Prescriptive analytics decision-making system for cardiovascular disease prediction in long COVID patients using advanced reinforcement learning algorithms

Abstract

In recent years Covid-19 impact is causing unprecedented difficulties worldwide, affecting lifestyle choices. The post-pandemic era has made this even more critical.COVID-19 triggers widespread inflammation throughout the body, potentially causing damage to the heart and other vital organs. Mortality data from COVID-19 clearly show that the highest death rates occur in individuals with chronic conditions, such as diabetes, pneumonia, cardiovascular disease (CVD), and acute renal failure.CVD is a particular concern in the medical field. The early detection of CVD remains a significant challenge, as early identification can prompt lifestyle changes and ensure appropriate medical interventions when needed. Individuals with CVD are at an increased risk for heart attack and other serious complications. There is a limited amount of data available to study the effects of COVID-19 on CVD in COVID-19 patients. However, it is essential to monitor these patients to ensure full recovery without complications. The proposed system is specifically designed for individuals experiencing prolonged symptoms following a COVID-19 infection, commonly referred to as long COVID patients. This research introduces a novel Decision-Making System for CVD Prediction, utilizing an improved dual-attention residual bi-directional gated recurrent neural network unit (DA-ResBiGRU) algorithm with AI-Biruni Earth Radius Optimization (ABER). The proposed system employs state-of-the-art predictive algorithms and real-time monitoring to assess individual patient risk profiles accurately. This research addresses the critical need for personalized risk assessment in patients with long-term COVID, aiming to assist healthcare providers in timely and targeted interventions. By analyzing intricate patterns in patient data, the decision-making system enhances the precision of CVD prediction. Additionally, the system's adaptive nature allows it to continuously learn from new patient data, ensuring that its predictions remain up-to-date and reflective of the evolving understanding of long COVID-related cardiovascular risks. The simulation findings of this research highlight the potential of the proposed algorithm to be integrated into clinical decision-making, helping healthcare professionals identify high-risk patients more effectively. The proposed method outperformed existing algorithms, such as Deep Neural Network (DNN), Long short-term memory (LSTM), Inception-v3, Xception, and MobileNetV2, achieving the highest accuracy (97.88%), sensitivity (95.50%), specificity (94.29%), precision (96.68%), and F-measure (95.85%).

Keywords

COVID-19 cardiovascular disease deep learning improved dual attention residual bi-directional gated recurrent neural network unit

Introduction

COVID-19 is the world's first global corona virus pandemic and public awareness is still growing. Furthermore, to improve medical technologies, big data is critical in preventing and controlling COVID-19.^1,2 Chronic cardiovascular and other health conditions frequently cause death in COVID-19 individuals. In the past decade, CVD has remained the leading cause of death and is the principal cause of mortality.³In India, severe heart disease claims approximately 1.7 million lives annually. The World Health Organization (WHO) has recognized heart disease as a significant contributor to global illness and death rates. In 2019, CVD were the cause of approximately 17.9 million deaths globally, representing 32% of all fatalities. Among these CVD-related deaths, heart attacks and strokes accounted for 85% of the cases. Every day, the healthcare industry generates massive amounts of data, including redundancy, multitasking, insufficient information, and close links with time. Such information is challenging to handle, and data-mining approaches aid in the intelligent use of this information to extract essential insights and generate conclusions. Consequently, these approaches can assist healthcare practitioners in making more effective patient treatment decisions in a shorter time.⁴

When evaluating the efficiency of hybrid models that incorporate diverse methodologies, several researchers have investigated numerous methods to improve the accuracy of predictions, such as neural networks and machine learning (ML).⁵ ML and deep learning (DL) technologies have shown significant promise in supporting clinical decision making, assisting in developing medical guidelines and management algorithms, and promoting evidence-based medical practice for treating CVD.⁶Although ML⁷ and DL⁸ systems offer potential results in CVD prediction, they are not without barriers. The primary challenge is the complexity and diversity of the CVD information, which is often complicated by disjointed datasets. Another crucial issue is interpreting the model results. Traditional ML and DL models may only occasionally provide clear information on how the model arrived at its predictions, which medical professionals frequently want. Additionally, early diagnosis of cardiovascular disease using ML algorithms may eliminate the requirement for expensive and extensive clinical and laboratory testing, thereby lowering the cost imposed on healthcare organizations and patients.⁹

As a result, transfer learning (TL) has become a highly effective approach for enhancing the accuracy of CVD prediction. This technique uses knowledge from related domains and tasks and applies it to a particular focus domain, even though the data distribution differs significantly. The specific form of this strategy has attracted considerable research attention. This enables an effortless exchange of information across areas, such as unifying knowledge from clinical images to genetic data, even if these data sources are unrelated to the same topic. This article explores the application of ML algorithms combined with various analytical methods to detect and diagnose cardiovascular diseases in post-COVID-19 patients.¹⁰

This study introduces an innovative approach using an enhanced DA-ResBiGRU model integrated with ABER for improved CVD classification. The proposed method focuses on predicting and classifying CVD in long-term COVID-19 patients by utilizing two distinct datasets. The first dataset comprises cardiac magnetic resonance (CMR) images, which undergo preprocessing steps such as median filtering, intensity normalization, and histogram matching. These images are then segmented using a deep autoencoder network (DAE) combined with Bayesian fuzzy clustering, followed by feature extraction using VGG19. The second dataset consists of tabular data, which is preprocessed by cleaning, detecting, and removing outliers using the interquartile range (IQR), and performing feature selection through sequential forward selection (SFS). Finally, the classification is performed using the proposed DA-ResBiGRU model optimized with ABER. This comprehensive framework aims to enhance the accuracy and reliability of CVD prediction in long-term COVID-19 patients.

The major contributions of this study are as follows.

To introduce a novel attention-based system for cross-modal transfer learning, enabling accurate forecasting of CVD. This method effectively addresses the complexities associated with analyzing CVD data by integrating multimodal datasets.

To enhance the generalization capability of the proposed model, two distinct datasets were utilized for training, ensuring robust performance across diverse scenarios.

To optimize the machine learning model's performance, hyperparameter tuning was employed, refining the selection of parameters during the training process.

To rigorously evaluate the proposed framework, its performance was compared against existing studies using key metrics such as accuracy, sensitivity, precision, F1 score, ROC, and MCC, demonstrating its effectiveness and reliability.

The structure of this paper is as follows: Section 2 provides a review of the literature, Section 3 describes the proposed method, Section 4 discusses the analysis and results, and Section 5 concludes with future research directions.

Literature survey

Pedro Ribeiro et al. (2024) examined three medical situations: low, moderate, and severe CVD. Two ECG signals were recorded for each situation from two different body postures. Then, ten nonlinear features were selected based on every recorded signal during each 1-s ECG time series and fed into 19 ML classifiers using a leave-one-out cross-validation approach.¹¹ Muhammad Ali Muzamil et al. (2024) suggest incorporating AI into ECG technology could transform cardiology by improving the detection and treatment of cardiac disorders. This progress can be achieved through scientific inquiry, cross-disciplinary collaboration, and the consideration of ethical ramifications. However, deploying AI-enhanced electrocardiograms requires a comprehensive evaluation of ethical issues.¹²

Pawan Singh et al. (2024) developed various ML techniques to correlate human gait metrics and better understand cardiac health. Current technology allows for a noninvasive and effective assessment of each individual's risk of developing heart disease.Multiple gait metrics, including step length, cadence, and speed, were initially experimentally measured using gait systems and retroreflective markers.The experimental datasets were used to train the ML model, which was then tested using different gait metrics.¹³ Mumita Moitra et al. (2023) created a CNN-based DL system that can predict CVD risk in COVID-19 patients with an accuracy of up to 97.97%. The efficacy of the proposed model was evaluated using measurements from cardiac CT scans, including the cardiothoracic ratio (CTR), pulmonary artery-to-aorta ratio (PA/A), and calcified plaque.¹⁴

Vaishali Baviskar et al. (2023) created a new Genetic Sine Algorithm (GSA) to identify optimal features while avoiding local optima. Recurrent Neural Network (RNN) classification technology influences the extracted features combined with the LSTM method. Deep Progressive Attention-RNN + LSTM (DPA-RNN + LSTM) was designed to increase the classification rate by filtering all incorrect information and emphasizing critical information.¹⁵ Morten Heath et al. (2023) conducted a survey of PubMed and Embase, supplemented with references to pertinent preceding research. This study included publications that compared one type of interpretation to another in a healthcare setting, including those that did not provide an interpretation or measure patient outcomes.¹⁶

Mahbub Jaafari et al. (2023) employed DL technologies to diagnose CVD using CMR data, a field that is now being extensively researched. This review presents an overview of the research that uses CMR imaging and DL approaches to detect CVD.The introductory section explains the types of CVD, diagnostic approaches, and most essential medical imaging modalities.This work discussed research on CVD identification using CMR images, as well as the most relevant DL algorithms.¹⁷ Saran Kumar et al. (2023) introduced a stacked ensemble framework designed for feature extraction, selection, and classification. Their approach utilized a novel sample-based neural network inference technique to develop classification and stacking models. To enhance the model's performance and achieve a global optimal solution, the study incorporated the Hawks Optimizer (HO). The dataset used to predict CVD was obtained from an open-site Kaggle CVD Prediction Dataset.The dataset class imbalance problem is also a significant factor that must be addressed to improve prediction quality.¹⁸

