3.1. Data acquisition

Data acquisition is a critical step in the research process, ensuring the availability of high-quality and relevant data for the study. In this case, the dataset was obtained from a reputable source, specifically from Kaggle, a platform known for hosting various datasets for research and analysis. The dataset’s link, provided https://www.kaggle.com/datasets/marcaubreville/mitosis-wsi-ccmct-test-set?select=1018715d369dd0df2fc0.dcm [31] indicates the specific location from which the data was sourced.

The data acquisition process involved retrieving digital pathology images in DICOM format, which is a standard format used in the medical imaging field. These images contain crucial information about cellular structures and abnormalities, making them ideal for studying mitotic activity. Digital pathology images provide a detailed view of tissue samples, allowing researchers to analyze various aspects, including cell morphology and mitotic figures.

3.2. Pre-processing

Once the dataset is acquired, pre-processing is employed to prepare the data for analysis. Pre-processing steps are essential for ensuring consistency, removing noise, and enhancing the quality of the images. In this study, the following pre-processing techniques were applied:

1. (i). Normalize Image Sizes and Color Channels: Ensuring uniform dimensions and color representations across all images is crucial for accurate analysis. Normalizing the sizes and color channels helps in standardizing the input data for subsequent processing.
2. (ii). Apply Customized Stain Normalization Techniques: Stain normalization techniques are employed to make the images consistent. Stain normalization ensures that variations in staining across different samples or slides do not affect the analysis, allowing for reliable comparisons between images.

The Stain Normalization Technique customized for mitosis detection is designed to address staining variations in pathology images and enhance the robustness of mitosis detection. The CDL normalization employs a unique and adaptive approach to learn and normalize staining differences specific to the dataset.

Stain normalization is a crucial preprocessing step in digital pathology, especially for tasks like mitosis detection, where consistent and accurate analysis of histopathological images is essential. Mitosis detection involves identifying cells that are undergoing the process of cell division, and stain normalization helps ensure that variations in staining across different images or within the same image do not hinder the detection process. The steps of stain normalization, specifically for mitosis detection are as follows:

1. Image Input:
   • Stain normalization begins with the input of histopathological images obtained from different sources, laboratories, or staining protocols.
   • These images may have variations in terms of color intensity, brightness, and overall staining characteristics.
2. Color Representation:
   • The images are represented in a color space, such as RGB (Red, Green, Blue).
   • In the case of mitosis detection, the stain normalization algorithm focuses on the color information associated with the tissue structures, particularly nuclei and chromatin.
3. Stain Separation:
   • The stain normalization algorithm separates the image into different stain components like hematoxylin and eosin (H&E) stains. Hematoxylin stains cell nuclei blue, while eosin stains the cytoplasm and other structures pink.
4. Reference Image Selection:
   • A reference image is selected as a representative target for normalization. This reference image is often chosen from a set of images that are considered standard or representative of the desired staining characteristics.
5. Color Transformation:
   • The stain normalization algorithm calculates the color transformation matrix needed to map the stain components of the input image to those of the reference image.
   • This transformation aligns the color characteristics, ensuring that the staining patterns in the input image become more consistent with the reference image.
6. Normalization Process:
   • The calculated transformation matrix is applied to the entire image, adjusting the color distribution and intensity to match the reference image.
   • This process helps in normalizing staining variations across different images, making them more comparable for subsequent analysis.

After stain normalization, the preprocessed images are more suitable for mitosis detection algorithms. The normalization enhances the visibility and consistency of nuclei and chromatin staining, making it easier for mitosis detection algorithms to identify and analyze cell division structures accurately. The output is a set of normalized images that have undergone color adjustments to ensure consistency in staining characteristics, facilitating more reliable and robust mitosis detection. By normalizing staining variations, the stain normalization process improves the accuracy and reproducibility of mitosis detection algorithms, contributing to more reliable pathology analysis and diagnosis.

1. (iii). Remove Artifacts and Noise using Median Filtering: Median filtering was used to eliminate artifacts and noise from the images. This process helps enhance the clarity of the images, making it easier to detect relevant features without interference from unwanted elements.
2. (iv). Split the Dataset: The dataset was divided into three subsets: training, validation, and test sets. This division is crucial for training and evaluating machine learning models effectively. The training set is used to train the models, the validation set helps in tuning hyperparameters and preventing overfitting, and the test set assesses the model’s performance on unseen data.

