplified
method omitted the PCA step but still applied the exact same lowpass filter and autocorrelation peaks
approach.
4
Physiol. Meas. 46 (2025) 035005 M C F Hostrup et al
Figure 3. Data snippet from a single participant recorded simultaneously from the accelerometer and flow meter during a normal
breathing pace segment. (a) Lowpass-filtered accelerometer data, with x-axis in blue, y-axis in red, and z-axis in yellow. (b)
Accelerometer data after projection onto the first principal component. (c) Reference flow meter data.
2.4. RR measurements from the flow meter
The flow meter was used as a reference for measuring RR. Every breath recorded by the flow meter created a
visible peak in the flow signal as seen in figure 3, which were marked by an algorithm, with following manual
visual confirmation of registered breaths.
2.5. Statistical analysis
Statistical analysis was performed using IBM SPSS (v28.0.1.1, Armonk, USA). Estimated RRs from the
accelerometer were compared to the RRs measured from the flow meter in the corresponding segment for all
statistical analysis types. Q–Q plots were created to assess normality. Mean absolute error (MAE), Pearson
correlation, a paired t-test, two-way repeated measures ANOVA, and Bland–Altman plots were conducted.
The LOAs from the Bland–Altman plots were 95% LOA. If a bias was statistically significant, a 95%
confidence interval (CI) was calculated. The LOAs were corrected for repeated measurements as described by
Bland and Altman (2007), when including multiple segments from the same participant.
Additionally, to compare the overall performance of the PCA-autocorrelation method with the single
z-axis method, the Wilcoxon signed-rank test was performed due to the non-normal distribution of the
absolute differences. Descriptive statistics were reported as mean (SD). P-values <0.05 were considered
statistically significant. To interpret the Pearson correlation coefficients, the naming convention described by
Schober et al (2018) was used.
3. Results
3.1. Data obtained from the experiment
Twenty-five healthy participants, with an overall mean age of 24.2 (2.4) years and a mean BMI of 22.4
(3.1) kg m−2, participated in the study. Eight participants (32%) were female. The mean age for female
participants was 24.3 (0.9) years, with a mean BMI of 21.4 (1.6) kg m−2. For male participants, the mean age
was 24.1 (2.9) years, and the mean BMI was 22.9 (3.5) kg m−2. An example of data recorded from the
accelerometer and flow meter for one participant is illustrated in figure 3. As the data allocated for testing
was 80% of the recorded data, the testing data set consisted of 100 segments, from 20/25 participants. Two of
the 100 segments were discarded due to the RRs measured from the flow meter (91 bpm and 105 bpm)
exceeding the exclusion criterion of RR >48 bpm. Hereby, 98/100 segments of the testing data were used for
statistical analysis. The 98 segments of testing data consisted of 20 segments of slow breathing, 60 segments
of normal breathing, and 18 segments of fast breathing. The included data had RRs ranging from 3–38 bpm,
as illustrated on figure 4. Based on an analysis of Q–Q plots, the recorded data were considered normally
distributed.
5
Physiol. Meas. 46 (2025) 035005 M C F Hostrup et al
Figure 4. Left scatterplot: RR estimates from the PCA-autocorrelation method and flow meter. Right scatterplot: RR estimates
from the z-axis method and flow meter. Each point represents the RR estimated in a single segment.
Table 1. Overview of results for RRPCA −RRflow and RRzaxis −RRflow . Bias, CI, LOA, and MAE are in bpm. ∗:p<0.05 ∗∗ :p<0.001.
Parameter Slow Normal Fast Total
PCA Bias 0.1 −0.1 0.3∗(CI:0.1; 0.5) 0.0
LOA [−0.7; 0.9] [−2.4; 2.2] [−0.6; 1.1] [−1.9; 1.9]
r0.99∗∗ 0.96∗∗ 0.99∗∗ 0.99∗∗
MAE 0.3 0.7 0.4 0.5
Z-axis Bias 9.8∗(CI:3.1; 16.5) 2.6∗(CI:0.6; 4.7) 0.6∗∗ (CI:0.4; 0.8) 3.7∗∗ (CI:1.8; 5.6)
LOA [−18.3; 37.9] [−13.8; 19.1] [−0.2; 1.3] [−14.9; 22.3]
r−0.05 0.27∗0.99∗∗ 0.44∗∗
MAE 10.0 3.3 0.6 4.2
The mean and SD of the RRs measured by the flow meter were 8.4 (3.7)bpm for slow breathing, 14.8
(3.6) bpm for normal breathing, and 27.6 (5.9) bpm for fast breathing.
