A density-based MS disease diagnosis model using the capuchin search algorithm and an ensemble of deep neural networks

Abstract

Multiple sclerosis (MS) is a severe brain disease that permanently destroys brain cells, impacting vision, balance, muscle control, and daily activity. This research employs a weighted combination of deep neural networks and optimization techniques for MS disease diagnosis. This method uses slices of magnetic resonance imaging (MRI) images as input. Then, after the pre-processing operation, the process of segmentation and identification of the region of interest (ROI) is performed using a combination of the fuzzy c-means (FCM) algorithm and the capuchin search algorithm (CapSA) algorithm. When the target view is detected, the features of each ROI are extracted through three techniques: local binary pattern (LBP), multi-linear principal component analysis (MPCA), and gray level co-occurrence matrix (GLCM). Each of these features is then processed by a deep neural network. In each deep neural network, the CapSA algorithm is used to determine the optimal topology structure and adjust the weight vector of the neural network. This means that in this process, the vector and topology of the deep neural network are adjusted using the CapSA algorithm in such a way that the training error is minimized. Finally, after creating the trained models, the weighted combination of the outputs of these three models is used for the final diagnosis. The implementation results showed that our method was successful in achieving 100% precision compared to other comparative methods. Also, in the average accuracy criterion, it showed a performance of 99.51%, which shows the high performance of our method in diagnosing patients.

Introduction

Chronic diseases are defined as conditions that often worsen over time, necessitating ongoing medical care and leading to limits and disability. The world health organization (WHO) estimates that chronic illnesses claim the lives of 41 million people each year¹. Multiple sclerosis (MS) is an autoimmune chronic demyelinating disease of the central nervous system (CNS). Its main features are inflammation and neurodegeneration. The disease’s pathological presentation is MS plaques or lesions. These are isolated areas of demyelination that mostly affect the white matter of the central nervous system. Progressive-relapsing MS (PRMS), secondary-progressive MS (SPMS), primary progressive MS (PPMS), and relapsing-remitting MS (RRMS) are the four types of MS². MS sufferers have a wide range of symptoms. Weakened limbs, weariness, tingling sensations, disorientation, and impaired eyesight are among the symptoms^3,4.

MS lacks a known etiology. Nonetheless, studies indicate that among genetically predisposed people, environmental variables may contribute to the onset of the illness⁵. At the moment, Magnetic Resonance Imaging (MRI) is the most helpful technique for identifying MS, monitoring the illness’s course, and assessing the effectiveness of different treatments in clinical trials^6,7. In addition to displaying demyelination (lesions or plaques), MRI of the brain and spine produces a number of pictures that help with the visual identification of MS lesions⁸. Even in cases when skilled manual annotations of lesions are feasible in reality, variation among observers in MRI interpretation might provide a challenge in many situations. Due to several constraints, including low resolution brought on by physical limits, visual inspection is especially challenging⁹. An automated, intelligent system for MS lesion detection and quantification could be useful when analyzing several MRI images clinically. Because it requires a lot of labor and experience, manual analysis is costly and time-consuming¹⁰. As a result, artificial intelligence (AI) is using machine learning (ML) and deep learning (DL) techniques to automate MS diagnosis^11,12. ML refers to a branch of AI in which computers possess the capacity to acquire knowledge and improve their performance without the need for explicit programming. On the other hand, DL represents a subset of ML that consists of algorithms enabling software to autonomously train itself to carry out various tasks by exposing complex neural networks to extensive datasets.

The research focuses on enhancing the diagnosis of MS disease through MRI images by integrating optimization techniques and deep learning models. Our method offers two key innovations, including: (1) A new segmentation technique based on combination of CapSA and FCM is proposed to efficiently segment the suspicious areas from MRI images (2) The CapSA is incorporated to refine the topology and weights of deep neural networks and then generate a weighted ensemble of deep neural networks to enhance the classification performance and reduce the risk of overfitting. Using such advancements, the proposed approach offers efficiency in MS diagnosis than the existing methods. Our main contributions can be summarized as follows.

• Introduction of a new algorithm for segmenting MRI images and identifying areas suspected of MS lesions through the combination of FCM and CapSA.

• Implementation of three feature description techniques, namely local binary pattern (LBP), multi-linear principal component analysis (MPCA), and gray level co-occurrence matrix (GLCM), to characterize the features of each region of interest (ROI).

• Development of a method to enhance the diagnosis of MS disease through MRI images by integrating optimization techniques and deep learning models.

The paper follows this progression: Section “Related works” reviews the previous works. Section “Proposed method” presents the proposed method, followed by Section “Research finding” research finding. Section “Discussion, limitations and future directions” discusses the research findings, limitations, and future works. Finally, Section “Conclusion” includes the conclusions.

Related works

By examining the properties of the lesions’ MRI images, Zhang et al.¹³ made predictions on whether clinically isolated syndrome (CIS) will converge into MS. 84 participants with CIS were included in the study. To decide whether to convert to MS, the McDonald criteria were applied. To segment brain lesions, three-dimensional fluid attenuated inversion recovery (FLAIR) and three-dimensional T1 pictures were utilized. Lesion masks were created using a manual segmentation method supported by a computer. To test the efficacy of various segmentation techniques, automated segmentations were also generated using the lesion segmentation toolbox for SPM. The segmented masks served as input data for training an oblique random forest (RF) classifier by automatically calculating shape and brightness attributes. An accuracy of 84.5% was attained by the classifier.

A comparison analysis of different machine learning approaches was carried out by Sacca et al.¹⁴ in order to identify the best approach for early MS diagnosis. They assembled 19 healthy volunteers and 18 MS patients from the neurological unit of the University Magna Graecia of Catanzaro, Italy. The independent component analysis network dataset was analyzed using RF, support vector machine (SVM), k-nearest neighbors (KNN), Naïve Bayes (NB), and artificial neural network (ANN) techniques. Both SVM and RF showed the same accuracy of 85.7% and specificity of 66.7% when using 5-fold cross-validation.

