# Cough Expired Volume and Cough Peak Flow Rate Estimation Based on GA-BP Method

Authors: Shuai Ren; Jinglong Niu; Zihao Luo; Yan Shi; Maolin Cai; Zujin Luo; Qihui Yu
Journal: Complexity
 (2020)

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## Abstract

Cough is a respiratory protective behavior for clearing the secretion. The cough process can be characterized by three features which are cough peak flow rate, peak velocity time, and cough expired volume. The cough expired volume (CEV) and the cough peak flow rate (CPFR) are important for medical diagnosis and cough effectiveness assessment. In this study, the CEV and CPFR values of 700 healthy participants were measured and collected by using a portable pulmonary function device. The gender, age, height, weight, and smoking status information of the 700 participants were also collected. Meanwhile, the integration of backpropagation neural network and genetic algorithm (GA-BP) method was developed to estimate CEV and CPFR values. The results showed that the estimation accuracy of GA-BP method exceeds 90%, which indicates that the GA-BP method could be effectively used for CEV and CPFR value estimation. Furthermore, the method proposed in this paper could be useful for medical diagnosis and medical device development.


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## Body

## 1. Introduction

Cough is a kind of respiratory reflex behavior. When the respiratory tract is stimulated by inflammation, dust, or some particulate matters, cough behavior is performed to clear respiratory secretions to keep the respiratory tract clean and unobstructed [1–5]. Because of the high pressure difference between the inside and outside of the thoracic cavity, a high airflow rate is generated to impose a great shear force on the surface of secretions and propel them to the mouth [6].According to previous studies, the cough process continued about 0.4∼0.6 s and can be characterized by three parameters which are cough peak flow rate (CPFR), peak velocity time (PVT), and cough expired volume (CEV) [7–10]. The CEV and CPFR are the total exhausted air volume and the maximum airflow rate measured in atmosphere normal reference during the whole cough process, respectively.The cough expired volume (CEV) and the cough peak flow rate (CPFR) are important for medical diagnosis, cough effectiveness assessment, and extubation decision [11–13]. However, as for the patients with mechanical ventilation, neuromuscular disease, or other diseases which impairs the cough ability, the CEV and CPFR values cannot be obtained and used for medical diagnosis. Therefore, establishing a relationship between the CEV, CPFR values and human physical information could be used for medical diagnosis for these patients. If the physical information is obtained, the CEV and CPFR values will be estimated.Previous studies have developed the relations between CEV and CPFR values and human genders, heights, and weights. Leiner et al. found that the CPFR is related to the height and age of human [14]. Mahajan et al. and Singh et al. involved the gender as an influence factor and developed relations between CPFR, CEV, and PVT [8, 9]. Their research involved 100 healthy and nonsmoking volunteers (50 females and 50 males) and showed a direct relationship between CPFR and CEV values [8]. The results showed that the maximum value of CEV reached 5 L with an average of 3 L. Zhu et al. measured the CEV values of three healthy subjects and found that the variation range from 0.8 to 2.2 L with an average of 1.4 L [15]. Gupta et al. investigated 25 healthy subjects (12 females and 13 males) and developed a first-order relation between CEV, CPFR values and genders, heights, and weights through the linear regression analysis method [7]. The results are performed as follows:(1)CPFRLs=−8.8980+6.3925hm+0.0346wkg,for male,CPFRLs=−3.9702+4.6265hm,for female,CEVL=0.138CPFRLs+0.2983m,for male,CEVL=0.0204CPFRLs−0.043m,for female.Brandimore et al. established a linear relation among CEV values, airflow rates, and number of coughs through analyzing the measured data of 25 participants (14 females and 11 males with an average of 23 years old). The results demonstrated significant linear relationships between expired volume, the total number of coughs, and cough airflow rates [6]. Particle velocimetry (PIV) method has been also used to estimate ranges of cough velocities. Chao et al. collected the average velocity of 50 coughs from eleven healthy volunteers (3 men and 8 women). The estimated maximum cough velocities of male and female were 13.2 m/s and 10.2 m/s, respectively [16]. VanSciver et al. performed over twenty-nine nonsmoking healthy volunteers (ten male and nineteen female volunteers) to obtain and analyze the cough velocity. The results showed that there is no correlation between cough velocity and sex and weight [10].In this study, 700 healthy participants were involved. The CEV values, CPFR values, genders, heights, weights, ages, and smoking status were measured and recorded. Meanwhile, the integration of backpropagation neural network and genetic algorithm, which is called the GA-BP method was developed to estimate CEV and CPFR values.


