Novel Methods of AI-Based Gait Analysis in Post-Stroke Patients

Featured Application

Potential applications of the findings presented in this article include low-cost, fast, and simple gait analysis systems for use by primary care physicians, orthopedists, neurologists, and geriatricians, enabling the screening of patients who require a further more accurate gait diagnosis, including as part of preventive medicine.

Abstract

Research on gait function assessment is important not only in terms of the patient’s mobility, but also in terms of the patient’s current and future quality of life, ability to achieve health goals, family life, study and/or work, and participation in society. The main methods used herein include a literature review and an analysis of our own original research and concepts. This study used the historical data of 92 ischemic stroke patients (convenience trial) undergoing two kinds of rehabilitation. An artificial neural network, fractal analysis, and fuzzy analysis were used to analyze the results. Our findings suggest that artificial neural networks, fuzzy logic, and multifractal analysis are useful for building simple, low-cost, and efficient computational tools for gait analysis, especially in post-stroke patients. The novelty lies in the simultaneous application of the three aforementioned technologies to develop a computational model for the analysis of a patient’s post-stroke gait. The contribution of this work consists not only in its proposal of a new and useful clinical tool for gait assessment, even in the most severe post-stroke cases, but also in its attempt to offer a comprehensive computational explanation of observed gait phenomena and mechanisms. We conclude by anticipating more advanced and broader future applications of artificial intelligence (AI) in gait analysis, especially in post-stroke patients.

1. Introduction

Gait is the primary means of human movement. Despite the apparent simplicity of the matter, there are many definitions of gait, as walking is one of the most complex activities performed by humans. It is also one of the most frequently performed activities, occupying on average 10% of an individual’s time each day.Gait is such an important activity in people’s daily lives that any deficit in it can seriously reduce their subjective health-related quality of life. Research on the assessment of gait function is therefore important not only in terms of the patient’s mobility, but also in terms of the patient’s future quality of life, ability to achieve health-related goals, family life, and study and/or work [1]. In addition, clinical studies have confirmed the relationship between various medical conditions and a patient’s gait characteristics [2].

The normal human gait is stereotyped—this means that the range of possible deviations from the global gait pattern is so narrow that both the normal gait pattern and the acceptable range of deviations from it can be established for the whole population. Furthermore, on the basis of the values of deviations from the global gait pattern, it is possible to make inferences about health and disease (pathological changes in gait pattern caused by disease or injury) in a given patient [3,4].

This also means that gait, despite differences among individuals, is characterized by a certain degree of repeatability and can be described in terms of norms (depending on many factors, such as length of lower limbs, age, state of health, etc.). Deviations from these norms, in turn, provide information on abnormalities, providing an opportunity for the appropriate choice of therapy. Thus, gait diagnosis can be performed on both healthy people (to ensure they are within normal limits) and people with a wide range of gait deficits. For the aforementioned reasons, the search is on for low-cost, accurate, and fast ways to analyze gait, not only for clinical purposes, but also, for example, to optimize the movements of athletes. It is imperative that gait-testing methods are selected in such a way as to ensure, among other things, ease and rapidity of testing and low cost while maintaining testing sensitivity [5,6].

The analysis of gait function in healthy individuals, the assessment of gait pattern pathology, and the targeted restoration (re-education) of gait function in patients with functional deficits places high demands on specialists. This is aided by the use of gait measures that are low-cost, quick and simple to use, accurate, reliable, reproducible, and independent of the patient and the therapist. These measures must be usable in everyday clinical practice in neurological, post-stroke, and rehabilitation wards, and in outpatient practice in rehabilitation.A good diagnostician is already able to perceive changes in a patient’s gait during observation and use these changes to make clinical inferences. However, such a model of clinical gait assessment requires experience and is difficult to transfer to another person and to standardize. Hence, the optimization of gait diagnosis is essential [7,8].

1.1. Clinical Gait Analysis

Gait analysis is defined as the analysis of human walking locomotion, oftenusing computerized and instrumented measurements of its constituent movement patterns [9]. Gait can be described using a large number of parameters, and their statistical and simulational analysis enables the relatively early detection of many abnormalities, the selection of an appropriate therapeutic method, and the evaluation of therapy progress. However, it must be remembered that, despite the importance of gait research, a mathematical model of gait was not developed until the 1990s. This is due to the fact that a comprehensive description of the human locomotor system is difficult, if not impossible: in a healthy person, more than 280 degrees of freedom may be observed.

