The Potential of Artificial Intelligence in Predicting Post-Stroke Rehabilitation Outcomes: Statistical Analysis Considering Rivermead Motor Assessment and Activities of Daily Living Indicators and Selected Demographic Variables

Abstract

Strokes are currently the third most common cause of death worldwide and the leading cause of disability in people over 50 years of age. The functioning of post-stroke patients depends primarily on well-conducted rehabilitation, both in stationary conditions and at home. The aim of this study was to evaluate the functional outcomes of patients after ischemic stroke who underwent home rehabilitation. The RMA (Rivermead Motor Assessment) and ADL (activities of daily living) scales were used for evaluation. A total of 20 patients underwent a 4-week home rehabilitation program in Cracow. In the studied group, most patients showed functional improvement after the 4-week rehabilitation period. Predictive models were created (Net1, Net2, Net3) using artificial intelligence algorithms, including regression and classification methods. The analysis results indicate that the best outcomes in predicting the RMA and ADL indicators. For Net2, the prediction accuracy for the ADL indicator was 94.4%, which is significantly higher compared to the other indicators. The RMA1-3 indicators achieved relatively low accuracy rates of 38.9–44.4%. In contrast, for Net3, the RMA1-3 indicators showed high accuracy, achieving 89.1–91.3% correct results. The conclusions of the study suggest that using a combination of the Net2 and Net3 models can contribute to optimizing the rehabilitation process, allowing therapy to be tailored to the individual needs of patients. The research proves that it is possible to predict the effect of rehabilitation by using AI. The implementation of such solutions can increase the effectiveness of post-stroke rehabilitation, particularly through the personalization of therapy and dynamic monitoring of patient progress.

1. Introduction

In today’s dynamic medical environment, where technological advancements go hand in hand with the growing needs of patients, there is a constant drive to improve rehabilitation processes. Rehabilitation is a key component of patient care, especially after various illnesses or injuries. In this context, the use of modern technologies, data analysis, and artificial intelligence methods has become an important area of research. Stroke is the leading cause of disability in people over 50 [1].

The rehabilitation process is a dynamic and individualized experience for each patient. The outcomes of therapy can depend on many factors, such as age, gender, or the level of depression. Therefore, it is crucial to explore new analytical methods to better understand the relationships between various variables and rehabilitation outcomes.

This study focuses on the application of artificial intelligence in predicting rehabilitation outcomes, particularly using the RMA (RMA1-3) and ADL indicators. Based on the statistical analysis of data collected before and after rehabilitation, the study aims to identify factors influencing therapy effectiveness. Additionally, the article focuses on developing a predictive model that uses artificial intelligence methods to forecast the values of RMA and ADL indicators based on demographic variables, such as age, gender, and the level of depression.

Despite the large number of studies on post-stroke individuals and their rehabilitation, there are few studies on models that predict rehabilitation outcomes. So, that was the purpose for this publication: to focus on developing such a model using AI tools. The objective of the research was to prove that the AI tools can be used as support of the rehabilitation process to predict the effect of rehabilitation. This prediction will help to choose the best method of rehabilitation for individual patients.

2. Related Works

In the scientific literature, there are numerous publications dedicated to RMA and ADL indicators [2,3]. For example, in article [4], a cross-sectional study was conducted to develop a tool for assessing children’s daily activities. In this study, the authors identified key elements that describe a wide range of activities of daily living (ADL) and subsequently developed a self-assessment questionnaire. In another article [5], the relationship between cognitive functioning and depressive symptoms in older adults in China was presented, along with the mediating role of daily living activities. The findings suggest that cognitive functions can affect depressive states through the ability to perform daily activities. Therefore, it is recommended to develop individualized intervention strategies for older adults to maintain or delay cognitive decline, preserve daily activity abilities, and reduce the risk of depression.

In the field of stroke rehabilitation, there are numerous studies focusing on various rehabilitation techniques. For example, article [6] analyzed the impact of early, intensive, in-hospital rehabilitation, initiated within two days of surgery and lasting up to seven days, on the improvement of daily living activities in patients with and without dementia. The paper [7] examined the impact of a triad approach—combining rehabilitation, nutritional support, and oral management—on health outcomes in post-stroke patients. This approach has gained increasing interest in improving health outcomes among older adults, although evidence of its effectiveness in stroke patients has been limited.

In paper [8], the effect of rehabilitation motivation on improving daily living activities in subacute stroke patients beginning intensive rehabilitation was explored. These results could contribute to the development of rehabilitation programs aimed at enhancing daily living activities in subacute stroke patients.

An interesting publication is article [9], which presented a novel robot-assisted mirror therapy (RMT) platform designed to support the rehabilitation of motor and vision abilities in stroke patients, particularly in cases of asymmetric limb function. Traditional mirror therapy involves using a mirror to stimulate the unaffected limb by watching its reflection. The proposed RMT platform expands the possibilities of traditional mirror therapy by enabling assisted coordination of both hands—paretic (affected by stroke) and healthy. Meanwhile, article [10] compared the level of independence in performing activities of daily living (ADLs) in stroke patients who underwent tele-rehabilitation with a control group that participated in traditional in-person rehabilitation.

A separate group of studies focuses on using the Rivermead Index (RMI). In article [11], the effectiveness of task-related training (TRT) and progressive resistive exercise (PRE) was compared in stroke patients. In article [12], the trunk muscle strength and their impact on motor function and balance in stroke patients were analyzed using the Rivermead Mobility Index (RMI) to assess mobility. The review [13] evaluated the psychometric properties of various motor assessment scales, including RMI and Rivermead Motor Assessment (RMA), confirming their utility in clinical practice and research. The systematic review in article [14] evaluated acupuncture therapies in older stroke patients.

