Common and unique brain aging patterns between females and males quantified by large‐scale deep learning

Abstract

There has been extensive evidence that aging affects human brain function. However, there is no complete picture of what brain functional changes are mostly related to normal aging and how aging affects brain function similarly and differently between males and females. Based on resting‐state brain functional connectivity (FC) of 25,582 healthy participants (13,373 females) aged 49–76 years from the UK Biobank project, we employ deep learning with explainable AI to discover primary FCs related to progressive aging and reveal similarity and difference between females and males in brain aging. Using a nested cross‐validation scheme, we conduct 4200 deep learning models to classify all paired age groups on the main data for females and males separately and then extract gender‐common and gender‐specific aging‐related FCs. Next, we validate those FCs using additional 21,000 classifiers on the independent data. Our results support that aging results in reduced brain functional interactions for both females and males, primarily relating to the positive connectivity within the same functional domain and the negative connectivity between different functional domains. Regions linked to cognitive control show the most significant age‐related changes in both genders. Unique aging effects in males and females mainly involve the interaction between cognitive control and the default mode, vision, auditory, and frontoparietal domains. Results also indicate females exhibit faster brain functional changes than males. Overall, our study provides new evidence about common and unique patterns of brain aging in females and males.

We employ a large‐scale deep learning framework followed by an explainable artificial intelligence technique to automatically discover brain functional connectivity (FC) relating to the aging and provides evidence about the shared and unique aspects of brain aging between females and males. The gender‐common and gender‐specific FCs are verified by the association between FCs and cognitive measures.

1. INTRODUCTION

As the global population rapidly ages, it is increasingly important to understand the effects of aging on the human brain. So far, we still do not have a complete understanding of how aging affects the human brain function, nor do we have clarity on ways to mitigate aging‐related brain decline. Moreover, although researchers found gender differences in the working memory, verbal abilities, and reasoning domains (Nichols et al., 2021) as well as in brain structure (Sanford et al., 2022) along with the aging, gender differences in the effects of aging on the brain function have not been established. It is therefore essential to investigate how females and males differ in their brain function aging, which could inform the development of gender‐specific interventions to delay negative effects of aging on the brain.

Previous studies have found aging‐related changes in specific brain functional networks by comparing young and old adults using statistical analysis methods (Campbell et al., 2013; Grady et al., 2016; Ng et al., 2016; Staffaroni et al., 2018). A few work (Meier et al., 2012; Sendi et al., 2020) used machine learning to reveal aging‐related functional connectivity (FC) that contributed mostly to classifying young and old populations. However, these studies cannot guarantee that the identified features are related to the progressive aging. Additionally, none of these studies used a large sample size to maximize the reliability of extracted FC features and validated aging‐related FC using independent cohorts. Furthermore, as gender difference in the brain has been well acknowledged (Allen et al., 2011; Biswal et al., 2010; Filippi et al., 2013), some studies have attempted to examine how females and males differ along with aging in the brain function (Goldstone et al., 2016; Scheinost et al., 2015; Stumme et al., 2020; Zonneveld et al., 2019). However, the findings were also often based on small sample size and statistical analysis methods, which may not accurately represent the distinguishing features. To the best of our knowledge, functional changes that are common to both genders and those specific to each gender across the entire brain during typical aging remain largely unexplored, and their associations with cognitive decline in females and males also remains unclear.

The integration of neuroimaging data with advanced methods can provide valuable avenue for comprehending the aging process of the brain. Given the superiority of deep learning in its automatic feature learning and powerful generalization ability, here we propose a large‐scale deep learning framework to investigate whole‐brain FC significantly associated with progressive aging. Moreover, our focus extends to exploring both the commonalities and distinctions in brain aging patterns between females and males. To ensure the reliability of our findings, we utilize brain FC estimated from resting‐state fMRI data obtained from a substantial cohort of 25,582 healthy participants. In contrast to previous studies that often compared young and old groups, we explore FC related to progressive aging by classifying between any two of seven age groups. This process includes 4200 classifiers on the main data for exploration and additional 21,000 classifiers on the independent data for verification. We employ an unbiased cross‐validation classification scheme to enhance generalizability of our identified FC to aging, and leverage explainable AI to offer a more intuitive understanding of the features learned by deep learning. Notably, we disclose stable gender‐common and gender‐specific changes in brain function associated with aging. Interestingly, these changes exhibit both shared and distinctive relationships with cognitive degradation. In summary, our work not only reveals the progressive functional changes along with aging but also highlights gender‐common and gender‐specific brain changes, which could potentially guide the development of treatments aimed at mitigating the adverse effects of aging on cognitive functions.

2. MATERIALS AND METHODS

2.1. Data

We analyzed the brain FC of 25,582 healthy participants (13,373 females and 12,209 males) from the UK Biobank dataset (Miller et al., 2016) after excluding the participants with any mental, neural system, or other diseases that could affect the brain function. Please find the subject selection method in the supplementary material and see Figure S1 for the demographic information of all remaining healthy participants. Our analysis specifically focused on the data from healthy participants aged 49–76 years who exhibited small head motions (less than 1.5 mm) during their resting‐state fMRI scans. The head motion was computed by averaging the motion parameters across space and time points. This age range was chosen to encompass middle‐aged and older adults, as the dataset contains very few participants outside this age range.

We downloaded the brain FC data from the UK Biobank website for our study. Since the processing was relatively complex, we include the details in the supplementary material and describe the primary steps as follows. The resting‐state fMRI data were preprocessed by the UK Biobank team. Fifty five brain functional networks were then obtained by performing a group ICA (Filippini et al., 2009; Smith et al., 2011) on the denoised fMRI data. Figure S2 and Table S1 provide details of these networks which were assigned into nine functional domains: attentional (AT), auditory (AU), cerebellum (CB), cognitive control (CC), default mode (DM), frontoparietal (FP), subcortical (SC), sensorimotor (SM), and visual (VI) domains. The network assignments are generally consistent to our previous work (Du et al., 2020) with seven domains and others' studies (Shen et al., 2018) with five domains. In this paper, we performed more detailed domain partitions for the 55 networks. We separated cognitive control and attention because they are two primary properties of information representation in working memory (Courtney, 2004), and highlighted FP since the FP network serves as the central hub for cognitive control functions (Zanto & Gazzaley, 2013). For each subject, a $55\times 55$ connectivity matrix reflecting the connectivities between brain functional networks was obtained by computing partial correlation between any two functional networks' time series, which measures the direct connectivity between two time series after regressing out effects from all the other time series. After that, the connectivity strengths were improved by using L2 regularization and further Gaussianized from correlations into z‐statistics. Due to the symmetricity of each connectivity matrix, only its lower triangular elements were used as the FC measures (size: 1 × 1485) for investigating aging‐related functional changes. It is worth pointing out that we further removed the effects of head motion by constructing a linear regression model for each FC measure taken as the dependent variable with the head motion as the explanatory variable. This processing is necessary because older participants tended to have greater head motions during scanning (see Table S2 for head motion information).

2.2. Classifying different age groups in females and males using large‐scale deep learning models

Based on the FC measures, we distinguished between paired age groups, with a focus on identifying key FC features influencing the classifications. We employed large‐scale deep learning models, rather than a unified deep learning model for all age groups, to investigate the impact of progressive aging on brain function. As outlined in Figure 1, we first applied deep learning to classify any two age groups for the females and males separately due to the promising applications of deep learning in the neuroscience field (Lundervold & Lundervold, 2019; Zhang et al., 2020), and then identified the FC features that are most relevant to the progressive aging for the females and males respectively using an explainable artificial intelligence (AI) technique (Sundararajan et al., 2017). After that, we extracted the aging‐related gender‐common and gender‐specific FC features and further validated the effectiveness of the features using additional classifications on the independent data. Moreover, we examined how the stable gender‐common (or gender‐specific) FCs similarly (or uniquely) changed along the aging process for females and males, and also evaluated whether the gender‐common (or gender‐specific) FCs show shared (or disparate) relations with cognitive measures.

FIGURE 1.