## 2. Materials and Methods

### 2.1. Experiment Setup

The CEV and CPFR values were measured by using a portable pulmonary function device (Contec Ltd.), which are presented in Figure1. The CEV and CPFR values acquisition range from 0 to 10 L and 0∼16 L/s, respectively. The acquisition errors are within ±0.05 L and 0.2 L/s, respectively. A disposable connector is installed in the front of the device during the collection. The human subjects hold the connector with their mouths and cough forcefully. After a single cough, the CEV and CPFR values will be displayed on the device screen and stored in the device.Figure 1
Portable pulmonary function device (Contec Ltd.). The CEV and CPFR values can be displayed on the screen and stored in the device. The data can be transmitted to the computer through Bluetooth function.All the participants were receiving the training of how to use this device before measurement. Sitting posture was adopted during measurement.


### 2.2. Ethical Statement

The CEV, CPFR values, and physical information of 700 human subjects were obtained by the doctor at the Chao Yang Hospital. All the human subjects were agreed to conduct these measurements and signed the informed content. The Chao Yang Hospital ethics committee and human subjects have approved these data collection (Approval number: 20175241).


### 2.3. Backpropagation Neural Network

BP neural network is a multilayer feedforward neural network with the forward signal transmission and reverse error transmission and could be used to estimate any nonlinear relations through training [17–20]. Typically, the BP neural network consists of the input layer, hidden layer, and output layer. The input signals are processed layer by layer from the input layer through the hidden layer to the output layer. If the expected output is not achieved, the signals transfer to backpropagation. According to the prediction error, the neural network weights and threshold values adjust to obtain the expected output values [21–24].In this study, five inputs which represent gender, height, weight, age, and smoking status, and two outputs which represent CEV and CPFR value are set up in the BP neural network. The structure of the BP neural network is presented in Figure2. The neuron number of hidden layers is set to 11 based on the Hecht–Nelson method.Figure 2
The BP neural network structure used in this study. A three-layer structure was adopted. There are five neurons in the input layer, eleven neurons in the hidden layer, and two neurons in the output layer.


