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The authors have no patents related to the presented topic. The authors have declared that no competing interests exist.

Conceived and designed the experiments: JMA MC GD HG WK. Performed the experiments: MC. Analyzed the data: MC HG WK GZ. Contributed reagents/materials/analysis tools: DD HG WK. Wrote the paper: JMA MC GD DD HG WK GZ.

The recommended method for measuring respiratory rate (RR) is counting breaths for 60 s using a timer. This method is not efficient in a busy clinical setting. There is an urgent need for a robust, low-cost method that can help front-line health care workers to measure RR quickly and accurately. Our aim was to develop a more efficient RR assessment method. RR was estimated by measuring the median time interval between breaths obtained from tapping on the touch screen of a mobile device. The estimation was continuously validated by measuring consistency (% deviation from the median) of each interval. Data from 30 subjects estimating RR from 10 standard videos with a mobile phone application were collected. A sensitivity analysis and an optimization experiment were performed to verify that a RR could be obtained in less than 60 s; that the accuracy improves when more taps are included into the calculation; and that accuracy improves when inconsistent taps are excluded. The sensitivity analysis showed that excluding inconsistent tapping and increasing the number of tap intervals improved the RR estimation. Efficiency (time to complete measurement) was significantly improved compared to traditional methods that require counting for 60 s. There was a trade-off between accuracy and efficiency. The most balanced optimization result provided a mean efficiency of 9.9 s and a normalized root mean square error of 5.6%, corresponding to 2.2 breaths/min at a respiratory rate of 40 breaths/min. The obtained 6-fold increase in mean efficiency combined with a clinically acceptable error makes this approach a viable solution for further clinical testing. The sensitivity analysis illustrating the trade-off between accuracy and efficiency will be a useful tool to define a target product profile for any novel RR estimation device.

Respiratory rate (RR) plays a fundamental role in routine clinical assessment for disease diagnosis, prognosis, and treatment in children

The current recommended method for measuring RR is to count the number of breaths in one minute. This method was promoted by the World Health Organization (WHO)

The user interfaces and the ubiquitous availability with health workers make mobile phones the ideal platforms for mobile health projects. A growing number of initiatives are leveraging the wide availability, affordability, portability, and usability of mobile phones to tackle the health challenges of developing countries

We propose a method of estimating RR in less than 60 s using a mobile phone application. RR is estimated by measuring the median time interval between breaths, and then dividing 60 s by this time interval. The time interval between breaths is measured as the user taps on the touch sensitive screen of a mobile device in time with the inhalation phase of breathing. The accurate measurement of the breath intervals using an electronic system allows for additional tests to validate the RR estimation. We use the measure of consistency (% deviation from the median tap time) to exclude aberrant breath intervals while the measurement process is ongoing. We hypothesize that:

RR estimations using median tap interval times can provide a RR in less than 60 s, therefore increasing efficiency compared to the recommended 60 s counting.

Accuracy improves when more taps are included in the calculation of the median RR.

Accuracy improves when inconsistent time intervals are excluded.

In this manuscript we present the development of the algorithms to calculate RR from tapping time intervals and demonstrate the gain in efficiency through experimental tests using standardized videos of children breathing at a wide range of RRs. A sensitivity analysis and optimization experiment for the novel algorithm will facilitate the definition of target product profiles and device specifications for the development of RR measuring devices that allow for shorter assessments to increase acceptance with health care practitioners.

RR is calculated from the median time interval

The consistency C of a measurement is reported as the maximum percentage of absolute deviation of each time interval

A RR calculated from a set is reported if the consistency C is equal or lower than a consistency threshold

The median time interval

A mobile phone application called

The application allows the user to measure at any RR between 2 and 140 breaths/min and displays the number of taps completed (

A button records taps and an indicator displays how many taps have been performed (bottom).

An animated (chest, shoulder and mouth) baby presents the RR. The timing of the animation can be reset with a tap. The consistency of the tap intervals is displayed on the bottom of the screen as blue dots.