3.3. Feature extraction

The pre-processed dataset is then utilized for feature extraction, where relevant information indicative of mitotic activity is extracted from the images. These features include texture patterns (such as Local Directional Patterns and Local Frequency Patterns), shape characteristics, and color features (represented through histograms). The process of feature extraction gives a complete set of 150 features per image, divided into three broad categories: texture, shape, and color. These include specifically the texture features like Local Directional Patterns (LDP) and local Frequency Patterns (LFP), that capture spatial relation and texture distribution characteristics of mitotic activity. Shape features emphasize morphological properties like area, perimeter, eccentricity, circularity, and solidity to distinguish mitotic figures from non-mitotic structures. Color features are based on histogram-based statistics in RGB and HSV color spaces, indicating intensity and color distribution differences between mitotic and non-mitotic areas. Feature selection methods are subsequently applied to reduce the dimensionality of the feature space and remove irrelevant or redundant features.

3.4. Feature selection

In the feature selection phase, a hybrid optimization algorithm is applied to efficiently reduce the dimensionality of the feature space and eliminate irrelevant or redundant features. This proposed hybrid optimization algorithm combines the JSO and the WaOA. The JSO component contributes global exploration capabilities, while the WaOA component enhances local exploitation strengths. Together, they form a synergistic approach to feature selection, aiming to retain informative features for mitosis detection while eliminating those that may not significantly contribute to the task. This innovative hybrid algorithm provides a well-balanced strategy to navigate the complex feature space and improve the overall efficiency of the mitosis detection model.

3.4.1. Jellyfish search optimizer.

The JFS optimizer draws inspiration from the movements of jellyfish and is structured around three fundamental principles. First, jellyfish movements can be influenced by ocean currents or their swarm dynamics. This influence is regulated through a time control (TC) mechanism, enabling the optimizer to switch between these two forms of movement. Second, jellyfish are naturally inclined towards areas with an ample food supply. They tend to settle in these locations once a sufficient amount of food is detected. Third, the quantity of available food is quantified through a specific objective function.

To initialize the jellyfish population, a chaotic logistic mapping approach is employed. This initialization process occurs randomly, ensuring a diverse and varied starting point for the jellyfish population within the optimization framework.

(1)

where represents the logistic chaotic value of the Jellyfish and the initial jellyfish population are denoted by , which can take a value from the range of 0–1.

For evaluating the fitness of the solution, the optimization process aims to maximize the F1 score as given in Eqn. (2), which, in turn, ensures a balance between precision and recall in mitosis detection.

(2)

The time control (TC) mechanism is governed by two crucial factors. The first factor is the time control function. , which is compared with a constant . The time control function is computed as follows:

(3)

where represents the current iteration number, and denotes the total number of maximum iterations in the optimization process.

The value of varies between 0 and 1 as the iterations progress. Simultaneously, is set to a constant value of 0.5. When surpasses , the jellyfish adjust their movement towards the ocean current. To determine this ocean current’s direction, the average of all vectors pointing from each jellyfish to the best jellyfish location is calculated. Consequently, the new location for each jellyfish is computed using the formula described in Eqn (4).

(4)(5)(6)

where represents the best location among the current jellyfish, and the parameter signifies the mean of all jellyfish locations within the swarm. stands for a random number falling within the range [0, 1].

When the value of is less than , the jellyfish exhibit movement within the swarm. This movement is categorized into two types: passive (Type A) and active (Type B). In Type A movement, most jellyfish move around their locations. Each jellyfish’s location is updated according to the following Eqn. (7):

(7)

where represents the upper bound of the search space, and represents the lower bound of the search space.

During Type B movement, a random jellyfish other than the one of primary interest is selected. The direction of movement is determined by a vector pointing from the jellyfish of interest. to the randomly selected jellyfish . The updated location of the selected jellyfish is computed as described in Eqn. (8). This type of movement represents an effective exploitation of the local search space:

(8)

where represents the objective function value associated with the jellyfish location .

The selection between Type A and Type B movement is determined by the TC mechanism. The term plays a crucial role in this decision-making process. It is compared with a random number within the range [0, 1]. If the random number is greater than the calculated value of , the jellyfish exhibits Type A motion. Conversely, if the random number is smaller than the calculated value, the jellyfish follows Type B motion. To clarify this concept, Type A motion is initially chosen when the TC function rapidly decreases from 1 to 0 over time. In contrast, Type B motion is favored as time progresses.