A study on the classification of MS patients with MRIs was carried out by Moghadasi et al.¹⁵ since 2D images are more effective for machine learning processing, they discovered that 3D scans may be transformed into 2D slices by the SVM methods. Using 72 brain MRI scans, they constructed four models with one-vs-all and 6 models with one-vs-one parameters.

Rezaee et al.¹⁶ developed a hybrid automated processing technique for MS identification based on features from MRI data. Information was obtained from 64 MS patients and 61 healthy volunteers during a period of 18 months. The differential evolution (DE) technique was used to pick the features after they were retrieved using the fractal and pseudo-Zernike moments approaches. The algorithm was shuffled frog-leaping algorithm (SFLA) optimized wavelet kernel parameters with extreme learning machine (ELM).

Ekşi et al.¹⁷ employed a computer-aided diagnostic (CAD) method to differentiate between MS and low-grade brain tumors using magnetic resonance spectroscopy (MRS) data from 51 MS patients as well as 39 patients with low-grade brain tumors. For feature extraction, peak integration and full-spectrum techniques were utilized, while for classification, SVM, ANN, and linear discriminant analysis (LDA) were applied. The 100% accuracy, specificity, and sensitivity which the ANN-based system was able to accomplish were determined using a very small sample of 90 records.

A study on the use of radiomics models to fluid-attenuated inversion recovery (FLAIR) images to predict unenhanced MS lesions was carried out by Peng et al.¹⁸ Recursive feature elimination, the ReliefF algorithm, and least absolute shrinkage and selection operator (LASSO) were employed for selecting features after they gathered data from 45 MRI images belonging to 36 patients. With average accuracy, sensitivity, specificity, and area under the ROC curve (AUC) of 82.7%, 80.9%, 84.1%, and 0.857, respectively, the SVM classifier showed the greatest performance out of the three machine learning classifiers used to build predictive models.

A hybrid machine learning model for MS lesion detection and lossless processing of unbalanced data was created by Elsebely et al.¹⁹ they made use of MRI scan textural information and two-dimensional discrete wavelet transformations. Using textural data, an ensemble ML model was created for MS identification. The best results were obtained with ensemble decision trees (EDT) and ensemble support vector machines (ESVM), which had accuracy rates of 98.2% and 98.5%, respectively.

A segmentation technique for MS diagnosis in MRI data was developed by Merzoug et al.²⁰ using SVM with RBF kernel and artificial immune systems (AIS). After the method separated brain tissues into three parts, an SVM model relying on the sequential minimum optimization (SMO) was utilized to categorize MS lesions. 100% sensitivity, 83.8% specificity, and 99.8% accuracy were attained by the method.

Using a hybrid watershed-clustering technique, Bonanno et al.²¹ created a CAD system that automates segmenting images to separate MS lesion regions from other regions. In order to find structures inside the MS lesion, they examined the MRIs of twenty patients and used a watershed technique. Based on the identified MS lesions, they additionally computed significant features for every area of interest. Unwanted oversegmentation was addressed via cluster analysis. 87% diagnostic accuracy, 77% sensitivity, and 87% specificity were attained by the approach.

Ashtiani et al.²² developed a machine learning method to differentiate among MS sufferers and healthy people using distinctive graph properties. In the initial phases of the trial, there were eight MS patients and twelve healthy subjects. The local metrics—node degree, subgraph centrality, K-Coreness, and PageRank centralities—achieved an accuracy of 85%. The global measures of modularity, individual betweenness centrality, and small-worldness index increased the detection of MS patients with a sensitivity of 81.25%.

Convolutional neural networks are used in a technique developed by Soltani et al.²³ to identify lesions associated with MS illness from MRI pictures. Using a 1 × 1 filter size in the convolutional layer, the method comprised two pooling layers, three ReLU layers, and four convolutional layers. The network was trained using the stochastic gradient descent with momentum approach. The method yielded 99.33% specificity, 99.98% sensitivity, and 99.66% accuracy.

In order to increase the diagnostic accuracy of MS lesions, Alijamaat et al.²⁴ used the Haar wavelet transform. They achieved this by combining the two-dimensional discrete Haar wavelet transform with a convolutional neural network (CNN) network. Based on experiments conducted on 20 healthy individuals and 38 patients, the method showed a sensitivity, precision, and accuracy of 99.14%, 98.43%, and 99.05%, respectively, using image data from the respective groups.

A wavelet-transform-based pooling method was used by Alijamaat et al.²⁵. This method breaks down the input image, makes it smaller, and highlights significant variations in the image. Because it highlights local specificities, this change may improve diagnosis. With six convolutional layers, two wavelet pooling layers, and a linked layer, the suggested approach produced results with 98.92% accuracy, 99.20% precision, and 98.33% specificity. Twenty healthy people and 38 patients were used to test this strategy. Research on MS diagnosis models is compiled in Table 1.

Table 1.

Studies on models for diagnosing MS.