Hatice et al. (2022) introduced COVID-DSNet, a DCNN to predict common types of pneumonia (bacterial and viral) as well as COVID-19, using CT scans, chest X-rays (CXR), and a integration of both imaging types. The proposed model is a cost-effective and practical DL network that can be easily utilized and further developed by data scientists.¹⁹ Karthick et al. (2022) aimed to create a hybrid dataset to improve the development of more accurate cardiovascular disease (CVD) risk prediction models. To achieve this, they combined multiple datasets to form the “Sathvi” dataset, which consists of 531 instances, 12 attributes, and no missing values.²⁰ In a related study, Nandakumar P et al. (2022) introduced the Hamming distance feature selection method for preprocessing and cleaning various heart disease datasets.DL models, such as deep belief networks with the bionic cuckoo search algorithm, are used to make precise predictions about heart diseases.²¹

Misha Urooj Khan et al. (2022) proposed detecting CVD via PCG signal processing with artificial neural networks (ANN) and spectral feature fusion. The input was processed, and the five spectral characteristics with the highest pairwise variability were selected. The proposed system offers advantages over current techniques, being noninvasive and dependable.²² Jyoti Metan et al. (2021) suggested that the full-depth convolutional neural network optimized with the Sand Piper optimization (FDCN-SPO) method demonstrated the highest accuracy and computational performance for myocardial mass, wall thickness, left and right ventricular volumes, and ejection ratio.²³

Essam H. Houssein et al. (2021) developed various ECG signal descriptors for feature extraction using one-dimensional local binary patterns (LBP), wavelets, higher-order statistics (HOS), and morphological information. A hybrid ECG arrhythmia classification method, MRFO-SVM, has been proposed for feature selection and classification.²⁴Table 1 presents a summary of the detailed survey.

Table 1.

Summary of the existing literature survey.

Ref No	Techniques used	Advantage	Limitation
¹¹	Various Machine learning classifiers	It shows a 7.57% improvement.	It is important to extract more feature.
¹⁵	DPA-RNN + LSTM	99.21% accuracy	Need to reduce the computational cost.
¹⁸	Hawks Optimizer (HO)	accuracy of 97%	Need to reduce the computational time
²⁰	CatBoost ML classifier	A mean accuracy of 94.34%	Proper training and understanding of the model are essential for accurate results
²¹	Deep Belief Network	High Accuracy	Need to improve the performance of classification models
²²	artificial neural networks (ANN)	99.99% accuracy	ANNs require careful tuning of hyperparameters to achieve optimal performance
²⁴	MRFO-SVM	Overall classification accuracy of 98.26%	High Computational Cost

Problem statement

Among the various complications associated with long-term COVID, there is a growing recognition of cardiovascular involvement in affected individuals.CVD prediction and classification in patients with long-term COVID-19 present a multifaceted challenge.First, the pathophysiological mechanisms underlying cardiovascular complications in Long COVID are not fully understood.While acute COVID-19 has been linked to inflammation, endothelial dysfunction, and hypercoagulability, the persistence of these factors in long-term patients poses unique challenges for the accurate prediction and classification of CVD.Second, the manifestation of cardiovascular symptoms may vary widely among individuals with Long COVID periods, making it difficult to establish a standardized set of parameters for prediction models.Some patients may experience persistent chest pain, arrhythmias, or myocardial inflammation, whereas others may display more subtle signs, such as exercise intolerance or fatigue.This heterogeneity complicates the development of predictive algorithms that can reliably identify individuals at risk of cardiovascular complications.

In addition, the longitudinal nature of Long COVID necessitates continuous monitoring and reassessment, as cardiovascular symptoms may evolve over time. Effective prediction and classification models must account for the dynamic changes in the clinical presentation of CVD in patients with long-term COVID-19. Addressing these challenges requires a comprehensive understanding of the interplay between viral persistence, immune response, and cardiovascular pathology, coupled with advanced ML techniques to develop robust predictive models tailored to the unique characteristics of Long COVID. The successful development of such models could significantly enhance early intervention strategies and improve outcomes for individuals at risk for cardiovascular complications in the extended aftermath of COVID-19.Existing cardiovascular disease prediction methodologies employing deep learning and machine learning algorithms for long-term COVID-19 patients have numerous limitations.Many models exhibit a lack of generalizability because they are trained on restricted datasets that may not represent a diverse patient population.Second, they frequently neglect to integrate real-time data, thereby constraining their efficacy in dynamic clinical settings.Moreover, the interpretability of the models is frequently inadequate, complicating the ability of healthcare professionals to comprehend the rationale behind the predictions.Ultimately, there exists a risk of overfitting, wherein models exhibit strong performance on training data, yet falter on novel instances.

Proposed methodology

Predicting and classifying CVD in patients with long-term COVID-19 is crucial for identifying the potential health risks associated with the aftermath of the virus.Researchers have employed a multifaceted approach that integrates information from both the CMR and tabular datasets.For the CMR dataset, a comprehensive preprocessing pipeline was implemented, starting with the application of a median filter to reduce noise, followed by intensity normalization and histogram matching for standardization.The data were then segmented using DAE with Bayesian fuzzy clustering to enhance the accuracy of delineating relevant cardiac structures.Feature extraction was accomplished using the VGG19 model, capturing high-level representations that contribute to the subsequent prediction model. Figure 1 shows the proposed block diagram. Simultaneously, a tabular dataset undergoes preprocessing steps to ensure data quality. Cleaning processes address missing or inconsistent values, whereas numerical reduction techniques identify and handle outliers using IQR.Furthermore, feature selection through SFS refines the dataset and retains the essential variables for the predictive model. The final classification step involves an Improved DA-ResBiGRU with ABER. This advanced model integrates attention mechanisms, residual connections, and bidirectional recurrent units to capture temporal dependencies and intricate patterns, ultimately providing a robust prediction and classification framework for cardiovascular risks in patients with long-term COVID-19.

Figure 1.

Proposed block diagram.

CVD prediction using CMR dataset

Advanced medical imaging techniques such as CMR imaging have emerged as promising avenues for CVD prediction.The process begins with meticulous pre-processing of the CMR dataset.Techniques such as median filtering are employed to mitigate noise, whereas intensity normalization ensures consistency across images.Histogram matching further aligns the intensity distributions, creating a standardized dataset for subsequent analysis.Segmentation is a crucial step in identifying relevant structures within CMR images.The DAE is deployed for segmentation owing to its ability to capture complex hierarchical features.Bayesian fuzzy clustering enhances the accuracy of segmentation by incorporating uncertainty measures, thereby allowing for a more robust delineation of anatomical structures.The segmented regions of interest provided a foundation for subsequent analyses.Feature extraction, a pivotal aspect of CVD prediction, was accomplished using a powerful VGG19 architecture. This CNN excels in capturing intricate spatial hierarchies within the segmented regions. The extracted features serve as discriminative indicators, capturing subtle patterns and variations that are indicative of potential cardiovascular abnormalities. Integrating these preprocessing, segmentation, and feature extraction techniques creates a comprehensive pipeline for CVD prediction, fostering accurate risk assessment and facilitating timely clinical interventions.

Pre-processing

In the pre-processing of CMR images for the detection and analysis of CVDs, several essential steps are employed to enhance image quality and facilitate accurate diagnosis. A common approach involves the application of a median filter to reduce noise and improve image clarity.This helps smooth out irregularities and artifacts present in the CMR images.Additionally, intensity normalization is crucial for standardizing pixel values across different images, ensuring consistency in their representation. This step aids in better comparability and interpretation of the images during subsequent analyses. Furthermore, histogram matching was applied to align the intensity distribution of the images with the aim of harmonizing variations in contrast and brightness. This normalization technique enhances the overall consistency and comparability of CMR images, contributing to more reliable and precise assessments in the context of cardiovascular disease diagnosis and research.

(a) Median Filter

Median filtering is a highly efficient noise reduction technique that is frequently utilized in image processing. Mean filtering replaces the pixel value at the center of the sliding window with the average value of the pixels in the window. The median's mathematical filtering is described as,

f (x, y) = m e d i a n_{(s, t) \in S_{x y}} {g (s, t)}

(1)

(b) Intensity Normalization

Preprocessing intensity normalization techniques can reduce fluctuations in the image signal intensity caused by technical factors (scanner specifications and sequence acquisition parameters).These approaches improve the intensity-based emission of the signal by “smoothing” the differences in intensity levels, that is, the repeatability of learning.Intensity normalization eliminates signal discrepancies between participants, MRI scanners, and sequence configurations by using signal values from nearby muscles.The normalized STIR spleen ratio was calculated using the same procedure as that used for T2-weighted STIR imaging.The intraclass correlation coefficient (ICC) was used to assess the interobserver agreement. To prevent division by zero, we normalize the image intensity between 0 and 1, subtract the minimum value, and then divide it by the range of values, using $ε$ as a tiny constant:

x * = \frac{x - (x) + ε}{m a x (x) - (x) + ε}

(2)

Histogram matching is commonly used to produce processed photos using particular histograms.Below is a formal explanation of histogram matching: Let S and T represent the source and target images’ continuous intensities, respectively (assumed as random parameters). $P_{S}$ and $P_{T}$ represent their respective continuous probability density functions (PDF). $P_{S}$ can be estimated from the source image, while $P_{T}$ represents the target PDF. Let r be a random number with the following properties.

r = M (S) = (L - 1) \int_{0}^{S} P_{S} (x) d x

(3)

Where L represents the intensity level numbers, and x represents a substitute variable for integration. We assume that a random value w possesses this condition.