In article [15], it was analyzed whether the RMI scale is suitable for comparing groups of stroke patients differing by age, gender, and side of brain injury. Article [16] assessed oxygen consumption and heart rate in stroke patients and healthy participants during tasks on the Modified Rivermead Mobility Index (MRMI). The findings suggest that stroke patients use more oxygen to complete these tasks, which may indicate the inclusion of these exercises in aerobic training protocols. Article [17] addresses the hierarchy of elements in the RMI scale, which allows for more efficient and quicker assessment of stroke patients. The established start-stop rules contributed to improving result interpretation and accelerating the assessment process. In article [18], MRMI was compared with the MAS scale as a tool for evaluating mobility in stroke patients.

In the area of prognostic models for predicting rehabilitation outcomes, significantly fewer studies have been conducted. In article [19], a predictive model for ADL (activities of daily living) scores upon discharge for patients with spinal cord injury was proposed, based on machine learning algorithms. The HHO-RF (Harris Hawks optimizer with Random Forest) algorithm was found to be more effective in predicting outcomes compared to traditional RF, suggesting the applicability of this model for developing more effective rehabilitation programs. A systematic review [20] investigated prognostic factors affecting upper limb recovery after stroke. Results suggest that task-oriented interventions have the greatest effect, especially in the subacute and chronic phases. In article [21], a retrospective study on mobile rehabilitation (mRehab) was conducted, analyzing data from stroke patients during a six-week home-based rehabilitation program. It was shown that combining clinical and demographic data with movement phenotype data significantly improved the accuracy of rehabilitation outcome predictions, which could be useful in developing personalized rehabilitation strategies. Study [22] aimed to identify the most effective milestones for predicting the complexity level of patient mobility at an early stage of recovery. The results showed that “maintaining balance while sitting” and “sitting unsupported” were the best predictors of future patient mobility, and these assessments can be performed in everyday clinical practice. Article [23] evaluated whether progress in balance, measured using the Berg Balance Scale, and hospitalization duration could serve as independent predictors of outcomes after inpatient rehabilitation. The results indicated that balance condition at the beginning of rehabilitation and progress made during rehabilitation were strong indicators of discharge balance outcomes, which could help tailor rehabilitation programs for patients with severe motor impairments.

The literature review suggests that various approaches to stroke patient rehabilitation, both using advanced machine learning tools and more traditional methods, are effective in different contexts. Predictive models such as HHO-RF can be valuable in clinical evaluation of rehabilitation programs, allowing for a more personalized approach to patient treatment. Moreover, simple milestones like “maintaining balance while sitting” are easily measurable predictors of rehabilitation outcomes, making them valuable in daily clinical practice.

3. Materials and Methods

3.1. Description of the Studied Patients

The rehabilitation effects were studied in a group of individuals after an ischemic stroke. Each patient stayed in the hospital in the neurology department following the stroke and was then rehabilitated for 4 to 6 weeks in the neurological rehabilitation ward. After being discharged home, each patient underwent home rehabilitation at various intervals. The patients were evaluated twice: before starting home rehabilitation (Assessment I) and after its completion (Assessment II). Due to the epidemiological situation, rehabilitation sessions took place in the home environment. The duration of home-based physiotherapy was four weeks, five days a week, excluding Saturdays and Sundays, with each session lasting about 1.5 h. All patients underwent similar exercises, including active-passive exercises, assisted exercises, breathing exercises, coordination exercises, PNF exercises, trunk muscle exercises using the Bobath method, training in daily living activities, and manual dexterity exercises. The patients were informed about their participation in the study and consented to it. Physiotherapy and assessments were conducted by the same physiotherapist in Cracow. The level of functionality was assessed using indicators such as ADL and RMA. Below, the statistics of input data regarding the patients are presented (Figure 1).

The studied patient groups were diverse in terms of gender, age, and the level of depression. Demographic characteristics are one of the factors that could impact rehabilitation outcomes.

3.1.1. The Gender

Among the studied patients, there is diversity in terms of gender, which is an important aspect when analyzing the effects of rehabilitation. Women comprised the majority of the study group (60%).

The gender of patients can significantly impact the rehabilitation process, and considering this factor is crucial for the following several reasons:

• Physiological Differences;
• Injury Predisposition;
• Pain Response;
• Psychosocial Aspects;
• Hormones and Aging;
• Rehabilitation Goals;
• Health Needs.

3.1.2. The Age

The patients represented a wide age range, from 54 to 78 years old. However, the group can be categorized as seniors. Age differences can influence the dynamics of the rehabilitation process, and analyzing these data helps identify potential correlations.

Age differences among seniors can significantly impact rehabilitation outcomes due to specific characteristics associated with aging. Below are some aspects that may be linked with age and can have a significant impact on rehabilitation results:

• Physiological Processes;
• Comorbidities;
• Psychosocial Aspects;
• Recovery Rate;
• Diverse Therapeutic Goals;
• Acceptance of Aging.

3.1.3. Other Demographic Data

Despite the availability of other demographic data, such as socio-economic status, place of residence, ethnicity, marital status, or medical history, these variables were not considered in this study phase. All patients came from the same locality, their socio-economic status was similar, and nearly all patients lived independently. Thus, the focus was on gender, age, and depression level to more accurately analyze the impact of these factors on rehabilitation outcomes.

The choice of specific demographic variables is justified by their potential impact on patients’ recovery ability and anticipated changes in RMA and ADL indicators.

3.1.4. Depression Level as an Important Factor

The Yesavage Scale, also known as the Geriatric Depression Scale (GDS), is a diagnostic tool used to assess depression levels in elderly individuals.

The scale consists of 15 questions covering various aspects of daily life and emotional well-being, with “yes” or “no” answers assigned points, resulting in a final score between 0 and 15. Higher scores indicate more severe depression symptoms.

Interpretation of scores is as follows:

• 0–4 points: no or minimal depression;
• 5–9 points: moderate depression;
• 10–15 points: severe depression.

The level of depression assessed using the 15-point Yesavage Scale is a key element in analyzing rehabilitation outcomes. The data shows varying levels of depression among patients before starting therapy.

