Influence of individual’s age on the characteristics of brain effective connectivity

Abstract

Given the increasing number of older adults in society, there is a growing need for studies on changes in the aging brain. The aim of this research is to investigate the effective connectivity of different age groups using resting-state functional magnetic resonance imaging (fMRI) and graph theory. By examining connectivity in different age groups, a better understanding of age-related changes can be achieved. Lifespan pilot data from the Human Connectome Project (HCP) were used to examine dynamic effective connectivity (dEC) changes across different age groups. The Granger causality method with time windowing was employed to calculate dEC. After extracting graph measures, statistical analyses were performed to compare the age groups. Support vector machine and decision tree classifiers were used to classify the different age groups based on the extracted graph measures. Based on the obtained results, it can be concluded that there are significant differences in the effective connectivity among the three age groups. Statistical analyses revealed disassortativity. The global efficiency exhibited a decreasing trend, and the transitivity measure showed an increasing trend with the advancing age. The decision tree classifier showed an accuracy of $86.67\%$ with Kruskal–Wallis selected features. This study demonstrates that changes in effective connectivity across different age brackets can serve as a tool for better understanding brain function during the aging process.

Introduction

As people age, their bodies undergo a natural and inevitable process of change. One of the most noticeable changes occurs within the brain. The human brain is constantly changing throughout different life stages. These changes can affect various aspects such as physical, cognitive, psychological, social, and emotional characteristics. The mental traumas frequently arise during the early stages of childhood and adolescence [1]. As individuals grow older, the brain gradually undergoes a reduction in size, resulting in changes to cognitive performance. The process of brain shrinkage, known as cerebral atrophy, involves the loss of neurons and the connections between them. As a result, various cognitive functions such as memory, attention, and information processing may become compromised [2]. Additionally, age-related changes in the cerebrovascular system can also contribute to cognitive impairment [3]. These changes have raised significant concerns regarding the overall well-being of the aging population. To prevent the occurrence of these diseases and identify the specific brain areas involved in such disorders, it is essential to study the changes that occur in the brain from adult to old age [4, 5].

Functional magnetic resonance imaging (fMRI) is a widely used and effective technique for understanding changes in the brain [6]. By examining alterations in neural activity, fMRI enables the investigation of brain functions and their corresponding characteristics. Among its various applications, fMRI is notably employed in the study of brain connectivity [7, 8]. Brain connectivity refers to the connections, both functional and structural, between different regions of the brain. Resting-state fMRI (rs-fMRI) is a commonly used technique for studying brain connectivity [9].

A promising approach in this field is the dynamic analysis of rs-fMRI, which focuses on examining the temporal fluctuations of brain functional connectivity during resting-state scans [4]. This technique involves dividing the fMRI data into shorter time segments, or windows, and computing the connectivity between brain regions within each window. By sliding the window along the time series, dynamic changes in connectivity over time can be assessed [10, 11].

The brain can be viewed as a network consisting of various forms of connectivity. Structural connectivity (SC) provides the framework for communication between brain regions [12]. Functional connectivity (FC) measures the temporal relationship between neural activation patterns in distant brain regions [13]. Effective connectivity (EC), in contrast to functional connectivity, examines the directed flow of information between brain regions, assessing the influence one region has on others [7, 13, 14].

Recent studies have shown notable alterations in functional and effective connectivity in the human brain [4–6, 11]. The connectome, which outlines the unique characteristics of individuals, defines the network architecture of brain connections [15]. The study of the human brain as a network has become increasingly popular as it provides insights into connections and changes within the brain [16]. This network is represented as a graph, with brain regions depicted as nodes and functional or effective connectivity as edges, allowing for a methodical and comprehensive study of the brain’s structure [7].

Several studies have been conducted in recent years to analyze fMRI data in relation to the aging process [2, 4, 5, 14, 17] One particular study examined the changes in effective connectivity between different brain networks and their connection to cognitive decline during normal aging [5]. The results showed that the functioning of three key brain networks—the default mode network (DMN), the frontal-parietal network (FPN), and the sensorimotor network (SMN)—changed with aging. Specifically, a greater number of interaction paths within these networks was associated with aging and cognitive decline. This suggests the presence of a compensatory mechanism, meaning that older individuals with lower cognitive abilities require more comprehensive communication networks [5, 17].

In another study on the dynamic connectivity of the brain, researchers utilized a sliding window technique in combination with graph theory to examine the rs-fMRI networks of healthy older individuals [4]. The study collected a total of $114$ rs-fMRI patterns from subjects aged $48$ to $89$ years. The time series of regions of interest (ROIs) were divided into overlapping windows, and a Pearson correlation matrix was computed for each window. Various network properties, including average degree, average path length, clustering coefficient, and small-world, were analyzed. Notably, the joint influence of age and time on these network properties in participants aged $75$ to $79$ years exhibited a curvilinear pattern, with a decrease in network density and an increase in the small-world coefficient during the middle of the recording period.

