# A Mobile Cough Strength Evaluation Device Using Cough Sounds

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^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Proposed Device

#### 2.1. Model

_{0,(1)}, α

_{1,(1)}and β

_{(1)}are the parameters predetermined by a non-linear regression analysis (the Levenberg-Marquardt method) using the mean square error between the CPS

_{proposed}and the measured CPF as the evaluation function. The CPSL represents the cough peak sound pressure level. This model indicates that the cough peak flow (estimated CPF (CPS

_{proposed})) and the CPSL are logarithmically related. The next section describes the preprocessing method used to derive the CPSL from cough sounds, which can be measured using a smartphone.

#### 2.2. Measurement Protocol and Preprocessing for Cough Sounds

_{proposed}).

#### 2.3. User Interface Software

_{1}), measured CPF, and results of an objective swallowing function test, such as the repetitive saliva swallowing test (RSST), which detects patients who experience aspiration [10,11,12]. The bottom of the screen shows the history of the estimated CPFs to inform the user of chronical changes in cough function.

_{proposed}) is classified into four risk levels based on previously reported cut-off values [3,4,5,11], as shown below and in Figure 3:

## 3. Experiments

#### 3.1. Participants

_{1}, and FVC, and excluded those participants with FEV

_{1}/FVC < 80% and those who could not perform the measurement. As a result, two elderly participants with FEV

_{1}/FVC < 80% were excluded, representing 3.3% of all participants.

#### 3.2. Methods

#### 3.2.1. Cough Flow and Sound Measurement Methods

_{proposed}and those estimated by the model shown in Equations (2)–(6) explained in the following subsections as CPS

_{X}, where the subscript X distinguishes the model used.

#### 3.2.2. Models for Age Effect Analysis

_{0,(Y)}to α

_{3,(Y)}and β

_{(Y)}are constant parameters determined by the Levenberg-Marquardt method using the mean square error between the CPS

_{X}and measured CPF as the evaluation function; the subscript, Y, distinguishes the model. The 95% CIs are also calculated for each parameter. In addition, the parameters included in Equation (2) are determined by calculating the CPS using a previous model, such as α = 70.98 and β = 0.022, based on our previous study [8]. The Wilcoxon signed-rank test was used to compare the absolute error between the previous and proposed models. Spearman’s rank correlation coefficient analysis was used to assess the relationship between each CPS

_{X}and measured CPF. Absolute reliability was investigated using the Bland-Altman analysis method to detect systematic bias, such as fixed and proportional bias.

#### 3.2.3. Analysis of Models for Body Weight, BMI, and Height

_{w}, α

_{B}, and d

_{0}are constant parameters determined using the same method described in the previous section; weight, BMI, and height represent the participant’s body weight, BMI, and height, respectively; and α

_{0,(1)}, α

_{1,(1)}, and β

_{(1)}are the same values as those determined for the proposed model. The second term in the exponential function of Equation (6) (the height model) represents the correction term for the attenuation related to the participant’s height. A decrease in the sound level, L

_{p}, can be calculated by the distance (r, r

_{0}) between the sound source and the microphone, as follows:

_{0}and r are constants. Thus, to correct the CPSL for additional sound attenuation, height was inserted in Equation (6) instead of r. In this analysis, the coefficient of determination and the 95% CI were calculated for comparison with the proposed model (Equation (1)).

## 4. Results

#### 4.1. Parameter Determination

_{0}, α

_{1}, and β are as follows: a

_{0}= 42.90 (95% CI: 7.84 to 77.96), a

_{1}= −0.282 (95% CI: −0.509 to −0.055), and β = 0.028 (95% CI: 0.020 to 0.037); the determination coefficient of the proposed model is 0.829. In Equations (3) and (4), the coefficients are determined in the same manner as in the proposed model. Equation (3) yielded a determination coefficient of 0.829. The determined parameters are as follows: a