Our analysis pipeline that identifies and validates aging‐related gender‐common and gender‐specific functional connectivity (FC) using the large‐scale deep learning method. In the procedure, 4200 deep learning models are trained to classify all paired age groups among seven age groups for females and males separately using whole‐brain FC as features, and then the gender‐common and gender‐specific FC features that are most relevant to the progressive aging are identified using our method based on an explainable AI technique, after that, we validate the effectiveness of the gender‐common, gender‐specific and the combined common and specific FC features using additional 21,000 classifications on independent data, and finally, we evaluate the association (Pearson correlation) between each stable gender‐common (or gender‐specific) FC and the age as well as the correlations between the FCs and cognitive measures (including fluid intelligence, numeric memory, and reaction time).

For females or males, we divided all participants aged between 49 and 76 years into seven groups, each comprising individuals within a four‐year age range. So, the seven age groups encompassed participants aged 49–52, 53–56, 57–60, 61–64, 65–68, 69–72, and 73–76 years. Subsequently, utilizing a set of 1485 whole‐brain FC measures as potential features, we executed 21 classification tasks for differentiating all paired groups within the seven age groups, separately for females and males. During this process, we assessed the performances of various classification tasks and pinpointed the FC features that significantly contributed to the classifications. By extracting the crucial FC features separately for females and males, we identified the aging‐related gender‐common and gender‐specific FCs. The overall procedure is outlined in Figure 2a.

FIGURE 2.

The framework of our large‐scale deep learning classification method. We use a nested cross‐validation to perform classification tasks and aging‐related FC identification. (a) The overview of our framework. (b) The nested cross‐validation procedure for classifying any two age groups. (c) The details of model training, model evaluation, and FC score computation.

For each pair of age groups, we performed the classification via a nested ten‐fold cross‐validation scheme (shown in Figure 2b) to maximize the reliability. Given the variability in sample sizes across genders and different age groups, we implemented a random sampling to ensure that the number of subjects was consistent across all age groups in the classification. Prior to each outer cross‐validation procedure, we randomly sampled female (or male) participants to equalize the subject numbers. Subsequently, each age group comprised 987 participants, resulting in a total of 6909 females (or males) across 7 age groups for the 21 classification tasks in each outer cross‐validation procedure. For the inner cross‐validation, the main data, consisting of the nine folds from the outer process, was partitioned into a ratio of 8:1:1 for the training, validation, and test sets, respectively. The training set was utilized for model training, while the validation set facilitated model selection. Subsequently, the trained model was assessed using both the test set of the main data and the independent data derived from the outer cross‐validation, as illustrated in Figure 2c. Because we randomly sampled the subjects before each outer cross‐validation procedure, the total data that we used included a large sample size (25,582 healthy participants including 13,373 females and 12,209 males), which benefited the exploration of reliable classifications and features.

We employed a multilayer perceptron (MLP) with two hidden layers and an output layer as the model. Specifically, the number of neurons for the first hidden layer was set to 128, the second hidden layer contained 32 neurons, and the output layer had 2 neurons for the two‐class (i.e., two age groups) classification. Furthermore, we utilized the early stopping, batch normalization (Ioffe & Szegedy, 2015), and dropout (Srivastava et al., 2014) techniques for avoiding overfitting, used rectified‐linear unit function as the nonlinear transform, and chose Adam (Kingma & Ba, 2014) as the optimizer. Specifically, the learning rate $\alpha =5\times {10}^{-4}$, the weight of L2 regularization $\lambda ={10}^{-6}$, the dropout probability $p=0.5$, and the epoch $e=100$.

In summary, using the data and model mentioned above, we trained 4200 classifiers through 100 cross‐validation runs, covering 21 classification tasks for each of the two gender groups. Consequently, we obtained the classification accuracy for each task, which involved classifying two age groups, utilizing data from females or males for both the test set of the main data and the independent data.

Additionally, we are interested in exploring whether a larger sample size of data and a more complex model would improve classification and generalization performance. Therefore, we conducted additional two‐class classification tasks only among four age groups (aged 57–60, 61–64, 65–68, and 69–72 years) using more data. For this goal, we randomly sampled 1736 females (or males) from the original participants for each of the four age groups in each outer cross‐validation. Besides, we implemented a five‐layer MLP model to classify any two age groups within the same cross‐validation framework. Identifying aging‐related gender‐common and gender‐specific FC via an explainable AI technique.

With the well‐trained deep learning models, our primary objective is to unveil the aging‐related gender‐common and gender‐specific FC. As our deep learning models were designed to differentiate between different age groups for females (or males), we extracted the crucial features that made the most significant contributions to the classifications with satisfactory performance. By examining the important features separately extracted from classifications using females and males, we sought to identify FC features that reflect the similarities and uniqueness in brain aging between the two genders. There are many approaches (Binder et al., 2016; Shrikumar et al., 2017) that can be used to interpret deep learning models. In this article, we opted for integrated gradients (IGs) to extract important features from our deep learning models due to its recognized sensitivity and effectiveness in interpretation (Sundararajan et al., 2017). The IG method serves to elucidate the relationship between a model's output and its input features. When provided with input data and the desired model output, IG computes importance scores for each input feature. For a specific feature, the magnitude of the score reflects the extent of its contribution to the classification; a larger absolute value indicates a more significant impact.

Figure 2c briefly illustrates the extraction of important aging‐related FC features for females or males using the IG method. In each run of the outer cross‐validation using females' (or males') data, we identified the important features that greatly contributed to classifying each two age groups when the classification achieved a satisfactory performance (>75% classification accuracy on the test set), and then evaluated the features' contributions across different classification tasks to find which FC features were relevant to the progressive aging. We only investigated the discriminative features for the classifications with high accuracies because those features worked well in differentiating different age groups and should be able to reflect brain aging. Specifically, we computed each feature's importance score by feeding the main data to each well‐trained deep learning model using the IG method, and then averaged the importance scores across all 10 inner cross‐validation runs and different classification tasks (with >75% accuracy) for each feature. After that, we took the absolute value of the mean importance score, and then normalized and sorted them across different features to select the top n FC (n = 300, nearly 20% of all FC) as the aging‐related FC for the females or males. It is worth pointing out that rather than feeding all data into the trained model to mine the important features, we only used the main data because this guarantees the unbiased property of additional classifications on independent data using extracted features.

Following the extraction of aging‐related FC features for females and males separately, the next step involved identifying FC features that were commonly associated with brain aging in both genders, as well as those that were uniquely relevant to each gender. To accomplish this, we assigned importance scores to all FC features, denoted as $S^{\mathrm{F}}$ and $S^{\mathrm{M}}$, estimated from the females' and males' data, respectively. By sorting the FC features separately based on these importance scores ($S^{\mathrm{F}}$ and $S^{\mathrm{M}}$), we selected the top n FC features for females and males, resulting in two sets of indices ($I^{\mathrm{F}}$ and $I^{\mathrm{M}}$). Then, we used these indices to determine the gender‐common FC (${\mathit{FC}}_{\text{common}}$), female‐specific FC (${\mathit{FC}}_{\text{female}}$), and male‐specific FC $\left({\mathit{FC}}_{\text{male}}\right)$ according to Equations ((1), (2), (3), (4), (5)). These designations allowed us to categorize and analyze the FC features that exhibited commonalities and distinctions between females and males.

$${\mathit{FC}}_{\text{female}}=\left(I^{\mathrm{F}}-I^{\mathrm{M}}\right)\cup \left\{\left.i\right|S_i^{\mathrm{F}}-S_i^{\mathrm{M}}>a,\forall iϵ\left(I^{\mathrm{F}}\cap I^{\mathrm{M}}\right)\right\}$$ (1)

$$\begin{array}{c}{\mathit{FC}}_{\text{male}}=\left(I^{\mathrm{M}}-I^{\mathrm{F}}\right)\cup \left\{\left.i\right|S_i^{\mathrm{M}}-S_i^{\mathrm{F}}>b,\forall iϵ\left(I^{\mathrm{F}}\cap I^{\mathrm{M}}\right)\right\}\end{array}$$ (2)

$$\begin{array}{c}{\mathit{FC}}_{\text{common}}=\left(I^{\mathrm{F}}\cap I^{\mathrm{M}}\right)-{\mathit{FC}}_{\text{female}}-{\mathit{FC}}_{\text{male}}\end{array}$$ (3)

$$\begin{array}{c}a=\frac{1}{\mid I^{\mathrm{F}}-I^{\mathrm{M}}\mid }\sum _{i\in \left(I^{\mathrm{F}}-I^{\mathrm{M}}\right)}\left(S_i^{\mathrm{F}}-S_i^{\mathrm{M}}\right)\end{array}$$ (4)

$$\begin{array}{c}b=\frac{1}{\mid I^{\mathrm{M}}-I^{\mathrm{F}}\mid }\sum _{i\in \left(I^{\mathrm{M}}-I^{\mathrm{F}}\right)}\left(S_i^{\mathrm{M}}-S_i^{\mathrm{F}}\right)\end{array}$$ (5)