References	Method	Data type	Pros	Cons
Zhang et al.13	RF	MRI	Focused on lesion features in baseline MRI, particularly shape and brightness Used 3-fold cross-validation to validate predictions made by the classifiers	Reliable features for small lesions may be impossible to extract from 2D images
Sacca et al.14	SVM, RF	MRI	Using mean signals extracted from Independent Component Analysis (ICA) of 15 brain networks	The feature space is larger than the number of records The risk of overfitting and misclassification of records
Moghadasi et al.15	SVM	MRI	Creating artificial models using SVM to classify MS and normal brain MRI images.	Only one 2D image was generated from each 3D image Proper hardware resources are needed for building models using the whole 3D dataset
Rezaee et al.16	ELM	MRI	Detection of MS lesions from magnetic resonance images. Promoting the feature vector structure by aggregating results from descriptors.	High resemblance of MS plaque-induced lesions to other lesions Time-consuming process and demands high expertise for lesion diagnosis
Ekşi et al.17	ANN	MRI	Availability of MRS in differentiation of low-grade brain tumors and MS lesions.	Not mentioned.
Peng et al.18	SVM	MRI	Developed machine learning models to predict unenhanced lesion evolution. Explored performance of different machine learning algorithms for monitoring MRI disease activity.	Multicenter investigations it is needed for analysis combined with other MRI sequences
Elsebely et al.19	EDT	MRI	Development of a fully automated hybrid model for detecting MS in the brain Solving the problem of imbalanced classification data	Time consumption, data acquisition, memory insufficiency, and low accuracy
Merzoug et al.20	AIS + SVM	MRI	Incorporation of standard deviation dependent filtering for better noise immunity Identification of the problem of MS lesions segmentation in supervised automatic approaches	Not mentioned
Bonanno et al.21	Hybrid Watershed-clustering algorithm	MRI	Applied cluster analysis to quantify and identify MS lesions	Not mentioned
Ashtiani et al.22	SVM	Cognitive task-related fMRI	fMRI can identify changes in brain architecture following brain damage in MS	Relatively low sensitivity in detecting MS patients Need for separating task blocks from rest blocks for connectivity analysis
Soltani et al.23	CNN	MRI	Use of stochastic gradient descent with momentum for weight correction Utilization of ReLU layer for handling negative values in the output	Not mentioned
Alijamaat et al.24	Two-dimensional discrete Haar wavelet transform	MRI	Used two-dimensional discrete Haar transform for feature extraction	Not mentioned
Alijamaat et al.25	Deep CNN	MRI	Location and number of lesions in the white matter of the brain are shown	Small sizes of lesions Dispersion of lesions in the brain Similarity of lesions to other diseases Overlapping of lesions

Proposed method

The accurate diagnosis of MS disease via MRI images necessitates the utilization of effective techniques for the identification of regions suspected of lesions and for the precise description of each region’s features. Concurrently, the features extracted from each region must be analyzed using a robust classification technique, enabling the diagnosis process to be conducted with minimal error. This research endeavors to fulfill these requirements by integrating optimization techniques and aggregating deep learning models. The proposed method encompasses the following steps:

1. Preprocessing.

2. Segmentation of MRIs and identification of ROI.

3. Feature description of the ROI.

4. Feature classification and disease diagnosis.

The algorithm is depicted in Fig. 1. The proposed method preprocesses each MRI slice to separate the image’s background regions from the brain tissue. Following the separation of the brain region, a histogram enhancement technique is employed to enhance the image’s contrast. Subsequently, each brain tissue slice is decomposed into its constituent regions using a novel segmentation strategy, enabling the accurate identification of regions suspected of lesions. The introduced approach combines FCM clustering and CapSA for image segmentation. In this approach, FCM is utilized for the initial approximation of regions and the formation of the initial population of CapSA, leading to a more accurate segmentation of brain regions based on entropy and silhouette index criteria. Upon completion of the second step, each region in the segmented image is scrutinized based on intensity and area features to identify regions suspected of lesions. These segments form the input to the next phase of the introduced approach, wherein three distinct techniques are utilized for describing the features of each ROI. In this step, the features of each ROI are described based on three techniques: LBP, MPCA, and GLCM. Each of these feature sets serves as input to one of the learning components in the proposed ensemble system, facilitating the disease diagnosis in the fourth step. In this step, an ensemble of three deep neural networks is employed for feature classification and disease diagnosis. Each of these learning models is trained utilizing CapSA. Ultimately, a weighted voting technique is implemented to ascertain the final output of the proposed diagnostic model.

Fig. 1.

Proposed method steps.

Preprocessing

The initial step of the introduced approach involves the preprocessing of MRIs to eliminate redundant information and enhance their quality. In this regard, the brain region in the input image is initially identified, followed by an improvement in the contrast of this region. Each slice of the MRIs is shown as . This slice employs a grayscale color system and comprises two primary parts: the region of brain tissues and the image background. The foremost process in the preprocessing step is the separation of these regions. As per the studies, the background part MRIs with a grayscale coloring system (in the brightness intensity scale of 0 to 255) possesses a maximum brightness intensity of 13. In this process, the image I is transformed to a black and white image using a threshold of 14. This action results in the pixels of the background region in the resulting binary image (and some parts of the brain tissues) having a value of 0, while other regions have a value of 1. The obtained black and white image is denoted as . Subsequently, all contiguous components in the image are extracted, and the largest contiguous region present in image B (based on the number of member pixels) is identified. An erosion operator is used to fine-tune the borders of the connected region, which is representative of the approximated brain region in black and white image B. The erosion operator may be defined as follows assuming the structural element is represented by the letter X²⁶:

1

According to the previously indicated relation, an eroded element Z is only taken into account in the event that the structural element X is a subset of the black and white image B. The structural element X is treated as a circle having a radius of three in the proposed approach. Z is the image that has eroded. In this image, the brain region is represented as a binary value of 1, and some of the inner parts of the brain tissue (which have a brightness less than the threshold 13) are represented as a value of 0. Given the continuity of the brain region, all existing cavities in the image Z are filled with values of 1. To perform this operation, all contiguous regions with values of 0 that are surrounded by values of 1 are replaced with a value of 1. The result of this operation is a binary mask of the brain region that, by applying it to the initial image I, can separate the brain tissue from the background:

2

Utilizing the aforementioned relation, all the pixels of the image background I are multiplied by the value 0. Subsequently, by cutting the bounding box of the non-zero values, the brain region is separated from the image. It should be noted that using the threshold of 14 is just used to estimate the region of brain and background. Some of the regions with low intensities, for instance, cerebrospinal fluid (CSF), may be excluded in the initial stage because of the threshold, but this is not much of a problem. The proposed preprocessing step employs the fill morphological operator to fill any of the holes that may be produced by the threshold in the binary mask of the brain. Taking into account that the brain is surrounded by the skull which has a high intensity, the fill operator restores the removed CSF regions into the brain mask. Also, in the worst-case scenario, where regions with intensities below the threshold are removed from the brain, these regions would likely be part of the CSF and would not contain any MS plaques, as plaques typically have higher intensities in MRI scans.