G (T) = (L - 1) \int_{0}^{T} P_{T} (x) d x = r

(4)

These two equations show that M(S) = G(T), which implies that T has to fulfill the requirement,

T = G^{- 1} [M (S)] = G^{- 1} (r)

(5)

Equations (1–3) demonstrate how a given image can be transformed into an image with a specific PDF.

Segmentation

Deep autoencoders learn the hierarchical representations of complex data.Integrating Bayesian fuzzy clustering with deep autoencoders enhances the segmentation process by incorporating uncertainty and flexibility in the handling of image variations.The deep autoencoder extracts features and reconstructs the input images, thereby capturing intricate patterns in CMR data.The Bayesian fuzzy clustering algorithm accommodates the uncertainty in assigning pixels to different clusters, providing a probabilistic framework for more accurate and robust segmentation.

(a) Deep autoencoder network (DAE)

A DAE is a primary deep network built of AEs with several hidden layers that generate significant energy.The Softmax classifier is sometimes called the output layer when dealing with classification challenges.An AE is an invalidated network that encodes the input data into specific illustrations.Consequently, the technique of rebuilding input samples with fewer mistakes is widely used.²⁵The training set was as follows:

(X, Y) = {(x^{(n)}, y^{(n)}) | n = 1, 2, \dots, N}

(6)

Among these, $y^{(n)}$ represents the equivalent sample trademark $x^{(n)}$ .

For each training data sample $x^{(n)}$ , encode $h^{(n)} = f (x^{(n)})$ , then decode $h^{(n)}$ to utilize for reconstruction $X^{(n)} = g (h^{(n)})$ , where g and f are decoding and encoding variables. These issues can be resolved by lowering the error between the input and reconstruction.

The sigmoid function and linear transformation were used to understand how the encoding and decoding processes work.

h^{(n)} = s (W x^{(n)} + b)

(7)

X^{(n)} = s (W h^{(n)} + B)

(8)

where s(·) represents the sigmoid function.A training dataset with the related energy usage is provided below.

J (θ) = \frac{1}{N} \sum_{n = 1}^{N} \frac{1}{2} | x^{(n)} - X^{(n)} |_{2}^{2}

(9)

The linear transformation, written as $θ = {w, W, b, B}$ , has missing parameters in s and θ.

The DAE design is based on the standard automated counter, which encodes $x^{(n)}$ in a hidden symbol $h^{(n, 1)}$ and sends it to the next input port. Repeat the layer process for $l = 1, 2, \dots, L$ , where L is the number of hidden layers.The output layer feature projection is critical for classifying various activities.

Individual design parameter training ensures that each layer provides the best possible outcome.Fine-tuning is a frequently used global optimization strategy in neural networks that improves DAE performance.The squared error cost for ideal samples is expressed as

J (w, b, x^{(n)}, y^{(n)}) = \frac{1}{2} | y^{(n)} - Y^{(n)} |_{2}^{2}

(10)

The fine-tuning process is defined by the energy function J(w,b), which forces the result to be close to the correct label throughout the preparation.

J (w, b) = \frac{1}{N} \sum_{n = 1}^{N} J (w, b, x^{(n)}, y^{(n)})

(11)

The integer layer encoding constraints are defined as $(w, b) = {(w^{(l)}, b^{(l)}) | l = 1, 2, \dots, L}$ . The first phase in the deep learning process is parameter initialization, which involves the use of a stochastic method to complete the DAE fitting with the energy-minimization constraint updates.

(b) Bayesian fuzzy clustering

The BFC²⁶ algorithm merges probabilistic and fuzzy approaches. The breadth of fuzzy indicators used in traditional fuzzy approaches has increased in light of prior information and Bayesian theory. The BFC approach solves the optimization problem using the Markov Chain Monte Carlo (MCMC) technique strategy²⁷ and the particle filter method.²⁸ Fuzzy clustering is handled using the maximum a posteriori probability (MAP) with the number of clusters predicted using the normal distribution.This drawback makes the BFC approach inappropriate for large-scale data, severely constrains its application area, and fails to satisfy current practical needs.The BFC technique is intended to address fuzzy clustering problems using a probabilistic approach.The BFC probability model comprises three parts: fuzzy prior membership (FCP), fuzzy data probability (FDL), and cluster center priority, as shown in the image below.The probability of the fuzzy data is expressed as follows:

p (U, C) = \prod_{k = 1}^{K} F D L (x_{k} | u_{k}, C)

(12)

= \prod_{k = 1}^{K} \frac{1}{Z (u_{k}, m, C)} \prod_{n = 1}^{N} f (x_{k} | μ = c_{n}, A = u_{k n}^{m} I)

(13)

$X$ is the training data matrix, U is the fuzzy members, C is the cluster center, K is the sample number, and N represents the cluster number. $u_{k n}$ represents the membership of data point $x_{k}$ in n .

m, $c_{n}$ , and I denote the fuzzy index, cluster center, and identity matrix, respectively. Z(u_k,m,C) represents the normalization constant and m represents the fuzzy index. There is no need to calculate $Z (u_{k}, m, C)$ , as it will be eliminated by equation (14) below.

The prior of fuzzy membership is expressed as,

p (C) = \prod_{k = 1}^{K} F C P (u_{n} | C)

(14)

= \prod_{k = 1}^{K} Z (u_{k}, m, C) (\prod_{n = 1}^{N} u_{k n}^{- m \frac{D}{2}}) D i r i c h l e t (u_{k} | α)

(15)

$p (C)$ has three parts: $F_{1} = Z (u_{k}, m, C)$ , $F_{2} = \prod_{n = 1}^{N} u_{k n}^{- m \frac{D}{2}}),$ and $F_{3} = D i r i c h l e t (u_{k} | α)$ . In the elimination equation (12), $F_{1}$ represents the normalization constant. $F_{3}$ represents the Dirichlet distribution and is explained as follows.

D i r i c h l e t (α) = \frac{Γ \sum_{n = 1}^{N} α_{n}}{\prod_{n = 1}^{N} Γ (α_{n})} \prod_{n = 1}^{N} x_{n}^{α_{n} - 1}

(16)

where

x_{n} \geq 0

, n = 1,…, N and

\sum_{n = 1}^{N} x_{n} = 1

. The Dirichlet prior parameter (α) determines the degree of sample membership. The BFC method employs Dirichlet distribution and eliminates the requirement that the fuzzy index in the FCM technique is higher than 1.

p (C) = \prod_{n = 1}^{N} f (c_{n} | μ_{c}, \sum_{c})

(17)

It should be noted that $p (c)$ corresponds to the high degree of membership provided by equation (4). $μ_{c}$ and $\sum_{c}$ represent the mean and variance of all samples, respectively.

μ_{c} = \frac{1}{K} \sum_{k = 1}^{K} x_{k}

(18)

\sum_{c} = \frac{γ}{K} \sum_{k = 1}^{K} (x_{k} - μ_{c}) (x_{k} - μ_{c})^{T}

(19)

The user sets the parameter $γ$ , which impacts the intensity of the prior. In this study, we utilize $γ = 3$ . To calculate the combined probability of X, U, and C, multiply equations (12), (14), and (16).

p (X, U, C) = p (U, C) p (U | C) p (C)

(20)

\propto e x p e x p {- \frac{1}{2} \sum_{k = 1}^{K} \sum_{n = 1}^{N} u_{k n}^{m} ‖ x_{k} - c_{n} ‖^{2}} \times [\prod_{k = 1}^{K} \prod_{n = 1}^{N} x_{n}^{α_{n} - 1} \times e x p e x p {- \frac{1}{2} \sum_{n = 1}^{N} \sum_{c}^{- 1} (c_{n} - μ_{c})}]

(21)

Based on map theory, the joint probability of equation (22) is a negative logarithm that can be simplified by multiplying by two.The joint probability formula is as follows:.

\begin{aligned} J (X, U, C) & = \sum_{k = 1}^{K} \sum_{n = 1}^{N} u_{k n}^{m} ‖ x_{k} - c_{n} ‖^{2} - 2 \sum_{k = 1}^{K} \sum_{n = 1}^{N} α_{n} \\ - 1 l o g u_{k n} + \sum_{n = 1}^{N} (c_{n} - μ_{c})^{T} (c_{n} - μ_{c})^{T} \sum_{c}^{- 1} (c_{n} - μ_{c}) \end{aligned}

(22)

Feature extraction

VGG-19 can automatically extract hierarchical features at different levels when applied to CMR images in the context of cardiovascular disease.This enables the model to discern intricate details of cardiac structures and abnormalities, facilitating the accurate identification and characterization of pathological conditions such as myocardial infarction, hypertrophy, or other cardiac anomalies.The use of VGG-19²⁹ in feature extraction for CMR images enhances the potential for automated and precise diagnosis, thereby contributing to the advancement of cardiovascular healthcare.

