The respiratory index (REX) used to classify the three levels.
The human walking behaviour can express the physiological information of human body, and gait analysis methods can be used to access the human body condition. In addition, the respiratory parameters from pulmonary spirometer are the standard of accessing the body condition of the subjects. Therefore, we want to show the correlation between gait analysis method and the respiratory parameters. We propose a vision sensor-based gait analysis method without wearing any sensors. Our method proposed features such as D′p, V′p and γυ to prove the correlation by classification and prediction experiment. In our experiment, the subjects are divided into three levels depending on the respiratory index. We run classifying and predicting experiment with the extracted features: V′p and γυ. In the classifying experiment, the accuracy result is 75%. In predicting experiment, the correlations of predicting the forced expiratory volume in 1 s (FEV1) and forced vital capacity (FVC) are 0.69 and 0.67, respectively. Therefore, there is a correlation between the pulmonary spirometer and our method. The radar system is a tool using impulse to record the moving of the subjects’ chest. Combining the features of radar system with our features improves the classification result from 75 to 81%. In predicting FEV1/FVC, the correlation also improves from 25 to 42%. Therefore, cooperating with radar system improves the correlation.
- gait analysis
- pattern recognition
- feature extraction
Walking behaviour can express information of human body-like pathological symptoms. For example, Parkinson’s disease patients are characterized by special pace rhythm .
People increase the respiratory ventilation when they are walking or exercising. However, those people who suffer from chronic obstructive airway disease (COAD) cannot increase their respiratory ventilation quick enough to maintain the exercising behaviour. Consequently, they change their behaviour such as walking slowly so that they can maintain their respiratory ventilation. We can perform gait analysis on COAD patients because their walking behaviours are different with normal people when they are exercising because of their respiratory function.
Chronic obstructive pulmonary disease (COPD) is one condition of COAD. Nowadays, there are many chronic diseases in our daily life. COPD is one of them. COPD is a chronic airway disease characterized by progressive going downhill of the breathing functions . One characteristic of COPD disease is the decreasing of forced expiratory volume in 1 s (FEV1) because of the obstructive airway . Depending on their disease severity, they have different walking behaviours. Therefore, gait analysis can be used to judge the COAD patients’ airway condition by observing their walking behaviour. However, it is difficult to collect the data of COAD patients without medical staff. Without clinical data, we cannot verify the correctness of our gait analysis algorithm.
By cooperating with Shuang-Ho Hospital in New Taipei, Taiwan, we set up an experiment. We film the side view of the subjects when they are performing a 6-min brisk walking test. By gait analysis, we can extract the features from walking behaviour such as pace distance and walking speed variation. However, in order to obtain that physiological information, we may need to wear sensors or markers on the subjects. Our method does not need to wear any sensors on the subjects.
In gait analysis, it is common to wear markers or sensors to record walking behaviour. In the experiment , the subjects need to wear a recorder on the ankle so that it could record the stride interval. In another experiment , the subjects also need to place a designed insole with 12 sensors into their own shoes.
However, there are some drawbacks of using makers or sensors. Firstly, it is inconvenient and uncomfortable of attaching them on human body and might affect the normal walking. Secondly, some sensors are heavy or hard to use for the elderly. Thirdly, some sensors have the electromagnetic interference that might affect and harm human body. In addition to the sensor problem, it is hard to tell a subject suffering from COAD disease or not by a single experiment. Without a complete examination, it is hard to judge whether the subjects are COAD patients or not. Consequently, we decide to access the respiratory function. By the pulmonary spirometer, we can obtain the tested subjects’ respiratory data. Nowadays, the parameters from pulmonary spirometer are the standard to access the respiratory function.
2. Related work
2.1. Chronic obstructive pulmonary disease
COPD is one condition of COAD and we introduce some studies of COPD disease. The research of the World Health Organization (WHO) and the global initiative for chronic obstructive lung disease revealed that nowadays the COPD is the fourth cause of death in the United States. For the entire world, the COPD can be considered the fifth cause of death . In another study, the COPD can be considered the fourth leading cause of death in the world  and is projected to be the fifth by 2020 as a worldwide burden of disease .