### 2.4. BP Neural Network Improved by Genetic Algorithm

Although BP neural network can obtain a good estimated result through the training process, the training time is too long and the results may converge to local optimal values. Genetic Algorithm (GA) is a parallel random search optimization method, which imitates the natural genetic mechanism and Darwin’s principle of biological evolution [25–27]. Therefore, the BP neural network is improved by genetic algorithm (GA) to solve this problem, which is called GA-BP [28–30]. The GA-BP algorithm is used to search for the most preferable weights and thresholds of neural network. The whole operation process includes initialization, calculating fitness values, selection, crossover, and mutation. This process repeats until the end condition is satisfied.The data set which consists of the connection weights and thresholds of neural network is regarded as an individual. As shown in Figure3, the real number coding was used to create the initial values for each individual which consists of ωij, a, ωjk, and b. The ωij and ωjk represented the weights between the input layer and hidden layer and the weights between the hidden layer and output layer, respectively. The a and b represented the thresholds of the hidden layer and output layer, respectively. The number of individuals was set ten in this study.Figure 3
The diagram of real number coding of individual. The weightsωij and ωjk and thresholds a and b are arranged serially in a single individual.The absolute error between predicted and expected output of BP neural network was used as the individual fitness value in this study. The fitness function is as below:(2)E=∑i=1mYi−Oi,where E is the individual fitness value, m is the number of neurons in output layer, and Yi and Oi are the predicted output and expected output of the network, respectively.The goal of selection is that individuals with lower fitness have a greater chance to inherit to the next generation. The roulette method was used for selection operation in this study, as shown in the following formula:(3)fi=kEi,pi=fi∑j=1Nfj,where p is the chosen probability of each individual, k is the coefficient, and N is the number of individuals.The crossover probability was set 0.5. The crossover operation for individualak and al at the j position was presented in equation (4). The diagram is shown in Figure 4.(4)akj∗=akj⋅1−α+alj⋅α,alj∗=alj⋅1−α+akj⋅α,where α is a random number between [0∼1].Figure 4
An example of crossover operation. The crossover operation for individualak and al performs at the j position. Part of the chromosome information has been exchanged for ak and al.The mutation probability was set 0.4 and the diagram is shown in Figure5. The new chromosome aij∗ is calculated through equation (5).where amax and amin are the upper bound and lower bound of gene aij, respectively. The r2 is a random number, g is the current iteration number, Gmax is the maximum evolution number, and r is a random number between [0∼1].Figure 5
An example of mutation operation. The chromosome information atj position of ai has been altered.(5)
a
i
j
∗
=
a
i
j
+
a
i
j
−
a
max
f
g
,
r
>
0.5
,
a
i
j
+
a
min
−
a
i
j
f
g
,
r
<
0.5
,
f
g
=
r
2
1
−
g
G
max
2
,The iteration was set 40. The operation process of GA-BP is presented in Figure6.Figure 6
The operation process of GA-BP. The GA-BP starts with GA which optimizes the initial values of weight and threshold of the BP neural network. Then, the BP neural network begins training with the optimized weights and thresholds until the end condition is satisfied.


## 2.1. Experiment Setup

The CEV and CPFR values were measured by using a portable pulmonary function device (Contec Ltd.), which are presented in Figure1. The CEV and CPFR values acquisition range from 0 to 10 L and 0∼16 L/s, respectively. The acquisition errors are within ±0.05 L and 0.2 L/s, respectively. A disposable connector is installed in the front of the device during the collection. The human subjects hold the connector with their mouths and cough forcefully. After a single cough, the CEV and CPFR values will be displayed on the device screen and stored in the device.Figure 1
Portable pulmonary function device (Contec Ltd.). The CEV and CPFR values can be displayed on the screen and stored in the device. The data can be transmitted to the computer through Bluetooth function.All the participants were receiving the training of how to use this device before measurement. Sitting posture was adopted during measurement.


## 2.2. Ethical Statement

The CEV, CPFR values, and physical information of 700 human subjects were obtained by the doctor at the Chao Yang Hospital. All the human subjects were agreed to conduct these measurements and signed the informed content. The Chao Yang Hospital ethics committee and human subjects have approved these data collection (Approval number: 20175241).


## 2.3. Backpropagation Neural Network

BP neural network is a multilayer feedforward neural network with the forward signal transmission and reverse error transmission and could be used to estimate any nonlinear relations through training [17–20]. Typically, the BP neural network consists of the input layer, hidden layer, and output layer. The input signals are processed layer by layer from the input layer through the hidden layer to the output layer. If the expected output is not achieved, the signals transfer to backpropagation. According to the prediction error, the neural network weights and threshold values adjust to obtain the expected output values [21–24].In this study, five inputs which represent gender, height, weight, age, and smoking status, and two outputs which represent CEV and CPFR value are set up in the BP neural network. The structure of the BP neural network is presented in Figure2. The neuron number of hidden layers is set to 11 based on the Hecht–Nelson method.Figure 2
The BP neural network structure used in this study. A three-layer structure was adopted. There are five neurons in the input layer, eleven neurons in the hidden layer, and two neurons in the output layer.


