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I. Introduction
Aging is a well-established independent risk factor contributing to vascular structural and functional impairments, ultimately leading to cardiovascular and neurological diseases [1–3]. Age-related vascular changes include decreased cerebral microvascular density, reduced vessel count, decreased capillary density, increased arteriolar tortuosity, and arterial stiffening. These changes are associated with thickened vessel walls, modest increases in vessel diameters, and outward hypertrophic remodeling. Arterial stiffening can decrease cerebral blood flow with advancing age, resulting in reduced oxygen and glucose supply to brain tissue. This sustained decline in cerebral blood flow may accelerate neurodegenerative processes, such as vascular dementia.
Numerous imaging tools are available to study age-related vascular and functional changes in the brain [4,5]. For instance, three-dimensional (3D) optical coherence tomography angiography has been employed to measure capillary vessel density and vessel tortuosity [3]. Positron emission tomography has demonstrated age-related declines in cerebral blood flow during brain activity [6]. Magnetic resonance angiography (MRA) image data are useful for assessing chronological age since aging is known to influence morphological characteristics of vessels [7]. Deep convolutional neural networks (CNNs) have been proposed to evaluate vascular aging using brain time-of-flight (TOF) MRA data from healthy subjects [8]. Additionally, combining MRA data with T1-weighted imaging has proven effective for predicting brain age with deep CNN models [9].
Arterial tortuosity, a characteristic associated with aging, is also influenced by factors such as female sex, high blood pressure, genetic disorders involving aortic dissection and dilation, and various other cardiovascular risk factors [10–12]. Recent studies have explored segmental arterial tortuosity and diameter as inputs for machine learning regression models for predicting age [13]. However, these studies have been limited to specific segments, primarily focusing on the left and right internal carotid arteries (ICAs) and the basilar artery (BA).
In the current study, we expanded this approach by incorporating not only ICA and BA segments but also additional arterial segments surrounding the circle of Willis. This broader inclusion of arterial segments facilitates a more comprehensive analysis of arterial morphological attributes relevant to age prediction. Given the increased number of available features, we further investigated the effectiveness of feature subset selection methods to enhance the performance of machine learning regression models.
II. Methods
Figure 1 illustrates the overall image preprocessing pipeline, including labeling of arterial segments and extraction of arterial tortuosity and diameter statistics features. Figure 2 summarizes the study as a flowchart outlining feature extraction, selection of relevant features, and development and validation of machine learning regression models. Each procedure is described in detail below.
1. Data and Labeling
The 3D MRA dataset was obtained from the IXI datasets (https://brain-development.org/ixi-dataset). After data exclusion, data from 171 subjects were used for analysis. Following manual identification of three seed points in the left and right ICAs and the BA, seeded region-growing was conducted for arterial segmentation [14,15]. The skeletonization function in the scikit-image library [16] was used to extract centerlines of the arteries in 3D. The Plotly Python library (https://plotly.com/python) was used to manually annotate arterial landmarks [14]. The Dijkstra algorithm was then employed to determine the shortest path between two identified endpoints [17]. Resulting segments of the centerlines were color-coded, as shown in Figure 3, and saved as .html files, which were visually inspected to ensure annotation accuracy. Data with incorrect pathfinding results were excluded from analysis. Centerline points underwent smoothing via spline interpolation. Missing centerlines in certain posterior communicating artery (PComm) segments were treated as missing values, imputed using the K-nearest neighbor (KNN) method from scikit-learn [18] with nneighbors = 5.
2. Feature Extraction
The features extracted from each arterial segment included six tortuosity metrics and seven diameter statistics.
1) Tortuosity metrics: The Euclidean length (l) between two endpoints, the curve length (lc), relative length, triangular index, sum of angles metric, and product of angle distance [19].
Relative length (RL):
where l is the Euclidean length, and lc is the curve length (Figure 4A).
Triangular index (TI):
where ai and bi are lengths of the two sides along the arterial segment, and ci is the length of the remaining side in the i-th triangle (Figure 4B).