Here, $i$ is the index of the $i$‐th FC, and $S_i^{\mathrm{F}}$ and $S_i^{\mathrm{M}}$ represent the importance scores of the $i$‐th FC for females and males, respectively. Gender‐specific FCs encompass features that are deemed important for one gender but not the other. For instance, considering ${\mathit{FC}}_{\text{female}}$, it comprises FC features included in the top n FCs for females but not present in the top n FCs for males ($I^{\mathrm{F}}-I^{\mathrm{M}}$ in Equation (1)), additionally, it includes FC features that are present in the top n FCs for both females and males, but the differences in their importance scores between females and males exceed specific thresholds ($\left\{\left.i\right|S_i^{\mathrm{F}}-S_i^{\mathrm{M}}>a,\forall iϵ\left(I^{\mathrm{F}}\cap I^{\mathrm{M}}\right)\right\}$ in Equation (1)). Here, $a$ and $b$ represent the thresholds for females and males, respectively, and are automatically estimated using Equations (4) and (5). Specifically, $a$ corresponds the mean value of the importance score differences of FC involved in $I^{\mathrm{F}}-I^{\mathrm{M}}$. Once the gender‐specific FC features are identified, the gender‐common FCs comprise the remaining FCs in both the first n FCs for females and males.

2.3. Verifying age‐related gender‐common and gender‐specific FC using independent data

As mentioned above, the extraction of aging‐related gender‐common and gender‐specific FC features was carried out using the main data within each run of the outer cross‐validation. Consequently, to ensure an unbiased evaluation, we utilized the independent data to assess two aspects. First, we examined whether the gender‐common features would lead to similar classification performances for both genders. Second, we assessed whether the gender‐specific features, such as female‐specific features, demonstrated a superior ability for one gender (e.g., female) compared to the other (e.g., male) in distinguishing different age groups.

For this goal, we conducted 21 classification tasks using the gender‐common, female‐specific, and male‐specific FC as inputs, respectively. Our aim was to evaluate how each set of features performed in classifying different age groups for females and males. Specifically, we anticipated that the gender‐common FCs would demonstrate similar effectiveness in classifying age groups for both genders. Meanwhile, we expected female‐specific FCs to outperform male‐specific FCs in classifying age groups for females, and conversely, male‐specific FCs to excel in classifying age groups for males.

Moreover, we carried out additional tests by combining the gender‐common and gender‐specific features. In other words, the gender‐common and gender‐specific (e.g., female‐specific) FC feature sets were utilized together for the 21 classification tasks using either the females' or the males' data. Our objective was to evaluate if combining gender‐common and gender‐specific features would lead to better performance compared to using only the common or unique features separately. To facilitate comparison with classifications using all FC features, we implemented a nested cross‐validation procedure with the same data organization as the aforementioned experiments.

Regarding each of five types of features (gender‐common, female‐specific, male‐specific, the combined gender‐common and female‐specific, and the combined gender‐common and male‐specific FC) extracted from each run of the outer cross‐validation, we conducted classifications to distinguish between each pair of age groups. These classifications involved the use of 10 deep learning models within the inner cross‐validation. To assess the performance of these classifiers, we evaluated their results on both the test set of the main data and the independent data using females' or males' data. In total, we trained 21,000 classifiers (five types of feature × 100 cross‐validation runs × 21 classification tasks × two gender groups) and evaluated their classification performance for both the test set of the main data and the independent data.

The IG method extracted important features that contributed greatly to the classification tasks, consequently disclosing the FC features that mostly relate to aging. To verify this point, we separately conducted the classifications with the same nested cross‐validation framework by separately using the important FC features with high importance scores identified by the IG method and the classifications using the less important FC features with low importance scores measured in IG for a comparison. It is worth pointing out that measured by Pearson correlation between FC and age, the two types of features were matched, meaning that they were equally important if using correlation‐based feature selection. Taking the classifications using the females' data for an example, as for the less important FC, we selected the FC features that had high absolute correlations (greater than 0.5) from the last n FCs in females (sorted by the FC importance scores using the IG method); as for the important FC, we chose the FC features from the combination of gender‐common and female‐specific FCs, with the condition that the selected FC had matched correlations with the less important FC.

2.4. Revealing property of the aging‐related gender‐common and gender‐specific FC

It is essential to consolidate and summarize the stable aging‐related gender‐common or gender‐specific FCs across multiple outer cross‐validation runs. This analysis aims to elucidate how FCs undergo similar or divergent changes with progressive aging in both genders. Therefore, we identified the gender‐common and gender‐specific FC features that occurred in more than 5 of the 10 outer cross‐validation runs as the stable gender‐common and gender‐specific FC features for further investigation.

To reflect the changing trend of each stable gender‐common and gender‐specific FC, we computed its mean FC strength of the subjects at the initial age (i.e., 49 years) as well as Pearson correlation between the FC's strengths at different ages and the ages for the females or males, respectively. Here, the FC strength at each age was measured by the mean FC strength of all participants at that age. Furthermore, to explore more details about the FC changing trends, six possible changing patterns were defined according to the mean FC strength at the initial age and Pearson correlation. We then summarized the FC features that coincide with each pattern. The six patterns included that positive FC strength increases along with aging (denoted by FC: +, corr: +), positive FC strength decreases along the aging but has no sign change of the FC strength (denoted by FC: +, corr: −), positive FC strength decreases with aging and has a sign change of the FC strength (denoted by FC: from + to −, corr: −), negative FC strength is enhanced along with aging (denoted by FC: −, corr: −), negative FC strength is suppressed along with aging but has no sign change of the FC strength (denoted by FC: −, corr: +), and negative FC strength increases along with aging and has a sign change of the FC strength (denoted by FC: from − to +, corr: −). After detecting the changing pattern for each FC, we compared it between females and males to investigate whether the gender‐common FC would present more similarity and the gender‐specific FC would present more differences. Due to this reason, we display the changing patterns of each stable gender‐common or gender‐specific FC in females and males for better visualization and easier comparison. In addition, regarding each pattern, we performed paired t test on the FC‐age correlations between the males and females to test the gender difference. Because the two genders could have different patterns for one FC, regarding the gender‐common FCs, we conducted two runs of paired t tests by taking the pattern of females and males as the standard separately, and regarding the gender‐specific FC (e.g., female‐specific FC), we performed one run of paired t test by taking the pattern of the related gender (e.g., female) as the standard.

To show the changes of each pattern‐related FC strengths during the aging progress in more detail, we computed the mean and standard deviation of those FC strengths in females and males separately as well as the covariance of FC strengths between females and males at each age to demonstrate the distribution of FC strengths at the age using an ellipse (Friendly et al., 2013). As such, the FC strength changes across different ages can be presented by ellipses with different colors. In this manner, it is convenient to observe the FC strength change of each pattern along with aging for the gender‐common or gender‐specific FC.

After that, for each type of FCs (the gender‐common, female‐specific, or male‐specific FCs), we computed the FC number and its percentage for each changing pattern to investigate which patterns are more occupied. In addition, we were also interested in unraveling what primary brain functions are commonly or uniquely influenced during the aging progress. So, we explored the gender‐common and gender‐specific FCs by looking into them through analyzing their linked functional domains. Since the 55 functional networks were assigned into nine functional domains, we separately summarized the gender‐common or gender‐specific FCs that belonged to each between‐domain or within‐domain. Specifically, for each between‐domain (e.g., CC‐DM) or within‐domain (e.g., CC‐CC), we computed the number of the FCs that were included by the between‐domain or within‐domain for each changing pattern. Next, we also summarized the FC number and percentage for the overall between‐domain or within‐domain for each changing pattern. Moreover, we defined the commonality and specificity measures to reflect the property of each FC. For each FC, we first calculated the FC‐age correlation difference between females and males. If the FC was taken as the stable gender‐common FC, the commonality was defined as 1 minus the absolute correlation difference; if it was taken as the stable female‐specific FC, the specificity was defined as the correlation difference by its correlation sign in females; if it was taken as the stable male‐specific FC, the specificity was defined as −1 by the correlation difference by its correlation sign in males. The overall commonality or specificity measure for each between‐domain and within‐domain for each changing pattern were subsequently calculated as the sum of the commonality or specificity measure of FCs that belonged to them. To maximize the reliability, we computed those measures by setting $n=300$ and by averaging results obtained under different settings ($n=100,200,\dots ,500$).

