Determination of the Rupture Risk of Cerebral Aneurysms via the Application of a Narrow Neural Network Classifier

With recent advances in technology, the number of fields suitable for the application of machine learning has gradually increased. This topic has frequently been addressed by researchers, especially in the field of medicine for the diagnosis of diseases [1-4]. Two main categories of machine learning have been studied in the literature: supervised and unsupervised learning methods. In supervised learning, the data set is divided into training and testing sets. The program is derived from the training set and an algorithm is developed, the accuracy of which is then evaluated using the test set. The purpose of the algorithm is to employ the developed algorithm to predict the outcome of new data [5]. Unsupervised learning aims to find the desired hidden structure in the data set without the use of accuracy data to predict the results [6].

 Brain aneurysms are protrusion-shaped enlargements of cerebral arteries [7]. Although unruptured aneurysms have been reported to occur in 3% of the population, recent studies have projected that the actual rate may be as high as 11% [8]. This condition affects the population and poses a potential risk of rupture [9]. Rupture of brain aneurysms causes subarachnoid hemorrhage, an adverse outcome known as hemorrhagic stroke [7]. Researchers have determined that small-sized intracranial aneurysms constitute 35-47% of ruptured aneurysms [8, 10, 11]. As there is currently no consensus on whether to intervene in an unruptured aneurysm, evaluating the risk of rupture constitutes a critically important parameter for disease treatment and follow-up [10-13]. In unruptured aneurysms, the risk of rupture can be prevented by microsurgery or endovascular treatment [13, 14]. In recent years, numerous studies in the literature have emphasized that the detection of intracranial aneurysms can be achieved with high accuracy using machine learning algorithms [1, 11, 15, 16]. The effect of hemodynamic factors on the rupture of Middle Cerebral Artery (MCA) aneurysms under different operating conditions has been investigated. The effects of mean wall shear stress, velocity in pressure distribution, and blood viscosity were examined. As a result, the average wall shear stress was observed to increase proportionally with the blood flow rate, and exceeding a value of 0.6 increased the risk of aneurysm rupture. In addition, another study demonstrated that an increase in blood velocity increases the risk of rupture in aneurysms [17]. In a study based on automatic detection of brain aneurysms, training was conducted by cross-validating TOF-MRA image data containing information on 284 patients using a deep learning model. 3D U-Net learning was performed with a total of 198 aneurysms in the data set consisting of 157 images with aneurysms and 127 without. Aneurysm location, such as ACA, MCA, and ICA (Anterior, Middle, and Interior Cerebral Artery, respectively), size (≤ 7 mm, 7-9 mm, 10-19 mm, and ≥ 20 mm), and age of the patient were also included in the study. The model was trained and evaluated on a GeForce RTX 2080 Ti GPU (11GB GDDR6) with TensorFlow 2.4.0. Performance metrics for the best model achieved a false positive rate of 0.8 per patient and a sensitivity of 83%. In addition, the PHASES scores for aneurysms were calculated and categorized as low, medium, or high-risk groups. Low-risk aneurysms were determined to require monitoring, while medium and high-risk aneurysms require treatment. The size and location of the aneurysm were observed not to present significant effects in terms of sensitivity to rupture [18]. For the PHASES score calculations, age, hypertension, history of subarachnoid hemorrhage, aneurysm size, and site predictors were evaluated in 230 patients and compared with populations from North America and Europe (excluding Finland). The risk of aneurysm rupture was found to be 3.6 times higher in Finnish people and 2.8 times higher in Japanese people [19]. In addition, prediction of sugarcane disease and early diagnosis of Alzheimer's disease can be made by using Convolutional Neural Network (CNN) models [20, 21]. In a study, the efficacy of deep learning methods was evaluated in the early, intermediate and advanced stages of Diabetic Retinopathy diagnosis using fundus images [22]. Additionally, an effective image segmentation approach and classification techniques have been devised for the detection and classification of Alzheimer’s and Parkinson’s disease [23].