_{0}

_{,}

_{(3)}= 42.32 (95% CI: 7.15 to 77.50), a

_{1}

_{,}

_{(3)}= −0.212 (95% CI: −0.713 to 0.289), a

_{2}

_{,}

_{(3)}= −0.001 (95% CI: −0.006 to 0.004), and β

_{(3)}= 0.028 (95% CI, 0.020 to 0.037). The 95% CIs of the coefficients, a

_{1,(3)}and a

_{2,(3)}, in Equation (3) include 0. Equation (4) yielded a determination coefficient of 0.832. The determined parameters are as follows: a

_{0}

_{,}

_{(4)}= 6.58 (95% CI: −70.33 to 83.49), a

_{1}

_{,}

_{(4)}= 2.366 (95% CI: −3.448 to 8.181), a

_{2}

_{,}

_{(4)}= 0.00 (95% CI: 0.00 to 0.001), a

_{3}

_{,}

_{(4)}= −0.048 (95% CI: −0.156 to 0.060), and β

_{(4)}= 0.028 (95% CI, 0.020 to 0.037). The 95% CIs of all parameters, except for β

_{(4)}in Equation (4), include 0. The 95% CI indicates that only α

_{0,Y}, α

_{1,Y}, and β

_{Y}are valid parameters because the 95% CIs of the other parameters include 0.

#### 4.2. Estimation Accuracy

_{proposed}and measured CPF in the young and elderly participants. To compare the CPF estimation accuracy of the proposed and previous models, Figure 4b shows a plot of the CPS

_{previous}against the measured CPF. Spearman’s rank correlation coefficient analysis showed a significant positive correlation between the CPS

_{proposed}and measured CPF in both the young participants (r = 0.780; p < 0.001; power > 0.99) and the elderly participants (r = 0.750; p < 0.001; power > 0.99). For all participants, the Spearman’s rank correlation coefficient is r = 0.913, with p < 0.001 and power > 0.99, as shown in Figure 4a. In addition, Spearman’s rank correlation coefficient analysis showed a significant positive correlation between the CPS

_{previous}and CPF (young participants: r = 0.795; p < 0.001; power > 0.99, elderly participants: r = 0.765; p < 0.001; power > 0.99, all participants: r = 0.314; p = 0.016; power, 0.68), as shown in Figure 4b. Moreover, in young participants, the Wilcoxon signed-rank test showed no significant differences in the absolute error between the CPS

_{proposed}and CPS

_{previous}(6.19% vs. 8.95%, p = 0.085) (Figure 5a); however, in the elderly participants and all the participants, the Wilcoxon signed-rank test showed significant differences in the absolute error between the CPS

_{proposed}and CPS

_{previous}(13.55% vs. 90.01%; p < 0.001, 9.96% vs. 17.92%; p = 0.001, respectively) (Figure 5b,c). In addition, Figure 6 shows the corresponding Bland-Altman plots for the proposed and previous models. Neither model showed fixed bias, but both models showed proportional bias (r = −0.318; p = 0.015; power, 0.693, r = −0.523; p < 0.001; power, 0.991, respectively).

#### 4.3. Effects of Body Weight and BMI on CPF Estimation Accuracy

_{w}, a

_{B}, and d

_{0}, were determined as explained in Section 3.2.2. The determined parameters are as follows: a

_{w}= 0.137 (95% CI: −0.021 to 0.295) and a

_{B}= −0.303 (95% CI: −0.717 to 0.110). The 95% CIs of coefficients, a

_{w}and a

_{B}, in Equation (5) include 0, indicating that these parameters are not valid. Equation (5) yielded a determination coefficient of 0.839.

#### 4.4. Effect of Body Height on CPF Estimation Accuracy

_{0}= 141.6 (95% CI: 122.8 to 160.5). Equation (6) yielded a determination coefficient of 0.833. Spearman’s rank correlation coefficient analysis showed a significant positive correlation between the CPS

_{height}and measured CPF (young participants: r = 0.797; p < 0.001; power > 0.99, elderly participants: r = 0.772; p < 0.001; power > 0.99, all participants: r = 0.916; p < 0.001; power, 1), as shown in Figure 7a. In addition, Figure 7b shows the corresponding Bland-Altman plot of Equation (6). Equation (6) did not show fixed or proportional bias (r = −0.200; p = 0.133).