(a) VGG-19

The VGG-19 network, as shown in Figure 2, has 19 layers, including 16 convolutional layers and three fully connected layers.As neural networks deepen, their precision improves, thereby enhancing the feature extraction.The convolutional layers perform convolutions and are connected to the max-pooling and dropout layers.These layers use 3 × 3 filters with max pooling to reduce the convolutional layer output dimensions.To limit false positives, the network was trained on a single lesion before testing all lesions.

m_{i}^{(x)} = B_{i}^{(x)} + \sum_{j = 1}^{b_{i}^{(x - 1)}} k_{i, j}^{(x - 1)} \times m_{j}^{(x)}

(23)

Figure 2.

Deep learning features using VGG19 model.

Where $k_{i, j}^{(x - 1)}$ is the filter size, $B_{i}^{(x)}$ is the matrix deviation, and $m_{i}^{(x)}$ is the feature map is created as a function of the output. Following the convolution operation, an activation function was utilized to produce a nonlinear transfer function, as shown below:

n_{i}^{(x)} = n (m_{i}^{(n)})

(24)

$n_{i}^{(x)}$ where denotes the activation function.The ReLU is commonly used because of its high computational efficiency. The ReLU function can be mathematically stated as

n_{i}^{(x)} = m a x (0, n_{i}^{(x)})

(25)

Activation functions decrease the nonlinear results and relations by transforming negative values to zeros and processing only positive values.Upsampling or max-pooling layers are combined with convolutional layers to minimize the dimensionality of the convolutional output. max pooling is used, with each block's maximum value serving as the final image pixel.

n_{i}^{(x)} = f (x_{i}^{(x)})

(26)

Where $n_{j}^{(x)}$ the weight functions and f is is the nonlinear transfer function. Supervised learning algorithms select the best hyperplane to split the feature space.High-dimensional hyperplanes are used to classify the training dataset into various groups. A kernel support vector machine transmits nonlinearly separable data to a different vector space. The linear classification decision function for a given training data set $D (x_{1}, y_{1}), (x_{2}, y_{2}), \dots, (x_{n}, y_{n})$ ) is as follows:

y_{i} = ((w Δ x_{i}) + b)

(27)

Among them, $x_{i} \in R^{n} \to h$ transforms the data into a high-dimensional space. $y_{i} \in \pm 1$ is the membership degree label of each activity in the dataset.

(w . x_{i}) + b = 0

(28)

The hyper planes are reformed if the margins are delineated and supplied as,

y_{i} = ((w Δ x_{i}) + b) \geq 1

(29)

According to the preceding functions, the factor that must be decreased to formulate the ideal hyper plane is presented as,

\frac{1}{2} ‖ w ‖^{2}

(30)

The results were generated using features from the previous layers.To prevent overfitting, the dropout function randomly deleted neurons during training. Table 2 provides the details of the layer architecture.

Table 2.

Proposed architecture layer details.

Layer	Size	Kernal Size	Feature map	Stride	Activation
Conv1_1	224 × 224 × 64	3 × 3	64	1	ReLU
Conv1_2	224 × 224 × 64	3 × 3	64	1	ReLU
Max pooling	112 × 112 × 64	3 × 3	64	2	ReLU
Conv2_1	112 × 112 × 128	3 × 3	128	1	ReLU
Conv2_2	112 × 112 × 128	3 × 3	128	1	ReLU
Max pooling	56 × 56 × 128	3 × 3	128	2	ReLU
Conv3_1	56 × 56 × 256	3 × 3	256	1	ReLU
Conv3_2	56 × 56 × 256	3 × 3	256	1	ReLU
Conv3_3	56 × 56 × 256	3 × 3	256	1	ReLU
Conv3_4	56 × 56 × 256	3 × 3	256	1	ReLU
Max pooling	28 × 28 × 256	3 × 3	256	2	ReLU
Conv4_1	28 × 28 × 512	3 × 3	256	1	ReLU
Conv4_2	28 × 28 × 512	3 × 3	256	1	ReLU
Conv4_3	28 × 28 × 512	3 × 3	256	1	ReLU
Conv_4	28 × 28 × 512	3 × 3	256	1	ReLU
Max pooling	7 × 7 × 512	3 × 3	256	2	ReLU
Conv3_1	7 × 7 × 512	3 × 3	256	1	ReLU
Conv3_1	7 × 7 × 512	3 × 3	256	1	ReLU
Conv3_1	7 × 7 × 512	3 × 3	256	1	ReLU
Conv3_1	7 × 7 × 512	3 × 3	256	1	ReLU
FCN 1	25,088	-	-	-	ReLU
FCN 2	4096	-	-	-	ReLU
FCN	1000	-	-	-	SoftMax

CVD prediction using UCI dataset

CVD prediction and classification have become increasingly crucial in the field of healthcare by leveraging advanced machine learning techniques to enhance early diagnosis and risk assessment.The process often begins with the utilization of tabular datasets containing diverse patient information including demographic details, medical history, and various risk factors.Preprocessing plays a pivotal role in preparing datasets for accurate modeling. Cleaning involves addressing missing values and standardizing data formats to ensure uniformity, while reduction techniques focus on enhancing model efficiency by refining the dataset. Identifying numerical values within a dataset is crucial, as they often represent key indicators of cardiovascular health. Subsequently, the dataset underwent outlier detection, which is essential for maintaining the data integrity.IQR is an effective method for identifying and removing outliers. SFS is used for feature selection, systematically adding features to the model one at a time and evaluating its impact on performance.By selecting the most relevant features, SFS enhances the model accuracy, reduces overfitting, and improves interpretability.This meticulous approach to preprocessing and feature selection not only refines the dataset, but also ensures that the subsequent ML model is robust and capable of making accurate predictions regarding an individual's susceptibility to CVD.

UCI dataset

As previously stated, researchers considered the UCI³⁰ repository as a typical clinical property for selecting features for investigation.Subsequently, class tags were used to clean the list of properties before collecting data from Google Forms. Table 3 lists the attributes of these datasets.We discuss 14 qualities and provide the appropriate measurements.

Table 3.

Cardiovascular dataset attributes.

No/Attribute	Description	Values/Ranges
Age	Age	29–77
Sex	Gender	Male = 1; Female = 0
Chest pain (CP)	Describes the level of CP	CP = 1 (typical angina)
		CP = 2 (atypical angina)
		CP = 3 (non-typical angina)
		CP = 4 (asymptotic)
RestBP	Patient's blood pressure while admitted in hospital	94–200
Chol	Cholesterol level recorded	126–564
FBS	Patient's Fasting blood sugar level and binary classified values (Depends on whether the patient has more than 120 mg/dl of sugar.)	1 (Yes)
FBS		0 (No)
Rest ECG	ECG from 0 to 2. It shows the severity of the pain	0, 1, 2
Heart Beat	Maximum value of heart beat	Between 71 and 202
Exang	angina or not	1 (Yes)
Exang	angina or not	0 (No
Old Peak	Describes the patient's depression status	0–6.2
Slope	Describes the patient's condition during exercise stress test	1 (up sloping)
		2 (flat)
		3 (down sloping)
CA	Fluoroscopy status	0–3
Thal	Chest pain or not	0–3
Target	No of Classes	1 (Yes)
Target	No of Classes	0 (No

COVID 19 CT dataset

The dataset comprised 746 CT scan images, categorized into two groups: COVID-19 positive and COVID-19 negative.Specifically, 349 images in the dataset represent patients diagnosed with COVID-19, whereas the remaining 397 images were from individuals not affected by the virus.

Data pre-processing

This is an approach to data mining that prepares, cleans, and organizes raw data before creating and training ML algorithms.Often, the data received from multiple sources are raw and unsuitable for fast analysis.Missing attributes, outliers, and noisy data are identified and eliminated from the dataset.This study employs cleaning techniques, such as locating missing numbers and searching for and deleting outliers.This study checked the dataset for missing values using the Python programming language in the Anaconda Jupiter environment and discovered no missing values. Outliers are values with more than three standard deviations apart from the mean. Recognizing, Identifying, and deleting outliers before using a predictive model may significantly decrease errors while enhancing the accuracy.This study investigates the 14 available attributes of outliers and uncovers their specific characteristics.The missing data preparation approach does not include any missing data. However, using the interquartile range method, we identified and deleted numerous outliers that showed standard deviation from the mean.

Detecting and eliminating outliers through the IQR method

The IQR³¹ method helps identify outliers that are spread across a dataset, with a larger IQR indicating that data points are more dispersed and a smaller IQR suggesting that data points are closer to the mean.To compute IQR, the first quartile (Q1) was subtracted from the third quartile (Q3).The formula for the IQR is Q3–Q1, which captures the middle 50% of the data.The IQR can be visually represented using a boxplot, where data points are divided into four equal parts corresponding to the quartiles from Q1 to Q3. This technique effectively separates the dataset into equal sections and identifies outliers between the first and third quartiles.

I Q R = Q 3 - Q 1

(31)

L o w e r b o u n d = Q 1 - 1.5 * I Q R

(32)

U p p e r b o u n d = Q 3 + 1.5 * I Q R

(33)

O u t l i e r > u p p e r - l o w e r

(34)

O u t l i e r < l o w e r - u p p e r

(35)

Outliers can be recognized using the algorithm described above by determining whether the value is above or below the range. The proposed algorithm discovered 256 outliers in the 1025 datasets used in this study after reducing outliers using the quartile approach.After removing the outliers, 769 data points were obtained.