Many hemodynamic parameters have been considered in determining the rupture risk status of aneurysms. However, separate evaluations have not been performed for each of these risk factors. In terms of morphological features, they are associated with the rupture risk status of the aneurysm, but the extent of the effect has yet to be clarified [24, 25], constituting a significant gap in the literature. Another major deficiency in the literature is the limited number of studies examining comorbidities. In order to address this issue, the present study examined morphological and hemodynamic characteristics and their relationships in 220 patients with aneurysms aged 22-94 years to determine the rupture risk of cerebral aneurysms. These relationships were evaluated using machine learning classification algorithms and then tested with the data of 33 external patients to assess the classifications. An additional gap in the literature is the partial lack of information regarding aneurysm location. In this study, this deficiency was eliminated by including right-left and segment (M1, M2, M3, M4) information for each aneurysm. Studies in the literature examining morphological and hemodynamic features for identifying and automatically detecting rupture risk by means of machine learning methodologies are shown in Table 1.

Table 1. Literature review

The major risk for patients with cerebral aneurysms is rupture of the aneurysm and resulting fatal subarachnoid hemorrhage. Therefore, treatment should be initiated prior to any rupture that may occur in people with cerebral aneurysms.

The objective of the present study was to determine the risk of rupture as a percentage by examining the morphological structure and hemodynamic factors of all cerebral aneurysms, whether rupture or not. Accuracy is of critical importance when determining the risk status, as the possibility of rupture for existing aneurysms was evaluated using machine learning classification algorithms. For this purpose, a detailed data set that had not been used previously was created. This data set contains information on the width, length, location, and type of aneurysm, which constitute morphological characteristics. Additionally, patient-specific age, sex, and comorbidity parameters were included in the data set as they represent predictors affecting the risk of rupture. In order to increase the transparency of this study, the numerical and categorical data sets incorporating these seven predictors are presented in Appendix 1.

This study is comprised of three stages. First, an updated data set was created by examining the medical records of patients with cerebral aneurysms. In the second stage, classification was performed using machine learning algorithms for each morphological and hemodynamic parameter that may affect the risk of rupture in the aneurysm. Performance analysis results were obtained by analyzing the accuracy, specificity, precision, and sensitivity parameter values of the system. The final stage consisted of testing the trained classification network. For this purpose, the risk percentages of rupture in patients with cerebral aneurysms were determined using the external data set.

When evaluated in terms of innovation and contribution to scientific knowledge, our research can be considered to have yielded important results. In this section, we will present the innovations generated by our study. First, seven parameters, consisting of hemodynamic and morphological features, as well as rupture status for 39 different comorbidities were examined. To date, the impact of this variety of rupture status for different comorbidity parameters has not been examined in the literature. Since this situation directly affects the risk of rupture, it highlights a significant gap in the literature. Another innovation of our study involves the fact that heretofore no research has been conducted incorporating right-left and segment information regarding the location of the aneurysm; this represents yet another major deficiency in the literature. More importantly, in the present study aneurysms of all sizes were evaluated, without any exclusion criteria. As this also directly affects the risk of rupture, another gap in the literature is revealed. In addition to eliminating these deficiencies, the present study compared 23 different machine learning classification methods and determined rupture status using the Narrow Neural Network (NNN) classifier for the first time. In achieving this, for the first time, the risk of rupture could be expressed as a percentage. The disease histories of three patients with aneurysms were examined, and from the radiology reports rupture was determined to have occurred at later dates. With the machine learning classification performed in this study, the risk status expressed as a percentage was compared with the time at which rupture would occur for the first time in these three patients, and a 100% accurate result was obtained.

The present study contributes to the literature by providing guidance for neurosurgeons in determining the treatment stages for patients with aneurysms. Furthermore, using NNN, a machine learning classifier algorithm, the rupture risk status was estimated for patients with aneurysms with a success rate of 81.8%. Additionally, in patients with saccular aneurysms, while the location of the MCA, a size of 2-10 mm, and the presence of heart disease and hypertension exerted major effects on the rupture status, other characteristics were observed to have a lesser effect.

In this study, a machine learning algorithm was modeled utilizing the morphological and hemodynamic characteristics of cerebral aneurysms. A data set was created by grouping the parameters for these features. These data were then applied as input to the neural network algorithm, a machine learning classifier, to determine the risk of rupture and non-rupture of cerebral aneurysms, referencing 220 cases with seven predictors. In instances of ruptured aneurysms, the connection with these features was examined and the importance emphasized. The architecture of the developed classification model proposed to determine the risk of rupture is shown in Figure 2.