More and more tools are being provided to enable clinical gait analysis to be performed reliably and reproducibly. The development of certain software and hardware has reduced the effort needed to perform even complex calculations or simulations and hasthus led to their increasing clinical use. Such tools (even simplified ones) can provide a better understanding of physiological gait and the whole spectrum of its possible disorders, both through the pervasiveness of their use in clinical settings and in studies on patients not previously subjected to them in gait laboratories [10,11,12]. Simplified procedures and computer support enable significant time savings as well as greater accuracy and reproducibility than traditional observational methods. Despite the current advances in clinical gait analysis, limitations are still apparent, and these mainly relate to the following factors:

• the large amount of acquired data, which areoften redundant or even useless;
• the need to match tools to observed clinical problems, conditions, and deficits;
• the needs and expectations of clinicians regarding the way in which the results of clinical gait analysis are examined, presented, and interpreted (e.g., it should be fast, accurate, efficient, and based on an individual patient model);
• Its time-consuming nature and the difference between input (time, effort, equipment) and effects (no step improvement in rehabilitation effectiveness) [11,12].

For the aforementioned reasons, even today it is difficult to consider clinical gait analysis as a routine test, despite the fact that gait assessment is undertaken routinely even by primary care physicians, e.g., visual analysis of abnormal gait and posture and the sources of associated pain [13]. However, this is difficult to carry out promiscuously and reproducibly in the patient’s natural environment [2], even using sophisticated statistical methods and comparisons with data for the general population [14].

The theory and practice of clinical gait analysis has been the subject of scientific interest since as early as the 1980s and 1990s [15,16], with early attempts at automation and the introduction of clinical decision support systems [17]. This also applies to clinical gait analysis in post-stroke patients [18,19]. Zveryev et al. showed approximately 1.6 times more gait cycle variability in hemiparetic patients than in controls [20]. Differences in approaches to clinical gait analysis among different medical specialists have also been investigated, and the need for standardization in this area has been demonstrated [21,22].

1.2. Specificity of Post-Stroke Gait Analysis

Patients with gait impairment require dedicated solutions for the following reasons:

• the significant prevalence of stroke (it is among the three most common causes of long-term disability, despite preventive measures implemented to reduce mortality) [23,24,25,26];
• disorders occurring in both motor (including motor control) and sensory areas, often associated with other conditions and secondary lesions (including in long-term rehabilitation);
• disorders of both gait and balance functions;
• varying areas and degrees of damage and deficits which require a personalized approach to patient improvement;
• the return of lower limb function is an important goal for patients and their families as it significantly increases independence and motivation for further work;
• the risk of repeat strokes and an associated continuing need for prevention;
• the lengthy duration and multistage nature of post-stroke rehabilitation;
• the search for more effective methods of stroke rehabilitation than those currently in use is ongoing because it is not always possible to return a patient to full function, but only to the maximum performance level achievable for them, whereas improved methods of gait analysis may enable better comparative assessments and the selection of rehabilitation methods better suited to the particular condition [27].

To date, there have been many attempts to classify the gaits of post-stroke patients. Where attempts have been made, however, most of these have involved subjective observations [28].

The main reported gait disturbances in post-stroke people include the following:

• weakness of muscle strength;
• disturbances in the regulation of muscle tone;
• disorders of superficial sensation;
• disorders of deep sensation.

These abnormalities affect gait disturbances and manifest themselves in altered gait parameters, e.g., gait cycle length, stride length, and gait speed.

1.3. Former Approaches to Post-Stroke Gait Analysis

Gait dysfunction is considered one of the most common and disabling effects of stroke [29]. To date, instrumental gait analysis has been used to analyze the causes of gait deviations in post-stroke patients, but it generates a large amount of complex data, which poses a problem when there is a need to generate a short, simple report [30]. To date, three main methodological shortcomings have been identified: small sample sizes, lack of testing and selection on the basis of the method/methods best suited for analysis, and lack of detailed validation procedures [30]. A fundamental problem that occurs in clinical gait analysis is that large amounts of data are generated by laboratory analyses of human gaits, and this results in alternative attempts at reliable gait analysis based on relatively limited data sets (including heuristic methods), e.g., for the needs of the Children’s Health Centre, based on the use of artificial neural networks. A separate issue is the problem of the physical interpretation of the obtained results. An attempt to solve this problem using decision trees, neural networks, and fuzzy logic was presented by Derlatka, Pauk et al. [31,32,33].

1.4. AI-Based Approaches to Gait Analysis

Eleven databases were searched and fifteen studiesinvolving stroke patients were identified. However, following this, no method of gait analysis that could be directly applied in clinical practice when assessing the gait of a stroke patient was identified [30]. The integration of smart, low-cost wearables and artificial intelligence (AI) has led to their use in clinical settings [21].