Many studies have utilized graph analysis to analyze age-related changes in the brain [4, 18, 19]. According to the findings, there is a negative correlation between memory performance and higher local clustering in older individuals [20]. Research indicates that older adults exhibit reduced local and global efficiency in comparison to younger individuals [21]. The brain becomes less segregated and more interconnected with age [21, 22], potentially reflecting compensatory mechanisms in response to age-related neural decline [17].

In a study that employed graph theory and fMRI data, the researchers examined changes in brain functional connectivity patterns across three different age groups from the Human Connectome Project [19]. The results revealed that in the resting-state brain network, there was a decrease in global efficiency and an increase in transitivity with age. Graph measures were also utilized for classification. The best classification accuracy was achieved using a combination of Fisher score and decision tree classifier.

This study investigates the brain dynamic effective connectivity (dEC) in three distinct age groups: adolescent ($8-15$ years), adult ($25-35$ years), and middle age and senior ($45-75$ years). The analysis was conducted using data from the Human Connectome Project (HCP) lifespan pilot study, which aligns with a previous functional connectivity study on these age groups [19]. In order to examine changes within different age groups, various graph measures were extracted and used for classification. A statistical analysis followed by a classification technique was conducted to accurately classify individuals into three distinct age groups. Using this method can improve our understanding of the differences observed among various age ranges.

Materials and methods

The process of analyzing dynamic effective connectivity using graph metrics during rs-fMRI in three different age groups is illustrated in Fig. 1.

Fig. 1.

Scheme of the proposed analysis steps. (A) The fMRI images were preprocessed and along with the Automated Anatomical Labeling (AAL) atlas were inputted into the DYNAMICBC software. A total of 19 dynamic effective connectivity matrices were obtained using the Granger causality method. (B) Proportional thresholding was performed, and 16 thresholded matrices were calculated. (C) The thresholded dynamic effective connectivity matrices were binarized. (D) Local and global graph measures were extracted. (E) Feature selection was performed using the Kruskal–Wallis and Fisher scores. (F) Classification was conducted using two machine learning algorithms: support vector machine (SVM) and decision tree (DT). (G) The three age groups were classified

Subjects

This study includes three distinct age groups—adolescent, adult, and middle age and senior—with each group consisting of data from $10$ individuals. The dataset consists of $30$ fMRI data obtained from healthy individuals participating in the Human Connectome Project (HCP). Twenty-five data were collected from the HCP lifespan pilot fMRI dataset [23].

Five additional subjects were chosen from 1200 subjects of the Human Connectome Project, who were within the $25$ to $35$ years age range and had the same data registration conditions as the lifespan pilot set. This allowed us to have a total of $10$ participants in the $25$- to $35$-year-old group (Table 1). These demographic groups were discussed in the previous study [19] as follows: those aged $8-15$ were defined as children and adolescents, those aged $25-35$ were categorized as young adults, and those aged $45-75$ were classified as middle-aged and old. The data is accessible to the public at https://db.humanconnectome.org.

Table 1.

Age group profile

Age groups (HCP, gender, age)
Middle age and senior (45–75)	Adult (25–35)	Adolescent (8–15)
Pilot/F/(45–55)	Pilot/M/(25–35)	Pilot/F/(8–9)
Pilot/M/(45–55)	Pilot/M/(25–35)	Pilot/F/(8–9)
Pilot/M/(45–55)	Pilot/F/(25–35)	Pilot/M/(8–9)
Pilot/F/(45–55)	Pilot/F/(25–35)	Pilot/F/(8–9)
Pilot/M/(45–55)	Young adult/F/(25–35)	Pilot/F/(14–15)
Pilot/M/(65–75)	Young adult/F/(25–35)	Pilot/M/(14–15)
Pilot/M/(65–75)	Young adult/F/(25–35)	Pilot/F/(14–15)
Pilot/F/(65–75)	Young adult/F/(25–35)	Pilot/F/(14–15)
Pilot/F/(65–75)	Young adult/F/(25–35)	Pilot/F/(14–15)
Pilot/M/(65–75)	Young adult/F/(25–35)	Pilot/F/(14–15)

Data acquisition

The lifespan pilot HCP data was collected using a $3$ Tesla Siemens Connectome MRI scanner at Washington University. The rs-fMRI had a voxel resolution of $2\times 2\times 2$ ${\text{mm}}^3$, a flip angle of $52$°, a multi-band factor of $8,$ a field of view of $810\times 936$ ${\text{mm}}^2$, and $72$ slices. Each run consisted of $420$ frames with a repetition time (TR) of $0.72$ s and an echo time of $33.2$ ms.

