Reconstruction of dual tasking gait pattern in Parkinson’s disease subjects using radial basis function based artificial intelligence

Abstract

Vertical Ground Reaction Force (VGRF) is a force obtained during gait cycle beneath the feet and is used to screen the severity of Parkinson’s disease (PD) patient’s in clinical environment. This article investigates the VGRF signals (left and right) semblance nature among PD patients and control subjects as a function of time and possibility of reconstructing dual tasking VGRF signal from normal walking VGRF signals using radial basis function (RBF) based artificial intelligence (AI). There are many traditional methods for gait analysis and these methods are purely subjective and none made semblance analysis of same subjects gait pattern in different tasking. In order to overcome the difficulties faced by PD patients, RBF based AI is proposed in this research to reconstruct the dual tasking VGRF signal from normal walking VGRF signal. 93 PD patients with mean age: 66.3 years (63% men), and 73 healthy controls with mean age: 66.3 years (55% men) datasets are used in this work. Proposed RBF network is trained on VGRF signals obtained in normal walking and dual tasking conditions from control. The network was trained with 60% of VGRF data and tested on remaining 40% data. Semblance analysis results are encouraging, and it shows that semblance is high in PD patients than control subjects during dual tasking (P < 0.05). In order to test the findings of semblance analysis, we explicitly reconstruct VGRF signal of clinically significant dual tasking from VGRF signal of normal walking by the proposed RBF method. Findings proved that the proposed RBF network can reconstruct dual tasking VGRF signal of PD patients from their normal walking VGRF signal with high cross correlation (P < 0.0001). These findings pave way for a new adjunct tool to diagnose the gait dynamics of PD patients using the proposed reconstruction method.

Keywords

Vertical ground reaction force signals semblance continuous wavelet transform k-means clustering

1 Introduction

Parkinson’s disease (PD) is a considered as a kind of neurological abnormality mostly occurs in elder population and one of its symptoms are disturbed gaits or freezing of gait. According to World Health Organization reports [1, 2], about 6.3 million PD people are there worldwide and increasing year by year. Presently, there are many intricate and very challenging clinical procedures that are used to screen and measure PD severity [3 –7]. Assessment based on gait dynamics were studied which allows the patient to walk in a confined area by making fast and short steps [4, 5]. Questionnaire obtained from PD subjects and their caretakers specifically on freezing of gait (FoG) on the frequency and severity of FoG episodes were studied [8 –10]. Most of these clinical methods are subjective and lack in defined protocols in clinical setting. Moreover, these methods fail to reflect the real situation and time taken for evaluation and would not reflect the gait variability and frequency of FoG. Single waist-worn tri-axial accelerometer with machine learning approach was proposed for home environments to monitor PD patients in real-time [10 –12]. In this method, the subject must wear the electronic gadget which transmits the signals pertaining to subject’s mobility and FoG. Though the method seems to be new and gives freedom from clinical environment nevertheless adds discomfort to the subjects in wearing the device all the time and it is highly a cumbersome task in continuing during rest of the life. Now days, the effect of cognitive tasks on PD severity is fetching progressively in PD subjects gait pattern screening. Experimentally, these facts are confirmed with evidences that there is a strong the relationships between cognitive function such as dual tasking and change in gait variability [8, 9]. Vertical Ground Reaction Force (VGRF) is a force obtained during gait cycle beneath the feet and is used to screen the severity of Parkinson’s disease (PD) patient’s in clinical environment. VGRF signals not only reflects the gait pattern and also it gives more information on gait cycle spatiotemporal details hidden in, it is imperative that these signals must be studied intensively in clinical procedures [5]. Our hypothesis is that if there is a strong physiological connection between individual’s cognitive tasks and their gait pattern, these cognitive tasks could perhaps manifest VGRF signals. In order to validate the hypothesis, similarity between cognitive dual tasking (subtraction of seven) and effect of that on VGRF signals of PD patients and control subjects are studied in this work. Discussing PD disorder physiologically and its connection with cognitive tasks are beyond the scope of this paper.