As a part of the preprocessing process, the image of the brain region is enhanced based on the adjustment of intensity values²⁷. In this approach, the intensity values in the grayscale image J are mapped to new values. In this condition, 1% of the lower and 1% of the upper values of all pixels are saturated to augment the contrast of the output image.

Segmentation and identification of ROI

A novel strategy is used in the second stage of the suggested approach to segment each image slice. For picture segmentation, the suggested approach combines the FCM algorithm with CapSA. By dissecting the brain area into its constituent tissues, this phase aims to reduce the complexity of the problem. Through this process, lesion regions in the image can be isolated as a cluster from other regions. The separation of various regions and tissues in brain images can be accomplished by analyzing the disparity in brightness intensity values. In this manner, by optimally setting threshold values for each region, the accurate method of segregating regions in images can be determined. The proposed approach models this step as a problem to be optimized and employs CapSA for solving it. For image segmentation, the suggested technique takes a similar approach to conventional FCM, with the exception that each region’s centroid is treated as a variable for optimization, and CapSA is used to find its ideal value. Additionally, the first collection of Capuchins is created using FCM in order to hasten the convergence of the suggested segmentation technique. In this section, the segmentation process is initially formulated as an optimization problem, followed by a detailed explanation CapSA application for problem-solving.

Consider an image denoted as X that we aim to decompose into C segments with non-overlapping pixels. The most feasible way to distinguish between two tissues in each slice of MRI is to look at the intensity and spatial data of the pixels belonging to the tissue. Thus, a region in X can be defined as a collection of neighboring pixels that differ in intensity from one another less than other neighboring sections (having a common border). On the other hand, two separated sections A and B that have comparable intensities can be thought of as two separate segments. This definition stipulates that to identify each segment, both spatial information and pixel brightness intensity should be taken into account. In the optimization problem addressed in this research, an optimization variable is considered for each ROI in the image, which determines the intensity threshold corresponding to that area. As a result, in the suggested approach, every vector of solution is represented as a vector of integers of length C. Each value in this vector represents the intensity level of the pixels that belong to the relevant segment and has searching bounds (0.255).

Using the thresholds specified in the solution vector, the variation in intensities is calculated to determine each pixel’s membership in a segment in the suggested approach. As a result, every pixel in the image is allocated to an area in the solution vector that has the least absolute disparity with the threshold associated to that region. In this manner, for each solution vector generated by the optimization algorithm, a candidate segmentation for the input image can be formulated. Finding the best segmentation solution amongst the generated possible solutions is the main goal of the optimization procedure. In order to do this, it should be possible to use a fitness assessment function to determine which segmentation state is better than others. The suggested approach uses two different criteria in combination to get the best segmentation state for every image:

1. Silhouette index.

2. Entropy.

The image X is first broken down into C areas using the solution S in order to assess each solution’s fitness using the previously specified criteria in the suggested technique. In the process, every pixel is given an area with the shortest fuzzy distance with the associated threshold based on the absolute difference it has across all of the C thresholds provided in S. Matrix Y is obtained by decomposing picture X into C regions by applying this operation to all pixels. The resulting segmentation ignores the spatial details of the regions and only takes into account the intensity data of picture X. As a result, using spatial information, the resulting regions are then distinguished from one another. The picture matrix Y is broken down into its adjacent areas in this instance. A new unique identification is then assigned to a contiguous region to be regarded as a separate segment if its area surpasses 0.05 of the area of the brain (the region discovered in the preprocessing stage). The potential segmentation picture according to the solution S is broken down into non-overlapping sections when this process is completed for each region. The entropy and silhouette index criteria are then used to assess the segmentation accuracy of these non-overlapping regions. Equation (3) is utilized in the suggested segmentation algorithm to determine the quality of the segmentation that arises from every solution vector.

3

where C represents the number of ROI in the image, and n represents the number of pixels in it. Also, describes the silhouette index value for pixel i, which can be calculated as follows:

4

Where is the average distance from point i to other points in the same cluster with i, and is the minimum average distance from point i to points in the nearest cluster. Also, in Eq. (4), the parameter represents the entropy of region i in the segmented image based on the current solution vector. For this purpose, the entropy of each segment is calculated separately:

5

Where V denotes the number of unique values in the current region of the image, and describes the frequency of value I in this region. The objective of the proposed segmentation algorithm is to formulate a state of image segmentation that minimizes entropy while maximizing the silhouette index. Minimizing entropy implies forming segments with maximum pattern uniformity. Maximizing the silhouette index ensures the achievement of a segmentation state in which any difference between two regions is maximized. The proposed method employs CapSA to discover a segmentation capable of minimizing Eq. (3).

It needed to be highlighted that a segmentation method utilizing optimization techniques must have a high rate of convergence. In this case, the way the initial population is formed is just as important as the search approach that is used. In the suggested approach, a subset of the population is identified using FCM in order to offer estimates of points close to the universal optimal for the optimization process. The likelihood that the algorithm will enter a local optimum can be raised by basing the entire starting population on the FCM method. According to the suggested strategy, other solutions in the first population are assigned random values, and FCM is used to decide 1/4 of the starting population in CapSA. The image X is transformed into a vector, and the resultant vector is decomposed into C regions to determine each starting FCM solution. Then, a solution vector is said to be represented by the central point of the generated clusters. The following are the stages involved in segmenting pictures using CapSA and FCM:

Step (1) The FCM algorithm is applied times consecutively on the input image, and the extracted centers in each iteration are considered as an initial solution. Also, solutions in the initial population are randomly valued.

Step (2) Using Eq. (3), the fitness of every solution (Capuchin) is determined.

Step (3) Each Capuchin’s starting velocity is determined.

Step (4) Among the Capuchin population, half are chosen at random to be leaders, while the other half are labeled as followers.

Step (5) Proceed to step 13 if the total amount of iterations exceeds the maximum G; if not, repeat the subsequent steps:

Step (6) The following formula²⁸ is used to get the lifespan parameter of CapSA:

6

where g is the number of iterations that are currently in progress, and the parameters , , and have values of 2, 21, and 2, respectively.