Preprocessing step

The HCP fMRI data underwent analysis using the FEAT fMRI analysis option on the FSL (FMRIB’s Software Library, www.fmrib.ox.ac.uk/fsl) toolbox [24, 25]. The preprocessing of the images involved several steps, including motion correction using MCFLIRT, spatial smoothing using a Gaussian filter with a full width at half maximum (FWHM) of 5.0 ${\text{mm}}^3$, high-pass temporal filtering, non-brain elimination using the brain extraction tool (BET), and alignment to the MNI space using FLIRT.

Anatomical parcellation

In order to examine each subject, the brain was divided into $116$ specific regions of interest (ROIs) using an automated anatomical labeling (AAL) atlas [26]. This atlas covers both cortical and subcortical regions numbered $1$ to $90$, as well as cerebellar regions numbered $91$ to $116$.

Dynamic effective connectivity (dEC))

Graph theory can be employed to examine brain networks. The initial step entails creating a graph that symbolizes the underlying brain network, comprising brain areas (nodes) and the connections (edges) between them. These edges can be binary (indicating the presence or absence of a connection), weighted (representing the strength of the connection), or directed (showing the direction of information transfer), depending on the research question [7, 27]. This method provides insights into the functioning and arrangement of brain regions, as well as how alterations in brain networks may associate with various neurological conditions.

In this study, the DynamicBC technique (Dynamic Brain Connectome, available at http://www.restfmri.net/forum/DynamicBC) was utilized to establish the adjacency matrix, which serves as a mathematical representation of the brain connectivity among different regions over time [10, 11, 28]. The method involves dividing fMRI data into short time windows and examining connectivity patterns between brain regions within each window. Unlike traditional approaches that assume a constant strength of connections between different brain regions, DynamicBC can identify temporary patterns of connectivity that change over time. Based on numerous studies, the optimal time period for assessing the dynamic relationship between regions is typically between $30$ and $60$ s [4, 29]. As a result, we decided to use a sliding window length of $50$ TR [10]. Following this approach, a total of $19$ windows were generated.

In order to obtain directed graphs of connectivity, several measures, such as Granger causality [30] or dynamic causal modelling (DCM) [31], are available. These measures produce asymmetric matrices that represent the effective connectivity (EC) of the brain and include information on the causal influence of one region over another. Granger causality analysis is applied to determine which brain regions influence changes in the activity of other regions throughout the time duration. It is commonly used in the analysis of fMRI data using vector autoregression [32]. Equations $(1)$ and $(2)$ represent this method, where $Y(t)$ and $X(t)$ are two time series, $A_{\text{k}}$ and ${\acute{A}}_{\text{k}}$ are signed-path coefficients, $B_{\text{k}}$ and ${\acute{B}}_{\text{k}}$ are autoregression coefficients, $E\left(t\right)$ and $\acute{E}\left(t\right)$ are residuals, and $Z\left(t\right)$ represents covariates (e.g., other factors).

$$\text{Y}\left(t\right)={\sum }_{k=1}^p{\text{A}}_{\text{k}}\text{X}\left(t,-,k\right)+{\sum }_{k=1}^p{B}_{\text{k}}\text{Y}\left(t,-,k\right)+CZ\left(t\right)+E\left(t\right))$$ 1

$$\text{X}\left(t\right)={\sum }_{k=1}^p{\acute{A}}_k\text{Y}\left(t,-,k\right)+{\sum }_{k=1}^p{\acute{B}}_k\text{X}\left(t,-,k\right)+\acute{C}Z\left(t\right)+\acute{E}\left(t\right)$$ 2

It is based on the idea that if one time series (e.g., the activity in one brain region) can predict changes in another time series (e.g., the activity in another brain region), then the former time series is said to “Granger-cause” the latter [32]. The resulting connectivity matrices for each time window can thereafter be utilized to create an adjacency matrix, effectively representing the strength and direction of connections between all pairs of brain regions throughout the entirety of the data. This study aimed to determine the level of Granger causal influence between the region of interest (ROI) and all voxels across the entire brain, within each sliding window. As a result, $19$ dynamic effective connectivity (dEC) matrices were formed for each individual.

Matrices thresholding

To compute the graph measures, the proportional thresholding (PTh) technique was employed. This method involved filtering the connectivity matrix to remove any irrelevant and noisy information [19, 33, 34]. In order to accomplish this, the connectivity (dEC) matrices were thresholded by selecting a certain proportion of the strongest connections. For this study, the PTh method was used to create threshold matrices ranging from $0.04$ to $0.34$, with an increment of $0.02$. This range was selected to achieve a balance between sparsity and density in the resulting graph. Each thresholded connectivity matrix was then converted into a binary format, where nonzero elements were represented as $1$ and zeros as $0$. The application of this method generated a set of $16$ binary thresholded matrices, within each time window. Graph theory measures were then extracted from these binary connectivity matrices for each individual subject.