Feature selection

In forecasting cardiovascular disease (CVD) using the UCI repository dataset, choosing suitable features is crucial for enhancing model efficacy and interpretability. Extraneous features can adversely affect the performance. Sequential Forward Selection (SFS) is a widely used technique. This method begins by identifying the most effective individual feature and then determining the optimal combination of two features, followed by the best set of three features, continuing until the desired number of relevant features is achieved. The SFS, a wrapper-based approach, gradually incorporates features into the model. At each stage, the performance of the model was evaluated, and the feature subset that yielded the highest predictive accuracy was selected. Figure 3 illustrates the workflow of the proposed model.

Figure 3.

Flow chart for the proposed work.

To apply SFS in the context of cardiovascular disease prediction, the process typically begins with an empty set of features, and the algorithm iterates through the available features, adding the most informative feature in each step. The feature subset that yielded the best performance is retained. This iterative procedure continues until a predefined number of features are selected or until further additions do not significantly improve the model's predictive capability. The selected features can provide insights into the key factors contributing to cardiovascular diseases, aiding healthcare professionals in better understanding and managing the risks associated with this critical health issue.

Classification

Precise categorization of CVD is essential for proper diagnosis and treatment.Recent progress in AI has resulted in advanced models, such as the Enhanced DA-ResBiGRU with ABER, which enhances CVD classification.This architecture utilizes two attention mechanisms that focus on crucial input data aspects.It detects complex patterns in heart signals and improves the model explainability.By utilizing a bidirectional GRU, the model examines past and future contexts, offering a thorough analysis of temporal relationships in cardiovascular information.Additionally, the incorporation of ABER optimization ensures that the Earth's radius is accurately considered in geospatial features, contributing to more precise predictions, particularly in epidemiological studies where geographical factors play a role in CVD prevalence.The synergy of the Improved DA-ResBiGRU with ABER optimization offers a sophisticated approach for CVD classification.

DA-ResBiGRU

After feature extraction, the DA-ResBiGRU model, which is a novel hybrid approach, as shown in Figure 4, can be used for CVD classification. This method combines ResNET 50, which uses deeper layers, with a GRU.³²It utilizes skip connections that bypass layers, connect residual mappings, and simplify the learning process.The performance of the model is reduced by skipping the layers through regularization.The residual function is asymptotically expressed by the following equation: $G (a) := R (a) - a$ becomes G(a) +a, causing the learning curve to alter. The framework was linked to the BiGRU to enhance the model.

Figure 4.

Improved dual attention residual bi-directional gated recurrent neural network unit.

To ensure high classification accuracy, CVDs were classified using a dual-attention technique and closed layers.The attention function focuses on the classification layer to obtain the best results.

Considering an input data: $R = [r_{1}, r_{2}, \dots, r_{n}] \in R e a l$ denotes the past data, n represents the length n. The target data is represented by $S = [s_{1}, s_{2}, \dots, s_{n}] \in R e a l$ , and m denotes the output data's length. S = MF(R) denotes the mapping function.

r e_{u} = σ (W e_{r} [h 1_{u - 1}, r_{u}])

(36)

Where $r e$ represents the reset gate, $W e_{r}$ represents the reset gate's weight matrix, and $h 1_{u - 1}$ represents the hidden gate. σ represents the sigmoid function employed to determine the gate's limit value. $C_{u}$ represents the current image value and will ignore the past state in the reset gate result $C_{u - 1}$ so that the estimate of $r_{u}$ corrects the invariance in the image.

C_{u} = t a n h (W e_{h q} [r e * h 1_{u - 1}, r_{u}])

(37)

The update gate $U g$ , as shown in the equation below, determines the set features to be obtained for classification.

U g_{t} = σ (W e [h 1_{u - 1}, r_{u}])

(38)

A GRU is a recurrent structured neural network that considers historical information. The classification is based on hidden states and is expressed as,

h 1_{u} = (1 - U g_{u}) * h 1_{u - 1} + U g_{u} * C_{u}

(39)

Two hidden layers are linked in the BiGRU network to the same output layer, which gives the following equation,

h i d = G R U (r_{u}, h i d_{u - 1})

(40)

h i d 1 = G R U (r_{u}, h i d 1_{u - 1})

(41)

C_{u} = w 1_{u}, h i d_{u} + w 2_{u}, h i d 1_{u} + h i d 3_{u}

(42)

where hid and hid1 represent the two hidden layers and w1 and w2 represent the weights of the layers used to determine the CVD in the present image.

(a) Attention mechanism in Encoder

The encoder module $h i d = F (R) = [h i d_{1}, h i d_{2}, \dots, h i d_{m}] \in R^{m * n}$ receives input data, where m represents the hidden layer dimension. BiGRU returns $S^{'} = S_{1}^{'}, S_{2}^{'}, \dots, S_{m}^{'} \in R e^{m * n}$ . The following equation provides the following conclusions.

N_{s t} = A^{d} t a n h (B h i d_{t} + C S_{s - 1}^{'} + b i a s)

(43)

s \in N u m, 1 \leq s \leq n, t \in N u m, 1 \leq t \leq n

A, B, and C represent the real numbers that represent the learning weight matrix, and the classification results are normalized using softmax activation. The following equation defines the normalizing function,

F_{r s} = \frac{e x p (S o f_{r s})}{\sum_{s = 1}^{m} e x p (S o f_{r s})}

(44)

The feature correlation, $F_{r s}$ , is multiplied by the hidden layer

S_{u}^{'} = F_{2} (C S_{u}, S_{u - 1}^{'})

(45)

$F_{2}$ where represents the network units of the decoder.The input terminal no longer has the original condition of the unit, but instead considers weighted information that influences the size .

(b) Attention mechanism in a Decoder

A mechanism for self-attention arises in this decoder that produces efficient outcomes.This method does not work recursively in RNNs; therefore, the information sequence is not fixed. Absolute position encoding is employed to change the position; $E p$ represents the intended position of the input data.

{\vec{L}}_{E p}^{(g)} = K (E p)^{(g)} := {s i n s i n (\frac{1}{10000^{\frac{2 m}{d i}}} E p), i f K = 2 m c o s c o s (\frac{1}{10000^{\frac{2 m}{d i}}} E p), i f K = 2 m + 1

(46)

The self-awareness layer encodes data using location embedding $\vec{L}$ , resulting in parallel attention and increased classification rate through twofold attention.

Al-Biruni earth radius optimization algorithm (ABER)

This technique enhances development and navigation by dividing the population into different groups and dynamically adjusting their sizes throughout the process.Initially, the population was divided into two main groups: developers and explorers. To optimize the fitness value of individuals within each group, the proportion of the population engaged in development began at 30% and gradually increased to 70% as the optimization progressed.Conversely, the proportion assigned to the navigation group began at 70% and decreased to 30% over time.This approach significantly enhances the overall fitness of the individuals.Selective strategies are also employed to maintain the primary process response when no better alternatives are found, thereby ensuring that the population optimization process ultimately converges.Repeating the BER optimization thrice is unlikely to substantially improve the solution quality.If the solution reaches a local optimum, a mutation operation is applied.

The ABER³³ algorithm selects the most effective solution in each iteration, yielding excellent results.Although this approach may converge prematurely owing to the multimodal nature of the problem, it remains highly efficient owing to the elite method.The mutation process in ABER, along with the subsequent search within the navigation group, resulted in superior navigation capabilities.These capabilities enable ABER to effectively delay convergence. Algorithm 1 presents ABER pseudocode.Before executing the ABER, the number of iterations, population size, and mutation rate must be defined.The algorithm then creates development and navigation groups, dynamically adjusting their sizes as the process moves toward the optimal solution.Each group performs its role uniquely, and enhances its diversity and navigation.Implementing the ABER's selective strategy reduces the likelihood of process repetition and maintains leadership stability.

Algorithm 1.

ABER optimization Pseudo code

Initialize BER population (i = 1,2, …, d), max iterations Max_itr, population size d, fitness function F_n, initial iteration t = 1, intermediates variables z, r1, r2, r3.

Calculate fitness function F_n for each P_i.

Find best solution as P^∗

While $t \leq M a x_{i t r}$ do

for each solution in the exploration group do

Update $r = h \frac{c o s c o s x}{1 - c o s c o s x}$

Calculate D = r₁(p(t) − 1)

Update p(t + 1) = p(t) + D(2r₂ − 1)

end for

for each solution in the exploitation group do

Calculate D = r₃(L(t) − p(t))

Update p(t + 1) =(r₁∗p1 (t) + z∗r₂∗ (r₂ (t) − r₃ (t)) + (1 − z) ∗r₃∗ (r∗ (t) − r₁ (t))

Calculate $k = 1 + \frac{2 * i^{2}}{M a x_{i t r^{2}}}$

Investigate area around best solution as r ′ (t + 1) = r₁(r∗ (t) + k)

Compare p(t + 1) and r ′ (t + 1) to select the best solution r* (t + 1)

if no change occurred to the best fitness for last two iterations, then

Mutate solution

end if

end for

Update fitness F_n for each position P

end while

Return r^∗ (t)

The ABER efficiently adjusts the hyperparameters of the improved dual-attention residual bidirectional gated recurrent neural network unit for CVD prediction. This method reduces prediction errors and enhances the capacity of the model to identify intricate temporal relationships in patient data. Ultimately, ABER enhances the precision and reliability of CVD prediction by utilizing the advantages of sophisticated deep-learning architectures.