3.2. Estimation of RR
An overview of the results from the statistical analysis can be seen in table 1. The Pearson correlation
coefficient was r=0.99 (p<0.001) which indicated a very strong correlation between the
PCA-autocorrelation method and the flow meter across all measured RRs as illustrated in figure 4.
As illustrated in figure 5, the results using the PCA-autocorrelation method for the segments for slow
breathing had LOA =[−0.7; 0.9 bpm], the segments for normal breathing had LOA =[−2.4; 2.2 bpm], and
the segments for fast breathing had LOA =[−0.6; 1.1 bpm]. Hereby, all segments were within the acceptable
error margin of ±3 bpm.
The paired t-test showed a statistically significant but small systematic bias of 0.3 bpm (p=0.02) for the
PCA-autocorrelation method when evaluating the segments with fast breathing. No significant systematic
bias was observed for the other breathing paces.
3.3. Comparison between the PCA-autocorrelation method and z-axis
When using the alternative z-axis algorithm, where the PCA step was omitted, the Pearson correlation
coefficient was r=0.44 (p<0.001). This indicated a moderate correlation between the z-axis and flow meter
across all breathing paces as seen in figure 4. Additionally, when using the z-axis, the best agreement was in
the segments for fast breathing with LOA =[−0.2; 1.3bpm] and the worst agreement was in the segments
6
Physiol. Meas. 46 (2025) 035005 M C F Hostrup et al
Figure 5. Bland–Altman plots of the difference between the RR estimates from the PCA-autocorrelation method and the flow
meter. The red dashed lines represent the LOAs. The bias is represented by the black line. The blue points each represent
compared RRs for one segment.
for slow breathing with LOA =[−18.3; 37.9 bpm]. The RRs estimated in the segments with fast breathing
were within the acceptable error margin of ±3 bpm, however, RRs estimated in segments with other
breathing paces were outside the error margin.
The Wilcoxon signed-rank test showed a statistically significant difference (p<0.001) between absolute
errors of the PCA-autocorrelation method compared to absolute errors of the z-axis when including all
segments.
The two-way repeated measures ANOVA indicated that the z-axis method resulted in significantly
different RR as compared to the PCA-autocorrelation method. A post-hoc test indicated that the z-axis on
average estimated 4.0 bpm (CI: 1.4; 6.6 bpm) more than the PCA-autocorrelation method (p=0.005). In the
segments with fast breathing, the z-axis on average estimated 0.3 bpm more than the PCA-autocorrelation
method, but the difference was significant (p=0.042).
4. Discussion
In this study, we presented a novel PCA-autocorrelation method for RR estimation using a tri-axial
accelerometer. The method was validated in 20 healthy participants with an accelerometer placed on the
abdomen and using a flow meter as the reference. The study design focused on including a wide range of RRs
to validate that the developed method was able to handle clinically relevant RRs. When using the developed
method, 99% of the estimated RRs were within ±2 bpm compared to the flow meter. There was a very strong
correlation between the PCA-autocorrelation method and the flow meter for all breathing paces.
4.1. Single-axis vs multi-axis
Fekr et al (2014) investigated a wide range of RRs (7–66 bpm) on 8 healthy participants and achieved a
Pearson correlation coefficient r=0.99 compared to spirometry, using a peak and valley detection on the
single z-axis. Thus the current PCA-autocorrelation method achieving r=0.99, is similar in estimating RR
compared to the results achieved by Fekr et al (2014) and is superior compared to using our z-axis achieving
only r=0.44. Consequently, we demonstrated that the PCA-autocorrelation method proved to be superior
to using a single axis.