Generally speaking, chronic disease is gradually rising because of the ageing population and changing habits. The treatment for COPD patients is pulmonary rehabilitation programmes, including when patients are discharged at home . Economic analyses have shown that over 70% of COPD-related health-care expenditures result from emergency room visits and hospital care for exacerbations; this translates to >$10 billion annually in the Unites States . COPD patients have a lower physical activity level than healthy peers . The reduced level of physical activity also related to an increased risk . Liao et al.  proposed a review that concentrated on describing wearable devices for measuring physical activity level in COPD patients. In , the authors evaluated a method for detecting an exacerbation onset in COPD patients. They used data collected through a pulse oximeter, permitting an easy way to the cohort of patients composed of elderly people affected by COPD. The study  provided a system, which offers an effective platform for the satisfaction of the clinical and the patient’s needs in the area of early diagnosis of patient’s health status. The portable system aims at the effective management in the health status of the patients who are suffering from COPD.
2.2. Gait analysis
Gait analysis plays an important role in accessing human’s walking behaviour and it aims to extract biomechanics information. The obvious disease on lower limbs is Parkinson’s disorder. In , they provided a feasible method image marker to measure gait with little skin movement. Then, they performed quantitative analysis to extract gait parameter. According to their analysis, the joint angle, rotation angle of lower limbs, stride velocity and stride length have significant difference between Parkinson’s disease patients and non-diseased subjects. The study  demonstrated that the gait variability in terms of statistical parameters of stride interval such as STCγ, would be increased in Parkinson’s disorder. In addition to Parkinson’s disease, Alzheimer’s disease (AD) also can be detected by gait analysis. The study  presents an inertial-sensor-based wearable device and its associated stride detection algorithm to analyse gait information for patients with Alzheimer’s disease.
The above methods all use markers or sensors to get interest points and then use gait analysis. With the advances in smart phones, Susu Jiang et al.  used a smart phone with an accelerometer and a gyroscope to collect human walking gait data in daily life. However, one smart phone only records one feature data. If we want to acquire many interest point data, testers need to tie many smart phones on the body, which might be inconvenient for walking.
Now, we proposed a gait analysis algorithm without any wearable marker or sensor. In addition, we also collect clinical COAD and control data to verify the correlation between pulmonary spirometer and our gait analysis method.
3. Vision sensor-based gait analysis
To avoid wearing sensors on the tested subjects, we propose a vision sensor-based gait analysis method. This method is composed of four parts: input video frame decomposition, pre-processing, feature extraction and gait analysis. The input video takes the side view of the subjects when they are performing a 6-min brisk walking test. Then, the input video is decomposed into individual frames for further processing.
In the pre-processing part, there are three components to extract the silhouette of the tested subject: background subtraction, shadow removal and connected component labelling (CCL). The background subtraction subtracts the background image by the current video frame to capture the moving object. Because the human shadow cannot be removed by background subtraction, we adopt Jamie and Richard’s method  to solve the shadow problem. Then, there are some noises that cannot be removed, so we use the connected component-labelling method to reduce the noises and obtain the maximum object.
In the feature extraction part, there are two steps to obtain the desired features: segmentation and feature extraction. In the segmentation part, we have to find the central of gravity (COG) first, and use the COG point to perform body segmentation and extract legs of the subjects. Then, we can get the features such as pace distance and pace velocity in the feature extraction part.
In the gait analysis part, we divide whole subjects into two groups as the Bad and Good by consulting the proposed respiratory index formula. We use support vector machine (SVM) to perform classification and use adaptive network-based fuzzy inference system (ANFIS) to perform prediction.
3.1.1. Background subtraction
We take the first frame of the input video as the background image. The background subtraction method is shown in Eq. (1). The components x and y are the pixel location. The factor t is the current frame number. I represents the RGB value of the pixel, which is located at (x, y) and F is the -subtraction result. In our experiment, we set the Th-value at 15
3.1.2. Shadow removal
After subtract background image, some interferences still exist. The result of background subtraction is shown in Figure 1. The human shadow is viewed as foreground and we need to remove it. We consult Jamie and Richard’s  method to solve the shadow problem. The method is divided into two parts: (1) brightness distortion and (2) chromatic distortion.