Paying attention to patients with different levels of depression before rehabilitation and tracking if these levels correlate with therapy outcomes is valuable. This, in turn, will enable a more personalized approach to therapy, tailored to the specific needs of patients.

3.2. RMA Indicator

The Rivermead Motor Assessment (RMA) is a widely used tool for evaluating the motor abilities of stroke patients. Its primary goal is a detailed analysis of a patient’s motor capabilities, focusing specifically on limb functions as well as basic mobility and coordination skills.

The RMA consists of the following three main sections:

• RMA1—Global Functions: This section assesses basic motor skills such as sitting, standing up, walking, and running short distances. It provides a fundamental measure of the patient’s motor abilities and balance, offering insight into their mobility level.
• RMA2—Lower Limb and Trunk: Focuses on the patient’s ability to control lower limbs and trunk stability, including specific tasks like standing on one leg or lifting a leg.
• RMA3—Upper Limb: Evaluates upper limb functions, including manipulations and precise hand movements, important for everyday tasks such as lifting an arm or holding objects.

The RMA uses a binary scoring system of 0 or 1, where 1 indicates the ability to perform a given activity, and “0” indicates the inability.

3.3. ADL Indicator

The ADL (activities of daily living) index is a fundamental diagnostic tool that assesses a patient’s ability to perform daily life activities, providing a measure of their independence. The ADL assessment provides insights into the level of patient autonomy in activities such as bathing, dressing, eating, moving around, controlling physiological functions, and using the toilet.

The ADL (activities of daily living) index includes the evaluation of six key daily activities as follows:

• Bathing: Measures the patient’s ability to perform hygiene activities independently.
• Dressing: Assesses the patient’s motor skills and independence in choosing and wearing clothes.
• Eating: Evaluates the ability to manipulate objects and eat independently.
• Mobility: Tests the patient’s ability to move, essential for independent functioning.
• Bodily Functions Control: Concerns the patient’s ability to control physiological functions.
• Using the Toilet: Assesses the patient’s independence in using the toilet and maintaining personal hygiene.

Each activity is rated on a scale of 0–2, where the total score reflects the overall level of the patient’s independence, highlighting areas requiring rehabilitation support.

4. Prediction of Progress in Rehabilitation—Predictive Model

4.1. Methodology

To predict the progress in patients’ health following post-stroke rehabilitation, machine learning methods in the MATLAB vR2023b environment were utilized.

The predictive modeling study involves several key steps. Below is an overview of the process:

• Data Collection:

The first step is gathering data for training and testing the model. These data may include patient information as parameters $X=\left\{x_{1,}{x}_2,\dots ,x_{m }\right\}$, where $x_i$ represents age, gender, depression level, and health outcomes measured on various scales such as RMA1, RMA2, RMA3, and ADL. Results before rehabilitation are marked as $X_{pre}$ and after rehabilitation as $X_{post}$. Ensuring the quality of the collected data is crucial to verify that it is representative of the studied population and free of errors.

2.

Data Preparation:

The collected data are processed in several steps as follows:

• Data cleaning, which includes removing errors and filling in missing values. The dataset before cleaning is $X$ and after $X_{clean}$.
• Normalization or standardization $x_i^{\prime }$ of data to ensure consistency and facilitate model training.

  $$x_i^{\prime }={\displaystyle \frac{x_i-{\mu }_i}{{\sigma }_i}}$$

  (1)

  where μ and σ i ${\sigma }_i$ means the value and deviation of the standard deviation x and $x_i$.
• Feature engineering, which involves creating new variables $f\left(X\right)=f_1,f_2,\dots ,f_k$ from existing data.

3.

Data Splitting

The data $X_{clean}$ is split into two sets: a training set, $X_{train}$, and a simulation dataset, $X_{sim}$. The training set is used for training and adjusting the model parameters, while the simulation set is used later to assess the model’s performance on new data that it has not seen before.

Training set $X_{train}$ with corresponding labels $Y_{train}$, used to optimize the model parameters. Simulation set $X_{sim}$, used to evaluate the model on data that the model has not seen before. The sets are disjoint, i.e., $X_{train} \bigcap X_{sim}=\varnothing$.

4.

Model Selection:

Before training, different predictive models are tested, such as decision trees, logistic regression, Random Forest, and XGBoost. These models are evaluated based on their ability to predict the outcome variables such as RMA1, RMA2, RMA3, and ADL.

The tested predictive models, denoted as $M=\{M_1,M_2,\dots ,M_k\}$, are evaluated based on their ability to predict the output variables $Y=\left\{RMA1,RMA2,RMA3,ADL\right\}$.

In the first stage, the type of prediction to be applied is determined—classification or regression—depending on whether the expected output is discrete or continuous. While data in the current analysis is discrete, continuous data produced by regression methods can be converted into discrete form through appropriate transformations. These transformations are carried out at the simulation stage. On this step, the following variables were determined:

• For classification: the predicted output values $Y_{pred}$ take on discrete values.
• For regression: the predicted values $Y_{pred}$ are continuous and may later be transformed into discrete values during the stage of transforming simulation results.

During the research, several predictive models with varying input and output data structures, as well as different parameters, were tested.

5.