Last but not least, for some important stable gender‐common, female‐specific, and male‐specific FCs, we plotted the FC strength across different ages in females and males separately to further specify the related subtle brain networks. Through sorting, we identified the top‐10 important FCs from all stable gender‐common FCs by choosing those with smaller differences of FC‐age correlations between females and males among the FCs with >0.5 absolute FC‐age correlations in both genders. From the stable gender‐specific FCs (e.g., female‐specific FCs), we also selected the top‐10 important FCs for investigation, each of which had >0.5 absolute FC‐age correlation in this gender (e.g., female) and also had a greater difference in FC‐age correlation between females and males.

2.5. Exploring the association between the aging‐related FC and human cognitive decline

Building upon the identified stable aging‐related gender‐common and gender‐specific FCs, our interest also lay in exploring the association between the alterations in these FCs and the declines observed in human cognitive functions. In our work, we included three cognitive measures including the fluid intelligence (FI), numeric memory (NM), and reaction time (RT). In the UK Biobank protocol, FI was assessed through a task comprising 13 logic/reasoning‐type questions, each with a two‐minute time limit. For NM evaluation, participants were presented with a two‐digit number and required to recall it after a brief pause. The difficulty increased incrementally until an error occurred or a maximum of 12 digits was reached. RT was measured through a timed symbol matching test, with the score representing the mean response time in milliseconds across trials containing matching pairs. For each aging‐related stable gender‐common or gender‐specific FC, we calculated the Pearson correlation between its FC strength at various ages and each cognitive measure at different ages, ranging from 49 to 76 years. This analysis was conducted separately using data from females and males. Given the numerous participants at each age, we averaged the FC strengths or cognitive measures for individuals of the same age prior to conducting the correlation calculations. Additionally, we sought to examine the age‐related decline of each cognitive measure for females and males. For each cognitive measure, we present its mean and standard deviation at each age. Furthermore, we computed the gradients following a linear fit to the cognitive measures, distinguishing between females and males.

3. RESULTS

3.1. Deep learning reveals that brain FCs change gradually along with the normal aging

Figure 3a shows the classification accuracies using females' data for both the test set of the main data and the independent data. It is evident that the accuracy matrix approximatively presents a symmetric pattern, meaning that the classification accuracy is quite consistent between the test set of the main data and the independent data. Thus, our results support that the trained models had a satisfactory generalization ability. It is also observed that the classification between the group aged 49–52 years and the group aged 73–76 years achieved the highest accuracy (over 89%), and the classification accuracy slowly decreased when the age difference between the two groups in the classification became small. This trend was still true when enhancing the sample size and model complexity (see the supplementary Figure S3a,c), although the accuracies had a slightly increase.

FIGURE 3.

Classification performance using whole‐brain 1485 FCs in distinguishing different age groups on the test set of the main data and the independent data. (a, b) The classification accuracy for the females and the males, respectively. In (a) and (b), the upper triangular elements include the mean accuracy (across 100 runs) for the test set of the main data, and the lower triangular elements include the mean accuracy (across 100 runs) for the independent data. It is seen that the classification accuracy for the same classification task (e.g., the classification between the 49–52 age group and the 73–76 age group) is very consistent between the test set and independent data. (c) The mean classification accuracy of the similar classification tasks on the test set of the main data and the independent data. Each bar reflects the averaged classification accuracy of similar classification tasks that are defined as those classifying two groups with the same age difference. The figure demonstrates that the classification accuracy gradually increases when the age difference between the two groups become large, meaning that aging gradually influences brain function.

We also performed similar classifications for the males using the same framework. Figure 3b demonstrates a similar pattern to Figure 3a, again supporting that classifying two groups with more age differences was easier than classifying two groups with fewer age differences using brain FC features. Similar to the females' data, using more samples or more advanced models yields a consistent conclusion (Figure S3b,d). For a further summary, we regarded the classifications that classified two groups with the same age difference as the similar classification tasks (for example, the classification between the 49–52 age group and the 57–60 age group and the classification between the 53–56 age group and the 61–64 age group were taken as the similar classification tasks, because the age differences both were 8 years), and then averaged their classification accuracies for the test set of the main data and the independent data, respectively. Figure 3c shows that the classification accuracy reached the highest value when classifying the youngest and oldest groups (that had an age difference of 24 years) for females (90.11%) and males (85.93%) using the test set of the main data, and for females (89.38%) and males (86.28%) using the independent data. In contrast, the accuracy was lowest when classifying two groups with the smallest age difference (i.e., 4 years) for females (53.92%) and males (52.92%) using the test set of the main data, and for females (53.72%) and males (53.29%) using the independent data. Since the higher classification accuracy reflects a greater degree of dissimilarity of two age groups in the brain FC, our findings provide support for gradually declining brain FC along the normal aging process.

3.2. Our method reveals the most important aging‐related gender‐common and gender‐specific brain FC

After successfully extracting the aging‐related gender‐common and gender‐specific FCs based on the main data (in each run of the outer cross‐validation procedure), we carried out the age group classifications again via the same nested 10‐fold cross‐validation framework using those features of females or males. Moreover, we not only evaluated each of the above‐mentioned three types of FCs, but also tested two types of combined FCs (i.e., the combination of the gender‐common and female‐specific features as well as the combination of the gender‐common and male‐specific features). Thus, using each of the five types of FCs, we obtained the accuracy in classifying any two age groups for the test set of the main data and independent data, separately. The supplementary Figure S4 and Tables S3 and S4 include the detailed results for using each type of FC.

To enable comparisons across various types of FC, we consolidated the results by averaging the classification accuracies for similar tasks within each type of feature. Figure 4a,b show the corresponding results for the test set of the main data and the independent data, respectively, indicating that the results were very consistent between the main data and independent data. Interestingly, regardless of any type of features, the classification accuracy in both females and males gradually increased when the age difference between the two groups became large, again confirming that our identified FCs reflect progressive brain aging. Furthermore, the gender‐specific FCs often yielded better classification performance for the related gender than the other gender, supporting the validity of the gender‐specificity. For instance, when looking into the classification between the 49–52 age group and the 73–76 age group, the female‐specific FCs obtained higher accuracy for the females (82.71% on the test set of the main data and 80.63% on the independent data) than for the males (69.02% on the test set of the main data and 70.98% on the independent data). Conversely, the male‐specific FCs attained higher accuracy for males (78.08% on the test set of the main data and 74.57% on the independent data) than for females (70.59% on the test set of the main data and 72.83% on the independent data). Indeed, this scenario remained consistent across all classification tasks, encompassing both the main data and the independent data. Additionally, our observations indicate that the simultaneous utilization of gender‐common and gender‐specific FCs yielded superior performance compared to using either gender‐common or gender‐specific FCs alone, for both females and males. This suggests that gender‐common FCs signify a shared aging mechanism between females and males, while gender‐specific FCs provide additional insights into the distinct changes in brain function experienced by females and males during aging.

FIGURE 4.

Performance of the classifications between seven age groups using different datasets based on various features. (a, b) Mean accuracy of similar classification tasks on the test set of the main data and the fully independent data. The used features included the gender‐common FCs, the female‐specific FCs, the male‐specific FCs, the combined gender‐common and female‐specific FCs, and the combined gender‐common and male‐specific FCs. For comparison, the results using all FCs are also shown. (c) The overall accuracy obtained using each type of feature on different datasets. Here, all accuracies across different classification tasks are averaged to represent the overall accuracy. We include the results for the test set (of the main data) and independent data, and also include the results for the females and males. (d) The efficiency matrix. Each element of the efficiency matrix is the proportion of the corresponding overall classification accuracy in the overall accuracy using all FCs as features. It is seen that the gender‐specific FCs tend to yield better classification performance for the related gender than the other gender, and the combined use of the gender‐common and gender‐specific FCs result in a greater accuracy than using the common or specific FCs alone.