_{proposed}and CPS

_{height}, the absolute error was calculated. The Wilcoxon signed-rank test showed no significant differences in the absolute error between CPS

_{proposed}and CPS

_{height}(9.96% vs. 8.44%; p = 0.195), as shown in Figure 8.

#### 4.5. Examples of Elderly Participants

## 5. Discussion

_{w}and α

_{B}) included 0 (see Section 4.3), indicating that weight and BMI have minimal effects on the CPF estimation accuracy.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgements

## Conflicts of Interest

## References

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**Figure 1.**Cough sound measurement protocol and software configuration. CPS represents the cough peak flow estimated using cough sounds. (

**a**) The posture of a user while recording cough sounds. (

**b**) The user interface for editing a personal profile. (

**c**) The flow chart for cough sound preprocessing and cough peak flow (CPF) estimation. (

**d**) The results display that demonstrates the graphs resulting from signal preprocessing and CPF estimation.

**Figure 2.**Editorial part. This screen prompts the user to complete their personal profile. BMI, body mass index, BMI = body weight/height

^{2}; VC, vital capacity; FVC, forced vital capacity; FEV

_{1}, forced expiratory volume in 1 s; RSST, repetitive saliva swallowing test.

**Figure 3.**Results display part. The blue solid line represents the measured cough sound signal. The light blue solid line represents the rectified sound signal. The purple solid line represents the moving average with a time window of 20 ms. The red dot represents the maximum point of the moving average.

**Figure 4.**Estimation accuracy of CPS

_{proposed}and CPS

_{previous}. (

**a**) The CPF estimated by the proposed model (CPS

_{proposed}) against the measured CPF. (

**b**) Plot of the CPF estimated by the previous model (CPS

_{previous}) against the measured CPF. The red and blue circles represent the elderly and young participants, respectively. The linear regression lines are drawn for the groups of young and elderly participants, and the corresponding equations are shown in the upper part of each figure, where the green letters indicate the equation of the regression line for all participants. The right lower side shows the correlation coefficients and P values for each participant group.

**Figure 5.**Comparison of the absolute error between the proposed and previous models. (

**a**) Young participants, n = 33. (

**b**) Elderly participants, n = 25. (

**c**) All participants, n = 58.

**Figure 6.**Bland-Altman plots of the measured and estimated CPFs. (

**a**) The estimation accuracy of the proposed model (CPS

_{proposed}). (

**b**) The estimation accuracy of the previous model (CPS

_{previous}). The horizontal line is the mean of the measured CPF and estimated cough peak flow (CPS

_{X}). The vertical line represents the difference between the measured CPF and CPS

_{X}. The bold black solid lines represent the mean differences between the CPF and CPS

_{X}, and the red dotted lines represent the mean differences ± 2 standard deviations.

**Figure 7.**Estimation accuracy of CPS

_{height}. (

**a**) CPS

_{height}against the measured CPF. The linear regression lines are drawn for the young and elderly participant groups, and the corresponding equations are shown in the upper part of each figure, where the green indicates the equation of the regression line for all participants. The right lower part shows the correlation coefficients and p values for each participant group. (

**b**) Bland-Altman plot of the measured CPF and CPS

_{height}. The horizontal line is the mean of the measured CPF and CPS

_{height}. The vertical line represents the difference between the measured CPF and CPS

_{height}

_{.}The bold black solid lines represent the mean difference between the measured CPF and each CPS

_{height}, and the red dotted lines represent the mean difference ± 2 standard deviation bands.