If a jellyfish moves beyond the boundaries of the search zone, it will reposition itself to the opposite limit, as indicated in Eqn. (9).

(9)

where represents the location of the jellyfish in the dimension. This location is updated after considering the constraints imposed by the limits of the search space.

3.4.2. Walrus optimization algorithm.

The WaOA draws inspiration from the social behaviors of walruses, marine mammals found in Arctic and subarctic waters. Adult walruses are easily identifiable by their large whiskers and tusks. They are social animals spending most of their time on sea ice, hunting for benthic bivalve mollusks. Walruses migrate to rocky beaches in late summer, and their social behaviors involve guiding members to feed, migrating, and fighting or escaping from predators. These intelligent behaviors serve as the basis for mathematical modeling in the development of the WaOA approach.

1. (i) Feeding phase (Exploration)

In the first phase of the WaOA, inspired by the walrus feeding strategy, walruses explore the search space for optimal solutions. Similar to how walruses search for food, the algorithm explores diverse areas of the search space. The walrus with the longest tusks represents the best solution, analogous to the quality of candidate solutions. The exploration process is mathematically modeled by generating new positions based on the guiding member’s behavior. If the new position improves the objective function’s value, it replaces the previous position, enhancing the algorithm’s exploration capability. The mathematical representation of this process is given by Eqns. () and ().

(10)(11)

where represents the new position for the walrus based on the 1st phase of the Walrus Optimization Algorithm and denotes its jth dimension. are randomly selected integers between 1 or 2. represents the strongest walrus with the best objective function value, signifies a random number chosen from the interval [0, 1], and represents its objective function value. This equation governs the generation of new positions for walruses during the exploration phase of the algorithm.

1. (ii) Migration

During Phase 2 of the Walrus Optimization Algorithm, the natural behavior of walruses migrating to outcrops or rocky beaches in response to late summer air warming is emulated. In the algorithm, this migration guides the walruses to explore different areas in the search space. In this phase, each walrus migrates to the position of another randomly selected walrus in a different area of the search space. Eqn. (12) governs the generation of the proposed new position, and if this new position leads to an improvement in the objective function value, it replaces the previous position of the walrus. This process facilitates exploration of the search space by encouraging walruses to move to potentially more promising locations.

(12)(13)

where represents the new position for the walrus based on the 2^nd phase of the Walrus Optimization Algorithm. Specifically, represents the dimension. The objective function value associated with this new position is denoted as ., denotes the position of this selected walrus during migrate, denotes the dimension, and its corresponding objective function value is .

1. (iii) Escape and Fight

In Phase 3 of the Walrus Optimization Algorithm, which simulates the natural behavior of walruses escaping and fighting predators like polar bears and killer whales, the algorithm focuses on exploiting the local search space around candidate solutions. To mimic this behavior, a virtual neighborhood is defined around each walrus. Within this neighborhood, new positions are randomly generated using Eqn. () and (). If the objective function value improves with the new position, the new position replaces the previous one. This approach enhances the algorithm’s ability to explore the vicinity of candidate solutions, ensuring efficient exploration and exploitation in the problem-solving space.

(14)(15)(16)(17)

where indicates the new position for the walrus based on the 3^rd phase and denotes its jth dimension. and are the upper and lower bounds respectively.

3.5. Benefits of hybridization

1. (i). Global Exploration: JSO’s exploration phase enables the identification of diverse and globally relevant features for mitosis detection.
2. (ii). Local Exploitation: WaOA’s migration and feeding phases allow the algorithm to refine and focus on locally optimal feature subsets.
3. (iii). Diversity and Balance: The hybrid approach combines the strengths of both algorithms, ensuring a balanced exploration-exploitation strategy for effective feature selection.
4. (iv). Adaptability: The algorithm can adapt to different characteristics of the feature space, making it robust for mitosis detection tasks.

This hybrid feature selection algorithm aims to enhance the efficiency and effectiveness of feature subsets for mitosis detection by synergistically leveraging the exploration and exploitation capabilities of JSO and WaOA. Fine-tuning and validation based on mitosis detection datasets are essential for optimizing the algorithm’s performance.

Algorithm 1: Hybrid Feature Selection Algorithm for Mitosis Detection (HJWOA)

Initialization:

• Initialize the feature set with a subset of features randomly.