To summarize the performance of each type of FC, we averaged all accuracies across the 21 classification tasks to obtain an overall accuracy. One interesting finding from the results (Figure 4c) is that using the gender‐common and gender‐specific FCs in combination almost yielded an accuracy as high as using all FCs, supporting that those FCs included the most pivotal aging‐related FCs. To further clarify, we assessed the efficiency of each type of feature by computing the proportion of its relevant accuracy in the accuracy obtained from using all FC features. The efficiency matrix (Figure 4d) shows that for the females' data, using the combination of the gender‐common and female‐specific FCs yielded the highest efficiency, that is, 0.98 for the test set of the main data and 0.97 for the independent data; for the males' data, using the combination of gender‐common and male‐specific FCs yielded the highest efficiency, that is, 0.99 for the test set of the main data and 0.97 for the independent data. The results again confirm the important role of the identified common and specific FCs in characterizing brain aging.

Our deep learning method demonstrated commendable classification performance by automatically extracting efficient features, surpassing the effectiveness of other straightforward feature selection methods such as correlation‐based approaches. We validated this point by performing reclassification by separately using the important FC features identified by the IG method and the less important FC features measured by the IG method. Here, both types of features fell into a similar range of correlation values with the ages. That means the importance of the two types of features was comparable if using the linear correlation‐based feature selection. However, it is evident from Figure S5 that using important features revealed by the IG method resulted in higher classification accuracies, indicating that our deep learning method is more powerful in disclosing the aging‐related FCs.

3.3. Aging‐related gender‐common FC changes primarily in the CC domain

Since using the identified gender‐common FCs resulted in close classification performances between females and males on the independent data in distinguishing different age groups, it is desired to investigate what brain functions commonly alter in females and males and further how they consistently change along with aging. In our work, we identified 95 FCs as the stable gender‐common FCs. The detailed information and changing patterns of those FCs can be seen in Table S5.

As stated in Section 2, in total, there are six possible changing patterns according to the FC strength at the initial age and correlation. We separately summarized the FC features that belonged to each changing pattern to investigate the similarities and differences between the two genders. Figure 5a visualizes the changing patterns of the stable gender‐common FC features for both the females' and males' data. We found that although there are a total of six possible changing patterns, there was no FC whose mean strength changed its sign (from + to − or from − to +) across all ages that we investigated (i.e., 49–76 years). Thus, there were only four changing patterns of FC important to the aging process. Interestingly, within the 95 stable gender‐common FC features, only three showed different changing patterns between females and males (Figure 5a). Through conducting a paired t test on the FC‐age correlations of the gender‐common FCs for each pattern to investigate differences between the males and females, we found that the difference was insignificant for all four changing patterns (see Figure 5 for the T‐values and p‐values). For an intuitional display, we also show the mean correlation across all gender‐common FCs with the same changing pattern in Figure 5a, clearly demonstrating that the mean FC‐age correlation was close between the two genders.

FIGURE 5.

Changing patterns of the stable gender‐common, female‐specific, and male‐specific FC features. (a), (b), and (c) include the results of 95 stable gender‐common FCs, 113 stable female‐specific FCs, and 101 stable male‐specific FCs, respectively. For each FC, we show its changing pattern using one circle dot, with its x‐axis and y‐axis are Pearson correlations between the FC strengths at different ages and the ages for males and females, respectively, and its coloring way in left and right parts denotes its changing pattern in males and females, respectively. Although there are six possible patterns defined, only four patterns occur for these FCs, including the pattern of (positive FC strength decreases along with aging but has no sign change of FC strength, denoted by FC: +, corr: −), the pattern of (negative FC strength is enhanced along with aging, denoted by FC: −, corr: −), the pattern of (positive FC strength increases along with aging, denoted by FC: +, corr: +), and the pattern of (negative FC strength is suppressed along with aging but has no sign change of FC strength, denoted by FC: −, corr: +). It is seen that the mean correlation is close between the two genders for the gender‐common FCs, and the mean correlation is stronger in the related gender than in the other gender for the gender‐specific FCs. In the right‐bottom part, we show the T‐value and p‐value obtained using paired t test between the males and females on the FC‐age correlations for each pattern for both the gender‐common and gender‐specific FCs. The paired t test results support that the difference in FC‐age correlation is insignificant for the gender‐common FCs but significant for the gender‐specific FCs.

Furthermore, regarding each changing pattern of the stable gender‐common FCs, we display how the associated FCs' strengths changed with the aging progress in Figure 6a and include detailed information in Table S6. In particular, for the FCs belonging to a pattern, we show the FC strength distributions at each age for males and females using a confidence ellipse (Friendly et al., 2013). It is observed that regarding the gender‐common FCs, the ellipses tend to move along the diagonal line, suggesting that the changes of FC strengths in females and males were consistent for the stable aging‐related gender‐common FCs.

FIGURE 6.

Changes of the stable gender‐common, female‐specific, and male‐specific FCs along with aging. (a), (b), and (c) include the results of 95 stable gender‐common FCs, 113 stable female‐specific FCs, and 101 stable male‐specific FCs. For the FCs belonging to a pattern, a confidence ellipse is used to show the strengths of FCs that belong to the pattern for one specific age. The FC strengths of females and males from age 49 to age 76 are represented by ellipses with different colors. The dotted box is the minimum box (edges parallel to x‐axis or y‐axis) which includes all the ellipses. Regarding the gender‐common FCs, the ellipses corresponding to different ages move along the diagonal line, suggesting consistent FC changes between females and males. Regarding the gender‐specific (e.g., female‐specific) FCs, the ellipses move more greatly along one direction (e.g., y‐axis) compared to the other direction (e.g., x‐axis), validating the gender specificity.

Because each FC reflects an interaction between two brain functional networks, we further summarized the stable gender‐common FCs according to their associated networks. Given all networks were assigned to nine functional domains, we display the number of those FCs that belonged to each between‐domain (e.g., CC‐DM) and within‐domain (e.g., CC‐CC) in Figure 7a to investigate what functional domains are mostly relevant to the common aging mechanism. Furthermore, we summarize the number and percentage of FCs for each changing pattern in Figure 7a. We found that the gender‐common FCs occupied the highest percentage for the pattern of (FC: −, corr: +), and the second highest for the pattern of (FC: +, corr: −), relative to the other two patterns including (FC: −, corr: −) and (FC: +, corr: +), which means that FC strengths were primarily suppressed along with aging. More interestingly, measured by the gender‐common FCs, aging suppressed the positive FCs within domains and the negative FCs between domains. In addition, we also calculated the commonality measure for each between‐domain and within‐domain for each pattern. Considering that the stable gender‐common FCs were identified under the condition of using the top n = 300 features in the classifications, we also report the commonality measures by combining different n in Figure 7d. A consistent conclusion can be drawn that in general, the CC‐CC is the most similar for the pattern of (FC: +, corr: −), and the CC‐DM is the most similar for both the pattern of (FC: +, corr: +) and the pattern of (FC: −, corr: +) between females and males.

FIGURE 7.

Summary of the stable aging‐related gender‐common, female‐specific, and male‐specific FCs according to the network domains to which the FC‐associated networks belong. The FCs that coincide with the same changing patterns are shown using the same color. (a, b, c) We show the number of FCs belonging to each within‐domain or between‐domain of each pattern for the gender‐common, female‐specific, and male‐specific FCs, respectively. In the left‐top boxes of (a), (b), and (c), we also list the overall number of FCs (and its percentage) for each changing pattern as well as the results of the overall within‐domain and between‐domain. (d) The commonality measure between females and males for each between‐domain and within‐domain for each pattern. (e) The female specificity measure for each between‐domain and within‐domain for each pattern. (f) The male specificity measure for each between‐domain and within‐domain for each pattern. In (d), (e), and (f), the measures are computed based on both n = 300 and the combination of different n. We also provide the information about which within‐domain or between‐domain has the highest measure value (listed in the left‐top boxes in d, e, and f) for both n = 300 and the combination of different n.