Step (7) Carry out the subsequent actions for every Capuchin (leader and follower), such as i:

Step (8) For a leader, update the speed using the following equation²⁸:

7

In this case, j stands for the number of segments (dimensions), for Capuchin i’s velocity in dimension j, for Capuchin i’s location for the jth dimension, and for its best position for the jth variable as of right now. Two random real numbers in the interval [0, 1] are also included as and . Ultimately, the parameter that determines the previous velocity is , and it is set to 0.7.

Step (9) Based on their movement manner and velocity, the Capuchin leaders’ new positions are modified.

Step (10) Based on their velocity and the leader’s location, the follower Capuchins’ new location is adjusted.

Step (11) Using Eq. (3), the fitness of every solution (Capuchin) is determined.

Step (12) If the entire population’s position has been updated, the process returns to step 5; otherwise, the algorithm repeats from step 7.

Step (13) the solution with the least amount of fitness is applied to the input image, and the result is returned as the segmented image.

The ROI is determined by using the segmented image that was created in the previous phases. The suggested approach uses the characteristics of MS plaque in MRI pictures to pinpoint areas that may be lesions. When compared to other brain regions, MS plaques in MRIs usually appear as connected patches with greater intensity (or at least around their margins). Based on this, the average intensity and area characteristics are used in the suggested method to determine ROIs. The third stage of the suggested technique uses the set of regions that were chosen in this phase as its input.

Description of ROI features

Following the identification of regions suspected of lesions in the segmented image, the corresponding area for each ROI is extracted from the preprocessed image. The accurate classification of these regions and the diagnosis based on them necessitate the use of efficient techniques for feature extraction. The proposed method employs three distinct techniques to extract the features of each region, aiming to achieve a more robust feature description model. The LBPs were used to capture the local texture information and the GLCM features captured information about the spatial relationship of the gray levels. In order to reduce the dimensionality of the extracted features and in order to make the further computation more efficient, MPCA was used. While the LBP technique is noise-sensitive, we have avoided this by using a multi-scale system. In this way, we incorporated LBP features computed at different scales in order to acquire the texture information at multiple resolutions to minimize the noise influence. Also, the application of the different feature sets– the GLCM and the MPCA – complemented each other in giving a better understanding of the ROIs. These techniques are elaborated upon in the subsequent sections.

• (A)Feature description based on LBPs.

The labels of adjacent pixels within a radius, R, are taken into consideration by the LBP operator when allocating a binary value to each pixel. The values of each nearby pixel and the value of the central pixel are compared to determine these labels. To be more precise, pixels having values that are higher or equal to the central pixel are assigned a label of 1, and pixels having values smaller than the central pixel are assigned a label of 0. An L-bit length vector is then created by placing these labels in a circular pattern. Following the LBP operator’s labeling of the image, the following defines a histogram of the labels:

8

The function s has the following definition, and n is the number of labels produced by the LBP operator:

9

Patterns in which there are at most two changes from 0 to 1 or vice versa when the bits are rotated are called uniform patterns. Storing uniform patterns creates a new operator that has 59 patterns for 8-pixel neighborhood. The suggested method extracts LBP features using an adjusted model that is based on strategy²⁹. The segmented picture is split into N non-overlapping units in the suggested technique, and each image cell’s characteristics of LBP are retrieved using²⁹. This gives each cell’s LBP characteristics a description as a histogram array of length B. Consequently, every image may be represented as a vector of length N×B. Note that each ROI’s characteristics of the LBP are retrieved for 3 radii values () and eight neighborhood counts in the suggested technique. As a result, each ROI’s characteristics for LBP are described by feature vectors that have a dimension of 3×N×B.

• (B)Feature description based on MPCA.

The second model employed for feature extraction of the ROI in the proposed method is MPCA. For this purpose, consider a set of ROI regions comprising N segments, each with dimensions equal to . By aligning each segment adjacent to one another, the entire set can be represented as . Upon applying to the MPCA algorithm, the feature matrix extracted for R is , where . In this manner, the features of each ROI are condensed to P features, and each row of the resulting matrix D signifies the corresponding sample in the database. The feature extraction process is depicted in Fig. 2.

Fig. 2.

Feature extraction process by MPCA.

The computational process for feature extraction using MPCA is detailed as follows. MPCA is presented as a multilinear extension of PCA. Given a set of training samples tensor , MPCA defines a multilinear transformation , which maps the original tensor space to the tensor space where . Where, are derived in a manner that the majority of the observed variances between the samples of the original tensor are obtained. This variance is defined as follows³⁰:

10

Where, represents the mean tensor, which is calculated as . The matrices , maximize the total tensor dispersion . These matrices are obtained by solving the optimization problem as defined in³⁰.

11

Given that there is no known optimal solution for the optimization problem in relation 11, let’s assume that is a new test tensor. The sub-dimension tensor obtained through MPCA, , can be utilized for representation or classification instead of . This technique, by concurrently considering the horizontal and vertical correlation of data for feature extraction, proves to be more effective in applications that describe images.

• (C)Feature description based on GLCM.

GLCM is a probabilistic model that is utilized to describe the distribution of brightness intensities of adjacent pixels in an image. GLCM is a two-dimensional probability function that takes into account the brightness intensity of pixel i at a specific position in relation to the brightness intensity of pixel j at another position. Features derived from the GLCM are statistical values that can be used to describe image characteristics. These features can be employed to classify suspicious regions in the image. Some of the GLCM features that can be used to describe these suspicious regions include:

• Correlation: This feature quantifies the correlation between the brightness intensities of adjacent pixels. A high correlation value indicates that the brightness intensities of adjacent pixels are similar, making this feature useful for identifying regions with regular patterns.

• Variance: This feature quantifies the data dispersion. A high variance value indicates that the data are widely dispersed, making this feature useful for identifying regions with a high of diversity.

• Flatness coefficient: This feature quantifies the uniformity of the brightness intensity distribution. A high flatness coefficient value suggests that the brightness intensity distribution is uniform, making this feature useful for identifying regions with a uniform brightness intensity distribution.