Jellyfish Search Optimizer for Exploration (JSO):

1. Use JSO to explore the feature space globally.

2. Leverage JSO’s ability to navigate large solution spaces to identify potential feature subsets.

Walrus Optimization Algorithm for Exploitation (WaOA):

3. Apply WaOA for local exploitation of promising feature subsets.

4. Utilize WaOA’s ability to refine solutions in local neighborhoods, enhancing the quality of feature subsets.

Hybridization of Exploration and Exploitation:

5. Combine the globally discovered features from JSO with the locally refined features from WaOA.

6. Create a diverse feature set that captures both global and local characteristics.

Objective Function Evaluation:

7. Evaluate the effectiveness of each feature subset using the objective function.

Feature Subset Selection:

8. Select feature subsets based on their performance in mitosis detection.

Update and Refinement:

9. Refine the selected feature subsets using the hybridized information from JSO and WaOA.

10. Iteratively improve the selected features for better discrimination of mitosis patterns.

Termination Criteria:

11. epeat the process until the convergence criterion is met or a predefined number of iterations are completed.

3.6. Deep learning-based mitosis detection

The proposed model, referred to as CDL, is a sophisticated neural network architecture designed for the task of mitosis detection in medical image analysis. It leverages the power of transfer learning, initiating its architecture with pre-trained layers from the VGG-VD 16 [32] model. This 16-layered network is known for its effectiveness in image-related tasks. The model incorporates custom convolutional transpose (CONV-TRAN) layers for upsampling, skip connections to enhance segmentation quality, and additional layers tailored for finer segmentation, crucial for detecting mitotic nuclei accurately. Furthermore, the architecture transforms into a Fully Convolutional Network (FCN) for segmentation purposes. The utilization of transfer learning facilitates faster convergence and aids in avoiding overfitting, particularly beneficial when dealing with small datasets and classes that closely resemble each other. The proposed model is an integral component of a comprehensive system for mitosis detection, showcasing a thoughtful combination of deep learning techniques for precise and efficient medical image analysis.

3.7. Transfer learning

Transfer learning is a technique where a pre-trained neural network model is utilized as the starting point for a new task. Instead of training the entire network from scratch, the knowledge gained by the pre-trained model on a large dataset (like ImageNet) is transferred and fine-tuned for the mitosis detection task. The rationale behind transfer learning is that the pre-trained model has already learned generic features from diverse images, making it a powerful feature extractor. By fine-tuning the model’s parameters using mitosis-specific data, the network can adapt its learned features to the nuances of mitosis detection.

The choice of a suitable loss function is crucial in training the neural network for mitosis detection. Focal loss is a specialized loss function often used in object detection tasks, especially when dealing with imbalanced classes. Focal loss addresses the problem of class imbalance by down-weighting well-classified examples during training. This means that the loss assigned to well-classified samples is reduced, allowing the model to focus more on misclassified or challenging samples. This focus on difficult examples enhances the model’s ability to learn and improve its performance, particularly in cases where mitotic cells might be rare compared to non-mitotic cells in the dataset.

The architecture of the proposed CDL network involves a combination of customized features and well-established principles to achieve accurate segmentation of mitotic nuclei. The architectural components are as follows:

1. Base Model: CDL is based on the VGG-VD 16 network, a 16-layered deep CNN. VGG networks are known for their simplicity and effectiveness in image recognition tasks. The base model consists of 13 convolutional layers and 3 fully connected (FC) layers.
2. Transfer Learning: The first two convolutional layers of VGG-VD 16 are initialized with pre-trained weights from a model that was originally trained on the ImageNet dataset. This transfer learning approach leverages the learned features from a large dataset to boost the model’s performance on the mitosis segmentation task. Transfer learning is particularly valuable when dealing with small datasets, as it helps prevent overfitting.
3. Adaptations for Mitosis Segmentation: The architecture undergoes specific modifications to tailor it for mitosis segmentation. The last FC layer, designed for ImageNet’s 1000 classes, is replaced with a new FC3 layer for the mitosis segmentation task. Additionally, a convolutional transpose layer (CONV-TRAN) is introduced to handle upsampling and cropping, crucial for achieving finer segmentation.
4. Skip Connections: Skip connections, inspired by the concept of residual learning, are introduced to facilitate better gradient flow and enhance the spatial resolution of the segmented image. Three skip connections (SKIP1, SKIP2, and SKIP3) use 1 × 1 convolutions to adjust the dimensions of the outputs from pooling layers, contributing to more accurate segmentation.
5. Segmentation Quality Improvement: The architecture strategically uses multiple convolutional transpose layers with skip connections to produce fine segmentation results. These layers have different filter sizes, upsampling factors, and cropping configurations, ensuring that the output maintains the spatial details necessary for accurate mitosis detection.