1.4.1. Previous Gait Studies Using Artificial Neural Networks

The use of artificial neural networks for gait analysis and clinical decision support in this area was implemented relatively late, with the spread of personal computers and the rise in popularity of clinical gait analysis. It introduced the possibility of classifying gaits into normal and pathological categories directly based on gait examples rather than on a pre-built gait model. Positive results in supportive gait classification were obtained by Gioftsos and Grieve using artificial neural networks [34], and this method was soon successfully applied in athletes [35] and animals [36]. The classification of gait patterns, as well as their ageing-related changes, was demonstrated by Belg and Kamruzzaman. Their method achieved 100% classification accuracy on a selected group of patterns and enabled the identification of risk factors and measurement errors [37,38], while only a decade earlier an accuracy of 75–80% was considered acceptable. This also led to the first papers on the qualitative (rather than just quantitative) assessment of gait using artificial neural networks, based mainly on self-organizing networks (Kohonen networks). These compared spatial–temporal gait patterns, recorded in the form of curves, and related them to the correct gait cycle extracted by the network (not explicitly stated). Artificial neural networks are also being adapted to solve classification tasks related to gait analysis in patients with hemiparesis or who are recovering from fractures. Research is underway on networks adapted for personalized therapy (patient-tailored therapy) in combination with rehabilitation robots, and for predicting gait patterns and therapy outcomes [39,40].

Some have argued that the artificial neural networks used for gait analysis, particularly in athletes, remain underutilized, and that their true value remains unknown. The absence of expert systems dedicated to the analysis of movements in athletes is evidence of this.

Collaboration between representatives of technical sciences and therapists is all the more important due to the pervasiveness of sensory networks and multi-agent systems in clinical practice approaches. More and more solutions of this type are emerging, providing artificial neural networks with additional data for analysis and prompting other solutions from the field of computational intelligence. Artificial neural networks are increasingly supported by the support vector machine (SVM) method. Increasingly, deep neural networks with up to 10 layers are also being used for similar analyses, enabling much more complex feature decomposition and the discovery of hidden correlations.

1.4.2. Previous Gait Studies Using Fractal Parameters

Only a handful of papers were found in the literature addressing the problem of analyzing and classifying gait using fractal parameters. Ripoli et al. proposed a fractal algorithm that calculates a number (in the range of 1–2) characterizing the geometry of a one-dimensional signal equivalent to a gait pattern. Once the algorithm was calibrated, the results were accurate, reproducible, and independent of the amplitude of the signal (though only of the dynamics of change in the analyzed waveform). It could be used to measure an individual’s gait while walking on flat terrain, walking uphill, and climbing stairs. It should be noted, however, that the authors intended to use the developed algorithm to compare its results with data obtained from pulse sensors, electrocardiograms (ECG), and other sources [41]. No further studies appear to have been conducted by the above authors in this area. Sekine et al. showed that in patients with Parkinson’s disease, acceleration signals change in a more complex pattern with ageing and disease progression, and that their fractal dimensions are higher than those observed in healthy subjects [42]. Wang et al. have proposed a gait pattern classification system which uses a decision tree and an algorithm for estimating gait distance using information on the duration of phases in the gait cycle. This has been applied to both horizontal and stair walking, and an accuracy of 95.00–98.87% was achieved for stair walking [43]. Phinyomark et al. analyzed the influence of run length and various parameters used in fractal time series analyses of step intervals. They showed that a careful selection of fractal analysis methods and parameters is required [44]. Si et al. proposed a wearable sensor system (sensory shoes) that can be used to study human gait dynamics using a support vector machine and fractal analysis. An accuracy of 93.57% was obtained, showing its significant potential in gait identification [45].

Fractal parameters have also been used to analyze the influence of various behaviors, including gait, on EEG changes, as well as to analyze the non-linear properties of surface electromyography (sEMG), not only for the analysis of muscle activity, but also for the control of prostheses and/or other devices [46].

1.4.3. Previous Gait Studies Using Fuzzy Numbers

Sagawa et al. used fuzzy logic to assess which gait characteristic measurements and combinations best reflected severe gait dysfunction in a group of patients with cerebral palsy. Their retrospective study was conducted on 155 children aged 11 ± 5.3 years. In the study, Quinlan’s Interactive Dichotomizer 3 algorithm predicted the Gait Deviation Index (GDI) value from data concerning range of movement, muscle strength, spasticity level, etc. The establishment of seven rules allowed the algorithm to achieve an accuracy of 90%. Straight thigh muscle strength, spasticity level, and posterior tibialis muscle strength were considered the most important predictors [47]. Fuzzy logic was also used in an intelligent algorithm for (real-time) gait phase detection based on kinetic and kinematic parameters extracted from foot pressure and knee joint angle sensors. The proposed algorithm and graphical user interface have proved useful to clinicians for both physiological and pathological gait assessment [48]. The classification of pathological toe gait patterns using a fuzzy number-based algorithm was the subject of a study by Armad et al. The study included 716 patients, of whom toe gait was observed in 240. Measuring parameters, such as range of movement, degree of spasticity, and muscle strength, as well as the application of 12 rules and the use of a fuzzy logic-based algorithm for their analysis allowed the recognition of toe gait with an accuracy of 81%, and while this increased the objectivity of the result, further research and an increase in the accuracy of the algorithm are required [49]. The results of as tudy by Keegan et al. are worth noting here: the authors showed the effectiveness of a fuzzy number-based algorithm in detecting spinal ataxia in horses based on their body position (recognition accuracy >70%). A limitation of the above-mentioned study was the small size of the groups (12 horses with spinal ataxia and 12 healthy horses) [50]. This study demonstrates that kinematic findings supplemented with modern analytical methods still have great untapped potential.