In this way, the above set of features is extracted as descriptive features of the ROI to be used alongside two other feature categories as input to the proposed ensemble model.

Feature classification and detection

In the final step of the proposed method, an ensemble model composed of deep neural networks is employed to process the extracted features for each ROI and classify its type. In this ensemble model, CapSA is used to tune and train each DNN classifier. Also, a weighted voting strategy is utilized to determine the final output of the ensemble system. In the continuation of this section, after mentioning the structure of the proposed ensemble system, the strategy used for optimizing each DNN model is described, followed by detailing the employed weighted voting mechanism for determining output.

Ensemble model architecture

To classify the extracted features for each ROI, we employed an ensemble model composed of three DNNs. Each neural network was designed to process one of the feature sets: LBP, MPCA, and GLCM. Each DNN is fed by one of the mentioned feature sets and attempts to predict the target variable based on them. In the proposed ensemble model, each neural network is independently optimized by CapSA. The DNNs do not have a specified structure and the role of CapSA is to tuning the structure of the DNN and also, training it by determining the optimal weight values which leads to the minimized training error of the DNN. This operation is described in the next section.

Neural network optimization

We applied the CapSA to optimize each neural network’s setup. CapSA was used to modify the neural network’s weights, number of hidden layers, and the amount of neurons in every hidden layer. This optimizer seeks to determine the ideal topology and weight for the relevant DNN by using the training error criteria as its fitness function. It’s important to note that the optimization procedures carried out by CapSA in this stage are similar to those described in Sect. 3.2, with the exception that the solutions use a distinctive fitness function and structure. As such, only the distinctions indicated above are explained in this section.

• (A)Solution vector and search boundaries.

The neural network’s topology, the weights of the links between its neurons, and the network’s biases are all determined in this stage by CapSA. As a result, each CapSA’s solution consists of two associated components. The network topology is specified in the first component of the solution, and the network weights and biases are designated in the second component, which corresponds to the topology found in the first component of the solution. As a result, the optimization algorithm’s solutions have a variable length that depends on the network’s architecture. The perceptron network can have an endless number of topological states, hence the network architecture portion of the solution must take certain restrictions into account. Consequently, these restrictions are taken into account for the initial portion of the solution in order to restrict the search space:

• Maximum number of hidden layers: Each deep neural network can have up to 5 hidden layers. Consequently, the first part of the solution vector consists of 5 elements. The numbers in this section of the solution vector denote the number of neurons set for each of the hidden layers of the neural network.

• Neuron count in hidden layers: Each hidden layer of the neural network can contain a minimum of 0 and a maximum of 10 neurons. If the number of neurons in a layer is set to zero, that layer is omitted from the neural network architecture.

It is essential to note that just the quantity of neurons in the hidden layers is provided in the first component of the solution (deciding on the the topology). This is so because the total amount of input features and the number of output classes, respectively, dictate the size of the neural network’s input and output layers. The length of the second component of the solution is likewise dictated by the structure in the first component, since the number of neuron in the network is established by the initial component of the solution. It’s crucial to remember that all of CapSA’s initial population is chosen at random in this phase. Additionally, the search bounds of the weight values of the neural network are considered in interval [− 1, + 1].

• (B)Fitness function.

A fitness function is used to determine which of the solutions is the most desirable. This procedure entails creating the network outputs for the training instances, and matching these outputs with the true goal values, after figuring out the neural network’s structure and weights for each solution. The neural network’s performance and the quality of the produced solution are then assessed using the training error rate. Thus, the following is the definition of the CapSA fitness function:

12

where N is the total amount of training instances, and E is the number of training instances for which the neural network’s predicted label contradicts the ground truth label.

Ensemble model fusion

Following the optimization of the neural network models, a weighted voting strategy is employed to ascertain the final output of the neural network. In the proposed method, the influence of each DNN model on the final output of the ensemble model is determined via a weight value. This weight value signifies the count of the DNN model’s output in the voting process. In the proposed method, each DNN model can accept an integer weight value within the range [0, 10]. For instance, a weight value of 0 implies disregarding the output of the DNN model, whereas a value of 3 implies that the DNN output is counted thrice in the voting process. To determine the weight value of each DNN, a comprehensive search approach is utilized. In this context, a weight combination for the DNN models is chosen that minimizes the final training error of the ensemble model.

Research finding

The studies were carried out using MATLAB^® R2020a (V 9.8.0.1323502) software accessible through (https://www.mathworks.com/products/new_products/release2020a.html), with an MRI slice applied for all database samples. The goal of this strategy was to avoid the overfitting problem. The research utilized anonymized data from the publicly available ‘Brain MRI Dataset of MS with Consensus Manual Lesion Segmentation and Patient Meta Information’ dataset on Mendeley Data³¹. This research adheres to the ethical guidelines established for this dataset. This dataset includes MRIs from 60 patients (46 females and 14 males), with age range of 15 to 56 years old. The average age of patients is 33 years. Also, in term of MS phenotype, the dataset includes 50 RRMS and 10 SPMS instances. Due to the low number of patients, multiple slices were chosen from each MRI instance. Slices were selected at least 35 mm apart horizontally within each patient, which led to significantly different samples. In this regard, 406 slices were selected with 192 slices having no plaques and the remaining 217 slices having at least one plaque. Table 2 summarizes the dataset information.

Table 2.

Dataset specifications.

Feature	Value
Data source	Mendeley data
Number of patients	60
Gender	Female: 46, male: 14
MS phenotype	RRMS: 50, SPMS: 10
Age range	15 to 56 years
Mean age	33 years
Localization of lesions	Periventricular: 70%, cortical: 20%, brainstem: 10%

In the segmentation phase of the CapSA algorithm, the number of ROI is considered to be 5, and the population size and number of iterations are set to 150 and 500, respectively. Additionally, in the optimization phase of each deep neural network, the population size and number of iterations are specified as 100 and 800, respectively. During the experiments, a cross-validation technique with 10 repetitions is employed, and the performance of the methods is evaluated using precision, recall, F-measure, accuracy, matthews correlation coefficient (MCC), critical success index (CSI). During each evaluation iteration, the classified samples by the proposed method, after comparison with context labels, fall into one of four possible scenarios.