The architectural choices, such as the utilization of VGG-VD 16, transfer learning, and skip connections, collectively aim to address the challenges posed by mitosis segmentation, including small object sizes and the need for high-resolution outputs. This hybrid architecture integrates powerful features from a pre-trained model with task-specific adaptations to achieve superior performance in mitosis detection. The architecture of CDL is given in Fig 2.

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Fig 2. Architecture of CDL Network.

https://doi.org/10.1371/journal.pone.0327567.g002

4.1. Comparative analysis

In the evaluation of the proposed model’s performance for mitosis detection, various metrics such as precision, recall, and F1-score are employed. These metrics play a crucial role in assessing the accuracy and effectiveness of the model in identifying mitotic figures accurately. Precision, also known as positive predictive value, measures the ratio of correctly predicted mitoses to the total predicted mitoses. Recall, or sensitivity, quantifies the ratio of correctly predicted mitoses to the actual mitotic instances in the dataset. F1-score is the harmonic mean of precision and recall, offering a balanced assessment of the model’s performance. These metrics are implemented and analyzed using the MATLAB tool, providing a comprehensive evaluation of the model’s ability to correctly identify mitotic figures in the medical image dataset.

Fig 3 shows the comprehensive analysis of markedness (MK) and negative likelihood ratio (NLR) across various methods, the proposed CDL method excels with an MK of 0.062 and an NLR of 0.011. In contrast, ResNet, SqueezeNet, AlexNet, and MobileNet exhibit MK values of 0.044, 0.035, 0.028, and 0.026, respectively. The corresponding NLR values for these methods are 0.017, 0.021, 0.026, and 0.029, respectively. A lower MK signifies a better equilibrium between precision and sensitivity, while a reduced NLR indicates heightened diagnostic accuracy. The proposed CDL method outperforms other architectures in both metrics, underscoring its superior ability to accurately identify mitotic cells while minimizing false positives. This enhanced performance is attributed to the innovative combination of features and the optimized deep learning architecture in the proposed CDL method.

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Fig 3. Markedness and NLR Analysis.

https://doi.org/10.1371/journal.pone.0327567.g003

In the evaluation of the proposed CDL method alongside other architectures as shown in Fig 2, the Comprehensive Sensitivity Index (CSI), Balanced Accuracy (BA), and Fowlkes-Mallows Index (FMI) provide valuable insights. The proposed CDL method demonstrates a superior CSI of 0.988, outperforming ResNet (0.982), SqueezeNet (0.978), AlexNet (0.973), and MobileNet (0.970). Additionally, the CDL method achieves a commendable BA of 0.987, surpassing the BA values of ResNet (0.983), SqueezeNet (0.979), AlexNet (0.972), and MobileNet (0.972). FMI, another crucial metric, attains an impressive value of 0.994 for the proposed CDL method, indicating strong agreement between the predicted mitotic cell instances and the ground truth. Collectively, these results show in Fig 4 highlight the robustness and accuracy of the proposed CDL method in mitosis detection, showcasing its ability to achieve high sensitivity, balanced accuracy, and overall performance compared to other considered architectures.

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Fig 4. CSI, Balanced accuracy, and FMI Analysis.

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From Figs 3–5, the proposed CDL method exhibits outstanding performance in mitosis detection. With an accuracy of 0.988, the CDL method surpasses ResNet (0.982), SqueezeNet (0.978), AlexNet (0.973), and MobileNet (0.970), indicating its efficacy in correctly classifying mitotic and non-mitotic instances. Furthermore, the F-measure of 0.994 attests to the precision and recall balance achieved by the CDL method, outshining the values obtained by ResNet (0.991), SqueezeNet (0.989), AlexNet (0.986), and MobileNet (0.985). The high accuracy underscores the model’s ability to make correct predictions, while the elevated F-measure reflects the method’s capability to maintain a balance between precision and recall, crucial for reliable mitosis detection. These results in Fig 5 underscore the effectiveness of the proposed CDL method in achieving accurate and well-balanced mitosis classification.