Ii is the ith pixel of the input frame which can be represented in RGB space by the vector Ii = [(IR(i), IG(i))] as shown in Figure 2. Ei is the ith pixel of the background image which can be represented as Ei = [(ER(i), EG(i), EB(i))]. The lengths of these lines are the intensity of the ith pixel. The projection of Ii onto Ei is denoted as αiEi. We call the αi as brightness distortion. We can solve αi by Eq. (2)
There is a threshold τBD. We take those pixels whose αi values are smaller than threshold τBD as foreground such as Eq. (3) expressing. In our experiment, we set the threshold τBD at 0.7.
In the same way, we also set a threshold τCD to determine this pixel as background or foreground such as Eqs. (5) and (6) expressing. Those pixels whose CDi values are greater than threshold τCD are viewed as foreground and those pixels whose values are smaller as background. In our experiment, we set the threshold τCD at 10.
After finishing these two parts above, we combine these two images and the background subtraction result together to have a result without shadow.
3.1.3. Connected component labelling
Connected component labelling is used to detect the connected components and label them. These components have their own label number. Figure 3 shows an example. Figure 3(a) shows three different regions and (b) shows the labels of the regions. We keep the largest group as our result. In this case, the region of label 3 is reserved and discards other regions.
Though we have an image without shadow, some noises exist. We perform connected component labelling method so that we can have an image without these noises. Figure 4 shows the flow of pre-processing.
3.2. Feature extraction
After the pre-processing, we get the complete target silhouette. In this section, we separate legs from extracted silhouette by segmentation. Then, we find out the gait features such as pace distance and pace velocity in the feature extraction part.
In the segmentation part, we need to find the central of gravity first. Then, we use the extracted silhouette to get the contour by edge detection in order to build the distance map (DM). We can separate legs from human silhouette by DM.
We find the central of gravity from the extracted human silhouette by Eq. (7). After finding the COG of the whole body (COGx, COGy), we use edge detection on human silhouette to extract human contour such as in Figure 5. Then, we draw a DM by computing the Euclidean distance between (COGx, COGy) and extracted human contour shown in Figure 6(b). We compute the distance map by Eq. (8) and xi,yi are the location of the ith pixel of the extracted human contour.
We find the Nlegs, Nb2(l), Nb2(r) three points from DM as shown in Figure 6. Connecting Nb2(l) and Nb2(r) divides human body into top and down two parts. Connecting (COGx, COGy) and Nlegs separates legs into leg(l) and leg(r) shown in Figure 7.
3.2.2. Gait features
In this part, we extract gait features such as pace distance, pace time and pace velocity. Figure 8 shows a pace cycle model and we can extract pace distance (Dp), pace time (Tp) and pace velocity (Vp) from this model and Eq. (9). The distance value of the pace model comes from the horizontal distance between leg(l) and leg(r) such as D1. If the feet are close, we calculate the distance of the closed feet such as D2. D1 and D2 are the longest and shortest distance values, respectively. T1 and T2 are the start and end frame numbers of this step, respectively, so we have to multiply the frame rate to get the actual Tp. The frame rate is 1/30 s per frame in our experiment. Then, Vp comes from dividing Dp by Tp.
3.3. Gait analysis
To verify that there exists a correlation between pulmonary spirometer and our system, we perform classification and prediction experiments. There are two groups, namely bad and good, which are classified by the parameters from pulmonary spirometer and it becomes our classification standard. We take support vector machine for classification and take adaptive network-based fuzzy inference system for prediction. Here, we introduce the tools: SVM and ANFIS.
3.3.1. Support vector machine
SVM comes from Vapnik’s statistical learning theory  and it is a machine-learning method, which can be a powerful tool for learning from data and for solving classification problem . In a two-group classification problem such as our study (Bad/Good), the target is to find the Hyperplane between the two data groups. SVM finds the Hyperplane by looking for the maximum margin between two groups. The main idea of SVM is to transform data into higher dimensions and then construct a Hyperplane between two classes in the transformed space. Those data vectors, which are nearest to the constructed line in the transformed space, are called the support vectors which contain information about Hyperplane. Figure 9 shows the concept about the SVM.
3.3.2. Adaptive network-based fuzzy inference system
ANFIS was presented by Jang in 1993 . Adaptive network-based fuzzy inference system can construct an input-output mapping based on human knowledge by a hybrid-learning algorithm. The fuzzy inference system is employed with adaptive network. ANFIS contains a five-layer forward neural network to construct the inference system.
Input space is mapped to a given membership function (MF). By membership function, the input becomes a degree between 0 and 1. With different membership functions and the number of membership functions, the results are different. Figure 10 shows the ANFIS structure with two inputs and four rules.