Results and discussion

This section evaluates the model's performance using metrics such as accuracy, precision, recall, and F1-score. The model's discriminative capability was analyzed using ROC curves and the AUC. To ensure a thorough assessment, the dataset was divided into training (70%), validation (15%), and testing (15%) subsets. This division allowed for model training, hyperparameter optimization, and performance evaluation on unseen data.

A c c u r a c y = \frac{T P + T N}{T P + T N + F P + F N}

(47)

S p e c i f i c i t y = \frac{T N}{T N + F P}

(48)

R e c a l l = \frac{T P}{T P + F N}

(49)

P r e c i s i o n = \frac{T P}{T P + F P}

(50)

F - m e a s u r e = \frac{2 * P r e c i s i o n * R e c a l l}{P r e c i s i o n + R e c a l l}

(51)

A U - R O C = \frac{1}{2 (\frac{T P}{T P + F N} + \frac{T N}{T N + F P})}

(53)

F P R = \frac{F P}{F P + T N}

(54)

T N R = \frac{T N}{T N + F P}

(55)

F N R = \frac{F N}{F N + T P}

(56)

R M S E = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {(x_{i} - {\hat{x}}_{i})}^{2}}

(57)

M A E = \frac{1}{N} \sum_{i = 1}^{N} | x_{i} - {\hat{x}}_{i} |

(58)

where,

x_{i}

and

{\hat{x}}_{i}

denotes the predicted and actual values, respectively, and Nspecifes the number of instances.

Performance comparison with ML models

An evaluation of the performance metrics for the various algorithms is presented in Table 4. Figures 5 and 6 in the provided images and table reveal the effectiveness of the suggested model compared to other existing models, such as the Decision Tree (DT), support vector machine (SVM), Random Forest (RF), multilayer perceptron (MLP), and Logistic Regression (LR).The proposed model achieved the highest accuracy of 97.88%, significantly outperforming the other models, which ranged from.45% to 88.36%. Specifically, the proposed model's sensitivity (95.50%), precision (96.68%), and F-measure (95.85%) demonstrate its capability.The high MCC value (92.53%) and AU-ROC score (95.39%) further confirm the ability of the model to handle imbalanced datasets and its effectiveness in distinguishing between classes.

Figure 5.

Performance metrics comparison for machine learning algorithm.

Figure 6.

MCC and AU-ROC comparison for ML algorithm.

Table 4.

Performance comparison of different ML algorithms.

Algorithms	Accuracy	Sensitivity	Specificity	Precision	F-measure	MCC	AU-ROC
SVM	82.45	86.35	81.36	84.88	85.82	70.82	85.97
DT	85.3	87.88	82.78	86.72	86.36	72.66	86.32
RF	86.52	88.97	84.97	87.91	87.93	76.54	87.36
LR	86.66	90.72	85.30	88.72	88.85	78.94	90.89
MLP	88.36	92.54	88.72	90.50	92.07	80.94	91.56
Proposed	97.88	95.50	94.29	96.68	95.85	92.53	95.39

Note: Bold letters indicates the proposed work.

In contrast, although models such as SVM and DT achieve acceptable results, they lag behind the proposed model, highlighting the advancements made by the proposed approach in improving the performance across multiple metrics. Specifically, it achieved the lowest FPR (4.78%) and FNR (2.45%) while maintaining the highest TNR (98%). Regarding RMSE and MAE, which quantify prediction error rates, the proposed method recorded the lowest values at 0.28 for RMSE and 0.21 for MAE, outperforming all other models. This further highlights the precision and dependability of the proposed method in predictive tasks.

Among the traditional algorithms, MLP performed relatively well, with the second-lowest FPR (14%), FNR (12.2%), and highest TNR (94.6%) after the proposed method.MLP also demonstrated a lower RMSE (0.32) and MAE (0.28) than other conventional algorithms such as SVM and RF. LR also showed good performance with a low FPR (15%), FNR (17.3%), and TNR of 94.3%. However, its RMSE (0.38) and MAE (0.30) were slightly higher than those of the MLP. In contrast, RF and SVM showed higher error rates and lower TNRs, making them less favorable for the given task.RF, despite being a commonly used ensemble method, exhibited relatively high RMSE (0.46) and MAE (0.34).Traditional models, such as MLP and LR, also show promise but fall short compared to the proposed method.Although they are commonly used, SVM and RF display higher error rates, making them less optimal for this scenario, as presented in Table 5 and Figures 7 and 8.

Figure 7.

FPR, FNR and TNR comparison for ML algorithm.

Figure 8.

RMSE and MAE comparison for ML algorithm.

Table 5.

Performance comparison of different ML algorithms.

Algorithms	FPR (%)	FNR (%)	TNR (%)	RMSE (%)	MAE (%)
SVM	17	21.26	90	0.45	0.38
DT	16.26	20	91	0.42	0.36
RF	15	19	92	0.46	0.34
LR	15	17.3	94.3	0.38	0.30
MLP	14	12.2	94.6	0.32	0.28
Proposed	4.78	2.45	98	0.28	0.21

Note: Bold letters indicates the proposed work.

Performance comparison with DL models

The performance of several DL models as shown in Table 6 and Figures 9 and 10, including DNN, LSTM, Inception-v3, Xception, MobileNetV2, and the suggested method. The suggested method demonstrated the best performance across all metrics, demonstrating its superiority over the other models. The highest accuracy (97.88%), sensitivity (95.50%), specificity (94.29%), precision (96.68%), and F-measure (95.85%) were achieved. These findings demonstrate that the proposed method is highly efficient in correctly identifying positive cases (high sensitivity), while maintaining a low false positives rate (high specificity and precision).In addition, the MCC value of 92.53% and the AU-ROC value of 95.39% of the proposed method highlight its robustness and reliability in classification tasks.

Figure 9.

Performance metrics comparison for DL models.

Figure 10.

MCC and AU-ROC comparison for DL models.

Table 6.

Performance comparison of different DL algorithms.

Algorithms	Accuracy	Sensitivity	Specificity	Precision	F-measure	MCC	AU-ROC
DNN	92	91.3	90.1	92	91.6	81.94	87.75
LSTM	93.4	93	91.3	92.9	92.5	85.78	87.11
Inception-v3	94.8	93.9	92	93	93.6	87.76	87.14
Xception	95	94.1	93.1	93.4	94	87.89	88.91
MobileNetV2	96.2	95	94	95	95	91.82	92.34
Proposed	97.88	95.50	94.29	96.68	95.85	92.53	95.39

Note: Bold letters indicates the proposed work.

Xception and Inception-v3 demonstrated strong performance, achieving accuracies of 95% and 94.8%, respectively. However, they lag behind the proposed method and MobileNetV2 regarding specificity, sensitivity, and MCC. Xception achieved a slightly higher AU-ROC (88.91%) than Inception-v3 (87.14%), making it a slightly better option for classification tasks in which distinguishing between classes is crucial.DNN and LSTM, although still effective, demonstrated lower performance metrics than the other models.DNN, in particular, had the lowest MCC (81.94%) and AU-ROC (87.75%), indicating that it may not be as reliable as other models for this particular task. Thus, the proposed method was the most effective and achieved the highest performance across all metrics. MobileNetV2 offers a competitive alternative, whereas Xception and Inception-v3 provide solid performance. However, the functional, DNN, and LSTM may not be the best choices for this classification task based on the given metrics.

The effectiveness of different algorithms, such as DNN, LSTM, Inception-v3, Xception, MobileNetV2, and the proposed approach, is presented in Table 7 and Figures 11 and 12. The proposed method emerges as the top performer across all evaluation criteria, recording the lowest false positive rate (FPR) at 4.78% and false negative rate (FNR) at 2.45%, along with the highest true negative rate (TNR) of 98%. Furthermore, the proposed method achieved the smallest root mean square error (RMSE) of 0.28 and mean absolute error (MAE) of 0.21, underscoring its superior efficiency and dependability in predictive tasks.

Figure 11.

FPR, FNR and TNR comparison for DL algorithm.

Figure 12.

RMSE and MAE comparison for DL algorithm.

Table 7.

Performance comparison of different deep learning algorithms.

Algorithms	FPR	FNR	TNR	RMSE	MAE
DNN	16	19.14	92	0.42	0.35
LSTM	14.15	18	93	0.40	0.34
Inception-v3	13	16	94	0.39	0.32
Xception	12	15.2	95.5	0.35	0.29
MobileNetV2	11	13.1	95.8	0.31	0.25
Proposed	4.78	2.45	98	0.28	0.21

Note: Bold letters indicates the proposed work.

In comparison, MobileNetV2 performed well, showing competitive results, with a TNR of 95.8%, FPR of 11%, and FNR of 13.1%.It also maintained a lower RMSE (0.31) and MAE (0.25) than the other traditional models.Xception and Inception-v3 also showed strong performance, with Xception outperforming Inception-v3 slightly in all the metrics.In contrast, DNN and LSTM lagged behind, with DNN showing the highest FPR (16%) and FNR (19.14%), along with the highest RMSE (0.42) and MAE (0.35).This highlights that while traditional models can still be effective, the proposed method offers significant improvements in minimizing errors and enhancing classification accuracy.