**Figure 9.**Examples of elderly participants. The grey line represents the measured cough sound signal. The light blue solid line represents the bandpass-filtered and rectified sound signal. The purple solid line represents the moving average with a time window of 20 ms. The red circle represents the maximum point of the moving average. (

**a**) Example of a 77-year-old female with a measured CPF below the reference value of 270 L/min. The respiratory function test showed slightly low values of %VC = 83.5% and FEV

_{1}/FVC = 83.0%, but these values exceed the reference value. (

**b**) Example of a 70-year-old male with a measured CPF above the reference value of 270 L/min. The respiratory function test showed normal values of %VC = 91.6% and FEV

_{1}/FVC = 94.9%.

Variable | Young Participants (n = 33) | Elderly Participants (n = 25) | p Value |
---|---|---|---|

Age, years | 21.3 ± 0.4 | 80.4 ± 6.1 | < 0.001 |

Male sex, n | 20 | 10 | 0.209 |

Height, cm | 164.6 ± 8.4 | 154.1 ± 8.3 | 0.093 |

Body weight, kg (male, female) | 58.5 ± 11.6 (64.5 ± 11.3, 51.0 ± 6.2) | 55.1 ± 11.9 (58.6 ± 6.3, 53.4 ± 15.1) | 0.156 |

BMI, kg/m^{2}(male, female) | 21.3 ± 0.5 (21.4 ± 0.6, 20.9 ± 0.5) | 23.3 ± 4.1 (22.5 ± 1.6, 24.0 ± 5.2) | 0.216 |

%VC, % | 97.0 ± 8.9 | 91.5 ± 17.5 | 0.438 |

FEV_{1}/FVC, % | 90.4 ± 7.6 | 91.8 ± 8.2 | 0.185 |

_{1}, forced expiratory volume in 1 s; FVC, forced vital capacity.

Model | Parameter | Determined Value | Standard Error | 95% CI | Determination Coefficient | |
---|---|---|---|---|---|---|

Lower | Upper | |||||

Equation (1) | α_{0,(1)} | 42.90 | 17.50 | 7.84 | 77.96 | 0.829 |

α_{1,(1)} | −0.282 | 0.113 | −0.509 | −0.055 | ||

β_{(1)} | 0.028 | 0.004 | 0.020 | 0.037 | ||

Equation (3) | α_{0,(3)} | 42.32 | 17.54 | 7.15 | 77.50 | 0.829 |

α_{1,(3)} | −0.212 | 0.250 | −0.713 | 0.289 | ||

α_{2,(3)} | −0.001 | 0.002 | −0.006 | 0.004 | ||

β_{(3)} | 0.028 | 0.004 | 0.020 | 0.037 | ||

Equation (4) | α_{0,(4)} | 6.58 | 38.34 | −70.33 | 83.49 | 0.832 |

α_{1,(4)} | 2.366 | 2.899 | −3.448 | 8.181 | ||

α_{2,(4)} | 0.000 | 0.00 | 0.00 | 0.001 | ||

α_{3,(4)} | −0.048 | 0.054 | −0.156 | 0.060 | ||

β_{(4)} | 0.028 | 0.004 | 0.020 | 0.037 |

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**MDPI and ACS Style**

Umayahara, Y.; Soh, Z.; Sekikawa, K.; Kawae, T.; Otsuka, A.; Tsuji, T.
A Mobile Cough Strength Evaluation Device Using Cough Sounds. *Sensors* **2018**, *18*, 3810.
https://doi.org/10.3390/s18113810

**AMA Style**

Umayahara Y, Soh Z, Sekikawa K, Kawae T, Otsuka A, Tsuji T.
A Mobile Cough Strength Evaluation Device Using Cough Sounds. *Sensors*. 2018; 18(11):3810.
https://doi.org/10.3390/s18113810

**Chicago/Turabian Style**

Umayahara, Yasutaka, Zu Soh, Kiyokazu Sekikawa, Toshihiro Kawae, Akira Otsuka, and Toshio Tsuji.
2018. "A Mobile Cough Strength Evaluation Device Using Cough Sounds" *Sensors* 18, no. 11: 3810.
https://doi.org/10.3390/s18113810