## 2.4. BP Neural Network Improved by Genetic Algorithm

Although BP neural network can obtain a good estimated result through the training process, the training time is too long and the results may converge to local optimal values. Genetic Algorithm (GA) is a parallel random search optimization method, which imitates the natural genetic mechanism and Darwin’s principle of biological evolution [25–27]. Therefore, the BP neural network is improved by genetic algorithm (GA) to solve this problem, which is called GA-BP [28–30]. The GA-BP algorithm is used to search for the most preferable weights and thresholds of neural network. The whole operation process includes initialization, calculating fitness values, selection, crossover, and mutation. This process repeats until the end condition is satisfied.The data set which consists of the connection weights and thresholds of neural network is regarded as an individual. As shown in Figure3, the real number coding was used to create the initial values for each individual which consists of ωij, a, ωjk, and b. The ωij and ωjk represented the weights between the input layer and hidden layer and the weights between the hidden layer and output layer, respectively. The a and b represented the thresholds of the hidden layer and output layer, respectively. The number of individuals was set ten in this study.Figure 3
The diagram of real number coding of individual. The weightsωij and ωjk and thresholds a and b are arranged serially in a single individual.The absolute error between predicted and expected output of BP neural network was used as the individual fitness value in this study. The fitness function is as below:(2)E=∑i=1mYi−Oi,where E is the individual fitness value, m is the number of neurons in output layer, and Yi and Oi are the predicted output and expected output of the network, respectively.The goal of selection is that individuals with lower fitness have a greater chance to inherit to the next generation. The roulette method was used for selection operation in this study, as shown in the following formula:(3)fi=kEi,pi=fi∑j=1Nfj,where p is the chosen probability of each individual, k is the coefficient, and N is the number of individuals.The crossover probability was set 0.5. The crossover operation for individualak and al at the j position was presented in equation (4). The diagram is shown in Figure 4.(4)akj∗=akj⋅1−α+alj⋅α,alj∗=alj⋅1−α+akj⋅α,where α is a random number between [0∼1].Figure 4
An example of crossover operation. The crossover operation for individualak and al performs at the j position. Part of the chromosome information has been exchanged for ak and al.The mutation probability was set 0.4 and the diagram is shown in Figure5. The new chromosome aij∗ is calculated through equation (5).where amax and amin are the upper bound and lower bound of gene aij, respectively. The r2 is a random number, g is the current iteration number, Gmax is the maximum evolution number, and r is a random number between [0∼1].Figure 5
An example of mutation operation. The chromosome information atj position of ai has been altered.(5)
a
i
j
∗
=
a
i
j
+
a
i
j
−
a
max
f
g
,
r
>
0.5
,
a
i
j
+
a
min
−
a
i
j
f
g
,
r
<
0.5
,
f
g
=
r
2
1
−
g
G
max
2
,The iteration was set 40. The operation process of GA-BP is presented in Figure6.Figure 6
The operation process of GA-BP. The GA-BP starts with GA which optimizes the initial values of weight and threshold of the BP neural network. Then, the BP neural network begins training with the optimized weights and thresholds until the end condition is satisfied.