1.4.4. Previous Gait Studies Using Other Methods, Techniques, and Tools

Other gait tests using methods, techniques, and tools other than those described above can be divided into those using a single method and those combining several methods.

Muniz and Nadal, in a study belonging to the first group, showed the possibility of discriminating between the vertical ground reaction forces (GRFs) on a treadmill of patients with lower limb fractures and those of a control group using principal component analysis (PCA). Based on their study, they proposed a scale to determine the degree to which a gait deviates from what is normal. The classification accuracy, which depended on the choice of parameters of the PCA algorithm, was 92.2–96.1% in a relatively small study group (13 patients with fractures and 31 healthy subjects) [51]. The above-mentioned study was followed up by Lozano-Ortiz et al., who used a group of 51 patients (13 with fractures and 38 healthy controls), combined analytical methods: they used PCA and two different neural networks (a multilayer unidirectional neural network and a self-organizing network). The use of PCA and a multilayer unidirectional neural network gave a better result: an accuracy of 96% [52].

Examples of studies from the second group include the following:

• an investigation of the possibility of using an independent component analysis (ICA) together with a fractal dimension analysis in the study of the sEMG of small movements and the recognition of movement patterns (useful for the control of robots and other rehabilitation devices);
• an investigation of the spectrum of analysis possibilities using non-linear methods;
• a study of neuromuscular disorders using a wavelet analysis;
• a number of book studies published in the field of practical biomedical signal analysis which discuss clinical gait analysis.

1.4.5. Our Own Studies on AI-Based Post-Stroke Gait Analysis

The in-house research cited in this paper on the methodology and tools for relatively simple, fast, and inexpensive clinical gait analysis using fractal parameters is among the first undertaken in this area. Due to its strong interdisciplinary nature, this research was carried out as a collaboration between the Department of Physiotherapy Ludwik Rydygier Collegium Medicum of the Nicolaus Copernicus University in Toruń, the Institute of Mechanics and Applied Informatics at Kazimierz Wielki University in Bydgoszcz, and the Neurocognitive Laboratory at the Interdisciplinary Centre for New Technologies at the Nicolaus Copernicus University in Toruń.

Our own research, cited in this paper, required previous work concerning themethodologies and tools for relatively simple, fast, and inexpensive clinical gait analysis using fuzzy logic, specifically ordered fuzzy numbers (OFNs, also called Kosińki’s fuzzy numbers (KFNs)), artificial neural networks, and multifractal analysis [53,54,55]. Our research is among the earliest attempted in this area. Further research results concerningthe use of fuzzy logic, including OFNs, to analyze health-related quality of life (HRQoL) in post-stroke patients are also in print.

The proposed computational tools have also shown their usefulness, effectiveness, reproducibility, and sensitivity in detecting cases of small and subtle changes in post-stroke patient outcomes during the rehabilitation process. This is very important as post-stroke rehabilitation is lengthy and requires the adequate motivation of the patient and family/carers.

A potential source of error or inaccuracy that may havelimitedour studies was the relatively small number of patients we were able to enroll. In addition, concerns were raised about the fidelity of the study/treatment and the rehabilitation methods used (Bobath method in the study group vs. traditional rehabilitation approach in the reference group). A detailed description of the examination and measurement methods, including professional preparation, is necessary. This will enable the replication of the study with the same research protocol.

The proposed measures based on artificial neural networks, fuzzy models, and fractal dimensions extend the existing capabilities of clinical gait assessment towards more objective clinical reasoning and future-proof them by taking into account the widespread use of wearable health devices [53,54,55].

1.5. Aim of the Study

The effectiveness of the in-house methods described above cannot be determined without further research intotheir accuracy, as well as the methodologiesthemselves. Therefore, this article presents further research on gait analysis and describes a novel combination of artificial neural networks, fuzzy logic, and multifractal analysis.

2. Materials and Methods

2.1. Materials

The study used the historical data of 92 patients who were recovering fromischemic stroke (convenience sample) (

Table 1. Characteristics of the study and reference groups.