In Layer(3), the label N indicates normalization. This layer can be represented by Eq. (14)
Layer(4) is the product of the normalized data which can be represented as Eq. (15). The parameters pi, qi and ri are determined during the training process
Layer(5) implements sum of all inputs such as Eq. (16)
4. Proposed gait features
We propose some gait features from Dp and Vp and call the ith step of Dp and Vp as Dpi and Vpi. The mean distance and mean velocity are denoted as and Vp, respectıvely. In addition, we divide all steps into S sections depending on the step counts in order to reveal the variation of the subject's movement during the 6-min brisk walking test. Figure 11 shows an example that we divide Dp of all steps into six sections and there are and of each section.
The mean of distance for section i is called as and the mean of velocity for section i is called as . The variance of distance for section i is called as and the variance of velocity for section i is called as . These parameters are listed in Eq. (17)
From and , we can calculate the mean of distance variance and the mean of velocity variance, which are denoted as and . The mean of distance variance for the first two sections and the mean of velocity variance for the first two sections are denoted as and respectively. The mean of distance variance for the last two sections and the mean of velocity variance for the last two sections are denoted as and respectively. In addition, we also calculate the distance variance ratio and velocity variance ratio, which are denoted as and . The distance variance ratio is defined as the multiplication of and the result of dividing by . The velocity variance ratio is defined as the multiplication of and the result of dividing by . Figure 12 shows the region of these parameters and these parameters are listed in Eq. (18)
5. Clinical experiment environment
5.1. Experiment set-up and flow
The experiments are run at Shuang-Ho Hospital in New Taipei, Taiwan. We film the side view of the subjects when they perform the 6-min brisk walking test. We set up a green curtain to exclude the interferences such as the movement of other people from our experiment. We film the walking subjects using Nikon P330 digital camera.
Firstly, the therapists ask the subjects’ profile including height, weight and age. Secondly, by using pulmonary spirometer, we can get respiratory parameters such as FEV1 and FVC data about the subjects. Thirdly, before the experiment starts, the therapist helps the subjects wear a pulse oximeter on the index finger, which is used to measure the oxygen and pulse. Fourthly, the subjects need to take a 2-min break so that the pulse oximeter can record the oxygen and pulse in normal condition. Fifthly, when the walking test begins, the subjects should walk along the trail as fast as possible. While the subjects start their walking test, we film the side view of the subjects. Sixthly, after the 6-min walking test, the subjects use the pulmonary spirometer to measure the respiration parameter after exercising again.
5.2. Data collection
We run the experiments from September 2014 to July 2015. In the experiments, there are 60 subjects who aged between 24 and 91 years. Among these 60 subjects, there are 48 men and 12 women.
There are two rooms: the subjects walk from the right room to the left one, then turnaround to walk into the right room. When the subjects walk to the other side of the trail, they need to turnaround and continue to walk along the trail. They decrease their walking speed so that they can turnaround easily when they are close to the border. To avoid recording those slowdown steps, we abandon those steps and keep normal steps. Taking Figure 13 as an example, there are six steps in this walking trail. We just consider steps 1 and 6 as the normal steps and abandon steps 2–5.
Depending on the respiratory index that comes from Eq. (19), these subjects are divided into three levels: level 1 (the worst respiratory function), level 2 (poor respiratory function) and level 3 (normal respiratory function). Table 1 shows the respiratory index used to classify the three levels. We call the respiratory index as REX. The smaller REX represents the worse respiratory function
|Group||Level 1||Level 2||Level 3|
The main item of REX formula is postFEV1 and other items are used to adjust it. The three items of , and are greater than one in normal respiratory function subjects but smaller than one in poor respiratory function subjects. The value of is lower than 0.75 in those subjects who have poor respiratory function. Figure 14 shows the lung capacity changes of respiratory factors.
The FEV1 is the volume that has been exhaled at the end of the first second of forced expiration. The FVC is the forced vital capacity that is used for the determination of the vital capacity from a maximally forced expiratory effort. The IC is the inspiratory capacity that is the sum of inspiratory reserve volume and tidal volume. The is the ratio that is used for the diagnosis of obstructive and restrictive lung disease.