We further investigated 10 important FCs among the 95 stable gender‐common FCs and show their trajectories in Figure 8a. The 10 FCs had >0.5 absolute FC‐age correlations for both genders and the closer FC‐age correlations between the females and males. We found that eight of the ten FCs were associated with the CC domain, and the other two involved the AU, VI, and FP domains. For example, the positive FC between IC 22 (CC, medial superior frontal cortex) and IC 16 (CC, insula) decreased. In addition, the interaction abilities between the CC and many other domains such as DM, VI, SM, CB, and FP (in six of eight FCs) were impaired during aging. For instance, for both genders, the positive connectivity between IC 48 (CC, middle frontal gyrus) and IC 53 (DM, angular) decreased; the negative connectivity between IC 16 (CC, insula) and IC 5 (VI, occipital regions) was inhibited; and the negative connectivity between IC 46 (CC, inferior frontal gyrus, triangular part) and IC 28 (SM, precentral gyrus) was suppressed.

FIGURE 8.

The trajectories of (a) the top 10 stable gender‐common FCs, (b) the top 10 stable female‐specific FCs, and (c) the top 10 stable male‐specific FCs. The stable FCs are sorted by differences in the correlations between the two genders. For the stable gender‐common FCs, the FCs with the small difference in the correlations are taken as the important stable gender‐common FCs. For the gender‐specific FCs, we consider the FCs with a big difference as the important stable gender‐specific FCs. For each FC, we show its trajectory for females (or males) using the mean and standard deviation at each age. For each FC, we also demonstrate two functional networks and their associated domains the FC linked as well as the FC‐age correlations in females and males. The result indicates that the trajectories in females and males are similar for the gender‐common FCs but divergent for the gender‐specific FCs.

3.4. Aging‐related female‐specific FC primarily in interactions within CC and between CC and DM/VI domains

Since we already demonstrated that the female‐specific FCs were more powerful in distinguishing different age groups in females than that in males, it is reasonable to infer the unique aging part of females from them. Figure 5b shows the changing patterns of those 113 female‐specific FCs, supporting that 22 of the female‐specific FCs presented disparate changing patterns between the two genders, including eight FCs presenting the pattern of (FC: +, corr: −) in females but the pattern of (FC: +, corr: +) in males, six FCs presenting the pattern of (FC: +, corr: +) in females but the pattern of (FC: +, corr: −) in males, six FCs showing the pattern of (FC: −, corr: −) in females but the pattern of (FC: −, corr: +) in males, and two FCs showing the pattern of (FC: −, corr: +) in females but the pattern of (FC: −, corr: −) in males (see Table S7 for details). Regarding the remaining FCs that had the same changing patterns in females and males, the FC‐age correlations tended to show greater absolute values in females than in males, indicating that those FCs changed faster in females than in males along with aging progression. Furthermore, for each of the four changing patterns, the difference in the FC‐age correlations between the males and females was significant (p‐value <.01, tested by paired t tests), and the absolute mean FC‐age correlation was bigger in females than in males (Figure 5b).

Regarding the stable female‐specific FCs, we display their strengths in females and males for each changing pattern (in females) at each age using a confidence ellipse in Figure 6b (information is listed in Table S8). It is evident that regardless of any changing pattern, the confidence ellipses that correspond to the FCs from young ages to old ages move more greatly along the y‐axis than along the x‐axis, suggesting that the changes of FC strengths along aging progress were more apparent in females than in males for these stable female‐specific FCs.

Regarding the stable female‐specific FCs, we also summarized them by looking into their associated functional domains. We found that most FCs belonged to the pattern of (FC: +, corr: −), meaning that female‐specific FCs were mainly related to the suppressed positive FCs. Compared to the other two patterns of (FC: −, corr: −) and (FC: +, corr: +), the pattern of (FC: −, corr: +) included more FCs, which supports again that FC strengths were primarily suppressed along with aging (see Figure 7b). Furthermore, the female specificity was evaluated using both n = 300 and different n combined. Figure 7b,e show that the FCs that had greater female specificity were from the CC‐CC for the pattern of (FC: +, corr: −), the CC‐DM for both the pattern of (FC: +, corr: +) and the pattern of (FC: −, corr: +), and the CC‐VI for the pattern of (FC: −, corr: −).

To explore what FCs are the most unique to female brain aging, among 113 FCs, we identified the top‐10 female‐specific FCs that had >0.5 absolute FC‐age correlations in females and meanwhile had greater differences between females and males in the FC‐age correlations. Figure 8b demonstrates that these FCs played an important part in females but not necessarily in males during aging or showed fully different aging paths between females and males. For example, the positive FC between IC 38 (CC, middle frontal gyrus) and IC 30 (CC, inferior parietal lobule) decreased in females but almost was unchanged in males. The positive FC between IC 12 (CC, middle temporal gyrus) and IC 37 (DM, precuneus) increased in females but slightly decreased in males. The negative FC between IC 32 (CC, middle frontal gyrus) and IC 37 (DM, precuneus) was suppressed in females but was almost unchanged in males. The negative FC between IC 32 (CC, middle frontal gyrus) and IC 43 (VI, inferior temporal gyrus) was enhanced in females but suppressed in males. Moreover, the positive connectivity within DM (between IC 53 and IC 6) decreased in females but increased in males.

3.5. Aging‐related male‐specific FCs primary in the interaction within CC and between CC and AU/FP domains

Figure 5c shows the properties of the 101 stable male‐specific FCs. Although some FCs of them had the same changing pattern between the two genders, their FC‐age correlations presented greater absolute values in males than in females, indicating that males decline faster than females in those FCs along with aging. Among the 27 FCs that showed different changing patterns between genders, nine FCs had the pattern of (FC: −, corr: −) in females but the pattern of (FC: −, corr: +) in males, five FCs had the pattern of (FC: −, corr: +) in females but the pattern of (FC: −, corr: −) in males, eight FCs presented the pattern of (FC: +, corr: +) in females but the pattern of (FC: +, corr: −) in males, and five FCs presented the pattern of (FC: +, corr: −) in females but the pattern of (FC: +, corr: +) in males (see Table S9 for details). Moreover, there were significant differences in the FC‐age correlations between the two genders for all the four patterns, and the absolute mean correlation was bigger in males than in females for each changing pattern (Figure 5c).

Regarding each changing pattern of the male‐specific FCs, we display the FCs' strengths of both genders across different ages using confidence ellipses in Figure 6c (see details in Table S10). Figure 6c remarkably differs from Figure 6b, because those ellipses that corresponded to different ages moved more greatly along the x‐axis than along the y‐axis for each changing pattern. The results support that during the aging progress, the changes of FC strengths were more significant in males than in females for these stable male‐specific FCs.

Among the stable male‐specific FCs (see Figure 7c), we also found that FCs occupied more percentages for the two patterns of (FC: +, corr: −) and (FC: −, corr: +), compared to the other two patterns of (FC: −, corr: −) and (FC: +, corr: +), which also means that FC strengths were primarily suppressed along with aging. By evaluating the male specificity based on the male‐specific FCs, we found that the FCs that had more male specificity involved the AU‐CC for the pattern of (FC: +, corr: −), the CC‐CC for both the pattern of (FC: −, corr: −) and the pattern of (FC: +, corr: +), and the CC‐FP for the pattern of (FC: −, corr: +) (see Figure 7c,f for the results).

In Figure 8c, we further show the trajectories of 10 important stable male‐specific FCs, which had a strong FC‐age correlation (absolute correlation >0.5) in males and meanwhile had a greater gender difference in the FC‐age correlations. We found that the negative FC between IC 41 (CC, middle frontal gyrus) and IC 34 (CC, temporal gyrus) was enhanced in males but slightly suppressed in females, the negative FC between IC 16 (CC, insula) and IC 12 (CC, middle temporal gyrus) was suppressed in males but almost unchanged in females, the positive FC between IC 49 (AU, inferior temporal gyrus) and IC 32 (CC, middle frontal gyrus) decreased in males but slightly increased in females, and the negative FC between IC 29 (CC, supplemental motor area) and IC 13 (FP, middle frontal gyrus) was suppressed in males but slightly enhanced in females.