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Figure 2. Machine learning classifier

The data set created in this study was applied as input to machine learning algorithms, with the desired output being the determination of the rupture status as a percentage. Since the neural network classification algorithm generated the best results in terms of accuracy during the classification process, it was used as a reference in the subsequent stages.

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Figure 3. The proposed algorithm of the study

The neural network classifier is a proposed model-supervised machine learning algorithm. This algorithm was implemented with classifiers employed in the MatLAB R2023a classifiers application. These classifiers consist of decision trees, support vector machines, ensemble learning, logistic regression, and Bayesian classifier methods. In this study, the NNN classifier was used because its accuracy rate yielded the best results, while support vector machines are next in terms of high accuracy ranking. Neural network models are utilized for multi-class classification and enjoy high predictive accuracy, although difficult to interpret. As the size and number of fully connected layers in the neural network increase, the flexibility of the model increases. The MatLAB “fitcenet” function was employed in the training model for the neural network classifier. The highest accuracy for this data set was obtained with the NNN classifier. Additionally, the area under the Receiver Operator Characteristic curve (AU-ROC), accuracy, sensitivity, and specificity parameters were also included when conducting performance analysis for the machine learning classifiers. The machine learning algorithm used in this study is given in Figure 3.

3.1 NNN classification

The Narrow Neural Network classifier algorithm relies on a neural network structure with a limited number of layers and neurons. Compared to larger neural networks, narrow networks contain fewer parameters and are computationally lighter. This approach is ideal for small datasets or systems with limited computational resources. Unlike traditional deep learning models, it employs a narrow structure to reduce the number of parameters and mitigate issues like overfitting. This classifier algorithm accelerates data processing by providing a simpler and more efficient learning model. The Narrow Neural Network algorithm is preferred for its ability to quickly learn from limited datasets and perform satisfactorily in classification tasks. Additionally, they are generally preferred when the dataset is small or when there is a risk of model overfitting. However, it may be inadequate for complex and large data sets.

3.2 The operating of NNN

Input layer: The input layer receives features from the dataset.

Hidden layers: These networks consist of only a few layers (typically 1-2), each containing a limited number of neurons. Activation functions are applied within these layers to process the input data.

Output layer: As a classification problem, the output layer returns the predicted class. Activation functions such as softmax or sigmoid are typically used in this layer.

3.3 Mathematical models and parameters

The following general equations are used in narrow neural networks:

Weights and biases: Each neuron is associated with a weight (w) and a bias (b) that apply to the input features.

z=w⋅ x+b

where, x denotes the input data. The z value is then passed through an activation function.

Activation functions: Activation functions such as ReLU or tanh are used in the hidden layers, while softmax or sigmoid functions are typically used in the output layer for classification tasks.

For example, a ReLU activation function is defined as:

f(z)=max(0, z)

Loss function: To evaluate model performance, loss functions such as cross-entropy or mean squared error are applied. The loss function is critical in the backpropagation algorithm, where it facilitates updates to the weights and biases.

The model's optimization involved several key parameters: a learning rate of 0.1, which controlled the step size for weight updates during training, and a total of 30 learners, indicating the number of base models in the ensemble. Additionally, the estimator count was set to 7, defining the number of predictors used per estimation. A 5-fold cross-validation was conducted to enhance model generalizability and reduce overfitting risk by systematically partitioning the dataset for training and validation. Finally, the total misclassification cost was set to 160, imposing penalties on incorrect classifications to prioritize model accuracy. These parameters collectively contribute to balancing model accuracy, computational efficiency, and generalization.

The data set used, incorporating the morphological and hemodynamic features obtained from the medical records of patients with ruptured and non-ruptured aneurysms, appears in Table 2. Raw data values for variable groups related to the various parameters are included in Appendix 1, while the graphic results generated by the training that affect rupture status are presented in Appendix 2. Accuracy rates and training times in determining rupture status for the different classification models are shown in Figure 6.

Among the 23 models that underwent training, the highest accuracy value, at 73.29%, was obtained with the neural network classifier, depicted as orange in the graph. In this decision tree, PCA1 was used to reduce the dimensionality of the prediction space. As a result, a new variable set was created by removing unnecessary dimensions. The model was developed by selecting features for the seven parameters determined in the study. The final result for the maximum accuracy rate of 75% in training is shown in purple in Figure 7, for model 17, which had a training time of 3.38 seconds.