Performance comparison with optimization models

Table 8 and Figures 13, and 14 illustrate the performance comparison of various algorithms:the Grasshopper Optimization Algorithm (GOA), Particle Swarm Optimization (PSO), Harris hawk optimization (HHO), Grey Wolf Optimizer (GWO), Ant Lion Optimizer (ALO), and the proposed algorithm. The proposed algorithm consistently outperformed the other algorithms, achieving a remarkable accuracy of 97.88%, which was significantly higher than that of the competing methods, which ranged from 80.23% to 86.14%.Additionally, the proposed method showed superior sensitivity (95.50%) and specificity (94.29%), indicating its robustness in efficiently identifying both positive and negative cases.The precision and F-measure values also highlight the reliability of the proposed method for balancing true positives with precision, thereby further emphasizing its effectiveness in classification tasks.

Figure 13.

Performance metrics comparison for different optimization algorithms.

Figure 14.

MCC and AU-ROC comparison for different optimization algorithms.

Table 8.

Performance comparison of different optimization algorithms.

Algorithms	Accuracy	Sensitivity	Specificity	Precision	F-measure	MCC	AU-ROC
GOA	80.23	84.13	79.14	82.66	83.60	68.60	83.87
PSO	83.1	85.66	80.56	84.50	84.14	70.55	85.98
GWO	84.30	86.75	82.75	85.72	85.71	74.32	85.12
HHO	84.44	88.50	83.21	85.50	86.63	76.72	88.95
ALO	86.14	90.32	85.50	88.32	90.16	78.89	90.51
Proposed	97.88	95.50	94.29	96.68	95.85	92.53	95.39

Note: Bold letters indicates the proposed work.

The proposed algorithm leads to an AU-ROC performance with a score of 95.39%, demonstrating its strong capability to accurately differentiate between classes. The MCC value of the proposed method (92.53%) was the highest among the compared algorithms, demonstrating a robust correlation among the original and predicted classifications. These results collectively highlights the efficacy of the proposed algorithm across all evaluated metrics, making it a more reliable and precise option than other optimization algorithms, such as PSO, GOA, HHO, GWO, and ALO. Such improvements in the performance metrics suggest that the proposed approach is well suited for applications requiring high precision, recall, and overall classification accuracy.

The confusion matrix in Figure 15 illustrates the efficiency of the suggested COVID-19 prediction model. In the confusion matrix, the model accurately identified 98.35% of the actual COVID-negative cases as negative and correctly predicted 97.25% of the actual COVID-positive cases as positive. The false positive rate was 1.65%, meaning 1.65% of COVID-negative cases were mistakenly classified as positive. Similarly, the false negative rate was 2.75%, indicating that 2.75% of the actual COVID-positive cases were incorrectly labeled as negative. Overall, the confusion matrix demonstrates a highly effective model with exceptional accuracy in distinguishing between positive and negative COVID-19 cases.

Figure 15.

Confusion matrix.

Analysis of learning rate, loss and batch size

Figure 16 demonstrates the impact of varying learning rates and batch sizes on the loss across training epochs. The first graph reveals that a smaller learning rate (0.001) results in a slower yet steady decline in loss over time. In contrast, higher learning rates (0.01 and 0.1) initially reduce the loss more quickly but eventually stabilize or show a slight increase as training continues.This indicates that, while higher learning rates may speed up the initial learning, they can also lead to suboptimal convergence or even overfitting.In the second graph, a comparison of batch sizes reveals that a larger batch size (16) results in a faster reduction in loss than a smaller batch size (8).However, both batch sizes showed a similar trend in loss reduction, suggesting that, while larger batch sizes may speed up training, the overall effect on convergence may not be drastically different.

Figure 16.

Loss over epoch for different learning rates.

Figure 17 shows that it steadily improved throughout the epochs, eventually converging around a high accuracy value of 97.88%.The loss values decreased significantly in the initial stages and stabilized in later epochs.

Figure 17.

Accuracy and loss graph for training and validation.

ROC analysis

Figure 18 illustrates the Receiver Operating Characteristic (ROC) curves for different models, showcasing the relationship between sensitivity and 1-specificity across varying thresholds. The Area Under the Curve (AUC) serves as a key performance indicator, where larger values reflect superior discriminatory ability. The proposed framework exhibited superior performance, attaining an AUC of 0.972 and demonstrating the highest classification accuracy.This outcome indicates that “Our Framework identifies true positives more accurately while reducing false positives compared to other methods.The other models, including MMT (AUC = 0.962), CMGAT (AUC = 0.966), MGNN (AUC = 0.960), and DCTA (AUC = 0.957), also demonstrated strong performance but were slightly shorter than the proposed framework.The close clustering of the curves for these models indicates that all methods perform well; however, the proposed framework has a slight edge in terms of overall accuracy and reliability.

Figure 18.

ROC curve.

Classification comparison pre-processing techniques

A comparative analysis of classification performance using different preprocessing techniques is presented in Table 9. The study examines unprocessed images, fuzzy color preprocessing, stacked images, and a novel “proposed” method. Performance metrics, including precision, accuracy, F1-score, and recall, were used for evaluation. The simulation results indicate that the proposed preprocessing method outperforms the other techniques across all performance categories. It achieved an overall accuracy of 97.88%, with perfect recall and precision for the normal class and near-perfect scores for other categories. This indicates that the proposed method significantly improves the system's ability to accurately analyze CMR images across all categories, establishing it as a highly effective approach for medical image analysis. Other techniques showed comparatively lower performance, with the raw method achieving an average accuracy of 93%, while the fuzzy color technique reached 94.52%. Although these methods still perform reasonably well, their results are inferior to those of the stacked image approach, particularly in terms of precision and recall.

Table 9.

Classification comparison for pre-processing techniques.

Image pre-processing	Accuracy (%)	Recall (%)	Precision (%)	F1-score (%)
Un-preprocessed	93	93.5	93.2	92
Fuzzy color	94.52	94.4	94	94.3
Stacked images	96.13	96.1	94.3	94.8
Proposed	97.88	96.68	95.50	95.85

State-of-the-art comaparison

A comparison of the performance metrics, as shown in Table 10 illustrates across various models with an accuracy of 97.88%, outperforming the other models. Additionally, it maintained strong performance in sensitivity, precision, and F-measure, with values of 96.68%, 95.50%, and 95.85%, respectively. This indicated the robustness of the model in effectively predicting true positives and ensuring consistent accuracy in its predictions. Although Srinivas et al.'s model achieved a close accuracy of 97.00%, the proposed model still holds an edge with a slightly better overall balance in the key metrics.

Table 10.

Comparison of performance metrics across different models.

Model	Accuracy	Sensitivity	Precision	F-measure
KrishnarajChadaga et al. (2024)³⁴	95.00	95.00	94.00	94.00
Krishna Kumar Joshi et al. (2023)³⁵	95.00	95.00	95.00	95.00
K. Srinivas et al. (2023)³⁶	97.00	96.00	96.00	96.00
Mouna Afif et al. (2023)³⁷	96.23	94.81	93.85	94.19
Sanzida Solayman et al. (2023)³⁸	96.34	96.00	95.00	96.00
Proposed	97.88	96.68	95.50	95.85

In comparison, the methods developed by Solayman et al. and Afif et al. achieved strong results, with accuracies of 96.34% and 96.23%, respectively. However, their sensitivity and precision were slightly lower than those of the proposed model. Similarly, the frameworks introduced by Chadaga et al. and Joshi et al., both achieving 95.00% accuracy, delivered consistent outcomes but fell short of outperforming the top-tier models. Collectively, the proposed framework exhibits a notable advancement in accuracy and a balanced performance across critical evaluation metrics, establishing it as a more dependable and efficient solution compared to current methodologies.

Discussion

The DA-ResBiGRU framework improves the model's capacity to concentrate on the most pertinent data features by utilizing its dual attention mechanism. This capability enables the system to dynamically emphasize critical inputs and accurately identify complex temporal relationships and detailed patterns within cardiac magnetic resonance imaging and structured tabular data. Additionally, the integration of residual connections mitigates the vanishing gradient issue, allowing the model to develop deeper and more meaningful representations while maintaining optimal performance. The ABER algorithm is instrumental in refining the hyperparameters of the model. By maintaining a balance between the exploitation and exploration phases, ABER prevents the model from settling into local optima and guides it toward achieving optimal solutions. This method fine-tunes key parameters, such as the batch size, learning rate, and network weight, contributing to the model's high accuracy, sensitivity, and specificity.

The model's integration of multimodal data, combining CMR imaging with tabular clinical data, allows for more comprehensive analysis. Preprocessing steps such as median filtering, intensity normalization, and histogram matching for imaging data, along with outlier detection and sequential forward feature selection (SFS) for tabular data, ensure that only clean and relevant information is used. This thorough data preparation enhanced the robustness and adaptability of the model across various patient populations.

Unlike many state-of-the-art models that rely on single data modalities or lack sophisticated optimization techniques, this hybrid framework is particularly adept at identifying nuanced patterns related to long-term COVID-associated cardiovascular risks. By incorporating bidirectional gated recurrent units (BiGRUs), the model can analyze data in both forward and backward directions, enhancing its capability to identify temporal patterns essential for precise cardiovascular risk assessment. Extensive testing against a range of machine learning models (SVM, RF, LR), deep learning architectures (LSTM, Inception-v3, MobileNetV2), and optimization algorithms (GOA, PSO, GWO, HHO, and ALO) consistently showed that the proposed model delivered superior performance across all evaluated metrics. Its strong generalization to new data, minimized error rates, and high precision establish its reliability and effectiveness for clinical decision-making.