3.6. Association between age‐related FC and cognitive function

It is widely recognized that human cognitive functions frequently exhibit a decline with aging. Therefore, our investigation also focused on examining the associations between the identified aging‐related FCs and the human cognitive functions across different ages. The cognitive functions were measured by FI, NM, and RT. As shown in Figure 9a, for the gender‐common FCs, the relationship between the FC strengths and cognitive measures presented a similar trend between females and males. For the female‐specific FCs, the FC change was more relevant to the decline of all three cognitive measures for females than males (Figure 9b). In contrast, for the male‐specific FCs, the FC change was more associated with the decline of all three cognitive functions for males than females (Figure 9c). For the females and males, we also demonstrate the cognitive measures along different ages to reflect how these cognitive functions decline along with aging. It is observed in Figure 9d that the FI and NM measures decreased and the RT measure increased along with aging for both females and males, but females tended to have lower cognitive levels than males for all ages. Furthermore, the decline rates of cognitive functions along with aging were slightly greater in females than in males, probably because of the faster brain aging of females.

FIGURE 9.

Association between the stable gender‐common, female‐specific, and male‐specific FCs and human cognitive functions measured by the fluid intelligence (FI), numeric memory (NM), and reaction time (RT). In (a), (b), and (c), each plane displays the correlation values of the FC strengths and one cognitive measure, with the x‐axis (rM) representing the correlations computed using the males' data and the y‐axis (rF) representing the correlations computed using the females' data. The coloring format of each FC is as same as Figure 4, in which different colors denote different FC changing patterns. For FCs corresponding to each pattern, the mean correlation of females and the mean correlation of males are exhibited using a “×.” For the gender‐common FCs, the relationship between the FC strengths and cognitive measures presents a similar trend between females and males. For the gender‐specific FCs, the FC strength is more relevant to the cognitive measures for one gender than the other one. In (d), we show the cognitive measures along different ages (49–76 years) for the females and males separately. Regarding each cognitive measure, we show its mean and standard deviation at each age. Also, we list the gradients after the linear fitting for females (F) and males (M) separately. The gradients of the three cognitive measures are greater in females than in males, suggesting a faster decline in females.

3.7. Aging‐related brain function decline is slightly faster in females than in males

Another noteworthy finding from this study is the observation that females undergo more rapid changes in brain function compared to males as they age. This finding was supported by several factors. First, the classification accuracies in differentiating two age groups in females were slightly higher compared to males when utilizing all whole‐brain FC features. This trend was observed in both the testing set of the main data and the independent data for each classification task (Figure 3a,b). Furthermore, similar patterns were observed when summarizing the results of similar classification tasks (Figure 3c). Second, when only using the aging‐related gender‐common FCs for the classification, there was a slightly higher ability to distinguish between different age groups in the female population compared to the male population (Figure 4c), as the overall accuracy using females' data was 62.72 and 62.84% and the overall accuracy using males' data was 61.48 and 61.76%, for the main testing and the independent data, respectively. Third, there is evidence suggesting faster brain aging in females, as indicated by the higher correlation between FC strength and age in females. Figure 5 shows that for the gender‐common FCs, the average correlation with age had a slightly larger absolute value in females compared to males for three out of four changing patterns. This finding is also supported by the results of paired t tests. Fourth, our findings showed that the relationship between the gender‐common FC and cognitive measures was more pronounced in females compared to males (see Figure 9a). Additionally, as depicted in Figure 9d, both females and males exhibited cognitive function decline with age, with females showing a faster rate of decline. These results collectively offer compelling evidence for the notion that females experience a more rapid decline in brain function than males.

4. DISCUSSION

With the growing elderly population, understanding brain functional changes as well as the similarities and differences between females and males during the normal aging is crucial for developing gender‐specific preventive approaches. In this study, we utilized resting‐state fMRI data from a super large sample of 25,582 healthy participants aged 49–76 years to investigate whole‐brain FC alterations with aging, with a particular focus on identifying and validating aging‐related FCs that are common or specific to females and males. Although there have been interests in exploring brain aging (Damoiseaux, 2017; Edde et al., 2021; Jockwitz & Caspers, 2021; Zuo et al., 2017), to the best of our knowledge, this is the first attempt that investigates the relationship between females and males in aging based on deep learning using whole‐brain FC from a super large sample of data. We used a large N fMRI data to achieve effective classification and explore reliable aging‐related brain functional changes, while most previous studies worked with, respectively, small sample sizes (Campbell et al., 2013; Goldstone et al., 2016; Grady et al., 2016; Meier et al., 2012; Scheinost et al., 2015; Staffaroni et al., 2018; Stumme et al., 2020). Deep learning with a nested cross‐validation procedure was employed to maximize the generalization ability of the identified gender‐common and gender‐specific FCs, thus consistent classification performance was achieved between the test data of the main data and the independent data. Moreover, we used an explainable AI approach to automatically interpret the efficient features from the well‐trained deep learning models, which ensured that the identified FCs are significantly relevant to the aging. Different from previous work that often only considered young and old adults for statistical analysis or classification, we comprehensively investigated seven age groups for paired‐group classifications, consequently allowing us to extract FC features relating to the progressive aging. More importantly, we evaluated the relationship between FC strengths and cognitive measures, aiming to understand how changes in brain function, as measured by FC, relate to declines in cognitive function along with aging process.

Our findings underscore the gradual decline in brain function as individuals age, which aligns with our intuitive understanding of normal brain aging. This is evident from the classification accuracy, which progressively improved as the age difference between two classified groups increased. The deep learning gained the highest classification accuracy in distinguishing the youngest and the oldest groups for both females and males, and its performance decreased as the age difference became smaller. The phenomenon not only occurred for both the test data of the main data and the independent data using the whole‐brain FCs, but also was true for using the gender‐common FCs, gender‐specific FCs, and the combination of gender‐common and gender‐specific FCs. Hence, our study provides neuroimaging evidence supporting the notion that brain function undergoes gradual changes as individuals age. These changes may contribute to the gradual decline observed in various cognitive abilities from mid to late adulthood (Hoogendijk et al., 2016; Nichols et al., 2021).

We found that females and males displayed significant similarities in brain aging. There are 95 common aging‐related FCs, which were extracted from the main data and validated using independent cohorts. Different from previous studies (Campbell et al., 2013, Goldstone et al., 2016, Grady et al., 2016, Meier et al., 2012, Scheinost et al., 2015, Staffaroni et al., 2018, Stumme et al., 2020) that often only focused on FC strength, our study comprehensively investigated them by considering the FC strength, the sign of FC, and the FC‐age correlation. Specifically, we divided the gender‐common FCs into six possible changing patterns. In addition, contrary to studies that summarize FC at a general level (Goldstone et al., 2016; Scheinost et al., 2015; Stumme et al., 2020), which typically involved averaging FC values between the same two functional domains, our study analyzed brain function at a whole‐brain level and subsequently conducted a thorough evaluation of within‐ and between‐domain changes to summarize the findings. In our research, we observed consistent changing patterns and degrees in most of the gender‐common FCs. Furthermore, these FCs also displayed similar correlations with age as well as associations with cognition in both females and males. We also observed that aging predominantly diminished functional connections in both males and females, suggesting a decline in the ability of different regions to interact among the older population. Interestingly, our results revealed that diminished interactions affected by aging primarily involved the positive connectivity within the same functional domain and the negative connectivity between different functional domains. It is worth noting that our study found changes in negative FC to be a key factor in brain aging. Previous research suggests that negative FC helps maintain the balance and stability of the resting‐state brain network (Saberi et al., 2021). As the brain ages, alterations in the values and quantity of negative FC (Mijalkov et al., 2023) may disrupt this balance, leading to a decline in cognitive abilities. Furthermore, since negative FC may be directly related to cognitive function (Chai et al., 2014), these changes can have a direct impact on cognitive performance. Although previous studies have reported a reduction in within‐network FC and an increase in between‐network FC, as well as a generally less segregated network structure (Betzel et al., 2014; Geerligs et al., 2015), they typically overlooked the sign of FC and only considered only magnitudes (e.g., in modularity computation). Our work comprehensively summarized the FCs by dividing them into different patterns, thus being able to provide more information. Interestingly, we found the CC domain related to the most commonality of aging effects. Indeed, there has been mounting evidence suggesting that older adults experience cognitive decline in various aspects of CC (Lufi & Haimov, 2019; Murman, 2015). Moreover, although it is acknowledged that age‐related changes could be partially reversed through physical exercise and cognitive training due to the brain neuroplasticity (Fountain‐Zaragoza & Prakash, 2017; Lauenroth et al., 2016; Pothier et al., 2021), it is still unclear which type of training is effective in mitigating cognitive decline in older adults. In our study, we provide neuroimaging evidence that certain FCs are impaired during the aging process. This knowledge could help identify specific strategies to delay the effects of brain aging. Our study suggests that maintaining positive connectivity between the middle frontal gyrus and angular gyrus, as well as preserving the negative connectivity between the insula and occipital regions and between the inferior frontal gyrus and precentral gyrus, may help preserve psychological well‐being in both females and males.