Model Training:

The training data are split into input and target data. There are three distinct stages during training, each evaluated as follows:

• Training:
  Data are passed through the network, and weights are updated according to a learning algorithm (such as feedforward backpropagation). The aim is to adjust the model to best represent the relationships in the training data.
  The training set $X_{train}$ is divided into an input dataset $X_{in}$ and an output dataset $Y_{target}$.
  During training, the cost function $L\left(Y_{target},Y_{pred}\right)$ is minimized

  $$\mathrm{L}(Y_{target},Y_{pred})={\displaystyle \frac{1}{N}}{{\displaystyle \sum }}_{i=1}^N\mathcal{l}\left(y_i,{\widehat{y}}_i\right),$$

  (2)

  where $\mathcal{l}$ means the chosen error metric (e.g., MSE for regression), $y_i$ represents the actual values, ${\widehat{y}}_i$ are the values predicted by the model, and N is the number of samples.
  During training, the model parameters θ are updated according to an optimization algorithm, such as the simple gradient descent method

  $$\theta \leftarrow \theta -\alpha {\nabla }_{\theta }L\left(Y_{target},Y_{pred}\right),$$

  (3)

  where α represents the learning rate.
  Goal: Minimize errors in training data.
• Validation:
  Based on the validation results, model parameters may be adjusted, or training may be stopped to avoid overfitting.
  Goal: Assess the model’s ability to generalize to new data.
• Testing:
  The test data are separate from the training and validation data, allowing for an unbiased evaluation of the model’s effectiveness.
  The model is evaluated on validation and test sets to monitor generalization. The final value of the error function on the test set is given by $L\left(Y_{test},{\widehat{Y}}_{test}\right)$, which allows for assessing the model’s effectiveness on unseen data.
  Goal: Provide an objective measure of the model’s quality on data not seen during training.

6.

Training Process Evaluation:

In this step, the training process is evaluated for accuracy in three stages: training, validation, and testing. The model is evaluated using appropriate metrics for prediction errors to understand its ability to generalize as follows:

• For regression: MSE (Mean Squared Error), RMSE (Root Mean Squared Error), MAE (Mean Absolute Error). The expression for MSE, RMSE, and MAE is given as [24]

  $$MSE={\displaystyle \frac{1}{N}}{{\displaystyle \sum }}_{i=1}^N{\left(y_i-{\widehat{y}}_i\right)}^2, RMSE=\sqrt{MSE}, MAE={\displaystyle \frac{1}{N}}{{\displaystyle \sum }}_{i=1}^N\left|y_i-{\widehat{y}}_i\right|.$$

  (4)
• For classification: accuracy, precision, recall, F1-score, and ROC AUC.
• The final evaluation of the learning process is based on the fit between the output data and target data, measured using the fit coefficient and R-value.

7.

Simulation:

After achieving a satisfactory model, it can be implemented to predict new data. In MATLAB, the obtained model can be used for predictions on new data using dedicated functions.

For this process, simulation data (which also consists of input and target data) is used, but for the simulation itself, only input data are utilized. The results from the output data from the simulation (sim output data).

The optimal model M*, tested on the simulation set $X_{sim}$, generates predictions $Y_{sim}=M\left(X_{sim}\right)$, which are continuous if the regression methods were used.

8.

Conversion of Continuous Results to Discrete Form

The simulation results (sim output data) from regression methods are in a continuous form. It is therefore necessary to convert them to a discrete form. This can be achieved using an appropriate algorithm or function. The simplest way to convert continuous results to discrete was to round the values to the nearest integer. Another approach was to define specific value ranges to represent particular discrete values. Ultimately, the simulation process produced results in a discrete form (sim-d output data).

The simulation results $Y_{sim}$ are transformed into discrete data $Y_{sim-d}$ using the following:

• Rounding: Rounding the continuous values to the nearest integer

  $$Y_{sim-d}=round\left(Y_{sim}\right).$$

  (5)
• Assigning to Intervals: The values in $Y_{sim}$ are assigned to intervals corresponding to integer values using the function P, where $P\left(Y_{sim}\right)$ returns discrete intervals.

9.

Simulation Evaluation—Final Assessment of Model Performance

Once the simulation results $Y_{sim-d}$ are converted to a discrete form, they are compared with the actual target values. The evaluation includes the following:

• Calculation of Percentage of Correct Classifications: This involves determining the percentage of correctly and incorrectly classified simulation results by counting those that matched the actual values and those that did not. This final evaluation verifies the quality of the model’s prediction of rehabilitation progress.
• Analysis of Metrics: Metrics such as F1-score, precision-recall, and confusion matrix allow for a comprehensive evaluation of the model’s effectiveness.

10.

Selection of Final Model Combination

Based on the simulation results, the final combination of models for predicting various rehabilitation outcomes is chosen as follows. For example:

• One model M_A may perform well in predicting RMA1, RMA2, and RMA3 but not ADL.
• Another model M_B may predict ADL better but struggle with other variables.

In this case, a decision is made to combine different models $M^{\ast }=\left\{M_A,M_B\right\}$, assigning them to specific output variables as follows:

• Model A for predicting RMA1, RMA2, and RMA3.
• Model B for predicting ADL.

Such a combination allows for better prediction accuracy, as each model is optimized for a particular subset of output variables.

Figure 2 presents a diagram presenting the above method of creating and selecting a prediction model.

4.2. Training and Simulation Set

The results from pre-rehabilitation assessments served as the dataset. The input data structure included features as presented in

Table 1. Input data.

No.	Age	Gender (1-Woman; 2-Men)	Depression (0–15)	RMA 1 * (0–13)	RMA 2 * (0–10)	RMA 3 * (0–15)	ADL * (0–6)
1	66	1	8	5	5	1	2
2	71	1	7	6	4	3	3
3	68	2	8	5	6	2	3
4	74	1	9	3	4	2	2
5	54	2	3	7	6	2	3
6	78	2	6	4	3	0	2
7	66	1	8	3	3	1	2
8	67	1	4	9	10	8	4
9	59	1	5	6	5	3	3
10	63	1	6	4	4	6	3

* Before rehabilitation.

.

The target data were divided into four types. In the first type, the target included four values corresponding to RMA1, RMA2, RMA3, and ADL after rehabilitation. The second type also consisted of four values, representing the difference between pre- and post-rehabilitation scores. The third type of target data included differences in the results of RMA1, RMA2, and RMA3, while the fourth type contained the difference in ADL scores.

Table 2. Models parameters.