Recently in clinical settings, gait pattern has been widely used to identify PD severity. On the other hand, only limited research has been carried out in our knowledge to estimate the correlation between VGRF signals of left and rights feet among PD patients in dual tasking/normal walking [13]. Hence, it is clinically more important to study the similarity of VGRF signals in dual tasking/normal walking and quantity the same based on PD severity. Statistically, VGRF signals obtained beneath the feet are non-stationary in nature like other physiological signals and any signal processing tools used for its analysis must capable of processing its non-stationarity such as wavelet transform [14].

Normally, semblance analysis (filtering) relates any two signals in terms of frequency based on their phase. In the past, such analysis has been used to relate geophysical data [14, 15]. This methodology has not been explored for analyses of VGRF signals of PD patients. Statistically, VGRF signals are non-linear in nature and it is advisable to use such analysis using continuous wavelet transform (CWT) will give best time-frequency resolution-based analysis and possible to quantify the similarity using wavelet coefficients [16–19 , 24].

In the past three decades, artificial intelligence (AI) based neural networks has turn out to be a prominent tool in numerical approximation and time-series prediction. Radial basis function (RBF) is one of the robust neural networks with high speed learning capability [21]. There are many studies carried out in the past which proves the superiority of RBF in approximating all kind of functions and predicting nonlinear systems [21, 22]. RBF neural networks are widely used in many biomedical researches; disease classification based on parameters extracted from physiological signals [21], diagnosis based on images and biomarkers [22]. A new approach of RBF based AI method to reconstruct the dual tasking VGRF signal from normal walking VGRF signal is proposed.

Table 1
Subject Characteristics

Parameters Control (n = 73) 55% men PD (n = 93) 63% men P-Value

Age (Years) 63.6±8.6413 66.3±9.44 0.507

Height (m) 1.68±0.085 1.67±0.085 0.889

Weight (Kg) 73.9±15.89 72.7±12.39 0.621

Education (Years) 13.9±3.79 13.7±1.99 0.912

Hoehn and Yahr Stage (0–5) 0 2.3±0.38

UPDRS 31.61±11.89 0.47±0.89 P < 0.001

UPDRSM 18.98±8.28 0.47±0.88 P < 0.001

Gait Speed (m/s) –Normal Walking 1.24±0.18 1.03±0.22 P < 0.001

Parameters	Control (n = 73) 55% men	PD (n = 93) 63% men	P-Value
Age (Years)	63.6±8.6413	66.3±9.44	0.507
Height (m)	1.68±0.085	1.67±0.085	0.889
Weight (Kg)	73.9±15.89	72.7±12.39	0.621
Education (Years)	13.9±3.79	13.7±1.99	0.912
Hoehn and Yahr Stage (0–5)	0	2.3±0.38
UPDRS	31.61±11.89	0.47±0.89	P < 0.001
UPDRSM	18.98±8.28	0.47±0.88	P < 0.001
Gait Speed (m/s) –Normal Walking	1.24±0.18	1.03±0.22	P < 0.001

2 Materials and methods

This section gives the description of signal processing and AI methods used to reconstruct VGRF signals proposed in the work and available literature. It also presents the details of datasets used in this research and methodology followed.

2.1 Data

Gait VGRF signals datasets from Physio Bank archives of Physio Net (collected at the Laboratory for Gait & Neurodynamics, Movement Disorders Unit of the Sourasky Medical Center) were used for this study and Table 1 presents the subject characteristics. Datasets consists of multichannel recordings from force sensors beneath the feet of 93 PD patients with mean age of 66.3 years (63% men), and 73 healthy controls with mean age of 66.3 years (55% men). Beneath each foot eight sensors (sixteen sensors from both feet), VGRF (measure gait force in Newton’s) signals were digitally recorded at 100 samples per second from eight sensors (measure gait force in Newton’s) at subjects usual, self-selected stride for roughly 120 seconds on level ground. Sum of eight sensors from each foot also recorded simultaneously.

The complete explanation of gait dynamics protocol followed while data acquisition is presented in [10]. Figure 1 pictorially represents the time series of gait variability of PD and control subject, in both dual tasking and normal walking conditions. Fig. 2 shows the sensor position on left and right foot, the average of all sensors was calculated and taken for analysis. Data were visually checked for its quality and few data were omitted because of its drift and discontinuity.

Fig.1

Gait variability time series of PD and control subjects in normal/dual tasking conditions. Variability increases during dual tasking in the subject with PD (CV = 6.5%), but not in the control subject (CV = 1.2%) –(From Yogev et al., 2005).