For conducting the present study, the ^{rd}

The protocol for this study (video recording and assessment of accuracy) was approved by The University of British Columbia/Childrens and Womens Health Centre of British Columbia Research Ethics Board, Vancouver, Canada (#H13-01116). Written informed consent was obtained from study subjects or in the case of minors, from their parent or guardian, before enrollment into the study.

De-identified video recordings were made of 23 anesthetized children, aged 0–5 years, breathing for a period of 3–5 minutes, at the British Columbia Children's Hospital, Vancouver, Canada. Only the exposed chest and abdomen were included in the field of view of the video. No facial features or any other identifying features were recorded.

Five cases of controlled and 5 cases of spontaneous ventilation were selected for use as standard videos. The RR ranged from 17 to 59 breaths/min (

Ventilation | Age (months) | RR (breaths/min) |

Controlled | 56 | |

23 | 33 | |

23 | 59* | |

36 | 47* | |

43 | 51* | |

Spontaneous | 23 | 30 |

23 | 38 | |

25 | 24 | |

53 | 17 | |

59 | 17 |

Adult subjects were recruited among trainee, volunteer and staff population from the British Columbia Children's Hospital. Their age, gender, education level, profession and mobile phone use familiarity _{C}_{C}

In Phase II the test for consistency was enabled to provide a more realistic use scenario. The parameters were set to a conservative threshold (z = 4, Th_{C}

We performed a sensitivity analysis on Phase I data where 60 s of tapping was available to study the effects of Th_{C}_{C}

The estimated RR was compared to the reference RR for accuracy. We used normalized root mean square error (NRMSE) as a measure for accuracy, such as_{ref}

The time taken for completing the tapping measurement depends on the RR to be measured, the number of tap intervals z required in a set, and the consistency threshold Th_{C}

In cases where a valid set was not completed for a given combination of parameters within 60 s, E was set to 60 s, no RR was reported and the completion rate (CR) was reduced, thus penalizing the parameter choice. CR was calculated such as

We built a linear regression model to determine the relationship between NRMSE, E and the number of consecutive time intervals z and the consistency threshold Th_{C}

There is a trade-off between accuracy and efficiency. While a small consistency threshold Th_{C}_{C}_{C}

gives the most accurate RR measurement (lowest NRMSE);

in the least amount of time (in terms of median and 95^{th}

with the highest CR (where a RR is reported in 60 s or less).

For this, we used a cost function analysis, such as^{th}

The optimization experiment was performed using a 15-fold cross-validation on the combined data set from Phase I and II. Two observations for each video were randomly assigned to one of 15 data bins. A single data bin was then selected as a test set and the remaining bins are used as a training set. This was repeated until all data bins, and consequently each observation, were used once as a test set. The parameters with the smallest costs were selected in each repetition. The optimal parameters from each repetition were then ranked and the most frequent occurrence was reported and selected to calculate the performance of the test sets. The performance of the RR from the median tap intervals of the selected tap interval number without consistency test (z = 4, no Th_{C}

Thirty-two adult subjects were recruited from the British Columbia Children's Hospital's trainee, volunteer and staff population. Twenty-two subjects measured RR using the mobile app for 60 s (Phase I). Ten subjects from the nursing staff measured RR using the mobile app until a consistent set was obtained (Phase II). Two subjects from Phase II were excluded for not completing all videos. Subject demographics and mobile phone use familiarity are summarized in

Phase I (60 s, no Th_{C}) |
Phase II (z = 4, Th_{C} = 6) |
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Category | Subcategory | n | % | n | % |