Sum of angles metric (SOAM):
where ϕi is the angle between two adjacent lines connecting the center and two endpoints for the i-th center (Figure 4C). Product of angle distance (PAD):
2) Diameter statistics: Mean, minimum, maximum, standard deviation, 25th percentile, 50th percentile, and 75th percentile values. Diameters were calculated along the centerline points using the distance_transform_edt() function from the SciPy library [20] on 3D binary vessel masks.
The 13 arterial segments were considered for feature extraction, and their names and anatomical locations are shown in Table 1 and Figure 3, respectively. Hence, the total number of features per subject was 13 segments × (6 + 7) features/segment = 169, which is equal to 13 arterial segments multiplied by 13 features (i.e., 6 tortuosity metrics and 7 diameter statistics).
3. Feature Selection
Two methods, correlation-based feature selection (CFS) and Relief-F, were applied to reduce dataset dimensionality.
CFS is a sophisticated multivariate filter method designed to optimize feature subsets for predictive modeling [21]. It selects subsets that correlate strongly with the target variable while minimizing inter-feature correlations, ensuring each feature uniquely contributes to prediction. By assessing predictive value and redundancy among features, CFS maximizes predictive accuracy. This method refines the predictive capability of models while simplifying feature selection, making it valuable in machine learning applications. It enhances the effectiveness of predictive models by focusing on essential and non-overlapping features.
Relief-F extends the earlier Relief algorithm, specifically tailored for multi-class datasets [22]. It selects features by choosing samples and identifying their closest matches within the same class. By comparing attribute values between these samples and their nearest hits (similar instances) and misses (dissimilar instances), Relief-F continuously refines relevance scores for each feature [23]. Features that consistently show similar values within a class and distinct values across classes are identified as highly relevant, thereby enhancing predictive accuracy.
Feature subsets comprising 70%, 50%, 30%, and 10% of the total 169 features were selected using both methods. Age, the target variable, was categorized into three groups (20–39, 40–59, 60–89 years). For CFS, subsets with the highest merit based on feature-class and feature-feature correlations were selected from all possible subsets. Relief-F utilized the Relief-F library (https://pypi.org/project/ReliefF/) with “n_features_to_keep” set to 118 (70%), 85 (50%), 51 (30%), and 17 (10%), fixing “n_neighbors” at 25. The “n_neighbors” parameter specifies the number of nearest neighbors evaluated when assessing feature significance. These selected subsets were subsequently input into machine learning models.
4. Model Development
Five machine learning regression models were compared for age prediction: random forest, linear regression, AdaBoost, XGBoost, and lightGBM regression. Random forest, linear regression, and AdaBoost models were trained and validated using scikit-learn [18]. XGBoost regression models were trained and validated using XGBoost [24] (https://xgboost.readthedocs.io/en/stable/). LightGBM regression models were trained and validated using LightGBM [25] (https://lightgbm.readthedocs.io/en/stable/). Each model was evaluated using four-fold cross-validation. For each fold, hyper-parameters were tuned via randomized search [26] using candidate parameter sets.
5. Model Evaluation
The machine learning regression models’ prediction performance was evaluated using the following metrics. When xi is the real age of the i-th subject, and yi is the predicted age of the i-th subject, the Pearson correlation coefficient is defined as
where χ̄ is the mean of the xi values, and ȳ is the mean of the yi values. The correlation coefficient r ranges from −1 to 1. Root mean square error (RMSE) is defined as
Mean absolute percentage error (MAPE) is defined as
The coefficient of determination or R2 is defined as
Feature importance was calculated for all models using the scikit-learn library.
6. Model Interpretation
The Shapley additive explanations (SHAP) method was used to interpret model predictions [27]. SHAP utilizes concepts from cooperative game theory, specifically Shapley values, to quantify the fair contribution of each feature to a model’s predictions. This approach measures each feature’s impact on individual predictions, thereby enhancing the transparency and interpretability of the model’s decisions [28]. SHAP values can be computed through various methods, including Kernel SHAP, Deep SHAP, and Tree SHAP. In this study, Tree SHAP was used, as it is specifically designed for tree-based machine learning models such as decision trees, random forests, and gradient-boosted trees [29]. SHAP values offer significant advantages in terms of both global and local interpretability. Unlike traditional feature importance metrics, SHAP assesses not only the overall importance of each feature but also indicates whether the effect of a feature is positive or negative on the prediction. Furthermore, SHAP values are calculated for each observation, providing personalized insights. Consequently, SHAP facilitates a comprehensive understanding of the model at both global and individual levels.