Fig.2

Pictorial representation of sensor positions on left and right foot and the average of all sensors were also simultaneously calculated for analysis.

Data are presented as mean±SD, as indicated.

2.2 Semblance analysis

There are many traditional methods such as cross-correlation or cross cross-spectral density could be used for statistically comparing two time series. Cross-correlation can take on values from 1 to –1 and is a measure of the similarity of the two datasets whereas semblance analysis compares two datasets based on correlations between their phase angles, as a function of frequency. Semblance is defined as the difference between the phase angles of the two datasets at each frequency. Two time series can be compared using semblance analysis based on inherent relationship in phase angles with respect to frequency. Traditional Fourier transform (FT) H (f) of a signal h (t) is given by [14, 15], $(f) = \int_{- \infty}^{\infty} h (t) e^{- 2 π ift} dt$ (1) where, t - time, f –frequency. H will be complex in nature with both magnitude and phase pertinent to major dominant frequency components. Such change in phase angles at each frequency can be calculated from: $S = Cos θ (f) = \frac{R_{1} (f) R_{2} (f) + I_{1} (f) I_{2} (f)}{\sqrt{R_{1}^{2} (f) + I_{1}^{2} (f)} X \sqrt{R_{2}^{2} (f) + I_{2}^{2} (f)}}$ (2) where R₁ (f) and I₁ (f) - real and imaginary parts of the FT of signal 1, in terms of frequency f (R₂ and I₂ are for signal 2). Semblance S takes values from –1 to +1. If the signals have very good phase correlation, it may take +1 and, 0 there is no such correlation exists, and –1 means seamless anti-correlation. Multi-scale version of the above Equation (2) was first derived by Cooper and Cowan [14] using the CWT and is given below for readers understanding.

CWT produces best time–frequency resolution analysis by including scale into main equation. Scale can be use shortened wavelet high-frequency details and stretched wavelet for lower frequencies. The CWT of a signal h (t) is given by, $CWT (u, s) = \int_{- \propto}^{\propto} h (t) \frac{1}{{| s |}^{0.5}} Ψ^{*} (\frac{t - u}{s}) dt$ (3) where s - scale, u –VGRF in our case, Ψ - mother wavelet, and * indicates complex conjugate. In this study, Complex wavelet called Morlet was incorporated as suggested in [16], which is written as, $Ψ (x) = \frac{1}{π f_{b}} e^{2 π {if}_{c} x} e^{\frac{- x^{2}}{f_{b}}}$ (4)

In Equation (4), f_b chooses wavelets bandwidth and f_c, called as center frequency of wavelet. For equalization of scale to wavelength, a factor of 1.0 will be used for f_c. Generally, the scale levels are associated to pseudo-frequencies (f_p) and it can be calculated from the center frequency (f_c) of wavelet, $f_{p} = \frac{f_{c}}{s Δ T}$ (5)

Where, ΔT is the sampling period in a time series. Comparison of two time series using cross-wavelet transform is given as, ${CWT}_{1, 2} = {CWT}_{1} {XCWT}_{2}^{*}$ (6)CWT_1,2 is a complex quantity with magnitude A (the cross-wavelet power) given by, $A = | {CWT}_{1, 2} |$ (7) and local phase θ: $θ = {tan}^{- 1} (\frac{ℑ ({CWT}_{1, 2})}{R ({CWT}_{1, 2})})$ (8)

In the above equation, θ (ranges from -π to +π) indicates signals relationship in phase. A corresponding equation based on Equation (4) is derived as, $S = {cos}^{n} (θ)$ (9) Where n > 0. From the above equation, –1 indicates inverse correlation; 0 indicates no correlation; +1 indicates very good correlation. Here S and θ relates only phase angles, an advantage of this equation is that the compared datasets not necessarily have to have alike entities. After incorporating cross-wavelet transform and is redefined as, $D = {cos}^{n} (θ) | {CWT}_{1} {XCWT}_{2}^{*} |$ (10) where n = 1. Hence D comprises, phase of S and magnitude A constitutes the D, this is advantageous when the phase correlations of the larger magnitude components of the dataset are of highest significance.