Conclusion

This study introduces an innovative decision-making framework aimed at forecasting CVD in long COVID patients by integrating state-of-the-art reinforcement learning techniques with prescriptive analytics. The system utilizes a DA-ResBiGRU model combined with ABER to enhance predictive precision. By incorporating CMR imaging and structured tabular data, the framework addresses complexities arising from diverse and unconnected datasets. Remarkably, the system achieved a peak accuracy of 97.88%, alongside sensitivity, precision, and F-measure values of 96.68%, 95.50%, and 95.85%, respectively. Additionally, it exhibited robust performance in Matthews correlation coefficient (MCC) at 85.75% and AU-ROC at 95.39%. These outcomes highlight the system's dependability in identifying cardiovascular risks in long COVID patients, offering a valuable tool for early detection and improved clinical management. Future research will focus on broadening the dataset to include a wider variety of patient demographics, enhancing the model's ability to generalize across diverse populations.

Footnotes

ORCID iD

Banumathi J

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

All data analysed during this study are included in this article.

References

Banerjee

, et al. Estimating excess 1-year mortality associated with the COVID-19 pandemic according to underlying conditions and age: a populationbased cohort study. Lancet 2020; 395: 1715–1725.

Mohamed

, et al. Impact of COVID-19 on cardiac procedure activity in England and associated 30-day mortality. Eur Heart J Qual Care Clin Outcomes 2021; 7: 247–256.

Groff

, et al. Short-term and long-term rates of postacute sequelae of SARS-CoV-2 infection: a systematic review. JAMA Netw Open 2021; 4: e2128568.

World Health Organization. Coronavirus disease (COVID-19) pandemic, https://www.who.int/emergencies/diseases/novel-coronavirus-2019 (2023, accessed 7 September 2023).

Global Burden of Disease Long COVID Collaborators; Wulf Hanson

Abbafati

Aerts

, et al. Estimated global propor- tions of individuals with persistent fatigue, cognitive, and respiratory symptom clusters following symptomatic COVID-19 in 2020 and 2021. JAMA 2022; 328: 1604–1615.

Lee

Baek

Kim

, et al. Cardiovascular outcomes between COVID-19 and non-COVID-19 pneumonia: a nationwide cohort study. BMC Med 2023; 21: 394.

Kim

JOR

Jeong

Kim

, et al. Machine learning-based cardiovascular disease prediction model: a cohort study on the Korean national health insurance service health screening database. Diagnostics (Basel) 2021 May 25; 11: 943. PMID: 34070504; PMCID: PMC8229422.

Tiwari

Chugh

Sharma

. Ensemble framework for cardiovascular disease prediction. Comput Biol Med 2022; 146: 105624.

Jafari

Shoeibi

Khodatars

, et al. Automated diagnosis of cardiovascular diseases from cardiac magnetic resonance imaging using deep learning models: a review. Comput Biol Med 2023; 160: 106998.

10.

Karthikeyan

. A novel attention-based cross-modal transfer learning framework for predicting cardiovascular disease. Comput Biol Med 2024; 170: 107977.

11.

Ribeiro

Marques

Pordeus

, et al. Machine learning-based cardiac activity non-linear analysis for discriminating COVID-19 patients with different degrees of severity. Biomed Signal Proces Control 2024; 87: 105558.

12.

Muzammil

Javid

Khan Afridi

, et al. Artificial intelligence-enhanced electrocardiography for accurate diagnosis and management of cardiovascular diseases. J Electrocardiol 2024; 83: 30–40. ISSN 0022-0736.

13.

Singh

Singh Kourav

Mohapatra

, et al. Human heart health prediction using GAIT parameters and machine learning model. Biomed Signal Proces Control 2024; 88: 105696. ISSN 1746-8094.

14.

Moitra

Alafeef

Narasimhan

, et al. Diagnosis of COVID-19 with simultaneous accurate prediction of cardiac abnormalities from chest computed tomographic images. PLoS One 2023 Dec 14; 18: e0290494. PMID: 38096254; PMCID: PMC10721010.

15.

Baviskar

Verma

Chatterjee

, et al. Efficient heart disease prediction using hybrid deep learning classification models. IRBM 2023; 44: 100786. ISSN 1959-0318.

16.

Heath

Hvass

AMF

Wejse

. Interpreter services and effect on healthcare - a systematic review of the impact of different types of interpreters on patient outcome. J Migr Health 2023 Jan 24; 7: 100162. PMID: 36816444; PMCID: PMC9932446.

17.

Jafari

Shoeibi

Khodatars

, et al. Automated diagnosis of cardiovascular diseases from cardiac magnetic resonance imaging using deep learning models: a review. Comput Biol Med 2023 Jun; 160: 106998. Epub 2023 May 6. PMID: 37182422.

18.

Kumar

Rekha

. An improved hawks optimizer based learning algorithms for cardiovascular disease prediction. Biomed Signal Proces Control 2023; 81: 104442. https://doi.org/10.1016/j.bspc.2022.104442.

19.

Reis

Turk

. COVID-DSNet: a novel deep convolutional neural network for detection of coronavirus (SARS-CoV-2) cases from CT and Chest X-Ray images. ArtifIntell Med 2022 Dec; 134: 102427. Epub 2022 Oct 17. PMID: 36462906; PMCID: PMC9574866.

20.

Kanagarathinam

Sankaran

Manikandan

. Machine learning-based risk prediction model for cardiovascular disease using a hybrid dataset. Data Knowl Eng 2022; 140: 102042.

21.

Nandakumar

Narayan

. Cardiac disease detection using cuckoo search enabled deep belief network. Intell Syst Appl 2022; 16: 200131. ISSN 2667-3053.

22.

Khan

Samer

Alshehri

, et al. Artificial neural network-based cardiovascular disease prediction using spectral features. Comput Electr Eng 2022; 101: 108094.

23.

Metan

Prasad

Ananda Kumar

, et al. Cardiovascular MRI image analysis by using the bio inspired (sand piper optimized) fully deep convolutional network (Bio-FDCN) architecture for an automated detection of cardiac disorders. Biomed Signal Proces Control 2021; 70: 103002. ISSN 1746-8094.

24.

Houssein

Ibrahim

Neggaz

, et al. An efficient ECG arrhythmia classification method based on Manta ray foraging optimization. Expert Syst Appl 2021; 181: 115131. ISSN 0957-4174.

25.

Amarbayasgalan

Lee

Kim

, et al. Deep autoencoder based neural networks for coronary heart disease risk prediction. 2019. https://doi.org/10.1007/978-3-030-33752-0_17.

26.

Zhang

Xue

. An online weighted Bayesian fuzzy clustering method for large medical data sets. Comput Intell Neurosci 2022 Feb 21; 2022: 6168785. PMID: 35237309; PMCID: PMC8885256.

27.

Andrieu

Freitas

Doucet

, et al. An introduction to MCMC for machine learning. Machine Learning 2003; 50: 5–43.

28.

Elvira

Djurie

Djurić

. Adapting the number of particles in sequential Monte Carlo methods through an online scheme for convergence assessment. IEEE Trans Signal Proces 2017; 65: 1781–1794.

29.

Raja

, et al. Synergistic analysis of Lung Cancer's impact on cardiovascular disease using ML-based techniques. IEEE J Biomed Health Inform. doi: https://doi.org/10.1109/JBHI.2024.3365176

30.

Janosi

Steinbrunn

Pfisterer

, et al. Heart disease [Dataset]. UCI Machine Learning Repository. 1989. https://doi.org/10.24432/C52P4X.

31.

Vinutha

Poornima

Sagar

. Detection of outliers using interquartile range technique from intrusion dataset. 2018. https://doi.org/10.1007/978-981-10-7563-6_53.

32.

Sreedevi

Kiran

Santhi Sri

, et al. Da-resbigru -brain tumor classification using dual attention residual bi directional gated recurrent unit using MRI images. Biomed Signal Proces Control 2024; 88: 105596. ISSN 1746-8094.

33.

El-kenawy

E-S

Abdelhamid

Ibrahim

, et al. Al-Biruni Earth Radius (BER) metaheuristic search optimization algorithm. Comput Syst Sci Eng 2022; 45: 1917–1934.

34.

Chadaga

Prabhu

Sampathila

, et al. Explainable artificial intelligence approaches for COVID-19 prognosis prediction using clinical markers. Sci Rep 2024; 14: 1783.

35.

Joshi

Gupta

Agrawal

. An efficient transfer learning approach for prediction and classification of SARS – COVID −19. Multimed Tools Appl 2024; 83: 39435–39457.

36.

Srinivas

Gagana Sri

Pravallika

, et al. COVID-19 prediction based on hybrid inception V3 with VGG16 using chest X-ray images. Multimed Tools Appl 2024; 83: 36665–36682.

37.

Afif

Ayachi

Said

, et al. Deep learning-based technique for lesions segmentation in CT scan images for COVID-19 prediction. Multimed Tools Appl 2023; 82: 26885–26899.

38.

Solayman

Aumi

Sultana Mery

, et al. Automatic COVID-19 prediction using explainable machine learning techniques. Int J Cogn Comput Eng 2023; 4: 36–46. ISSN 2666-3074.