Parameter	Study Group n = 46 (100%)	Reference Group n = 46 (100%)
Age (years):
mean	64.70	66.67
SD (standard deviation)	9.99	10.75
min	41	43
Q1 (lower quartile)	58	57
median	66	68
Q3 (upper quartile)	72	74
max	81	83
Gender:
female (F)	23 (50.00%)	22 (47.82%)
male (M)	23 (50.00%)	24 (52.18%)
Side affected:
left (L)	21(45.65%)	23 (50%)
right (P)	25(54.34%)	23 (50%)
Time after cerebrovascular accident (weeks):
mean	63.22	64.17
SD (standard deviation)	15.87	15.21
min	6	6
Q1 (lower quartile)	24	19
median	61	62
Q3 (upper quartile)	103	107
max	151	155

).

Rehabilitation method used:

• The Bobath method was used in the study group;
• The traditional rehabilitation approach was used in the reference group.

2.2. Methods

The software used in this study was MatlabR2023a with the Neural Networks toolbox (MathWorks). An analysis using fuzzy numbers (including directed fuzzy numbers) was also performed by Piotr Prokopowicz using MU-FEG software.

The use of a neural network in this study allowed us to extract from the studied parameters (spatial–temporal, fractal, fuzzy) associations and features given indirectly, classify and present the results in a form enabling their use in assessing a patient’s condition (patients qualified for a specific group according to whether they were healthy or sick, including patients with hemiplegia), and to direct the further rehabilitation process, including by assigning the studied patient to a group with specific gait characteristics. Asystem developed in this way could become the basis of a future artificially intelligent therapeutic decision support system or so-called second opinion.

The fractal dimension (FD) is included among the tools of chaos theory, as is entropy. It is an alternative to variance, standard deviation, or coefficient of variation. In the present study, the fractal dimension complements the measurement of step duration irregularity for the measurement of the traditional spatial–temporal parameters of gait: speed, pace, and gait cycle (two-step length),as well as their normalized values. In response to rehabilitation, post-stroke patients (e.g.,those with hemiplegia) exhibit a qualitative change in gait characteristics which is reflected in the time intervals of their gait cycle (typically, their gait becomes smoother).

The analysis of gait parameters using directed fuzzy numbers allows a targeted aggregation of gait parameters into a single number in the range 0–1which denotes the degree to which the gait parameters deviate from the norm for a healthy population. This approach enables the quick assessment of whether a patient’s parameters are within the normal range, and, if not, how far they deviate from this norm.

The gait quality of a healthy personis at least 0.5 on a scale of 0 to 1. However, in order to obtain a value of 1, the person tested must have gait parameters that are equal to the mean for all the gait parameters considered. The patterns of norms are thus part of a fuzzy system that is generated automatically by the MU-FEG program on the basis of data from a file, and it is possible to generate new norms by replacing the data file.

The results obtained were subjected to statistical analysis. Data were archived using a Microsoft Excel 2013 spreadsheet. Statistical calculations were performed using the Statistica 12 computer program from Statsoft (including Medical Kit) and IBM SPSS Statistics 24.

In both groups of patients undergoing rehabilitation, changes in the values of individual parameters were determined by subtracting the results of measurement one (before therapy, BP) from the results of measurement two (after therapy, AT).

The aforementioned results were interpreted as follows:

• AT − BP > 0: improvement
• AT − BP = 0: no change
• AT − BP < 0: deterioration

The exception was the fractal dimension, for whichthe results were interpreted as follows:

• AT − BP > 0: deterioration
• AT − BP = 0: no change
• AT − BP < 0: improvement

The arithmetic mean or median was used to determine the central tendency in the set of variables on the interval scale. To measure dispersion in a set of variables, the standard deviation or minimum and maximum values and lower and upper quartile values were used.

The Shapiro–Wilk test was used to determine the nature of the distribution of the variables. Interval scale variables with a distribution close to normal were presented using the arithmetic mean and standard deviation (SD). Interval scale variables whose distribution was not normal were presented using the median, minimum, and maximum valuesas well as the values of the lower quartile (Q1) and upper the quartile (Q3) (25th and 75th percentile, respectively).

When the distribution of results showed the characteristics of a normal distribution, parametric tests were used; otherwise, non-parametric tests were used.

The parametric Student’s t-test, or its non-parametric equivalent for dependent variables (the Wilcoxon signed-rank test), was used to assess the significance of differences between the initial and final measurements within the same group. When differences were found to be significant in the data obtained using the parametric tests, their magnitudes were assessed on the basis of arithmetic means. When differences were found to be significant in the data obtained using the non-parametric tests, their magnitudes were assessed on the basis of medians. Where necessary, the following methods were used to assess the significance of differences between several measurements: the parametric test, one-way analysis of variance for repeated measures to compare dependent samples, Anova or its non-parametric equivalent, and Friedman’s Anova test.

For the data analyzed using parametric tests, the Tukey post-hoc test was used to examine the nature of the differences that were observed. For the data analyzed usingnon-parametric tests, the Anova Friedman post-hoc test was used to examine the nature of the differences that were observed.