2.3 Radial basis function based signal reconstruction network

Radial Basis Function (RBF) based AI are widely used in approximation and regularization theories [22, 23] which comes under supervised learning neural networks. Fig. 3 shows the basic structure of RBF which comprises three layers: input layer which takes input variables; hidden layer (non-linear) forms centers of clusters of data in the input space; and output layer (linear) brings out the output variables. Euclidean distance is calculated by the activation function of each hidden unit between input vector and the center of the hidden unit.

Fig.3

Architecture of Radial Basis function.

The description of learning algorithm is presented in this section. The input data Z is a p-dimensional vector, Z = [z₁, z₂, z₃ … . z_p] ^T. In RBF’s architecture, the input layer aids only as a distributor to the hidden layer. The response from the j^th hidden unit for the jth input data z_i has the following form:

$φ_{i} (z_{i}) = φ (∥ z_{i} - c_{j} ∥) j = 1, 2, 3 \dots \dots . N_{h}$ (11) where ∥□ ∥ denotes the Euclidean norm, c_j is the center of the jth unit in the hidden layer, φ (□) is the activation function, N_h is the number of hidden units. In RBFs, the activation function φ (□) of hidden units is symmetric in the input space and the output of each hidden unit depends only on the Euclidean distance between the input and center of the hidden unit. There are various forms of activation function, the popular Gaussian function is considered in this work: $φ (z) = \exp (- \frac{∥ z_{i} - c_{j}^{2} ∥}{2 β^{2}})$ (12) where β- center width, which can be obtained from, $β = \frac{d_{\max}}{\sqrt{2 N_{h}}}$ (13) where d_max□ gives the maximum distance across the centers of hidden units. The activity of the rth unit in the output layer $\hat{y_{r}}$ can be obtained from $\hat{y_{r}} = w_{0} + \sum_{q = 1}^{N_{h}} W_{qr} \emptyset_{q} (z) r = 1, 2, \dots N_{R}$ (14) where ∅_q (z) is the response of the qth hidden unit resulting from all input data, W_qr is the connecting weight between the q^th hidden unit and the rth output unit, w₀ is the bias term, and N_R is the number of output units. Once the centres and widths of hidden units are determined, each weight in Equation (14) can be determined by the method of minimizing least-square error [22]. The centers of the RBF functions were estimated by k-means clustering algorithm which is commonly used in pattern recognition [23]. K-means is considered as unsupervised clustering algorithm which finds a set of r centers that iteratively minimizes the mean squared distance from each data point to its closest center. A detailed mathematical approach and its description of k-means algorithm can be found in [23].

Here we propose a new method of reconstruction of the dual tasking gait dynamics from normal walking of PD patients using RBF networks. Because dual-task exercise is considered clinically important and is one of the therapies given during treatment of motor function in PD patients [25]. The VGRF data used in this study were sample data 100 samples per second and hence the time interval between two consecutive samples becomes 0.01 sec. The proposed RBF networks were modeled like a window of samples in such a way that the past six samples of normal walking VGRF signal predicts the current sample of dual tasking VGRF signal and shown in Fig. 4. This window is moved throughout the times series recorded during normal walking and dual tasking. In order to train this model, 60% of PD patients VGRF signals of dual tasking and normal walking conditions were used. Optimization of network (number of RBFs and sigma factor) were carried out in order to achieve good correlation by maintaining other parameters constant. Upon optimization, 150 hidden units and center spread, of 15 were chosen finally for this study (refer Table 2). The RBF model was tested with 40 % of remaining data.

Fig.4

RBF model proposed for reconstruction of dual tasking gait dynamics from normal walking.

Table 2

Optimization of RBF network parameters (number of hidden units and center spread) based its network performance

Size of	β Center	Correlation
hidden units	Center spread
60	2	0.75
85	4	0.79
110	6	0.84
125	11	0.88
150	16	0.93

3 Results

There were many experimental studies carried out on PD patients gait analysis using various signal processing methods. In this work, CWT based semblance analysis measures phase relationships of two VGRF signals obtained beneath the feet. This method allows the clear visualization of stand and swing phase based on VGRF signals amplitude. MATLAB release R2018b (The Math Works co. MATLAB^® version 2018b) licensed version is used for this research. CWT based semblance results of control and PD subjects in normal/dual task walking conditions are shown in Figs. 5–8. These are results obtained from one subject data from each category and comparable results were obtained from all other datasets. For clear visualization of signals and semblance results 1000 samples from the average of all signals from each foot is presented in this article.