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Fig 5. Accuracy and F-Measure Analysis.

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In the evaluation of Sensitivity and Specificity, as given in Fig 6, the proposed CDL method showcases remarkable performance in mitosis detection. With a Sensitivity of 0.988, CDL outperforms ResNet (0.982), SqueezeNet (0.978), AlexNet (0.973), and MobileNet (0.970), illustrating its ability to accurately identify mitotic instances. Additionally, the Specificity of 0.986 further underscores the CDL method’s capacity to precisely recognize non-mitotic cases. These results highlight the robustness of the proposed CDL approach in achieving high sensitivity for mitosis identification while maintaining a strong specificity for accurate discrimination of non-mitotic instances. The superior performance in both sensitivity and specificity positions the CDL method as an effective solution for mitosis detection in histopathological images.

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Fig 6. Sensitivity and Specificity Analysis.

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In the assessment of False Positive Rate (FPR) and False Negative Rate (FNR) in Fig 7, the proposed CDL method demonstrates commendable performance, contributing to its overall efficacy in mitosis detection. FPR represents the proportion of non-mitotic instances wrongly classified as mitotic, while FNR indicates the fraction of actual mitotic instances misclassified as non-mitotic. With a low FPR of 0.013, CDL excels compared to ResNet (0.015), SqueezeNet (0.019), AlexNet (0.029), and MobileNet (0.025). This indicates the CDL method’s ability to minimize the occurrence of false positives, reducing the chances of misclassifying non-mitotic instances as mitotic. Furthermore, the FNR of 0.011 for CDL surpasses other methods, emphasizing its capacity to minimize false negatives and enhance the identification of actual mitotic instances. The CDL method’s superior performance in both FPR and FNR highlights its proficiency in achieving a well-balanced trade-off between precision and recall, essential for robust mitosis detection in histopathological images. Table 2 provides a comprehensive overview of the performance metrics for mitosis detection methods, including the proposed CDL, ResNet, SqueezeNet, AlexNet, and MobileNet. The proposed CDL method consistently outperforms other approaches across various metrics, affirming its efficacy as an advanced mitosis detection solution.

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Table 2. Comparative Analysis of Mitosis Detection Method.

https://doi.org/10.1371/journal.pone.0327567.t002

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Fig 7. FPR and FNR analysis.

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A learning rate of 0.001 yielded the best accuracy of 98.8% as well as an F1 score of 0.994. A batch size of 32 gave the optimal balance between precision (98.5%) and recall (98.3%). Eight convolutional layers generated the best accuracy, whereas increased dropout rates (i.e., 0.5) resulted in underfitting. These results identify the most important parameter settings responsible for the general success of the model in detecting mitosis.

The CDL model greatly improves the accuracy and efficiency of mitosis detection, assisting pathologists by automatically identifying mitotic figures, decreasing diagnostic time, and eliminating human error. This has the potential to enhance cancer staging and directly influence clinical treatment decisions by providing more accurate evaluations of tumor aggressiveness. The model’s capacity to deal with issues such as class imbalance and image variability improves its resilience in a wide range of clinical situations. It assists in minimizing inter-observer variability, leading to more uniform diagnoses across institutions. Additionally, the potential for the model’s real-time deployment will enable faster decision-making, enhancing patient outcomes. In the end, CDL is an important asset in the integration of AI-based diagnostics into everyday clinical workflows, facilitating personalized cancer care.

4.2. Database analysis

The accuracy comparison across four publicly available mitosis detection datasets highlights the effectiveness of the proposed Customized Deep Learning (CDL) model over existing architectures such as ResNet-50, SqueezeNet, AlexNet, and MobileNet. The four datasets used in this study are:

1. Mitosis WSI CCMCT Training Set [33] A whole-slide imaging (WSI) dataset designed for mitosis detection in histopathological images.
2. Mitosis-AIC [34] A dataset containing annotated mitotic figures used for artificial intelligence-based mitosis detection.
3. Mitosis Detection [35] A curated dataset for training deep learning models to classify mitotic and non-mitotic cells.
4. Mitosis and Non-Mitosis [36] A dataset with a clear distinction between mitotic and non-mitotic cells, useful for training robust classification models.