Another significant contribution of this study is that we uncovered prominent gender differences in the process of brain aging. We identified 113 stable female‐specific FCs and 101 stable male‐specific FCs, which demonstrate the distinct impact of aging on each gender. Since the gender‐specific FCs that we identified by separately classifying females and males showed greater discriminatory ability in classifying different age groups within one gender than the other gender in the independent dataset, they can be considered as representative of the specific aging patterns in each gender. Regarding some of the gender‐specific FCs, it was observed that females and males were affected by the aging process in a totally different manner. This can be attributed to the distinct changing patterns observed in FC strength, sign, and FC‐age correlation between the two genders. In contrast, for certain gender‐specific (e.g., female‐specific) FCs, it has been observed that aging has a more pronounced effect on one gender (e.g., females), while the other gender (e.g., males) may be less susceptible to the effects of aging. This is due to the fact that the gender that is more affected (e.g., females) exhibited a stronger correlation between FC and age compared to the less affected gender (e.g., males) despite the same changing pattern. Among the stable gender‐specific FCs, more FCs came from the patterns of (FC: +, corr: −) and (FC: −, corr: +) compared to the other two patterns, again confirming that FC strengths were primarily reduced along with aging, consistent with previous findings on both healthy human (Gallen et al., 2016) and mouse brain (Egimendia et al., 2019). Surprisingly, we found many biomarkers that manifest gender‐specific brain function decline. Regarding the female specificity, the positive FC between the middle frontal gyrus and inferior parietal lobule decreased in females but was almost unchanged in males; the positive FC between the middle temporal gyrus and precuneus increased in females but slightly decreased in males; the negative FC between middle frontal gyrus and precuneus was suppressed in females but almost unchanged in males; the negative FC between middle frontal gyrus and inferior temporal gyrus was enhanced in females but suppressed in males; the positive connectivity within DM decreased in females but increased in males. Regarding male specificity, the negative FC between the middle frontal gyrus and temporal gyrus was enhanced in males but slightly suppressed in females, the negative FC between the insula and middle temporal gyrus was suppressed in males but almost unchanged in females, the positive FC between the inferior temporal gyrus and middle frontal gyrus decreased in males but slightly increased in females, and the negative FC between the supplementary motor area and middle frontal gyrus was suppressed in males but slightly enhanced in females. In our study, gender differences were primarily found within the interaction between CC networks and DM/vision/AU/FP domains. A few studies have focused on gender differences in aging, but there is not a clear consensus. A study by Goldstone (Goldstone et al., 2016) analyzed data of 20 young and 20 old adults and only found the gender difference of greater FC in the anterior cingulate cortex‐dorsal attention network in males. Utilizing 2878 participants aged from 50 to 95 years (54.1% women), Zonneveld et al. (2019) found that males showed higher within‐network FC in the FP, dorsal attention, and SM networks, and the between‐network difference was mainly in AT and SC networks. Stumme et al (Stumme et al., 2020) analyzed the FC of 772 participants (aged 55–85 years, 421 males) using graph theory and found that females showed higher within‐network FC in the DM and ventral attention networks, and males showed higher inter‐network FC in the SM network. Scheinost et al. (2015) used intrinsic connectivity distribution based on small samples (51 females and 52 males, aged 18–65 years). They found that both females and males showed decreased FC in the DM network, but females and males showed divergent trajectories in FP, sensory, subcortical, and limbic networks.

We also found that females showed a slightly faster changing trend in whole‐brain function than males along with aging. The conclusion is supported by the better classification performance in females than in males when using whole‐brain FCs or using gender‐common FCs to distinguish different age groups. Furthermore, gender‐common FCs showed higher associations with both the age and the cognitive functions in females than in males, which also indicates faster brain changes in females along with aging. In our work, even directly measured by the cognitive measures including FI, NM, and RT, the decline rate was also a little bit greater for females than males, coinciding with our conclusion that females have slightly faster brain aging decline than males. Our finding is consistent with considerable literature that shows worse performance on cognitive measures in women than in men (Lee et al., 2014; Lei et al., 2012), and is also supported by previous studies that found faster cross‐sectional FC changes with age in females (Zhang et al., 2016), although a recent work (Mijalkov et al., 2023) using multilayer network to study the sex and age relations supports a faster decline in males than females. It is also known that women have a greater prevalence of Alzheimer's disease (AD) than men (Au et al., 2017; Laws et al., 2016), which might be partly due to the gender differences in brain aging since age is a major risk factor for AD.

In this work, the identified aging‐related gender‐common and gender‐specific brain FCs were further verified by investigating the association between FCs and the cognitive measures, as it is widely acknowledged that human cognitive functions often decline along with aging. We found that the relationship between the FC strengths and cognitive measures is consistent between females and males for the gender‐common FCs, but divergent for the gender‐specific FCs. In more detail, regarding the identified gender‐common FCs, the relationship between their strengths and typical cognitive measures showed similar trends between females and males; however, regarding the identified gender‐specific FCs, the relationship between their strengths and cognitive measures was stronger in one gender than the other one. Therefore, the results validate the shared and unique decline in the brain along with aging.

There are some limitations that could be addressed in future. First, although the identified aging‐related FC features from the IG method were superior to those derived from linear correlation‐based feature selection (Figure S5), it is essential to acknowledge that interpreting deep learning models, especially in complex tasks like age classification, can be challenging. Given the variety of interpretability methods available, future work could benefit from combining different techniques or exploring alternative approaches to enhance the reliability of discriminative features contributing to age group classification. Second, to streamline the result summary and facilitate gender comparison, we only computed linear FC‐age correlations, while overlooking the intricate nonlinear associations. Since some studies have explored both linear and nonlinear trajectories of FC throughout the aging (Betzel et al., 2014; Luo et al., 2020; Ng et al., 2016), incorporating nonlinear analyses holds potential for a more comprehensive exploration. Third, similar to our previous work (Du et al., 2021), we employed the linear regression to mitigate the impact of head motion on FC measures. However, the adoption of a more sophisticated motion removal technique could enhance the validation process. Additionally, we did not consider genetic factors in our analysis. Given that studies (Li et al., 2022; Zhu et al., 2019) have indicated genetic factors may have complex influence on the FC, aging and sex, it is crucial to integrate genetic factors into future analyses to achieve a more comprehensive understanding of FC in aging. Finally, utilizing longitudinal data (Hoogendijk et al., 2016) would be preferable for studying brain aging compared to using cross‐sectional data, although there is an inherent challenge in collecting longitudinal data, particularly for participants without a history of brain or related diseases in late life.

In summary, our study pinpointed both shared and distinct brain functional changes during the normal aging between females and males. While the gender‐common and gender‐specific FCs displayed common and divergent trajectories of change between genders, it is interesting to note that the identified FCs aligned with cognitive decline in similar and unique ways. Therefore, our study enhances the understanding of complex brain aging from a neuroimaging perspective.

AUTHOR CONTRIBUTIONS

Conceptualization: Yuhui Du. Methodology: Yuhui Du. Investigation: Yuhui Du and Zhen Yuan. Writing—original draft: Yuhui Du and Zhen Yuan. Writing—review and editing: Yuhui Du, Zhen Yuan, Jing Sui, and Vince D. Calhoun.

CONFLICT OF INTEREST STATEMENT

The authors declare no competing interests.

Supporting information

DATA S1: Supporting Information.

Du, Y. , Yuan, Z. , Sui, J. , & Calhoun, V. D. (2024). Common and unique brain aging patterns between females and males quantified by large‐scale deep learning. Human Brain Mapping, 45(13), e70005. 10.1002/hbm.70005

DATA AVAILABILITY STATEMENT

We used data from the UK Biobank datasets with the agreement of project 34175 (PI: Yuhui Du) that do not allow for redistribution; however, the UK Biobank data can be accessed directly from the UK Biobank repository. All codes for the data analysis are available upon reasonable request.