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Figure 6. Training time and accuracy values of the different classification models

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Figure 7. Training times and accuracy values for the proposed NNN classifiers

The improved NNN classifier used in this study, wherein morphological and hemodynamic features were considered in tandem, yielded the greatest accuracy with respect to rupture status. In this connection, training for the model was performed using the neural network classifier. The model results obtained for the NNN classifier, developed by applying PCA1, with the number of learners set to 30 and a learning rate of 0.1, are presented in Figure 8. Positive Predictive Value (PPV) represents the proportion of correctly classified observations for a given predicted class. Conversely, the False Discovery Rate (FDR) indicates the proportion of incorrectly classified observations within the predicted class. PPV is shown in blue for correctly predicted points in each class, while FDR is displayed in orange for incorrectly predicted points in each class. The relationship between PPV and FDR in model training is presented in Figure 8(b). The TPR (True Positive Rate) and FNR (False Negative Rate) metrics are fundamental measures used to evaluate a model’s classification performance:

TPR (True Positive Rate): This is the rate at which positive instances are correctly classified as positive. Also known as "Sensitivity" or "Recall," this metric indicates the model’s ability to identify true positive cases and is calculated as follows:

TPR=TP/TP+FN

FNR (False Negative Rate): This represents the rate at which true positive instances are incorrectly classified as negative. This metric indicates the model's tendency to miss cases that belong to the positive class and is calculated as:

FNR=FN/TP+FN

Here,

TP (True Positive): The number of instances that are truly positive and correctly classified as positive by the model,

FN (False Negative): The number of instances that are truly positive but incorrectly classified as negative by the model.

TPR and FNR help evaluate the model’s performance in correctly identifying positive class instances. High TPR and low FNR values indicate strong model performance in accurately recognizing instances belonging to the positive class. The relationship between TPR and FNR in model training is presented in Figure 8(a).  

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(a)

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(b)

Figure 8. True positive-false negative rates of the NNN classifier

Here, the false negatives are shown in pink while true positives are depicted in blue. The highest accuracy value was calculated as 75%, with 46 true positives (tp) and 29 false positives (fp) for patient data indicating ruptures, and 86 true negatives (tn) and 15 false negatives (fn) for images without ruptures. The true positive rate (TPR) varied between 61.3%-85.1%, the false negative rate (FNR) ranged from 14.9%-38.7%, positive predictive values (PPV) were 75.4% and 74.8%, and false discovery rates (FDR) were calculated to be 24.6% and 25.2%.

Since rupture from cerebral aneurysms constitutes a major life-threatening risk, parameters that may cause rupture should be carefully considered. In this study, the classification of risk factors was performed incorporating such parameters. Graphs of the data on rupture in cerebral aneurysms for each risk factor are shown in Appendix 2. By applying the improved NNN classification algorithm, which yielded the best results in terms of accuracy, rupture was predicted to be detected in advance with an accuracy of 81.8% in the external testing process. This rate represents a level of accuracy that can prevent permanent damage and death in serious life-threatening illnesses. As a result of the machine learning classification process applied to the seven risk factors determined based on the medical records of patients diagnosed with cerebral aneurysms, rupture can now be predicted with great accuracy.

Ruptures, affected by morphological and hemodynamic parameters, induce subarachnoid hemorrhage. Such rupture can also occur in cases of head injury. Determining whether rupture is caused by an aneurysm or is a result of trauma presents difficulties. If rupture status can be established with high accuracy using machine learning, risky aneurysm surgeries can be avoided [1]. The machine learning classifier model employed in the present study incorporated the morphological and hemodynamic parameters of cerebral aneurysms in its analysis. Based on the resulting classification, the major risk factors triggering the rupture of saccular aneurysms were identified as MCA location and the comorbidities of heart disease and hypertension. Representing the estimated risk of rupture for cerebral aneurysms as a percentage demonstrates the applicability of this system, as do the relevant performance metrics obtained in this study.

In the future, the number of data points will be increased and information regarding the parameters of this data set will be expanded. With the use of different classification methodologies, it is anticipated that more general results can be obtained.

The authors would like to thank Sait Öztürk, Bekir Akgün and Ahmet Cemil Ergün for their contributions to the data set.