Network Name	Data Structure (Target Structure)	Number of Layers	Neurons in Layers and Transfer Functions
Net1	1	3	Layer 1: 7 (tansig), Layer 2: 4 (tansig), Layer 3: 4 (tansig)
Net2	2	4	Layer 1: 7 (tansig), Layer 2: 7 (tansig), Layer 3: 7 (tansig), Layer 4: 4 (purelin)
Net3	2	3	Layer 1: 7 (tansig), Layer 2: 4 (tansig), Layer 3: 4 (tansig)
Net4	3	3	Layer 1: 7 (tansig), Layer 2: 7 (tansig), Layer 3: 3 (tansig)
Net5	4	4	Layer 1: 7 (tansig), Layer 2: 7 (tansig), Layer 3: 7 (tansig), Layer 4: 1 (purelin)

presents the target data used for the developed machine learning models.

4.3. Parameters of the Tested Models

During the research, dozens of predictive models with different structures of input, output data, and varying model parameters were tested. The models that yielded the best simulation results featured the following functions:

• Training Function (trainlm): The Levenberg–Marquardt algorithm (trainlm) is used to adjust weights during training. It optimizes by minimizing error through weight modification and is known for its fast convergence, especially in regression.
• Adaptive Learning Function (adaptwb): This function handles adaptive weight modification during training. It allows adjustment of learning rates over time, accelerating convergence and enhancing adaptability.
• Performance Function (MSE): The Mean Squared Error (MSE) is used to assess performance by measuring the average squared differences between actual and predicted values. Minimizing MSE means better model representation of real data.

Additionally, selected models included the following transfer functions:

• tansig (Hyperbolic Tangent): A nonlinear transfer function often used in hidden layers of neural networks. It transforms input values within a range of −1 to 1.
• purelin (Linear): A linear transfer function that outputs the input value directly. Commonly used in output layers for regression problems where a linear relationship is expected.

Below are the remaining parameters of the models that provided the best results during simulations.

The parameters for splitting the training data were uniformly set for all the tested models. They define how the available dataset is divided into three main parts: training, validation, and testing as follows:

• TrainRatio (Training Data Ratio): Specifies the percentage of data used for training the model. It constitutes 70% of the training data. These data are used to update the model’s weights and learn from examples.
• ValRatio (Validation Data Ratio): Indicates the percentage of data used for model validation. Validation data accounts for 15% of the training data and is used during training to assess performance and improve model generalization.
• TestRatio (Testing Data Ratio): Specifies the percentage of data used for model testing. These data, also constituting 15% of the training data, are used to objectively evaluate the model on unseen data.

The sum of all three ratios should equal 1, meaning the entire dataset is appropriately divided. Correctly configuring data split parameters helps in optimizing the model, minimizing overfitting, and achieving a model capable of generalizing to new data beyond the training set.

5. Results

5.1. Test Results Before and After Rehabilitation

5.1.1. Statistical Analysis of Results

The results from the studies evaluating the health status of post-stroke patients before and after rehabilitation are presented in tabular form, showing the variance results for the RMA1, RMA2, and RMA3 indices, differentiated by gender (

Table 3. F-test: two-sample variance test for the RMA1, RMA2, and RMA3 indicators.

	RMA 1 Difference		RMA2 Difference		RMA3 Difference
	Female	Male	Female	Male	Female	Male
Mean	0.964286	0.888889	0.857143	0.611111	0.50000	1
Variance	0.850529	0.810458	0.645503	0.486928	0.481481	0.470588
Observations	28	18	28	18	28	18
Degrees of freedom (df)	27	17	27	17	27	17
F-statistic (F)	1.049443		1.325663		1.023148
P(F ≤ f) one-sided	0.469968		0.275796		0.492730
One-sided F-test	2.166593		2.166593		2.166593

).

If we compare the significance of the F-tests [24] in the context of p-values for all three indicators (RMA1, RMA2, RMA3), we can observe that none of the tests reaches the traditional level of statistical significance (e.g., p < 0.05). Following are the p-values for each indicator:

• RMA1 Indicator—p-value: 0.469968;
• RMA2 Indicator—p-value: 0.275796;
• RMA3 Indicator—p-value: 0.492730.

None of these p-values is less than the traditional significance level of 0.05. This means that there are no statistically significant differences between the variances for women before rehabilitation and men for any of the indicators studied.

For the ADL indicator, an analysis between genders was also conducted using a two-sample variance test (

Table 4. F-test: two-sample for the variance of the ADL index.

	ADL Difference
	Female	Male
Mean	0.964286	0.833333
Variance	0.257937	0.147059
Observations	28	18
Degrees of freedom (df)	27	17
F-statistic (F)	1.753968
P(F ≤ f) one-sided	0.114754
One-sided F-test	2.166593

). The mean value for women is 0.964, while for men it is 0.833. The variances for both groups are 0.258 and 0.147, respectively. The analysis includes 28 observations for women and 18 for men, resulting in degrees of freedom (df) of 27 and 17. The F-statistic value is 1.754, with a one-sided p-value (P(F ≤ f)) of 0.115. The results are not statistically significant at the 0.05 significance level since the p-value is greater than this level. The one-sided F-test also does not allow us to reject the null hypothesis.

5.1.2. Correlation Between Variables and Rehabilitation Outcomes

The correlation analysis between variables presented in

Table 5. Correlation between variables and rehabilitation progress measured using RMA1, RMA2, RMA3, and ADL indicators.

	RMA1 Difference	RMA2 Difference	RMA3 Difference	ADL Difference	Depression	Age
RMA1 Difference	1
RMA2 Difference	0.555	1
RMA3 Difference	0.104	−0.214	1
ADL Difference	−0.120	−0.373	0.184	1
Depression	−0.003	0.007	−0.212	0.165	1
Age	−0.342	−0.061	−0.167	−0.028	0.287	1
Gender	−0.041	−0.159	0.340	−0.140	−0.087	0.079

provides significant insights into the relationships among them.

There is a moderate positive correlation between the change in RMA1 and RMA2 (r = 0.555). This suggests that individuals experiencing greater changes in one variable tend to experience greater changes in the other as well. This is common after strokes, where motor function limitations often affect one side of the body. The relationship between the improvement in global functions (RMA1) and the condition of the lower limbs appears relatively consistent for both indicators.