6. Experimental results
In this chapter, we use the features that we get from Chapter 4 to perform our experiment. There are three experiments: classification with support vector machine, prediction with adaptive neural fuzzy inference systems and cooperating with radar system.
In the first experiment, we choose one feature from , and the other feature is . There are two combinations. Among these two combinations, we find the best one according to the classification results and it becomes the inputs of the prediction experiment. In the second experiment, we use the features that we find in the first experiment as the ANFIS inputs and calculate the correlation, MSE, regression slop under different membership functions. In the third experiment, we combine the features of radar system with our features to perform classification and prediction again.
6.1. Classification with support vector machine
Support vector machine is one of the most widely used machine-learning algorithms for classification problems .
We group the subjects of level 1 and level 2 into the Bad group, and the subjects of level 3 belong to the Good group. There are 32 subjects in the Bad group and 28 subjects in the Good group. Those subjects who belong to the Good group are marked with blue triangles and those subjects who belong to the Bad group are marked with red circles.
According to the above chapter, we divide all steps into S sections. In order to find the S-value, we perform different S-values in SVM classification. The inputs are and because these two parameters are affected by the S-value. Table 2 lists the SVM accuracy in different S-values and the highest accuracy is 0.61 when S equals six. Therefore, the S-value is six in our experiment. In this article, the bold values in all the tables means the best result in the experiment.
From Table 3, the subjects of level 3 have larger and than that of levels 2 and 1. The values of each level are the mean of and of the subjects who belong to the level. Therefore, the and become our choices of input features. Figure 15 shows the and of all subjects.
The subjects who have better respiratory function have larger and than those who have poor respiratory function. In Table 4, the values of level 3 are higher than those of levels 1 and 2. The values of each level are the mean of and of the subjects who belong to the level. Figure 16 shows the and of all subjects.
In addition, people have lower variance after they exercise. Figure 17 shows the pace distance of a person in three different conditions: normal walking, walking after a short run and walking after a long run. The variation of walking after a long run is smaller than others.
The is the mean of velocity variance of the hind of the test and is the mean of velocity variance of the front of the test. To those subjects who have poor respiratory function, the is smaller than because they feel like walking after a long run in the hind of the test. On the other hand, for those subjects who have better respiratory function feel like normal walking in the hind of the test.
Therefore, the of those subjects who have poor respiratory function should be smaller than those subjects who have better respiratory function. From Table 5, the value of level 3 is greater than levels 1 and 2. The values of each level are the mean of of the subjects who belong to the level. Figure 18 shows the of all subjects.
The considers the mean of velocity variance value and the velocity variance ratio , so become our choices of the input features. Figure 19 shows values of all subjects. Table 6 lists the SVM results with different features.
The accuracy of input features () is better than the other input features (). Therefore, we use () as the best inputs of the classification experiment. Figures 20 and 21 show the SVM result with the inputs () and (), respectively. In Figure 20, the subjects of the Good group have higher and than those who are in the Bad group.
6.2. Prediction with adaptive neural fuzzy inference systems
We utilize adaptive neural fuzzy inference system to help us predict the parameters from pulmonary spirometer. The ANFIS system comes from the toolbox of Matlab.
Because we only collect about 60 cases so far, it is not enough for ANFIS to perform prediction. In order to increase the training samples, we adopt Leave-one-out cross-validation method. Leave-one-out cross-validation is used in analysing small datasets. It uses one sample as the validation set and the remaining as the training set. Repeat on this way for all samples. We can use this method to solve the insufficient data problem.
In ANFIS, it is important to choose a correct membership function. In addition, we also need to choose the input sections. In the experiment, we use six different membership functions including trapmf, gbellmf, gaussmf, gauss2mf, pimf and dsigmf. Figure 22 shows the membership functions we use in our prediction experiment. The inputs of the experiment are and . In our results, we show the correlation, normalized Mean Square Error (MSEN) and regression slope under different membership functions. The formula of MSEN is shown in Eq. (20). The Targeti are the measured values from pulmonary spirometer and the Predicti are the values come from ANFIS.
We try to predict three different parameters that come from the pulmonary spirometer: post , postFEV1 and postFVC. The ‘post’ name means the parameters after the 6-min brisk walking test. In the following part, for the convenience, we call post , postFEV1, postFVC as, FEV1, FVC, respectively. and FEV1 are used to access the respiratory function, so we choose these two parameters as our predicting targets.