Four different mitosis detection datasets showed a higher accuracy value for the Customized Deep Learning (CDL) model compared to previous architectures, such as ResNet-50, SqueezeNet, AlexNet, and MobileNet. The results acquired are manifested in Table 3. The CDL model reached the highest accuracy in all datasets, achieving a maximum of 98.8% accuracy on WSI CCMCT, 98.5% accuracy on Mitosis-AIC, 98.3% on Mitosis Detection, and 98.1% accuracy on Mitosis and Non-Mitosis. The CDL model performed at very high accuracy across all the datasets, with very little performance variance (98.1% to 98.8%). Such low variance testifies to the model’s power in coping with different data distributions, such as different staining procedures, resolutions, and appearances of tissues occurring in histopathological images. On the other hand, the accuracy of ResNet-50 (the second-best performing model) does not exceed 94.8%, implying a performance gap of almost 4–5%, which becomes pretty significant in medical image analysis, where high accuracy is absolutely critical. Further, among lightweight models, SqueezeNet, AlexNet, and MobileNet range from 89% to 92% accuracy, indicating that while computationally efficient, these architectures fail to deal with the challenging aspects of mitosis detection, such as severe morphological variations and class imbalance issues. Also, the hybrid optimization algorithm (JSO + WOA) adds robustness through dynamically selecting the most discriminatory features, in effect reducing the impact of noisy or redundant information. Skip connections integrating within the network also enhance mitotic figure localization, reducing the model’s sensitivity towards morphological variability and class imbalance — two common issues in mitosis detection. These are solid evidences that CDL, working on class imbalance problems through advanced feature selection and improving cytological figure detection, emerges as a potential assisting tool to pathologists in cancer diagnosis-and-prognosis. The generalization ability of the CDL model was tested by its consistent performance on four independent, publicly available datasets. The very slight performance drop (only 0.7% from best to worst accuracy) suggests that the model generalizes well across various data sources. In contrast to traditional models that tend to overfit for particular dataset features, applying transfer learning in CDL enables the model to use pre-trained wisdom as well as learn from new, unobserved data. The transfer learning-based feature extraction prevents loss of critical image patterns despite exposure to histopathological differences of color, texture, or mitotic morphology. Future work can be undertaken to tune the model for real-time clinical application, also exploring multimodal learning approaches for better generalization over diverse histopathological datasets. For greater quantification and robustness in this generalizability, next studies can engage cross-dataset validation (learning on one and testing on the other), and assess the model’s robustness with introduced image noise and data augmentation, then test its ability on external clinical datasets in practice.

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Table 3. Comparative Analysis of Mitosis Detection Method for diverse database.

https://doi.org/10.1371/journal.pone.0327567.t003

4.3. Accuracy comparison of CDL with other deep learning models

From the Table 4, we observe that CDL has produced an accuracy far higher than all the other models examined, such as ReCasNet, FMDet, SMDetector, YOLOv5, ResNet-50, and DenseNet-201. The considerable improvement in performance of CDL is due to the intervention of a skip connection-based transfer learning detection module. The fine localization of mitosis by this module is further complemented by the application of a hybrid feature selection mechanism (Jellyfish Search Optimizer + Walrus Optimization Algorithm) that improves the classification procedure. On the other hand, models such as FMDet and Densenet-201 came close but were around 2–4% less accurate than CDL; thus, there is space for improvement in feature selection and class imbalance handling. The reason DNN and YOLOv5 have produced low performance levels is that both architectures intend to use an application of classical deep networks and object detection and therefore stand poorly against the challenging variability posed by mitotic figures.

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Table 4. Accuracy Comparison of CDL with Other Deep Learning Models.

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4.4. Robustness evaluation of CDL on diverse pathological conditions

The Dedicated Deep Learning (DL) model was put to the test under different circumstances in order to see how robust it is. In this regard, datasets annotated by different pathologists and pathological subtypes, including the varying quality of images used, were taken into consideration. The results acquired are manifested in Table 5.