Graph-theoretical measures

Once the adjacency matrices were constructed, the commonly utilized global and local graph measures were computed for each binary network in order to compare three distinct age groups. The Brain Connectivity Toolbox (BCT) was utilized to extract various measures and characteristics related to brain networks [16]. Segregation measures such as transitivity and clustering coefficient were obtained to examine the brain’s tendency to form specialized, independent subunits. Integration measures, namely global efficiency and flow coefficient, were derived to assess how well these subunits are interconnected for effective information processing. Additionally, local graph measures and assortativity coefficient were calculated to identify regional differences between various age groups.

Degree refers to the total connections that a node possesses in the brain [27]. A node with a high degree is extensively linked, which implies its significance in transmitting and processing information within the network. The in-degree and out-degree specifically target the direction of connections. The in-degree denotes the quantity of connections a node receives from other nodes, whereas the out-degree signifies the quantity of connections a node sends to other nodes [33]. Betweenness centrality measures the importance or centrality of a node within a network [35]. It quantifies how often a particular node acts as a bridge connecting other nodes in the network.

The flow coefficient is an essential metric for evaluating the capacity of individual nodes (local flow coefficient) and the overall network (global flow coefficient) in facilitating the transmission of information. The global flow coefficient is calculated by averaging the local flow coefficients of all the nodes in the network [33, 36, 37]. Global efficiency refers to how efficiently information flows between different brain regions [38]. It is measured by the shortest path length between any two regions in the network. On the other hand, local efficiency describes how effectively information can be transmitted within the immediate area surrounding a node, enabling efficient information processing within the network while maintaining segregation [7, 16].

Clustering coefficient calculates the proportion of connections between a node’s nearest neighbors out of all possible connections [27]. A high clustering coefficient suggests localized segregation. The participation coefficient determines if a node’s connections tend to cluster within a single module or bridge different specialized modules [39]. PageRank, as a measure of centrality, can be applied to explore the functional organization of the brain, uncovering patterns of neural activity and identifying key regions that play crucial roles in information processing [33–40]. Transitivity is a metric that determines the percentage of node triangles in a network, where higher values suggest a higher level of segregation [41]. It represents the network’s tendency to separate into distinct groups. Assortativity assesses the tendency of networks to include nodes that connect with other similar nodes, ranging from $-1$ to $1$ [42]. This metric is used to evaluate the resilience of a network, which refers to its capacity to withstand disruptions and attacks.

Statistical analysis of graph measures

Once the brain network measures have been extracted, it is important to identify the measures that vary among groups. The goal is to perform a significance test on the groups in order to ascertain whether the observed differences in the extracted measurements are statistically significant or simply a result of random chance. The Kruskal–Wallis test [43], a non-parametric method, was employed to examine the significant variations among three different age groups.

To decrease the number of false positive results in multiple hypothesis testing, a statistical technique called FDR (false discovery rate) correction was applied [44]. Multiple hypothesis testing is commonly conducted when investigating discrepancies in brain activity or connectivity between various groups or conditions [45]. Graph measures that showed P-values below a significance level of $0.05$ were identified.

Feature ranking and classification

The metrics derived from graphs can serve as features in machine learning models to distinguish between different age groups. Two methods were employed to rank the acquired graph measures. The first method involved utilizing the Kruskal–Wallis statistical test [46] to sort the features in ascending order based on their P-values. The features with the lowest P-values were then selected for the feature selection process.

In the second method, Fisher score [33, 46, 47] was used to identify the features that exhibited the strongest discrimination power across groups. Fisher score can be calculated using the following expression:

$$\text{fisher}-\text{score}=\frac{{\sum }_{i=1}^c{n}_{\text{i}}{(m_{\text{i}}-m)}^2}{{\sum }_{i=1}^c{n}_{\text{i}}{{\sigma }_{\text{i}}}^2}$$ 3

Here, $m$ and $\sigma$ represent the mean and standard deviation of the entire dataset, while $m_i$ and ${\sigma }_i$ represent the mean and standard deviation of the features within each class. Additionally, $c$ refers to the number of classes, $i$ denotes the label of each class, and $n_i$ signifies the number of subjects in class $i$. A larger Fisher score indicates a greater ability to differentiate between classes.

In this study, classification methods such as support vector machine (SVM) [33, 46, 47] and decision tree (DT) [46] were utilized to classify the mentioned three age groups. The “Leave one subject out” cross-validation method was employed to assess the performance of the machine learning model. This approach involves training the model on all data except for one subject, evaluating the model’s performance on the omitted subject, and repeating this process for all subjects [48]. The average performance across all subjects is then reported. The classification was performed on an individual measure as well as the combination of measures.