However, the correlation between changes in RMA1 and RMA3 is low (r = 0.104), indicating no strong relationship between these two variables. There is also no significant correlation between the change in RMA1 and the change in ADL (r = −0.120). A somewhat stronger negative correlation exists between the change in ADL and the change in RMA2 (r = −0.373).

5.1.3. The Influence of the Level of Depression on the Effects of Rehabilitation

In the case of depression, there is no strong correlation between the change in RMA1 and the level of depression (r = −0.003). Similarly, the correlation between the change in RMA2 and the level of depression is minimal (r = 0.007). However, the correlation between the change in RMA3 and the level of depression is moderately negative (r = −0.212), indicating that depression may negatively impact improvements in RMA3, which reflects overall physical condition. The correlation between changes in ADL and depression level is weakly positive (r = 0.165) but strongest from different factors, suggesting that individuals with higher levels of depression may have a tendency towards greater improvements in the ADL indicator. Pearson correlation interpretation in the medical field is as follows [25]:

• <0.29—weak correlation;
• 0.30–0.59—moderate correlation;
• 0.60–0.79—moderate to strong correlation;
• 0.80–0.99—very strong correlation;
• 1—perfect correlation.

5.1.4. The Influence of Age on the Effects of Rehabilitation

The impact of age on individual indicators is as follows: there is a moderate negative correlation between changes in RMA1 and age (r = −0.342). This suggests that older individuals may experience smaller changes in RMA1. There is also no correlation between changes in RMA2 and age (r = −0.061), as well as between changes in RMA3 and age (r = −0.167), which is weakly negative, and ADL and age (r = −0.028) show no correlation. This means that older individuals may experience less improvement in these indicators.

5.1.5. The Role of Gender in Rehabilitation

The correlation between gender and changes in RMA1 is minor (r = −0.041). It is important to note that females were labeled as “1” and males as “2”. A slightly weak negative correlation is seen with RMA2 (r = −0.159). There is no strong relationship between gender and changes in RMA1 or RMA2. However, the correlation between gender and changes in RMA3 is moderately positive (r = 0.340), suggesting that gender might influence changes in RMA3 (with greater improvement observed in men), although this relationship is not strong.

5.2. Results from Testing Predictive Models

The results from the training process, specifically the graphs illustrating the degree of fit between the output values and targets during the training of selected predictive models (as specified in Table 2), are presented in Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7.

The first tested model, Net1, aimed to predict target values for the indicators RMA1, RMA2, RMA3, and ADL.

The training results for each of the models are presented as follows:

• Net1:

  ○

  During training, a very high fit score of R = 0.99998 was obtained, indicating excellent adaptation of the model to the training data.

  ○

  During validation, the result was R = 0.8665, meaning the model performed slightly worse on unseen data but still maintained a high level of fit.

  ○

  A result of R = 83,381 for the test set suggests potential overfitting to the training data, possibly leading to poorer generalization to new data.

• Net2:

  ○

  The training result was 0.50367, indicating a moderate fit of the model to the training data.

  ○

  During validation, the result was R = 0.77451, meaning the model performed better than Net1 on new data, but there are still areas for improvement.

  ○

  A result of R = 0.50028 for the test set suggests that the model struggles on new data, indicating a generalization problem.

• Net3:

  ○

  The model achieved a training result of 0.67851, suggesting moderate fit.

  ○

  Validation result was 0.62192, indicating similar model performance on validation data as on training data.

  ○

  A test set result of R = 0.73999 is fairly good, suggesting the model has the ability to generalize to new data.

• Net4:

  ○

  The model achieved a training result of 0.49892, indicating moderate fit.

  ○

  The validation result was 0.33994, suggesting that the model does not perform well on new data, possibly due to overfitting on training data.

  ○

  A test set result of R = 0.55212 suggests moderate model generalization capability.

• Net5:

  ○

  The model achieved a very high training result of 0.87627, indicating a strong fit to the training data.

  ○

  The validation result was 0.95191, suggesting the model performs well on new data.

  ○

  However, a test set result of R = 0.0 is concerning and may indicate a problem with the model or the test data.

None of the models tested yielded satisfactory results during the training process, which should be explicitly noted: these results relate to the so-called training process. Nevertheless, the assessment of simulation results, as part of the subsequent steps of the presented methodology (Section 4.1), provided interesting findings.

6. Choosing the Optimal Model

The selection of the optimal predictive model within the presented methodology requires the evaluation of simulation results obtained for the five considered models (Net1 to Net5), taking into account the indicators RMA1, RMA2, RMA3, and ADL. The results from the training process alone, which, as indicated in the previous chapter, are overly satisfactory, are not sufficient for the final model selection. Based on experience in predicting, among other things, technical conditions [26] or process predictions [27,28], the authors decided to apply an analogous method for predicting rehabilitation outcomes.

This chapter presents the simulation results that enabled the selection of the best model or combination of models that could provide the most reliable forecasts for each of the rehabilitation indicators. The key challenge was to ensure that the chosen model exhibited high accuracy, precision, and Cohen’s Kappa coefficient.

The results of the simulation process required transforming the regression outputs from continuous to discrete values (stages 7 and 8 in the methodology). This transformation allowed for a more effective evaluation of prediction accuracy, particularly for the RMA and ADL indicators, which had a defined number of discrete classes. This was a crucial step, as the continuous results obtained from training the regression models did not allow for direct comparison with the actual outcomes.

6.1. Analysis of Simulation Results

As a result of the conducted simulation, confusion matrices were obtained for each of the models and for the indicators RMA1, RMA2, RMA3, and ADL. Below are the simulation results for the best of the analyzed models.

6.1.1. Net2

The analysis of the results for the Net2 model demonstrated very high effectiveness, particularly for the ADL indicator, with an accuracy of 94%. The model exhibited high precision at 92% and recall at 96%, suggesting an excellent ability to detect positive cases. Cohen’s Kappa value was 0.93, indicating a high level of agreement between actual results and predictions.