Fig.5

Normal walking time series of left and right VGRF signals of control subject and its CWT based semblance analysis.

Fig.6

Dual Task walking time series of left and right VGRF signals of control subject and its CWT based semblance analysis.

Fig.7

Normal walking time series of left and right VGRF signals of PD subject and its CWT based semblance analysis.

Fig.8

Dual Task walking time series of left and right VGRF signals of PD subject and its CWT based semblance analysis.

Figures 5 and 6 shows the left and right VGRF signals, its CWT plot and semblance plot (at bottom of Figs. 5–8) of control subjects and Figs. 7 and 8 for PD subjects. In control subjects, dual tasking semblance decreases compared to normal walking. On the other hand, in PD subjects, dual tasking semblance increases compared to normal walking. These findings support existing literature that cognitive effect influences gait pattern of PD subjects. In order to quantify the semblance and make it understandable, mean of the absolute value squared of the wavelet coefficients (power) of semblance were calculated for all data to estimate a new parameter called ‘Semblance power ratio (PR_SEM)’. PR_SEMis defined as ration of signal power in normal walking to dual tasking signal power (e.g., PR_SEM = Power of normal walking semblance coefficients/ Power of dual tasking semblance coefficients). Similar power ratio concepts have been used in the past in quantifying the parameters in other physiological signals analysis [19] and to our knowledge none have explored to use this concept in PD analysis. Based on the results derived from existing data, it is observed that decrease in PR_SEMis a good index of PD and it may have an impact in clinical screening. Control subjects has PR_SEM values of greater than 1 and is ≤1 for subjects with PD. Table 3 presents the average of PR_SEM values for control and PD subjects.

Table 3

Average of Power Ratio (PR_SEM)

Subject	Control (n = 60)	PD (n = 60)
PR_SEM	1.23±0.18	0.89±0.15
Values are shown as Mean±SD,
as shown P < 0.05

Fig.9

Heat Map of correlation between the various sensors signals.

A detailed heat map shown in Fig. 9 was developed using machine learning method in Python platform using Sea born library to understand the correlation between the VGRF signals obtained from various sensors across two feet. Heat map shows that the correlation between VGRF signals of same regions on either foot, i.e. R1-L1, R2-L2 \dots R8-L8 are high. This suggests that from this heat map one could easily understand and predict the other side from one side, either right or left would suffice to predict if a patient is normal or suffers from PD. It would really help clinicians and make their job easier in screening of PD. Upon establishing a structured heat map method, it would be sufficient to reconstruct the dual tasking as proposed from the normal walking. The reconstructed dual tasking (time series) from normal walking by the proposed trained RBF networks are presented in Fig. 10 (Right foot) and Fig. 11 (Left foot) shows the reconstructed dual tasking (red color) of a PD Subject from actual dual tasking (blue color) of both feet. In Fig. 11, the target (blue color) is the subject’s actual dual tasking VGRF signal and the output (red color) was obtained from the proposed RBF reconstruction model.

Fig.10

Reconstructed Dual Tasking (red color) of a PD Subject from actual dual tasking (blue color) of Right foot.

Fig.11

Reconstructed Dual Tasking (red color) of a PD Subject from actual dual tasking (blue color) of Left foot.

The cross-correlation between the actual and reconstructed dual tasking VGRF signals were found to be high and the correlations coefficients of 20 PD subjects testing data is shown in Fig. 12. These results strongly support our hypothesis of reconstruction of dual taking gait pattern. In this correlation estimation, frequency and phase correlations were not considered because it involves the VGRF signals of same foot. These are results obtained from one PD subject data and comparable results were obtained from all remaining datasets.

The correlation coefficient between the actual dual tasking VGRF signal and reconstructed dual tasking signal was higher irrespective of the foot (i.e., left or right). Totally 60 PD subject’s data were considered in this study, out of which 40 PD subjects were used for training the proposed RBF network. After training, remaining 20 PD subject’s data were used for testing the proposed RBF network and corresponding correlation values are displayed in Fig. 12. Average correlation value of 0.89±0.09 and 0.89±0.09 were obtained for PD subjects in left and right foot respectively.