Statistical analysis of dynamic effective connectivity

In order to gain a deeper understanding of the age-related changes in the dynamic effective connectivity within the brain, in this section, the 19 dEC matrices that were formed for each individual were analyzed. Statistical analyses were performed using the Kruskal-Wallis test to identify any significant variations among the three different age groups. To address the issue of false positive results, the FDR correction technique was applied.

Graph measures across age groups: examining the influence of gender

The statistical analysis can be influenced by various factors. This section concentrates on gender as a variable that may affect the results. The sample is divided into three age categories: adolescent, adult, and middle-age/senior, with 10 individuals in each group. The gender distribution includes 20 female and 10 male participants. ANCOVA (analysis of covariance) is used to analyze the local graph measures.

In the analysis, gender is treated as an independent variable, while the age groups are the dependent variables. ANCOVA allows for the examination of the relationship, while controlling for any potential confounding variables. This statistical approach provides a more robust and comprehensive understanding of the factors influencing the observed differences.

Result

The BCT toolbox was employed to extract graph metrics from brain data, enabling the examination of the brain’s segregation and integration measures, as well as regional variations between different age groups. The first two sections present the findings of an investigation into dEC in different age groups, using graph metrics during rs-fMRI. The initial section will focus on the results of the statistical analysis conducted on dEC. The second part will detail the outcomes of the classification analysis.

In the third section, the statistical analysis of dEC for three age groups will be presented to identify age-related differences. Finally, in the last part, the differences in local graph measures will be presented to identify variations between age groups, considering the effect of gender.

Statistical analysis results

To examine the significant differences in global and local measures among the three age groups, the Kruskal–Wallis test was utilized, with the false discovery rate (FDR) applied as a correction method. The findings of the statistical analysis were categorized into two sections: global graph measures and local graph measures.

Statistical evaluation of global measures

In this study, the assortativity coefficient was found to be the most statistically significant global measure. It was found that there was no significant difference in the global flow coefficient measure across the three age groups. The assortativity coefficient was found to be significant in more than half of the time windows (lowest P-value was $P=0.0013\text{at TH}=15,\text{TW}=12[221-270]$). Figure 2 illustrates the significant values of this measure for the fifth window ($81-130$), which had the highest number of significant P-values across all thresholds.

Fig. 2.

Changes in the assortativity coefficient within the time window (TW) with the most significant P-values at thresholds of 4 to 34% in different age groups. The adolescent group (represented in red), the adult group (represented in green), and the middle age-senior group (represented in blue)

By analyzing different time windows, it was observed that global efficiency tends to decrease with age (lowest P-value was $P=0.002\text{at TH}=3,\text{TW}=14[261-310]$). For instance, in window $14$ ($261-310$), which had the highest number of significant P-values across all thresholds, the highest global efficiency was observed in the adolescent group, followed by a decrease in the adult group, and the lowest value was observed in the middle age and senior group.

The analysis revealed that the transitivity measure in the time window number $8$ ($141-190$) had the highest number of significant values across most thresholds. The lowest P-value was $0.0046$, observed at a threshold of $13$ and a time window of $3[41-90]$. Transitivity was lowest in the adolescent group, with an increase observed in the adult group and a slight additional increase in the middle-aged and senior group. This suggests that transitivity tends to rise with age.

Statistical evaluation of local measures

The results of the statistical analysis using the Kruskal–Wallis test on local graph measures are presented here. These measures were calculated for $116$ brain regions identified from the AAL atlas. It is essential to examine local graph measures, as the interconnections between brain regions are crucial in understanding age-related and disease-related changes.

Statistical analysis results on local graph measures in $116$ regions of the AAL atlas are presented in Table 2. Table 2 outlines the lowest significant P-value (FDR-corrected), the corresponding brain region, the threshold (TH), and the time window (TW) for each local graph measure. These findings identify the brain regions that have been localized on more than half of the thresholded matrices (thresholded matrices from $4$ to $34\text{\%}$ of strongest connections). The threshold percentage (TH%) represents the percentage of all evaluated thresholds that have demonstrated statistically significant results for the specified local measure, area, and TW. The comparison between some local measures, between three different groups, is shown in Fig. 3.

Table 2.

Statistical analysis results on local graph measures in 116 regions of the AAL atlas (FDR-corrected)

TH %	TW	TH	P-value	AAL area	Local measures
100	[101–150]	0.12	< 0.0009	Frontal_Med_Orb_R	In-degree
100	[101–150]	0.04	< 0.0005	Putamen_R	Out-degree
93.75	[181–230]	0.32	< 0.0002	Frontal_Med_Orb_R	Sum-degree
81.25	[21–70]	0.04	< 0.0001	Precuneus_L	Betweenness centrality
62.50	[121–170]	0.20	< 0.0003	SupraMarginal_R	Flow coefficient
81.25	[41–90]	0.30	< 0.0002	Thalamus_L	Local efficiency
75	[221–270]	0.24	< 0.0003	Vermis_4_5	Clustering coefficient
81.25	[121–170]	0.26	< 0.0005	Putamen_L	Page-rank centrality
68.75	[121–170]	0.12	< 0.0009	Putamen_R	Participation coefficient

Fig. 3.