Age | 15 | 68.18 | 0 | 0.00 | |

31–40 y | 5 | 22.73 | 1 | 12.50 | |

41–50 y | 1 | 4.55 | 3 | 37.50 | |

51–60 y | 1 | 4.55 | 4 | 50.00 | |

Gender | Female | 13 | 59.09 | 8 | 100.00 |

Male | 9 | 40.91 | 0 | 0.00 | |

Highest Education | High School | 4 | 18.18 | 0 | 0.00 |

Undergraduate | 10 | 45.45 | 4 | 50.00 | |

Postgraduate | 8 | 36.36 | 4 | 50.00 | |

Profession | Researcher | 9 | 40.91 | 0 | 0.00 |

Medical Student | 7 | 31.82 | 0 | 0.00 | |

Engineer | 6 | 27.27 | 0 | 0.00 | |

Registered Nurse | 0 | 0 | 8 | 100.00 | |

Type of Mobile User |
Voice/Text Fanatic | 10 | 45.45 | 4 | 50.00 |

Mobile Elite | 5 | 22.73 | 1 | 12.50 | |

Minimalist | 5 | 22.73 | 3 | 37.50 | |

Display Maven | 2 | 9.09 | 0 | 0.00 |

There was a clear reduction of NRMSE with increased number of intervals (z) used to calculate the median respiratory interval, without using a Th_{C}_{C}_{C}

The normalized root mean square error (NRMSE) of counting taps in 60 s is depicted as a dashed line; the NRMSE of the RR obtained from the median tap times of all taps in 60 s is depicted as a dotted line.

NRMSE decreased (accuracy improved) with tighter consistency thresholds and with increasing number of intervals in a set. At lower Th_{C}

The linear regression model for NRMSE indicated that 97% of the variability in NRMSE can be accounted for by z and Th_{C}_{C}

Accuracy improved (smaller NRMSE) when Th_{C}_{C}^{2} to y^{2} for y =

The mean time taken for measurement increased when the number of time intervals in a set increased, and when Th_{C}_{C}_{C}^{th}

_{C}

Improving the accuracy (smaller NRMSE) was at the cost of increasing the time taken for measurement (_{C}

Increasing the accuracy (smaller NRMSE) is at the cost of increasing

The cost function analysis revealed that the parameter combination z = 4, Th_{C}_{C}^{th}

Adding a Th_{C}

The mean difference (bias) is −0.13 breaths/min and the standard deviation (SD) is 1.98 breaths/min. The number of observations is displayed as marker intensity. The dashed lines represent the 95^{th}

15 repetitions | z = 4, Th_{C} |
z = 4, no Th_{C} |

NRMSE (%) | 5.6±1.1 | 7.4±1.4 |

8.1±1.2 | 6.9±0.1 | |

9.9±0.6 | 7.9±0.2 | |

17.6±2.7 | 14.9±0.2 | |

CR (%) | 100 | 100 |

We developed a mobile phone application that calculates the RR by measuring the time intervals between breaths by tapping the screen of a mobile device. Efficiency E was significantly improved compared to conventional methods that require counting for 60 s. The introduction of a consistency threshold Th_{C}

The mobile phone application ^{th}

Accuracy increased with the number of breaths included in a set of taps to calculate the median. When ignoring the Th_{C}_{C}

The sensitivity analysis showed that excluding inconsistent tapping improved the estimation for a large range of tapping interval numbers. The measurement of consistency (maximum deviation of the median) allowed for instant rejection of aberrant taps. It also gave a measure of confidence to the performed measurement. The consistency between the taps performed depended on the natural variation of breathing and the accuracy of the taps performed by the user. An excessively restrictive consistency threshold would exclude natural variation of breaths and impact the usability of the method, forcing the user to tap for longer than 60 s. On the other hand, an overly relaxed consistency threshold would allow for user mistakes and negatively impact accuracy. Similarly, including a large number of breaths in a set would be detrimental to efficiency by increasing the minimum number of times a user had to tap before obtaining a RR, while using very few breaths to calculate the median would decrease accuracy. In previous work we have shown that accuracy of RR estimations obtained simultaneously from three independent sources can be improved when testing for agreement and excluding observations with large deviations from the mean RR

The standard videos used for the sensitivity analysis contained a wide spectrum of RRs, including fast breathing. However, these videos do not represent all possible breathing patterns. For example, in neonates the breathing variation is increased through periodic breathing, a normal breathing pattern characterized by alternating between regular breathing and short periods of apnea _{C}

The improvement in estimation of a rate using the continuous analysis of time intervals instead of counting of events in a fixed time interval is not entirely new and has been shown to be effective in improving efficiency and accuracy of rate estimations

Mobile technology is ubiquitous, even in developing countries and rural parts of the world

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We would like to thank Jim Phillip for generously contributing his work on the development of the counting methods