## 3. Results

The statistical results of collected physical information (gender, age, height, weight, and smoking status), CEV, and CPFR values of 700 human subjects are presented in Table1.Table 1
Statistical results of data for 700 subjects.
Parameters
Value
Number of males
430
Number of females
270
Number of smokers
106
Number of nonsmokers
594
Average of age
23.71
Standard deviation of age
8.36
Average of height (cm)
171.01
Standard deviation of height (cm)
7.68
Average of weight (kg)
66.60
Standard deviation of weight (kg)
13.41
Average of CEV (L)
1.54
Standard deviation of CEV (L)
0.77
Average of CPFR (L/s)
6.25
Standard deviation of CPFR (L/s)
1.72In order to testify the GA-BP method, the ten times tenfold cross-validations method was adopted. 700 groups of data were randomly divided into tenfolds, each fold contains 70 groups of data. Ninefold data were used to train the GA-BP network. The remaining onefold data is used for validation. Through ten different random groupings and exchanging the training and test data, we conducted ten times tenfold cross-validations. The statistical results of data for ten times tenfold cross-validations from test 1 to test 10 are presented in Tables2 and 3.Table 2
Statistical results of data for ten times tenfold cross-validations (test 1 to test 5).
Parameters
Test 1
Test 2
Test 3
Test 4
Test 5
Training group
Validation group
Training group
Validation group
Training group
Validation group
Training group
Validation group
Training group
Validation group
Number of males
390
40
391
39
384
46
391
39
389
41
Number of females
240
30
239
31
246
24
239
31
241
29
Number of smokers
95
11
97
9
96
10
93
13
94
12
Number of nonsmokers
535
59
533
61
534
60
537
57
536
58
Average of age
23.87
22.30
23.73
23.50
23.70
23.86
23.72
23.67
23.53
25.33
Standard deviation of age
8.41
7.70
8.48
7.15
8.43
7.64
8.34
8.52
8.29
8.74
Average of height (cm)
171.02
170.89
171.00
171.07
171.07
170.47
171.03
170.74
171.00
171.01
Standard deviation of height (cm)
7.62
8.25
7.64
8.07
7.86
5.84
7.70
7.56
7.67
7.84
Average of weight (kg)
66.76
65.09
66.66
65.99
66.60
66.56
66.62
66.39
66.70
65.71
Standard deviation of weight (kg)
13.08
15.99
13.50
12.53
13.42
13.30
13.39
13.54
13.61
11.33
Average of CEV (L)
1.55
1.46
1.54
1.61
1.54
1.58
1.55
1.51
1.54
1.57
Standard deviation of CEV (L)
0.76
0.82
0.77
0.76
0.78
0.65
0.77
0.80
0.77
0.75
Average of CPFR (L/s)
6.26
6.08
6.23
6.37
6.25
6.24
6.26
6.15
6.24
6.29
Standard deviation of CPFR (L/s)
1.71
1.85
1.72
1.70
1.76
1.37
1.71
1.79
1.71
1.78Table 3
Statistical results of data for ten times tenfold cross-validations (test 6 to test 10).
Parameters
Test 1
Test 2
Test 3
Test 4
Test 5
Training group
Validation group
Training group
Validation group
Training group
Validation group
Training group
Validation group
Training group
Validation group
Number of males
385
45
382
48
382
48
388
42
388
42
Number of females
245
25
248
22
248
22
242
28
242
28
Number of smokers
99
7
95
11
94
12
100
6
91
15
Number of nonsmokers
531
63
535
59
536
58
530
64
539
55
Average of age
23.62
24.53
23.63
24.47
23.73
23.50
23.73
23.57
23.86
22.39
Standard deviation of age
8.21
9.51
8.21
9.58
8.49
7.00
8.27
9.10
8.42
7.67
Average of height (cm)
171.02
170.87
170.83
172.60
170.93
171.64
171.12
169.97
171.03
170.79
Standard deviation of height (cm)
7.68
7.68
7.67
7.63
7.63
8.09
7.67
7.71
7.69
7.62
Average of weight (kg)
66.66
66.04
66.21
70.08
66.42
68.15
66.61
66.52
66.73
65.43
Standard deviation of weight (kg)
13.50
12.57
13.26
14.19
13.48
12.62
13.39
13.58
13.43
13.18
Average of CEV (L)
1.55
1.46
1.52
1.73
1.53
1.67
1.56
1.44
1.56
1.43
Standard deviation of CEV (L)
0.77
0.75
0.76
0.81
0.77
0.77
0.77
0.78
0.77
0.73
Average of CPFR (L/s)
6.26
6.10
6.20
6.65
6.21
6.54
6.27
6.03
6.27
6.01
Standard deviation of CPFR (L/s)
1.73
1.65
1.70
1.86
1.71
1.83
1.73
1.64
1.74
1.56The relative errors between estimated and test values for CEV and CPFR in ten times tenfold cross-validations are calculated and presented in Figures7 and 8, respectively.Figure 7
The relative errors between estimated and test CEV values in ten times tenfold cross-validations. The relative errors within 10% were marked green circles while beyond 10% were marked blue circles. (a) Test (1). (b) Test (2). (c) Test (3). (d) Test (4). (e) Test (5). (f) Test (6). (g) Test (7). (h) Test (8). (i) Test (9). (j) Test (10).Figure 8
The relative errors between estimated and test CPFR values in ten times tenfold cross-validations. The relative errors within 10% were marked yellow squares while beyond 10% were marked blue squares. (a) Test (1). (b) Test (2). (c) Test (3). (d) Test (4). (e) Test (5). (f) Test (6). (g) Test (7). (h) Test (8). (i) Test (9). (j) Test (10).