Furthermore, when using a single axis, the positioning of the accelerometer is crucial, since the
orientation of the axis must align with the respiratory movements. PCA reduces this requirement of precise
positioning of the accelerometer, thus healthcare professionals can be less attentive when positioning the
7
Physiol. Meas. 46 (2025) 035005 M C F Hostrup et al
accelerometer. Additionally, changes in patient position, and thereby a change in the axis of interest as
described by Bates et al (2010), will also be addressed by using PCA, as demonstrated by Schipper et al (2021)
in their study on the robustness of PCA in different positions.
Schipper et al (2021) proposed a novel form of PCA combined with a frequency domain method for RR
estimation. In 20 healthy participants who were lying in a supine position and measuring an RR range of
approximately 9–23bpm, they reported an agreement interval of 0.67 (0.33) bpm across all participants.
While this metric is not directly comparable to our 95% LOA, our study obtained a total LOA =[−1.9;
1.9 bpm] but included a larger range of RRs (3–38 bpm).
The larger LOA was primarily located in the segments with normal breathing. This might be due to
two-thirds of the normal segments following either a fast or slow segment, causing a transitional period
where breathing rates did not immediately stabilize to a normal pace. This transitional adjustment may have
introduced additional variance in the normal segments, potentially affecting the algorithm’s performance in
accurately estimating RRs.
Previous studies have predominantly applied a single accelerometer for the measurement of RR (Bates
et al 2010, Fekr et al 2014, Hung 2017, Preejith et al 2017, Doheny et al 2020, Jacobs et al 2021, Schipper et al
2021, Romano et al 2022). However, Ashe et al (2024) recently reported results using six accelerometers,
yielding accuracy estimates as high as LOA =[−0.9; 0.9bpm] in exercising healthy adults during controlled
laboratory conditions, with flow signals as the reference. While this multi-sensor approach demonstrated
excellent agreement, it relies on placement at multiple key anatomical landmarks, which may introduce
practical challenges, including increased complexity, cost, and considerations for ease of setup and patient
comfort. Our findings indicate that clinically acceptable performance can be achieved with a simpler
single-accelerometer setup. Specifically, we introduced a novel yet simple combination of PCA and
autocorrelation, tested on a clinically relevant range of RRs. This method achieved results within the
acceptable error margin of ±3 bpm for clinical use proposed by Breteler et al (2020).
4.2. Advantages and limitations of autocorrelation
Respiratory signals are generally regarded as periodic sinusoidal signals, simplifying the task of analyzing
their periodic components (Shen et al 2018). Autocorrelation was chosen for RR estimation because it
identifies repeating patterns within a signal by measuring its similarity with lagged versions of itself. This
makes it highly adaptive to variations in breathing patterns and differences between patients, as it only
requires consistent periodicity within the same breathing segment rather than strict uniformity across
signals. An additional advantage of autocorrelation is its independence from signal amplitude, eliminating
the need for predefined thresholds. This makes it a robust choice for RR estimation. Autocorrelation has also
been successfully applied in other domains, such as HR estimation and radar-based RR estimation (Shen et al
2018, Laurino et al 2020). However, an important limitation is its reliance on periodicity within the analyzed
segment. Irregularities, such as those caused by apnea, is expected to reduce its accuracy in estimating RR.
4.3. Effective range for RR estimation
Due to the implemented lowpass filter, the developed PCA-autocorrelation method was limited in the
maximal measurable RR. Therefore, the trade-off between the maximal measurable RR and the amount of
noise reduction by the filter was an important consideration. Even though the accelerometer was placed on
the abdomen, and not on the chest, as done in most articles (Fekr et al 2014, Hung 2017, Preejith et al 2017,
Schipper et al 2021, Romano et al 2022), the noise from the heart was still contaminating the respiratory
signals. Increasing the cutoff frequency, and thereby the maximal measurable RR, the noise from the heart
would not be attenuated sufficiently, and the PCA-autocorrelation method would likely register the HR
instead of the RR.