Group comparison of the local measures. Significant P-values from Kruskal–Wallis are indicated

The most frequently observed brain regions with significant differences among age groups in local graph measures include the right and left putamen ($PUT.R\&PUT.L$), left superior frontal gyrus/dorsolateral ($SFGdor.L$), left superior frontal gyrus/medial ($SFGmed.L$), right superior frontal gyrus/medial orbital ($ORBsupmed.R$), left paracentral lobule ($PCL.L$), left precuneus ($PCUN.L$), right calcarine $(CAL.R)$, vermis lobule $IV/V$ ($vermis45$), vermis lobule $\mathit{III}$ ($vermis3$), vermis lobule $\mathit{VII}$ ($vermis7$), and right cerebellum lobule $\mathit{VIIb}$ ($CRBL7b.R$) from the AAL atlas. Figure 4 shows the brain regions that exhibit the most statistically significant differences in local graph measures across different age groups.

Fig. 4.

Brain regions with significant differences in local graph measures between the three age groups (A, B and C indicate different brain views)

Network measures’ classification results

The Kruskal–Wallis test and Fisher score were utilized for feature selection in order to identify the best measures. Classification was carried out using SVM and DT algorithms. The accuracy of the best model is presented in this section.

Classification on the set of local measures

In terms of the classification of local measures, Table 3 displays the highest accuracy, best graph measures, and most common brain regions within the respective TW and TH. The machine learning classification on the set of local measures indicated that the DT achieved the highest accuracy of $86.67\%$ by employing the top seven features selected through the Fisher score and the Kruskal–Wallis test. On the other hand, the SVM algorithm achieved an accuracy of $73.33\%$ using the top seven features selected through the Kruskal–Wallis test.

Table 3.

Classification results

Classifier	Feature selection	Best accuracy	TW	TH	Best measures	Best area
DT	Kruskal–Wallis	86.67%	[21, 70]	0.04	Clustering coefficient, participation coefficient	Precuneus_L Heschl_L
	Fisher score	86.67%	[21, 70]	0.04	Clustering coefficient, participation coefficient	Precuneus_L Rectus_L
SVM	Kruskal–Wallis	73.33%	[281, 330]	0.1	In-degree, total-degree, page-rank centrality, betweenness centrality, local flow coefficient	Postcentral_R Frontal_Sup_L FrontI_Sup_MedL_L SupraMarginal_L Frontal_Inf_Orb_R
	Fisher score	70%	[281, 330]	0.3	Local flow coefficient	Cerebelm_Crus2_R

In Figs. 5 and 6, the highest accuracy for each classifier is depicted in relation to the number of features selected within the optimal TW and TH. The highest accuracy achieved for each classifier was obtained by selecting the top seven features through feature selection.

Fig. 5.

The highest accuracy obtained from SVM classifier with feature selection using A Kruskal–Wallis test and B Fisher score

Fig. 6.

The highest accuracy obtained from DT classifier with feature selection using A Kruskal–Wallis test and B fisher score

Based on the information provided in Table 3, the DT classifier, utilizing both the Kruskal–Wallis test and Fisher score for feature selection, achieved an accuracy of $86.67\%$ during the second TW and first TH. However, as illustrated in Fig. 6, the DT classifier incorporating the Kruskal–Wallis test for feature selection demonstrated better performance when selecting a larger number of features and overall appeared to be more suitable.

The most commonly used graph measures in the feature selection process for both classifiers and feature selection methods were degree, betweenness centrality, flow coefficient, and clustering coefficient. These measures had discriminative ability in the age group classification. The brain regions that were most commonly involved in this process were left superior frontal gyrus/dorsolateral ($SFGdor.L$), right superior frontal gyrus/medial orbital ($ORBsupmed.R$), right calcarine $(CAL.R)$, the right and left putamen ($PUT.R\&PUT.L$), vermis lobule $\mathit{III}$ ($vermis3$), and vermis lobule $IV/V$ ($vermis45$). Figure 7 shows these frequent brain regions in the feature selection process for classifying age groups based on the AAL atlas.

Fig. 7.