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Table 5. CDL Performance on Different Robustness Testing Scenarios.

https://doi.org/10.1371/journal.pone.0327567.t005

4.5. Analysis on accuracy and loss vs. epochs

The provided Fig 8 go a long way in shedding light on the training dynamics of the proposed Customized Deep Learning (CDL) model. The accuracy versus epochs plot shows a steady increase in accuracy on both training and validation sets, supporting that the model can learn the underlying patterns present in the mitosis detection task. The model appears to be converging stably, without much fluctuation, indicating well-set hyperparameters and a smooth training process. Likewise, the loss vs. epochs plot shows a decline of training losses, which also demonstrates effective weight adjustment and learning of meaningful representations. The validation loss follows very closely to the training loss, indicating that the model is well-generalizing on unseen data and is not suffering from overfitting. This improvement can be attributed to the use of transfer learning, skip connections, and a hybrid optimization method (Jellyfish Search Optimizer + Walrus Optimization Algorithm) for feature selection, which aids in the refinement of the learning process. Importantly, compared to these trends in comparative traditional deep learning approaches like ResNet, SqueezeNet, AlexNet, and MobileNet, the CDL shows smoother convergence curves, higher final accuracy, and lower final losses. This attests to the model’s efficiency in detecting mitotic figures with precision and robustness. Future progressions may be attempted to increase the speed of convergence by utilizing adaptive learning rates, dynamic augmentation techniques, and/or attention mechanisms to enhance feature learning. Other aspects include testing the robustness of the model across datasets with differing staining protocols, with different pathologist annotations, and multi-center histopathological images to further cement its generalization ability.

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Fig 8. Accuracy vs loss for varying epochs.

https://doi.org/10.1371/journal.pone.0327567.g008

7.1. Future research directions

Following up on this initiative; it could be advanced in future research:

Integration with Explainable AI (XAI): Enhance clinical trustworthiness through the addition of attention mechanisms or visual explanations to improve model interpretability. This will enable pathologists to interpret model predictions, making decision-making transparent.

Federated Learning Approach: Utilize privacy-protecting technologies to develop the model across different institutions without exposing sensitive patient information. This approach can enhance data diversity and model generalizability while keeping patient confidentiality intact.

Real-Time Deployment: Adapt the Customized Deep Learning (CDL) model to edge computing with the goal of real-time pathology use cases. With TinyML and hardware-aware neural network compression, this would provide on-site mitosis detection faster with less latency, suitable for point-of-care applications.

Multi-Task Learning: Extend the model to both detect mitosis and classify different cancer grades. This multi-task approach could simplify diagnostic pipelines, offering not only mitotic figure detection but also comprehensive cancer staging data to support prognosis and individualized treatment regimens.

Transfer Learning from Multimodal Data: Adapt the CDL model to include multimodal data, e.g., genomic, transcriptomic, and radiomic data. By fusing imaging data with molecular biomarkers, the model would present a more integrated understanding of cancer development, leading to more accurate and personalized diagnosis.

Self-Supervised Learning: Investigate self-supervised learning methods to learn deep learning models on unlabelled data. This would assist in overcoming the problem of the lack of abundant annotated datasets in medical imaging, enabling robust model learning even in low-data settings.

Augmented Reality (AR) Integration: Explore the implementation of augmented reality (AR) to visualize results of mitosis detection in 3D or project model predictions onto real tissue samples. This would facilitate greater ease for pathologists to interpret results in real-time and enhance decision-making at the time of surgery or biopsy examination.

Quantum Computing for Medical Imaging: In the long term, quantum computing might be used to fine-tune complicated deep learning models and speed up the processing of large-scale medical data. Through the use of quantum algorithms, training and inference times for mitosis detection can be greatly accelerated, further enhancing real-time applications.

7.2. Final remarks

The study provides a rigorous basis for detecting mitosis using deep learning, showing remarkable superiority over existing models. Nevertheless, more studies are needed to increase the robustness, generalizability, and real-life applicability of the model. With the resolution of the limitations identified here and looking for aggressive optimization strategies, CDL can be honed to evolve into a strong clinical tool in the hands of the pathologist to assist in cancer diagnosis and prognosis. The model experiences challenges in identifying mitosis in atypical cases or images with unusual morphological appearances, resulting in misclassifications. Furthermore, its accuracy can decline when it works with poor-quality images, including noisy, low-resolution, or preparation artifacts on the slide. Cross-dataset generalization is also a challenge, as the model might not generalize as well to datasets with varying staining protocols or imaging techniques. Although measures to counter class imbalance are taken, some datasets might still lead the model to bias towards the majority class. Lastly, the computational demands for real-time deployment might require additional optimization to guarantee efficient processing in clinical use.