Fig.12

Correlation of Reconstructed Dual tasking Signal with actual VGRF dual tasking signal of PD subjects (Data are presented as mean±SD, as indicated. P < 0.05).

4 Discussion

VGRF signal was considered as marker for Parkinson’s disease [13] in many past researches and clinical screening and reconstruction of physiological signals were studied based on RBF networks [19]. Firstly, focus of this study was to measure the semblance of VGRF signals using CWT based semblance analysis to understand the cognitive dual tasking effect on PD subjects gait pattern and quantification through PR_SEM . Semblance analysis allows the local phase relationships between the left and right foot VGRF signals as a function of both scale (and wavelength) and time. These findings also make the swing and stance phases clearly visible through the CWT plots. Based on the PR_SEM results derived from existing data, it is observed that decrease in PR_SEM is a good index of PD and it may have an impact in clinical screening. Based on the heat map developed in this study, one could easily understand and predict the VGRF nature in other side just from one side signal alone, i.e., either right or left would suffice to predict if a patient is normal or suffers from PD. It would really help clinicians and make their job easier in screening of PD. Moreover, this heat map concept enhances the conceptualization of reconstruction of the dual tasking gait dynamics from normal walking of PD patients using RBF networks.

It is observed that the similarity of left and right foot signals is high in normal walking and decreases in dual tasking for control subjects and is vice versa for patients with PD. Our findings also support the fact that there is a good connection between cognitive task and gait pattern of PD patients [8, 9]. Discussion of the physiological reason behind this analysis is out of scope of this article and it can be further investigated clinically. We restrict ourselves in analyses of these findings in signal processing perspective. Technically, semblance analysis allows us to study local phase relationships between the left and right foot VGRF signals as a function of both scale (and wavelength) and time. Secondly, we presented a new method of reconstructing dual tasking VGRF signal from normal walking of PD subjects using RBF. In the proposed methodology, the RBF networks were modeled as the previous six samples of PD patient normal walking envisages the current sample of PD patient dual tasking. This window of 6 samples is moved throughout the length of the signal recorded in normal walking and dual tasking. The window size is decided based on signal sampling frequency. The results show that dual tasking signal reconstructed by this method has good correlation with normal walking signal. Accuracy of the proposed reconstruction method was clearly demonstrated by training and testing. This article presented a new approach for screening PD and its gait pattern. It should be remembered that the accuracy the approach is also associated with the VGRF signal recording and optimization of RBF parameters used to train the network.

5 Conclusions

In conclusion, semblance analysis proves that high cross-correlation exists between VGRF signals (left and right feet’s) of patients with PD in normal walking and dual tasking than control subjects and PR_SEM helps in quantifying the same. From these findings, we can conclude that the CWT based semblance method could pave way for as another tool in diagnosis of PD severity. Meanwhile, it can be used as an adjunct tool in addition to other existing tools in clinical environments. It was found that the proposed RBF reconstructed VGRF signal of PD patients during dual tasking shows similar high cross correlation with normal walking (P < 0.0001) than control subjects. These findings pave way for reconstruction of dual tasking gait dynamics of PD patients from a normal walking using simple RBF method. The present data set is small, and more data and methodologies as mentioned above needs to be tried and validated as a tool. In order to improve sensitivity and specificity other algorithms/ methods or combination of such methods is to be tried. In conclusion, outcomes of research show that RBF method proposed here can effectively reconstruct dual tasking VGRF signals from normal walking VGRF signals. With these results, in future we expect to have an elegant noninvasive clinical tool for screening PD severity. This new method will give more comfort to PD subjects during screening and diagnosis and lesser the burden on physicians. This research opens a lot of space for further improvement using deep learning in reconstructing PD cases with various degrees of severity. In future, this research can be further extended to identify foot pressure distribution in-terms of VGRF signal magnitudes and phase through specialized machine learning models to screen and early predict the progress of PD severity. Also, PD severity classification according to clinical standards can also be carried out in future using the proposed reconstruction method.

Footnotes

Acknowledgment

The authors sincerely acknowledge the support by King Abdulaziz City for Science and Technology (KACST), Graduate Students Research Program, Project Number: 1-18-02-018-0001 and also the authors extend their appreciation to the Deanship of Scientific Research at Majmaah University for funding this work under Project Number R-1441-63.

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