Table 6. Prediction accuracy for the Net2 model for simulation data. The best result is marked by blue color.

	RMA1	RMA2	RMA3	ADL
Correct result	44.4	44.4	38.9	94.4
Incorrect result	55.6	55.6	61.1	5.6
All cases	100	100	100	100

presents the percentage share of correct and incorrect outcomes obtained using the Net2 model for predicting the indicators. The Net2 model achieved its best performance for the ADL indicator, with a classification accuracy of 94.44%, while the RMA1, RMA2, and RMA3 indicators had lower effectiveness (44.44%, 44.44%, and 38.89%, respectively).

Figure 8 presents the confusion matrices for the Net2 model, allowing for visualization of its effectiveness in distinguishing correct and incorrect classifications for each of the indicators. The analysis of the confusion matrices shows that the Net2 model achieved its best performance for the ADL indicator, with an accuracy of 94% and an F1-score of 94%. The high Cohen’s Kappa value (0.93) indicates that this model has very high agreement between actual results and predictions, making it highly useful in clinical practice.

6.1.2. Net3

The Net3 model demonstrated high effectiveness in predicting the RMA3 indicator, with an accuracy of 91%. The model had high precision at 89% and recall at 93%, which suggests a good ability to detect true positive cases. The F1-score was 91%, and Cohen’s Kappa value was 0.89, indicating a high level of agreement between actual results and predictions.

Table 7. Prediction accuracy for the Net3 model for simulation data. The best results is marked by blue color.

	RMA1	RMA2	RMA3	ADL
Correct result	83.3	83.3	94.4	44.4
Incorrect result	16.7	16.7	5.6	55.6
All cases	100	100	100	100

presents the results of the Net3 model for different indicators. The best performance was achieved for the RMA3 indicator, with an accuracy of 94.44%, while the RMA1 and RMA2 indicators also achieved high accuracy at 83.3%. In contrast, the ADL indicator had the lowest accuracy, at 44.44%.

Figure 9 presents the confusion matrices for the Net3 model, allowing visualization of its effectiveness in distinguishing between correct and incorrect classifications for each of the indicators. These results show that the Net3 model achieved the best results for the RMA3 indicator. Additionally, the results for the RMA1 and RMA2 indicators are also satisfactory, making this model highly effective in the context of motor rehabilitation.

6.2. Summary of Simulation Results

The classification metrics results (for both the training process and the simulation) are presented in

Table 8. The classification metric results for the training process and the simulation. The best result is marked by blue color.

Model	Feature	Accuracy	Precision	Recall	F1-Score	Cohen’s Kappa
N1	RMA1	67.4%	71.1%	73.1%	64.4%	67.4%
N1	RMA2	58.7%	55.9%	62.8%	54.4%	58.7%
N1	RMA3	58.7%	57.5%	65.9%	57.3%	58.7%
N1	ADL	71.7%	57.9%	45.0%	45.0%	71.7%
N2	RMA1	54.3%	33.3%	32.6%	31.7%	54.3%
N2	RMA2	50.0%	40.1%	41.0%	36.8%	50.0%
N2	RMA3	54.3%	56.3%	54.9%	54.0%	54.3%
N2	ADL	93.5%	89.4%	87.1%	88.0%	93.5%
N3	RMA1	91.3%	91.7%	87.1%	88.1%	91.3%
N3	RMA2	89.1%	84.0%	80.1%	81.6%	89.1%
N3	RMA3	91.3%	92.4%	90.1%	90.0%	91.3%
N3	ADL	39.1%	20.8%	24.9%	20.6%	39.1%
N4	RMA1	0.0%	0.0%	0.0%	0.0%	0.0%
N4	RMA2	0.0%	0.0%	0.0%	0.0%	0.0%
N4	RMA3	4.3%	0.4%	9.1%	0.8%	4.3%
N4	ADL	87.0%	66.2%	76.0%	69.6%	87.0%
N5	RMA1	39.1%	36.8%	31.4%	31.1%	39.1%
N5	RMA2	60.9%	57.1%	66.3%	57.9%	60.9%
N5	RMA3	39.1%	32.0%	33.9%	31.7%	39.1%
N5	ADL	0.0%	0.0%	0.0%	0.0%	0.0%

. Based on these results, it can also be observed that, similar to the simulation process alone, the best results for RMA1, RMA2, and RMA3 were provided by the Net3 model, while the best results for ADL were obtained with the Net2 model.

Based on the conducted analysis of the simulation results, as well as the combined results from the training process and simulation compared to actual outcomes, the optimal model was chosen as a combination of the Net2 and Net3 models. The Net2 model proved to be the best for predicting the ADL indicator (Figure 10), achieving very high accuracy and precision. Meanwhile, the Net3 model was the most effective for the RMA1, RMA2, and RMA3 indicators (Figure 11), which suggests its usefulness in assessing patients’ motor progress.

Based on the presented results, it can be observed that the prediction accuracy for the ADL indicator is 94.4%, which is significantly higher compared to the other indicators. The RMA1, RMA2, and RMA3 indicators achieved relatively low accuracy of 44.4%, 44.4%, and 38.9%, respectively, suggesting that the model had difficulties predicting these values. In particular, the RMA3 indicator achieved the lowest accuracy, indicating the need for further research to improve the model’s prediction capabilities in this area. Overall, the model demonstrated the highest effectiveness for the ADL indicator.

Based on Figure 11, the following conclusions can be drawn regarding the accuracy of predicted outcomes in different categories:

The RMA1, RMA2, and RMA3 indicators showed high accuracy, achieving 91.3%, 89.1%, and 91.3% correct results, respectively. These indicators also have a small percentage of incorrect results, ranging from 8.7% to 10.9%.

For the ADL indicator, the results were less precise, with an accuracy of 26.1%, while 73.9% were incorrect predictions. This suggests difficulties in predicting the ADL indicator compared to the other variables.