## 4. Discussion

There were 700 participants (430 males and 270 females) involved in this study. There were 106 smokers, accounting for about 15% of the total. The age, height, weight, CEV, and CPFR values were collected and analyzed. The average of CEV and CPFR were 1.54 L and 6.25 L/s, respectively. It is adapt to the statistical results of physical information of participants which presents a young state.The ten times tenfold cross-validations method was adopted to verify the GA-BP method. From Tables2 and 3, we found that the average and standard deviation values of age, height, weight, CEV, and CPFR values of training groups were approximate with that of validation groups in all ten times validations. It indicated that all the training and validations groups were selected randomly and the estimated results were reliable.It is considered that the estimated value is acceptable and relatively accurate when the absolute error is within 10% in this study. From the ten times validation results in Figures7 and 8, we find that the relative errors of a large number of test samples are within 10% for both CEV and CPFR values. The accuracy of ten times validations and the average values for CEV and CPFR estimations are calculated and presented in Table 4. From Table 4, we found that the accuracy of CEV and CPFR value estimations exceeded the 90% in all ten times validations. The averages of CEV and CPFR estimation accuracy were 95% and 94.57%, respectively. The results indicated that the GA-BP method has a high accuracy and could be effectively used for CEV values and CPFR values estimation.Table 4
The accuracy of ten times validations and the average values for CEV and CPFR values estimations.
Test group
CEV estimation accuracy (%)
The average of CEV estimation accuracy (%)
CPFR estimation accuracy (%)
The average of CPFR estimation accuracy (%)
Test (1)
91.43
95.00
91.43
94.57
Test (2)
95.71
92.86
Test (3)
94.29
94.29
Test (4)
92.86
98.57
Test (5)
97.14
94.29
Test (6)
91.43
92.86
Test (7)
95.71
91.43
Test (8)
95.71
97.14
Test (9)
98.57
97.14
Test (10)
97.14
95.71Considering the low sampling frequency of the portable pulmonary function device, the PVT value estimation is not completed in this study. Even the estimation accuracy is high under current condition and more data especially in a large span of age, height, weight, and other physical information should be involved and used for improving the generalization ability.


## 5. Conclusions

The heights, weights, ages, smoking status, CEV, and CPFR values of 700 participants were collected and analyzed in this paper. The GA-BP method which integrates backpropagation neural network and genetic algorithm was developed to estimate the CEV and CPFR values. Additionally, the ten times tenfold cross-validation method was adopted to testify the GA-BP method. The results show that the estimation accuracy of GA-BP method used for CEV and CPFR values both exceeds 90%. The averages of CEV and CPFR estimation accuracy reached 95% and 94.57%, respectively. The estimation results verified the accuracy of the GA-BP method.In the future study, the PVT value estimations will be completed. More information such as compliance and resistance will be measured and used in the GA-BP method to improve the generalization ability.



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*Source: 9036369-2020-02-26.xml*