Most frequent brain regions in the decision-making process (A, B and C indicate different brain views)

To evaluate the results of classifying different age groups, a confusion matrix for DT classifier with the Kruskal–Wallis test in the best TW $[\text{21,70}]$ and the best TH $(0.04)$ is illustrated in Table 4. In this table, $C1$ represents the adolescent group, $C2$ the adult group, and $C3$ the middle age and senior group. The rows of the confusion matrix contain the true known values, while the columns contain the predicted values. For identifying values related to each group, class $1$ has correctly identified labels at $90\%$, class $2$ at $66\%$, and class $3$ at $73\%$. In identifying values corresponding to classes $2$ and $3$, class $1$ has never made a misidentification, whereas misclassifications occurred between groups $2$ and $3$. In other words, the identification of group $1$, meaning the adolescent group, has been well executed and distinguished from the other groups.

Table 4.

Confusion matrix for DT classifier with Kruskal–Wallis feature selection method in the best TW and TH

	Predicted
		C1	C2	C3
Actual	C1	0.9	0.085	0.015
	C2	0	0.66	0.34
	C3	0	0.27	0.73

Considering the higher accuracy of the DT classifier with the Kruskal–Wallis test in the second TW $[\text{21,70}]$ and the first TH $(0.04)$, the sensitivity, specificity, accuracy, and precision metrics for this classifier are plotted in Fig. 8. As can be observed, for adolescent (blue graph), the best results have been obtained across various feature selections, indicating a higher discriminative power. The adults, however, have relatively weaker results compared to the other two classes.

Fig. 8.

Sensitivity analysis, specificity, accuracy, and precision for DT Classifier with Kruskal–Wallis feature selection method in the best TW [21, 70] and the best TH (0.04)

Classification with single local measures

In this section, we aimed to analyze and identify the most effective measures and distinct regions among various age groups. For this purpose, each set of local measure was individually presented to the DT classifier. Since the DT classifier exhibited the best classification outcomes in the previous section using the local measure set, it was employed to evaluate the classification results for each local measure. The results of the DT classifier, which utilized feature selection techniques such as the Kruskal–Wallis test and Fisher score, are presented in Table 5.

Table 5.

Classification results for each local measure

Decision tree		Local measures
Kruskal–Wallis	Fisher score
80% (TH = 0.34, TW = [221, 270])	80% (TH = 0.34, TW = [221, 270])	In-degree
83.33% (TH = 0.1, TW = [221, 270])	76.67% (TH = 0.3, TW = [121, 170])	Out-degree
76.67% (TH = 0.04, TW = [361, 410])	76.67% (TH = 0.04, TW = [361, 410])	Total-degree
86.67% (TH = 0.12, TW = [261, 310])	83.33% (TH = 0.12, TW = [261, 310])	Betweenness centrality
80% (TH = 0.24, TW = [81, 130])	76.67% (TH = 0.18, TW = [81, 130])	Local flow coefficient
73.33% (TH = 0.08, TW = [361, 410])	76.67% (TH = 0.04, TW = [41, 90])	Local efficiency
76.67% (TH = 0.3, TW = [41, 90])	80% (TH = 0.3, TW = [41, 90])	Clustering coefficient
76.67% (TH = 0.26, TW = [321, 370])	76.67% (TH = 0.26, TW = [341, 390])	Page-rank centrality
73.33% (TH = 0.06, TW = [341, 390])	76.67% (TH = 0.06, TW = [341, 390])	Participation coefficient

The betweenness centrality measure achieved the best accuracy of $86.67\%$ when the DT classifier with the Kruskal–Wallis feature selection technique was used. Additionally, graph measures such as degree, betweenness centrality, flow coefficient, and clustering coefficient displayed the best accuracy in distinguishing and differentiating among age groups using the DT classifier.

Statistical evaluation of dynamic effective connectivity findings

To investigate the interactions between different brain regions, the statistical analysis aimed to examine age-related differences in the dynamic effective connectivity within the brain network. The Kruskal–Wallis test was used to identify any significant variations among the three age groups under investigation.

The results are summarized in Table 6, which presents the brain regions that showed the most repetition within each time window ($19TW$), the connections those regions had with other regions, and the associated P-values. This provides the key brain areas and their interactions that exhibit age-related differences. Figure 9 provides a visualization of the significant regions and their connections. The nodes represent the significant brain regions, while the edges depict the connections between them.

Table 6.