3. Results

The analysis using neural networks resulted in an excellent fit of the learned network to the complex model. Errors in the healthy/post-stroke patient classification were not observed. An attempt was made to extend the model to include the calibration of the hemiplegic gait (the fractal dimension played a decisive role as a discriminator of gait irregularity), and this was successful. A multilayer perceptron (MLP)-type neural network with three layers was used for classification due to its simplicity (Figure 1). The following six inputs related to the six basic spatial–temporal gait parameters were defined: velocity, cadence, stride length, normalized velocity, normalized cadence, and normalized stride length. Only one output indicated probability of stroke. All inputs and outputs were normalized to arange of [0,1].

The network learning process used all the data and parameters (spatial–temporal, fractal, and fuzzy) available for the 100 post-stroke patients. The data were divided into a learning set (70% of the data), a validation set (20% of the data), and a test set (10% of the data). Network training errors with the following values were obtained: learning error: 0.001; validation error: 0.003; test error: 0.005 (Figure 2,

Table 2. Selected quality assessments of the artificial neural network (the best is in bold).

Network Structure	Accuracy (Learning) (%)	Quality (Testing) (%)
MLP 6-8-1	89.02	89.68
MLP 6-9-1	91.41	92.31
MLP 6-10-1	92.81	93.13
MLP 6-12-1	91.16	92.37
MLP 6-14-1	88.46	88.74

and

Table 3. RMSE values for the best neural networks in the study.

Network Structure	RMSE (Learning) Value (–)
MLP 6-8-1	0.02
MLP 6-9-1	0.01
MLP 6-10-1	0.001
MLP 6-12-1	0.01
MLP 6-14-1	0.02

).

The changes in the fractal parameters calculated before and after therapy in the study group were statistically significant (p< 0.05). The differences in the changes in parameters measured before and after therapy in the study group and the reference group were statistically significant (p <0.05). Thus, one of the above-mentioned therapy modalities was clearly superior to the other, as is reflected in the results of the study.

A comparison of means and medians shows that, for all parameters studied, greater improvement occurred in the study group than inthe control group (

Table 4. Comparisons of changes in fractal parameters before and after therapy in the study and reference groups.

Change in study group	Mean	0.08
	SD	0.02
	Min	0.02
	Q1	0.04
	Median	0.07
	Q3	0.08
	Max	0.09
Changein reference group	Mean	0.07
	SD	0.02
	Min	0.03
	Q1	0.08
	Median	0.07
	Q3	0.08
	Max	0.09
Distribution		Not normal
p		0.042

).

The changes in the fuzzy parameters calculated before and after therapy in both groups werestatistically significant (p <0.05) (

Table 5. Comparisons of changes in fuzzy parameters before and after therapy in the study and reference groups.

Change in study group	Mean	0.07
	SD	0.01
	Min	0.01
	Q1	0.05
	Median	0.07
	Q3	0.13
	Max	0.29
Change in reference group	Mean	0.05
	SD	0.01
	Min	0.01
	Q1	0.03
	Median	0.05
	Q3	0.09
	Max	0.40
Distribution		Not normal
p		0.021

).

Correlations among the traditional (spatial–temporal) and novel (fractal and fuzzy) gait parameters are shown in

Table 6. Correlations of parameter changes before and after therapy in the study group.

	Velocity	Cadence	Stride Length	Normalized Velocity	Normalized Cadence	Normalized Stride Length	Fractal Dimension	Fuzzy Parameter
Velocity	−	0.656 p = 0.001	0.672 p = 0.003	0.942 p = 0.012	0.746 p = 0.014	0.659 p = 0.015	−0.476 0.012	0.423 0.015
Cadence		−	0.634 p = 0.005	0.816 p = 0.007	0.945 p = 0.041	n.s.	−0.561 p = 0.001	0.645 p = 0.012
Stride length			−	0.689 p = 0.006	0.366 p = 0.022	0.412 p = 0.011	−0.614 p = 0.003	0.613 p = 0.011
Normalized velocity				−	0.734 p = 0.004	0.618 p = 0.017	−0.338 p = 0.002	0.367 p = 0.008
Normalized cadence					−	0.523 p = 0.034	−0.452 p = 0.001	0.399 p = 0.005
Normalized stride length						−	−0.491 p = 0.007	0.423 p = 0.001
Fractal dimension							−	−0.478 p = 0.004
Fuzzy parameter								−

n.s.: not significant.

and

Table 7. Correlations of parameter changes before and after therapy in the control group.