• True positive (TP): sick individuals accurately classified as sick.

• True negative (TN): healthy individuals are correctly classified as healthy.

• False positive (FP): healthy individuals are mistakenly classified as sick.

• False negative (FN): sick individuals mistakenly classified as healthy.

Accuracy is a commonly used measure for classification performance, defined as the ratio of properly classified samples to the total number of samples:

13

Precision is the proportion of correctly classified positive samples to the total number of positive anticipated samples, as shown in Eq. (14).

14

The F-measure is also called the F1-score, and it represents the harmonic mean of precision and recall. The value of the F-measure ranges from zero to one, and high values of the F-measure indicate high classification performance. The following equation is displayed:

15

It represents the correlation between observed and predicted classifications and is generated directly from the confusion matrix using Eq. (16). A coefficient of + 1 implies flawless prediction, − 1 denotes absolute difference between prediction and true values, and zero means no better than random prediction.

16

CSI determines the percentage of correctly anticipated positive occurrences for every event, with a range of 0 to 1. It is also known as the threat score or the true talent statistic. The CSI is calculated using

17

We looked at three different ways to check and diagnose the disease. The first method, which is our proposed method, was presented in the third section and all related techniques were used to perform disease diagnosis operations. The second mode, as Convolutional Ensemble, uses a simple ensemble system for disease diagnosis. This method uses DNN model statically for training with train SCG algorithm and then performs the recognition results through majority voting. In the third mode, we used the DNN (MPCA) method, in which the utilization of a singular DNN is solely based on the acquisition of MPCA features. Our suggestion is to use a combination of these features with image segmentation and then use a DNN to determine the impact of each combination of features on the final output, instead of using a DNN that only uses the MPCA feature. In addition, we compared the suggested method to previous works on CNN-SM²³, Wavelet-CNN²⁴, and W-Pooling²⁵.

Figure 3 shows the graph of average accuracy for different methods. As can be seen in the graph, our proposed method has a 1.9% and 0.97% superiority in disease diagnosis compared to the comparative methods of CNN-SM and Wavelet-CNN. These results show that our proposed method has improved the accuracy of disease diagnosis.

Fig. 3.

Comparison of average accuracy in different methods.

Based on the confusion matrix plot in Fig. 4, it is evident that the proposed method achieved an impressive accuracy of 99.01% in identifying samples from the negative class (healthy individuals), successfully classifying all these samples. On the other hand, for the samples in the positive class (individuals diagnosed with MS), the proposed method demonstrated an accuracy of 99.01%, contributing to an overall diagnostic accuracy of 99.5%, showing an approximately 1% increase compared to the comparative methods. Therefore, this analysis indicates that the proposed method outperforms the comparative methods in the classification of both sample classes, leading to higher reliability in its outputs.

Fig. 4.

Comparison of confusion matrix in different methods.

Figure 5 shows the classification quality diagram. This graph shows that our proposed method has full precision and its f-measure and recall are still higher than the comparative methods. An accuracy of one means that when our proposed model detects a sample as positive, this detection has a 100% probability of being correct. Also, recall also shows that our proposed method was able to identify a higher proportion of samples with MS more accurately; the probability of extracting samples belonging to the positive category by the proposed method is higher than other methods. The f-measure also shows that the coordinated average of these two measures is higher than the comparative methods. Therefore, the output of the proposed method for the positive category (individuals with MS) is more reliable than the comparative methods.

Fig. 5.

Comparison of classification quality in different methods.

The MCC, CSI, and AUC criteria in Fig. 6 are used to evaluate the accuracy and effectiveness of MS disease diagnosis methods. Higher values of these criteria indicate better method performance, meaning the method can more accurately identify samples related to the target. The graph illustrates an improvement in the proposed method’s performance in disease diagnosis.

Fig. 6.

Comparison of MCC, CSI, AUC in different methods.

Figure 7 shows the receiver operating characteristic (ROC) curve. According to this diagram, the suggested value of AUC is equal to one; because its false positive value is zero and its true positive value is complete. This makes the ROC curve for the proposed method to be in the shape of a perfect square and the area under the curve is equal to one. This graph is scaled from 0.5 to 1 to better show the difference between the compared methods. Also, from the comparison of the AUC value of the proposed method with the compared methods, we conclude that our proposed method has been able to increase the performance by about 2.1% compared to the CNN-SM method and about 0.5% compared to the Wavelet-CNN method in the positive category or category of individuals with MS.

Fig. 7.

Comparison of ROC curve in different methods.

Table 3 demonstrates the findings of the proposed approach and the alternative approaches. In this table, the proposed method has also been compared with several well-known deep neural network architectures, widely used for medical image classification tasks. These neural network architectures include LeNet-5³², AlexNet³³, VGG-16³⁴, and ResNet50³². ResNet50 architecture has been shown to achieve high performance in different image classification tasks including the medical image analysis. These residual connections assist to lessen the vanishing gradient issue, which makes it possible to train extremely deep networks. The next CNN architecture used for comparison is the VGG-16, which is characterized by its depth and simplicity of the architecture. It has been used in many applications of image classification including in medical imaging. AlexNet was one of the first models that made a significant breakthrough in the field of deep learning for image classification and is also employed in the classification of medical images in different studies. LeNet-5 is one of the first CNN architectures and is quite shallow compared to today’s CNNs; thus, it is not well suited to MS diagnosis, which is a more complicated task. However, we considered LeNet-5 in the comparisons to have a study on the relation between complexity of the neural networks and their performance in MS diagnosis. The proposed approach exhibits superior values for all assessment metrics, encompassing Precision, Recall, F-Measure, Accuracy, MCC, CSI, and AUC, in contrast to the other methods. For instance, the suggested approach exhibits a precision of 1, recall of 0.9908, F-size of 0.9954, precision of 99.5110, cross-correlation coefficient of 0.9902, CSI of 0.9908, and AUC of 1.0000, while the other methods possess lesser magnitudes.