III. Results
Figure 5 presents a histogram depicting the age distribution grouped in 10-year bins. The largest age group was 60–70 years, comprising 40 subjects, while the smallest group, aged 80–90 years, included only four subjects.
Table 2 summarizes the prediction performance of the five machine learning regression models. The random forest regression model combined with 50% correlation-based feature subset selection exhibited the best overall performance, with the lowest average RMSE (14.001 years), highest average R2 (0.275), and highest average Pearson correlation coefficient (0.560). Conversely, linear regression had the poorest performance, indicated by the highest average RMSE (15.756 years), lowest average R2 (0.065), highest average MAPE (0.301), and lowest Pearson correlation coefficient (0.454). However, linear regression performance improved (lower RMSE) as the feature subset percentage decreased, suggesting that feature selection positively affected its accuracy. Across all models, the correlation-based feature selection method consistently outperformed the Relief-F method. Among the tested models, the LightGBM regression model achieved the lowest average MAPE (0.273).
Table 3 shows the five most important features identified by each regression model. In the random forest and Ada-Boost models, L-P1_TI (triangular index of the left posterior cerebral artery P1 segment) was consistently the most important feature across all degrees of feature subset selection. L-P1_TI also frequently appeared among the top features in the XGBoost and LightGBM models, occurring in 4 out of 5 instances for XGBoost and in 3 out of 5 for LightGBM. In the XGBoost model, L-P2_TI (triangular index of the left posterior cerebral artery P2 segment) was identified as the most important feature in 2 of the 5 feature subset selections. L-P2_TI frequently appeared as an important feature, specifically 4 out of 5 times in random forest, AdaBoost, and XGBoost models. Notably, arterial diameter-related features were identified as important less frequently, appearing in only 32 of the 125 cases analyzed, predominantly within the right ICA segment (25 of 32 cases).
Figure 6 displays box plots for the two most important features, L-P1_TI and L-P2_SOAM, obtained from training the random forest regression model using a 10% feature subset selection (see Table 3). The correlation-based feature selection method was applied to select the top 10% (17) features. Feature importance determined by the random forest regression model was ranked as follows: L-P1_TI, L-P2_SOAM, L-P1_SOAM, R-ICA_d_min, L-P2_RL, and L-P1_PAD, with importance values of 0.152, 0.111, 0.074, 0.073, 0.071, and 0.007, respectively. Three age groups were compared: Group A (20–39 years, n = 56), Group B (40–59 years, n = 57), and Group C (60–89 years, n = 58). Figure 6A demonstrates that the L-P1_TI value increased with age. Mean values for Groups A, B, and C were 1.000271, 1.000317, and 1.000495, respectively. Although the range of TI values was narrow, clear differences in median values are noticeable in the box plots. Similarly, Figure 6B indicates that L-P2_SOAM values increased with age, with mean values of 5.005, 6.052, and 6.865 for Groups A, B, and C, respectively.
Figure 7 displays a Shapley dot plot calculated from a validation dataset. For each feature, individual points on the plot are positioned along the horizontal SHAP value axis, with color indicating the magnitude of the feature value. The SHAP values show that higher feature values correspond to higher predicted age for the L-P1_TI, L-P1_PAD, and L-P2_PAD features. This relationship is expected because larger TI and PAD values indicate increased arterial tortuosity, a feature anticipated in older age groups. Conversely, higher feature values correspond to lower predicted age for the L-P2_RL and R-P2_RL features. This result aligns with expectations because, according to Eq. (1), a smaller RL value indicates greater arterial tortuosity, typically associated with older age.
IV. Discussion
This study evaluated the performance of machine learning-based age prediction using TOF-MRA data with features derived from tortuosity and diameter measurements of 13 arterial segments in the circle of Willis. Multiple regression models were tested using various feature subset selection methods, and their performance was assessed using metrics such as RMSE, Pearson correlation coefficient, R2, and MAPE.