	Velocity	Cadence	Stride Length	Normalized Velocity	Normalized Cadence	Normalized Stride Length	Fractal Dimension	Fuzzy Parameter
Velocity	−	0.597 p = 0.001	0.629 p = 0.000	0.912 p = 0.002	0.624 p = 0.003	0.489 p = 0.007	−0.467 0.005	0.412 0.021
Cadence		−	0.520 p = 0.003	0.518 p = 0.004	0.756 p = 0.000	n.s.	−0.576 p = 0.002	0.642 p = 0.004
Stride length			−	0.523 p = 0.003	0.491 p = 0.011	0.771 p = 0.001	−0.629 p = 0.032	0.657 p = 0.022
Normalized velocity				−	0.634 p = 0.001	0.351 p = 0.013	−0.387 p = 0.004	0.387 p = 0.016
Normalized cadence					−	n.s.	−0.487 p = 0.012	0.432 p = 0.005
Normalized stride length						−	−0.423 p = 0.006	0.412 p = 0.005
Fractal dimension							−	−0.489 p = 0.001
Fuzzy parameter								−

n.s.: not significant.

.

In the study group, high and very high correlations were observed between changes in the studied spatial–temporal gait parameters, with the exception of a statistically insignificant association between change in pace and change in the normalized gait cycle, as well as moderate to high correlations between the fractal dimension, the fuzzy parameter and the spatial–temporal gait parameters. The negative correlations for the fractal dimension are due to the fact that an improvement in this parameter implies a decrease in this parameter (inversely to the other parameters studied).

In the control group, high and very high correlations were observed between changes in the studied spatial–temporal gait parameters (with the exception of a statistically insignificant association between change in pace and change in normalized gait cycle), and moderate to high correlations were observed between the fractal dimension, fuzzy parameter, and spatial–temporal gait parameters.

4. Discussion

These findings suggest that artificial neural networks, fuzzy logic, and multifractal analysis can be useful for building simple, low-cost, and efficient computational tools for gait analysis, especially in post-stroke patients. The novelty of this finding lies in the simultaneous application of the three aforementioned technologies to develop a computational model for the analysis of a patient’s post-stroke gait. The contribution of this work consists not only in its proposal ofa new and useful clinical tool for gait assessment, even in the most severe post-stroke cases, but also in its attempt to offer a comprehensive computational explanation of observed gait phenomena and mechanisms.

4.1. Comparison with Results of Current Research

The use of modern technology in gait analysis can be of great help in both clinical diagnosis and the assessment of risk and severity of pathology. In this paper, we focus on the application of AI as a simple gate-analysis solution, replacing complex gait analysis laboratories with primary care physicians and physiotherapists. The distinguishing features of our method have already been partially described in previous papers, and the evidence of its superiority over traditional methods is unequivocal. We compared our results with findings from publications [56,57,58] dedicated to the application of modern technology to the diagnosis of gait disorders resulting from neurologic and neurodegenerative conditions. The results of this comparison showed that our solution allows a more comprehensive assessment of both the state of the gait function in patients with neural deficits and its changes following rehabilitation. Nowadays, more and more attention is being paid to preventive medicine (medicine for healthy people), including the observation of non-age-related changes, which are becoming important indicators of physiological gait (with normal function), and are important for assessing the mobility and functional capacity of healthy people and those using assistive technologies.

Because of the interest shown byclinicians in the applicability of the proposed methods, including correlations with clinical data and points focusing on real patient data, our solution has also been used in clinical trials [59,60]. However, the fast and reliable assessment of gait quality and, after aggregation, HRQoL in post-stroke patients is still a significant problem for scientists and clinicians on a global scale. Hence, semi-automatic and automatic tools for the supplementary initial assessment of patient functioning and the subsequent cyclical re-evaluation of gait to assist in the rehabilitation process are constantly being developed.

Clinical gait analysis in telemedicine and telerehabilitation primarily involves the application of established devices, such as the Kinect (Microsoft), the PlayStation Eye (Sony), and the Nintendo Wii. Adapting proven devices for biomedical purposes in this way issuitable for the development of a commercial off-the-shelf (COTS) strategy, which will involve lower research and customization costs and shorter deployment times [61,62]. A summary of the development of rapid and low-cost gait diagnostics should also include wearables and virtual reality (VR) devices.

Better testing and analytical tools and more extensive testing infrastructure can enable preventive interventions that do not require the use of complex testing procedures and specialized gait analysis laboratories [63]. Gait analysis in the natural environment, i.e., preventive testing of children at school, or of athletes or soldiers during normal activity, may become the norm. The additional capabilities of mobile applications are already enhancing the capabilities and safety of sportspeople (e.g., runners), and solutions such as smartbands, smartwatches, and breath sensors are easily integrated into telemedicine applications. The development of wearable sensors has been progressing for about 15 years, but developers have tended to focus on solutions that do not process data in real time, are not intended for people under 40 years of age; the accuracy of these sensors are typically similar to that of marker-based video image analysis, and they are used to monitor patients during the activities of daily living, e.g., stair climbing and cycling. The key issue here is the standardization of sensor mounting, and the systems described still need further research [64,65].