Table 3.

Comparison of several methods.

Methods	Precision	Recall	F-measure	Accuracy	MCC	CSI	AUC
Proposed	1	0.9908	0.9954	99.5110	0.9902	0.9908	1.0000
Prop. (Conv.Ensemble)	0.9401	0.9401	0.9401	93.6430	0.8724	0.8802	0.9396
DNN (MPCA)	0.9810	0.9493	0.9649	96.3325	0.9271	0.9303	0.9781
CNN-SM23	0.9814	0.9724	0.9769	97.5550	0.9510	0.9537	0.9790
Wavelet-CNN24	0.9953	0.9770	0.9860	98.5330	0.9708	0.9723	0.9945
W-Pooling [25]	0.9772	0.9862	0.9817	98.0440	0.9608	0.9633	0.9859
LeNet-532	0.8531	0.8295	0.8411	83.3741	0.6671	0.6826	0.8370
AlexNet33	0.8784	0.8986	0.8884	88.0196	0.7594	0.7770	0.8939
VGG-1634	0.9726	0.9816	0.9771	97.5550	0.9509	0.9542	0.9812
ResNet5032	0.8860	0.9309	0.9079	89.9756	0.7993	0.8168	0.9241

As shown in Table 3, the proposed weighted ensemble model could draw an edge over the compared CNN architectures such as LeNet-5, AlexNet, VGG-16, and ResNet50. The results demonstrated that using simple and shallow CNN architectures such as LeNet-5 or AlexNet could lead to model under-fitting, observable through their relatively higher error rates during the training and testing phases. On the other hand, the ResNet50 with considerable deeper architecture than other CNN models, resulted in model over-fitting. This situation is observable from the training loss of 0 and low accuracy while observing unseen test instances. In contrast, the VGG-16 provides a balance between the model complexity and its performance, leading to competitive results in diagnosing MS.

Discussion, limitations and future directions

The main goal of this work was to create a new accurate approach to MS diagnosis based on MRI data. To achieve this goal we incorporated efficient methods in segmentations, optimization algorithms and deep learning models in order to come up with a more robust tool that can be used by the clinicians. In this section, we discuss the results which have been obtained for the proposed method and analyze its performance in comparison with the baseline methods. We also point out the research limitations and directions for future research.

• (A)Performance evaluation.

The results have shown that the proposed method outperforms the baseline methods in all the evaluation metrics. In particular, it obtained the results of precision equal to 1, recall equal to 0. 9908, F-measure equal to 0.9954, accuracy equal to 99.5110, MCC equal to 0.9902, CSI equal to 0.9908, and AUC equal to 1. These results were higher than the recent methods such as CNN-SM²³, Wavelet-CNN²⁴, and W-Pooling²⁵; and the diagnosis accuracy of our method is at least 0.97% higher than these approaches. The reasons for this superiority can be explained by the following reasons:

• Segmentation: the proposed segmentation algorithm helped in correctly determining ROIs from brain MRIs, and the result was a clean and accurate input for further processing steps (feature extraction and classification).

• Feature extraction: the features extracted using LBP, GLCM and MPCA covered the regions of interest effectively and the deep neural networks could learn the discriminative patterns from them.

• Deep learning: the deep neural networks which has been optimized using CapSA was able to learn complex relationship between the extracted features and the disease labels.

• Ensemble model: this was followed by the application of the weighted ensemble of deep neural networks that enhanced the robustness and accuracy of the classification. More importantly, the use of ensemble approach led to a decrease in the overall dimensionality of the model as opposed to the use of a single deep neural network architecture. Such simplification can be explained with the fact that the ensemble is capable of utilizing the strengths of various models while at the same time minimizing their shortcomings.

As for the accuracy, the proposed method is much higher than the well-known deep neural network architectures including ResNet, VGG, and AlexNet; showing a superiority of at least 2%. Despite the fact that these architectures have demonstrated high accuracy in other image classification tasks, they might not be compatible with the needs of MS diagnosis. The proposed ensemble model along with the optimized feature extraction and segmentation techniques were able to offer better accuracy compared to these high complexity models.

• (B)Limitations and future work.

The current research includes several limitations which should be mentioned and planned to be addressed in future studies:

• Dataset size: the present study possessed a small sample size, which could have possibly restricted the generality of the conclusions drawn.

• Feature engineering: it is also important to mention that the current set of features is not the only possible one; other features or different feature engineering strategies might have a positive impact on the model’s performance.

• Model complexity: as mentioned earlier, the proposed ensemble of DNNs is less complex compared to the well-known deep learning architectures. However, the employed ensemble model is still computationally expensive compared to the classical ML models, thus making it hard to apply them in real-time clinical practice.

In future work, it would be more beneficial to compare our method on larger and more diverse sets. Further, it would be beneficial to experiment with other feature extraction methods and come up with more effective deep learning models that would improve the effectiveness of our approach.

Conclusion

This study presents a novel approach for diagnosing MS using a weighted combination of deep neural networks and optimization techniques. The method utilizes MRI image slices, initially processing them through segmentation and region of interest region of interest identification using the FCM and CapSA algorithms. Subsequently, features from the ROIs are extracted through LBP, MPCA, and GLCM techniques and processed using deep neural networks, each optimized using the CapSA algorithm to minimize training error. The final diagnosis is determined by a weighted combination of the outputs from these models. The experimental results demonstrate the method’s outstanding performance, achieving 100% precision and displaying an average accuracy of 99.51% when compared to other diagnostic approaches. These results demonstrate how our suggested approach, which offers an automated and objective evaluation to assist in the clinical diagnosis of MS, might be a useful adjunct for clinicians. Although the primary diagnosis for MS remains clinical, our method presents a viable way to enhance diagnostic precision and uniformity.

Author contributions

All authors wrote the main manuscript text. All authors reviewed the manuscript.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.

Ethical statement

This study did not involve human subjects research as defined by Belmont Report. Data was collected through a voluntary anonymous questionnaire that did not pose any risks beyond those encountered in daily life. Informed consent was obtained from all participants.