Compared to a previous study [13] that focused solely on the ICA and BA segments, this study, which incorporated 13 arterial segments, demonstrated improved prediction performance. For instance, the random forest regression model in the current study achieved lower average RMSE (14.001 ± 0.444 years) and higher R2 (0.275 ± 0.065) compared to the earlier study’s RMSE (14.867 ± 0.515 years) and R2 (0.186 ± 0.031) [13]. These results highlight the value of incorporating additional arterial segments and employing feature subset selection methods. One notable exception was the linear regression model, which performed worse in the current study, showing higher average RMSE (15.756 ± 1.919 years) and lower R2 (0.065 ± 0.258) compared to the previous study (RMSE 15.000 ± 1.032 years; R2 0.162 ± 0.140). This suggests that linear regression may not effectively handle the increased complexity introduced by additional features.
The difference in performance between linear regression and other machine learning models can be attributed to inherent model characteristics. Linear regression assumes a straightforward linear relationship between features and the target variable (age), making it difficult to capture complex interactions embedded within the features. Consequently, linear regression exhibited poorer performance as the number of features increased. Conversely, non-linear models such as random forest and XGBoost effectively handled feature selection due to their capability to capture complex, non-linear relationships between features and the target variable.
Regarding feature selection, we considered filter methods that select features prior to training machine learning models. Although embedded and wrapper methods, which integrate machine learning algorithms directly into the feature selection process, are available [30], they were not explored in this study. These alternative methods might be valuable in future studies aimed at further enhancing predictive performance.
Although numerous missing values existed in the PComm arterial segments, applying data imputation methods such as KNN imputation improved performance while preserving the total number of data samples. Given the high dimensionality of features (169 features) in this study, investigating more advanced imputation methods could potentially further enhance prediction performance. Additionally, certain subjects’ data were excluded due to insufficient field of view in the superior-inferior direction affecting ICA or BA. Interestingly, ICA-related features were not dominant in feature importance in this study. Thus, future studies should consider including these previously discarded subjects’ data with insufficient fields of view and evaluating their impact on the machine learning regression models’ performance.
Previous studies have also investigated age prediction using MRA image data [8,9] and reported better prediction performances compared to our approach. However, those studies employed end-to-end deep convolutional neural network models, characterized by black-box behavior, which limits model interpretability. In contrast, our approach explicitly performs feature extraction based on anatomical structures of segmental arteries, allowing machine learning models to directly identify and interpret important features.
Our study underscores the potential of segmental feature extraction to generate numerous morphological features available for analysis, and highlights the utility of feature subset selection for enhancing age prediction accuracy. Moreover, machine learning-derived feature importance scores directly pinpoint anatomical features most relevant to age prediction. For instance, the L-P1_TI consistently emerged as one of the most significant features across most models.
This study has several limitations. First, the sample size was relatively small. Expanding the dataset might require correcting inaccurate arterial centerlines and including data with smaller fields of view along with suitable imputation strategies. Second, clinical information such as history of stroke, hypertension, and dyslipidemia was unavailable. This clinical information was intentionally excluded from our model since our goal was to develop machine learning models based exclusively on morphological vascular features. Third, the complexity of image processing tasks— including segmentation, skeletonization, and measurements of tortuosity and diameter—poses practical challenges for large angiography datasets and requires manual correction of arterial centerlines.
In conclusion, this study demonstrated the feasibility of machine learning-based age prediction using high-dimensional features derived from arterial tortuosity and diameter measurements across 13 segments of the circle of Willis. Among tested models, random forest regression with 50% correlation-based feature subset selection achieved the best performance, characterized by the lowest RMSE and highest average R2. Although linear regression showed the weakest overall performance, it improved when using reduced feature subsets, highlighting the importance of effective feature selection. Evaluation of feature importance suggests future studies might benefit from including previously excluded data with missing or incomplete information due to limited fields of view in the inferior portions of the brain. Future research should also explore more sophisticated imputation methods and advanced feature selection techniques to potentially further enhance the performance of machine learning-based age prediction.
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