FEV1-FVC is an index which is used to access the severity of airway obstruction. The lower value means that the airway obstructs severely. Table 7 shows our prediction results and we use [2 2] as the input sections. The and are the experiment inputs. Figure 23 shows the predicting results and regression slope under different membership functions.
FEV1 is also a parameter to access the respiratory function. The higher FEV1 value means that the subjects have better respiratory function. Consequently, we also predict the FEV1 value. Table 8 shows the prediction results and we use [3 2] as using 3 nodes for the first input and 2 nodes for the second input in the ANFIS system. The features and are the experiment inputs. Figure 24 shows the predicting results and regression slope in different membership functions.
The correlation and regression slope of predicting do not perform well under all membership functions. However, the correlation and regression slope of predicting FEV1 perform well under trapmf. From the two results above, we infer that our system is good at predicting the respiratory parameter from pulmonary spirometer (FEV1). However, it is hard to predict the computed value (). Consequently, we also predict the FVC value. Table 9 shows the prediction results and we use [3 2] as using 3 nodes for the first input and 2 nodes for the second input in the ANFIS system. and are the experiment inputs. Figure 25 shows the predicting results and regression slope in different membership functions.
Table 10 shows the best results of predicting , FEV1 and FVC. The correlations of FEV1 and FVC are all good and close and the regression slope of FEV1 is better than FVC. However, the correlation and regression slope of do not perform well. The MSEN of is smaller than other two parameters. Our system is good at predicting the parameters of pulmonary spirometer but do not perform well in predicting the ratio. Nevertheless, the high correlations of FEV1 and FVC verify that there is a correlation between pulmonary spirometer and our gait analysis system.
|Predicting target||Correlation||MSEN||Regression slope|
6.3. Cooperating with radar system
In this section, we combine the features of radar system with our features and . The radar system is a tool using impulse to record the moving of the subjects' chest and analyse the features of respiration. It uses the and the to analyse respiration. These two features are listed in Eq. (21). The Amp is the respiratory intensity of the subject. The and are the inspiratory speed and expiratory speed, respectively. The names ‘post’ and ‘pre’ mean the parameters after a 6-min brisk walking and before a 6-min brisk walking, respectively. We use these two features with and to perform SVM classification and ANFIS prediction experiments.
In the SVM experiment, there are still 32 subjects in the Bad group and 28 subjects in the Good group. Because we use () as the SVM inputs, we cannot draw a two-dimensional (2D) figure. The accuracy with () is 81.6% and it is higher than the accuracy with () (75%).
|Target (features)||Correlation||MSEN||regression slope|
In the ANFIS experiment, we also predict and FEV1 parameters and use () as the ANFIS experiment inputs. The input sections we used is [3 3 3 2] that means the number of nodes used in the four inputs are 3, 3, 3, and 2 respectively. Table 11 shows the results of predicting , FEV1 and FVC with (), () and (). We only list the best results among the six different membership functions. Figure 26 shows the best results of predicting , FEV1 and FVC with (), () and (). In predicting , the correlation and regression slope improve strongly though the MSEN value increases slightly by using (). In predicting FEV1 and FVC, it does not improve the effects on correlation and regression slope by using (). Therefore, the features of radar system cannot improve the results of predicting FEV1 and FVC.
Radar system improves our analysis results on both SVM classification and predicting the parameter FEV1/FVC. With radar system's help, there is a higher correlation and accuracy between the combined system and the pulmonary spirometer.
We propose a vision sensor-based gait analysis method without wearing any sensor on human body. In our approach, the proposed gait features analyse the subjects’ respiratory function. We also perform a clinical experiment on COAD patients and normal people with our vision sensor-based gait analysis method. With the extracted features, and , the classification result is close to the classification by the parameters of pulmonary spirometer. The SVM accuracy is 75%. In ANFIS experiment, the correlations of ANFIS prediction on FEV1 and FVC achieve 0.694 and 0.678.
In addition, by combining the features of radar system (ΔAmp and Δβratio) with our features (and ), the SVM accuracy and predicting on ratio () both improve strongly. The SVM accuracy goes to 81 from 75% and the correlation of ANFIS on predicting goes to 0.428 from 0.25. From the experiment above, we verify that there exists a correlation between the pulmonary spirometer and gait analysis system.