An important element is full digitization and the purposeful and planned use of data already collected. New analytical capabilities, combined with the wealth of patient records, can contribute to significant advancements in knowledge, not on lyin the field of gait biomechanics, but in the planning and implementation of therapy and sports training in general [63].

The proposed AI-based methods and techniques can be effective clinical and home-based tools for monitoring and rehabilitating gaits resulting from neurological and neurodegenerative disorders.

4.2. Limitations of Current Studies

Gait analysis is usually a complementary test, supporting a diagnosis made on the basis of other tests, especially in the diagnosis of various diseases and the evaluation of rehabilitation progress. Gait parameters are influenced by many different factors (height, age, gender, lower limb structure, etc.). Furthermore, the above-mentioned basic gait parameters are not sufficient, especially in medical diagnosis, so the classical gait regularity test includes the following:

• static examination;
• measurement of joint mobility;
• gait analysis.

When it comes to diagnosis and the evaluation of rehabilitation results, there is no single universal tool, technique, or method. Old solutions are constantly being improved and new ones developed for specific (mostly narrow) applications. The field of technical solutions for diagnostic support is developing particularly rapidly. This poses a challenge for medical staff, as they must be familiar with all of these solutions in order to ensure that the optimal diagnostic method is selected for each specific patient, disease, or therapy phase. There are several reasons for this:

• there are no universal methods;
• simple and quick methods are not very accurate;
• accurate, reliable, and reproducible methods are time-consuming, costly, and require complex procedures;
• some methods require organizational changes for their successful implementation.

Given this context, there is a need to pre-define the requirements of clinicians so that the designers of diagnostic systems (other clinicians, scientists, engineers) can propose more appropriate solutions. The development of smartphone apps and wearable devices means that some runners and triathletes are already using simple gait analysis solutions.

More advanced studies may include:

• the measurement of kinematic parameters (the analysis of human movements without analyzing the forces causing these movements), i.e., ranges of movement in the joints measured during gait as a trajectory of selected points on the body,
• the measurement of kinetic parameters, i.e.,the measurement of forces and moments of forces causing human movement, orthe measurement of muscle activity during gait using electromyography (EMG).

4.3. Directions for Further Research

Solutions based on computational intelligence can complement traditional methods of clinical gait analysis. Leading-edge solutions can be successfully implemented in the following cases:

• where data are difficult to acquire and must be obtainedfrom the patient during their normal activity (e.g., in children when they are uncooperative or unable to understand commands);
• where there are no data audit or the data are duplicated, incomplete, or subject to errors (including errors of unknown origin);
• where data do not permit the construction of a mathematical model and have to be analyzed by other means;
• where data must be obtained quickly, cheaply, and from a large sample.

Directions for the development of the described solutions include the following:

• investigating the long-term effects of different treatment programs;
• investigating the impact of individual characteristics (e.g., obesity);
• investigating the impact of medical conditions (e.g., diabetes);
• investigating the impact of orthopedic supplies;
• investigating the possibility of an integrated platform for automated clinical gait analysis (with online or offline video) that can be used on a mobile device (smartphone, tablet, etc.) [64,65,66,67,68,69].

One possible modification of the fuzzy analysis would be to change the fuzzy number from triangular to trapezoidal, i.e.,to extend the interval of the ‘ones’ and thus relax the ‘ideality’ criterion. The group of values close to the mean would then be evaluated as a quality equal to 1. In contrast, the use of directed fuzzy numbers (i.e., with the rising and falling slope of the fuzzy number altered) makes it possible to take into account the different speeds of influence of the ‘down’ and ‘up’ directions of change. The authors are currently involved in further research in the above area.

The proposed solution can provide practical, accurate, and rapid support for medical professionals, helping them make effective clinical decisions based on good prognoses. It could eventually become the basis for the development of new or upgraded clinical decision support systems. To date, many algorithms have followed such a development path [70,71,72,73,74], and we therefore plan to conduct further research using these algorithms to diagnose gait deficits in different groups of apparently healthy individuals and in patients with different conditions to obtain more accurate results.

5. Conclusions

The above analysis indicates the likelihood of more advanced and broader future applications of AI in gait analysis, especially in post-stroke patients.

The combination of multiple technologies from the field of AI, including artificial neural networks, fuzzy logic, and multifractal analysis, is useful for building simple, low-cost, and efficient computational tools for gait analysis, especially in post-stroke patients.

The computational post-stroke gait model we developed can be used as a basis for the development of a whole family of computational gait models for a wide range of conditions affecting the human locomotor system, especially those with a neurological basis. This may be particularly relevant for neurodegenerative changes resulting from ageing.