A solution to extending the maximal measurable RR, while avoiding the HR, would have to involve a
different type of filtering. However, similar articles (Bates et al 2010, Fekr et al 2014, Preejith et al 2017,
Doheny et al 2020, Schipper et al 2021) all used lowpass filters. In our study, the design of the filter combined
with the PCA-autocorrelation method was able to accurately estimate RR in a range of 3–38 bpm and
theoretically would be able to estimate up to 48 bpm, before being attenuated by the corresponding cutoff
frequency of 0.8 Hz. However, it can be argued that in a general ward setting, a respiratory monitoring
system should issue a warning well before reaching 48 bpm, as such a high RR is unusual for a resting adult
patient and could indicate a critical situation requiring clinical intervention. That said, the upper limit of
48 bpm poses a limitation for pediatric applications, where higher RRs are common. For example, in infants
(1–12 months), normal RRs can reach up to 60 bpm (Ambekar and Prabhu 2015).
Nevertheless, despite the limitations imposed by the lowpass filter, the developed method can still
estimate RRs outside the normal RR range of 12–20 bpm for adults.
8
Physiol. Meas. 46 (2025) 035005 M C F Hostrup et al
4.4. Study limitations
Our study included 25 healthy participants with an overall mean age of 24 (2) years and a mean BMI of 22.4
(3.1) kg m−2. Of these, 8 participants (32%) were female. This gender imbalance in the composition of our
participant group is similar to those reported for similar studies (Preejith et al 2017, Breteler et al 2020,
Doheny et al 2020). The accelerometer was placed consistently at 3 cm above the umbilicus for all
participants, minimizing the potential impact of anatomical differences between genders on the recorded
respiratory-induced accelerations. Comparable BMI and age between genders further reduce the likelihood
of this imbalance affecting the findings.
Only one position was investigated in our study, with participants lying still in a supine position in a
controlled laboratory setting. Conducting a study with multiple positions, as done in other articles (Hung
2017, Doheny et al 2020, Schipper et al 2021, Romano et al 2022), would be beneficial. Nevertheless, it is
expected that the PCA handles the problem of patients changing their position, as shown by Schipper et al
(2021).
To ensure accurate reference RR measurements, a flow meter with a mouthpiece and nose clip was used.
While this setup enables precise validation, it is known to slightly lower RR and increase tidal volume (Tobin
et al 1983a). Additionally, participants were instructed to voluntarily alter their breathing to achieve a wide
range of RRs, a necessary approach to validate the method across clinically relevant ranges. Whilst expectedly
more natural than metronome-paced breathing, voluntarily controlled slow or fast pace might not fully
replicate natural breathing.
Our method has not yet been evaluated in a clinical setting, where irregular breathing patterns, such as
apnea, can occur. This could potentially be a challenge for the PCA-autocorrelation method, as the
autocorrelation algorithm operates under the assumption of regular breathing within a given time segment.
5. Conclusion
Our study advances the field of accelerometer-based RR estimation by presenting a novel, simple
PCA-autocorrelation method which proved to be superior to using a single axis. RR was measured on healthy
participants in a clinically relevant range of RRs. The results indicate a very strong correlation, with clinically
acceptable agreement between the developed PCA-autocorrelation method and a flow meter used as the
reference. A clinical study should be conducted to explore performance in a clinical setting.
Data availability statement
The data that support the findings of this study cannot be made publicly available upon publication.
However, in accordance with the Danish Data Protection Act, § 10, these data can be shared upon reasonable
request for research purposes, provided that such processing is solely for statistical or scientific studies of
significant societal importance.
The data that support the findings of this study are available upon reasonable request from the authors.
Acknowledgment
The author’s have confirmed that any identifiable participants in this study have given their consent for
publication.
ORCID iDs
Mads C F Hostrup https://orcid.org/0009-0009-9620-991X
Anne Sofie Nielsen https://orcid.org/0009-0006-4843-0810
Freja E Sørensen https://orcid.org/0009-0000-3985-6971
Jesper O Kragballe https://orcid.org/0009-0002-8206-6611
Morten U Østergaard https://orcid.org/0009-0004-0839-8305
Emil Korsgaard https://orcid.org/0009-0006-0847-021X
Samuel E Schmidt https://orcid.org/0000-0002-0917-634X
Dan S Karbing https://orcid.org/0000-0001-8632-6180
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