The combination of the Net2 and Net3 models allows for optimal results across different aspects of rehabilitation. The Net3 model can be used for predicting rehabilitation outcomes related to motor functions, while the Net2 model provides detailed forecasts regarding improvements in activities of daily living (ADL).

The decision to combine the models stems from the observation that each model specializes in different areas of prediction. This hybrid combination allows for maximizing the potential of each model and increasing the overall effectiveness of predicting rehabilitation outcomes.

7. Discussion

The study results demonstrated the significant potential of artificial intelligence (AI) in post-stroke rehabilitation, but there are certain challenges that must be considered for practical implementation of this technology. Below, key aspects regarding future research, improvements in predictive models, and potential applications in clinical practice are discussed.

7.1. The Need for Dataset Expansion

To increase the effectiveness of AI models, it is necessary to expand the input dataset used to train the algorithms. Currently, the utilized data may not be sufficient to fully capture the complexity of post-stroke rehabilitation for patients belonging to different demographic groups (e.g., distinguished by age or residence). Therefore, future research should focus on expanding the dataset and considering additional variables, such as pre-rehabilitation physical activity, social/family support, the patient’s attitude toward the illness, and detailed data regarding the medical history and other aspects that may prove crucial during treatment and rehabilitation processes, relating to individual patient characteristics, beliefs, or biases. Diversifying the data will undoubtedly contribute to improving the accuracy and reliability of predictive models, as well as help better understand the factors that influence rehabilitation effectiveness.

7.2. Development and Optimization of Hybrid Models

Hybrid models that combine different predictive approaches have great potential in the context of rehabilitation. Such an approach could help in more accurately predicting therapy outcomes by using the most appropriate predictors based on the individual needs of the patient and the effectiveness of predicting a given indicator by a particular model. An essential aspect of developing such models is the use of advanced predictor selection methods that identify the most valuable features among a wide range of available data, thus increasing the accuracy of predictions.

7.3. Benefits and Limitations of AI Application in Rehabilitation

The introduction of artificial intelligence into post-stroke rehabilitation can bring numerous benefits, but it can also present certain challenges.

7.4. Benefits

• Personalization of Therapy: The implementation of AI can enable the customization of the rehabilitation process according to the individual needs of each patient. Based on a wide range of data, the intensity and type of exercises could be tailored to the patient’s specific characteristics and capabilities, which would enhance the effectiveness of the therapy.
• Monitoring Progress: The ability to automatically monitor patient progress would facilitate dynamic adjustment of the therapy plan. This would allow for quick responses to changes in the patient’s condition, resulting in more effective management of the rehabilitation process.
• Greater efficiency: Based on the patient’s data—such as age, gender, depression level, and assessed ability for independent functioning and mobility (parameters RMA and ADL) before rehabilitation—the therapist can utilize the developed model. Depending on the input data and recommended rehabilitation program, the model will determine if the chosen program will yield the expected benefits. If not, the model (in an extended version) will suggest a new rehabilitation program that offers a higher chance of recovery. The developed model can also be used by doctors to select the appropriate rehabilitation program after evaluating the patient’s motor skills. This approach will help reduce costs associated with ineffective rehabilitation treatments and prevent unnecessary extension of the rehabilitation process.

7.5. Limitations

• Data Quality: AI models require large amounts of high-quality data that must be representative of the target patient population. Lack of access to appropriate data or insufficient data quality can lead to incorrect predictions. Human error, such as patients’ reluctance to provide honest answers, points to the need for the implementation of appropriate methods and techniques for acquiring such data.
• Interpretation of Results: The results generated by AI models can be difficult for medical staff to understand, especially if they are not adequately explained. Therefore, it is crucial to develop tools and applications that are intuitive to use and easy to interpret, which will increase their acceptance and effectiveness in clinical practice. In addition to improving algorithms, it will also be necessary to properly train medical staff. An important aspect is ensuring algorithm transparency so that medical personnel can trust the decisions made by AI-based systems.

In summary, artificial intelligence holds great potential in post-stroke rehabilitation, particularly in terms of personalizing therapy and dynamically monitoring patient progress. However, to fully realize this potential, further research is needed to expand and improve the quality of data, optimize models, and ensure their interpretability and acceptance in clinical practice.

8. Conclusions

8.1. Summary of Main Findings

The results of this study indicate the potential for using artificial intelligence as a tool to support the rehabilitation process for stroke patients, particularly in predicting therapy outcomes. The potential of AI models lies in better adapting rehabilitation programs to individual patient needs, which could lead to a more personalized approach to therapy; however, further research is needed to fully validate this effectiveness.

Despite challenges related to overfitting and difficulties in generalizing the results, the approach proposed by the authors—combining several predictive models—appears to be an effective solution. The best results were achieved by combining the Net2 model for the ADL indicator with the Net3 model for RMA indicators, suggesting the possibility of creating a hybrid predictive tool that accounts for both daily living activities and motor functions progress. The use of regression methods for classification, incorporating all examined indicators in both the input and output datasets, and focusing on predicting the change rather than the indicator value itself, provided the best results in the conducted studies.

8.2. Practical Implications

The introduction of a combined method, where the trained model contains more input data but only certain data points are considered based on fitting accuracy, can help improve the effectiveness of predicting outcomes, including rehabilitation outcomes. However, this type of approach requires more advanced post-processing methods to identify the most suitable indicators. As demonstrated in this article, analyzing results from the training process alone for regression models can yield unreliable outcomes. This is due both to the challenge of classifying continuous values into discrete ones and the inconsistency of the results, which can be very good for one indicator but less accurate for others.

Future research directions should include enhancing algorithms in terms of their ability to generalize to new data and considering a broader range of variables, such as psychological aspects, social support, and the overall health status of the patient. Introducing AI into clinical practice could significantly improve the effectiveness of rehabilitation, but further research is needed to optimize models and establish standards for their use.