Statistical analysis of dEC across 116 regions of the AAL atlas (FDR-corrected)

P-value	Significant connections	Rep	AAL area	TW
0.003	Cerebellum-10-L $\to$ Occipital_Sup_R	21	Cerebellum-10-L	1
0.0003	Fusiform_R $\to$ Temporal_Mid_L	18	Fusiform_R	2
0.0002	Fusiform_R $\to$ Temporal_Mid_L	25	Fusiform_R	3
0.003	Vermis-4–5 $\to$ Frontal_Inf_Orb_R	23	Vermis-4–5	4
0.0006	Putamen_R $\to$ Frontal_Mid_L	37	Putamen_R	5
0.0007	Putamen_R $\to$ Vermis-4–5	24	Putamen_R	6
0.002	Amygdala_R $\to$ Temporal_Sup_R	24	Amygdala_R	7
0.01	Insula_L $\to$ Rolandic_Oper_R	17	Insula_L	8
0.009	SupraMarginal_L $\to$ Temporal_Inf_L	13	SupraMarginal_L	9
0.004	Frontal_Med_Orb_R $\to$ Postcentral_R	17	Frontal_Med_Orb_R	10
0.001	Vermis-3 $\to$ Cerebellum-Crus2-R	23	Vermis-3	11
0.0005	Vermis-1–2 $\to$ Cerebellum-Crus2-L	29	Vermis-1–2	12
0.003	Heschl_L $\to$ Temporal_Inf_R	24	Heschl_L	13
0.0001	Amygdala_L $\to$ Cerebellum-Crus2-L	27	Amygdala_L	14
0.0006	Frontal_Mid_Orb_R $\to$ 51	34	Frontal_Mid_Orb_R	15
0.002	Olfactory_L $\to$ Cerebellum-Crus2-L	24	Olfactory_L	16
0.004	Frontal_Inf_Tri_L $\to$ Cuneus_R	20	Frontal_Inf_Tri_L	17
0.001	Heschl_L $\to$ Temporal_Sup_R	24	Heschl_L	18
0.0006	Cerebellum-10-L $\to$ Frontal_Mid_L	26	Cerebellum-10-L	19

Fig. 9.

Brain regions and their connections with significant differences in dynamic effective connectivity between the three age groups. A Inner and inter-hemispheric connectivity and B inter-hemispheric connectivity

Analysis of graph measures across age groups: the impact of gender

The observed patterns in the statistical findings were influenced by factors such as gender and specific brain regions. In this section, the focus is on examining the potential influence of gender as a covariate in the age analysis.

Table 7 presents the key results of the ANCOVA analysis for each local graph measure. This includes the lowest significant P-value (FDR-corrected), the corresponding brain region, the threshold (TH), the time window (TW), the F-statistic (F), and the effect size (partial eta-squared). These findings identify the brain regions that have been localized on more than half of the thresholded matrices (ranging from $4$ to $34\%$ of the strongest connections). The degree of freedom (df) for the total model is $29$.

Table 7.

Age-dependent trends in local graph measures (df = 29, FDR-corrected)

Effect size	F	P-value	TW	TH	AAL area	Local measures
0.452	11.15	$2.9e^{-4}$	[101–150]	0.16	Frontal_Med_Orb_R	In-degree
0.547	16.29	$2.2e^{-5}$	[221–270]	0.04	Pallidum_L	Out-degree
0.485	12.72	$1.2e^{-4}$	[361–410]	0.04	Frontal_Sup_L	Sum-degree
0.486	12.76	$1.2e^{-4}$	[21–70]	0.04	Precuneus_L	Betweenness centrality
0.510	14.10	$6.4e^{-5}$	[161–210]	0.08	Cingulum_Post_R	Flow coefficient
0.488	12.87	$1.1e^{-4}$	[101–150]	0.20	Frontal_Sup_Medial_R	Local efficiency
0.495	13.26	$9.7e^{-5}$	[361–410]	0.34	Heschl_L	Clustering coefficient
0.546	16.24	$2.3e^{-5}$	[221–270]	0.22	Pallidum_L	Page-rank centrality
0.513	14.23	$6.1e^{-5}$	[121–170]	0.12	Putamen_R	Participation coefficient

The ANCOVA analysis allowed us to statistically control for the potential confounding effects of gender on the relationship between age and the local graph measures. By including gender as a covariate, we were able to isolate the unique effects of age, above and beyond any gender-related differences.

Discussion

This study aimed to investigate age-related changes in brain dynamic effective connectivity using graph theory and machine learning techniques applied to rs-fMRI data. The research approach was similar to a previous study that examined functional connectivity in the same dataset [19]. Graph measures were calculated from all subjects, and a statistical analysis was performed. This research employed machine learning techniques to differentiate between three distinct age groups. The selection of relevant features was done through a Kruskal–Wallis test and Fisher score. The classification methods used in this study showed acceptable accuracy results, indicating that the approach employed for selecting appropriate measures was successful.

The Kruskal–Wallis test was used to examine the statistical significance of the global graph measures across different age groups. Among the different global measures, the assortativity coefficient exhibited a significant distinction among the three age groups. However, in the previous study, which examined functional connectivity, this measure was not significant and did not differ across any of the proportional thresholds [19]. Studies conducted on the assortativity coefficient measure in biological networks have revealed a significant trend towards disassortativity [49, 50]. This indicates that nodes in these networks tend to be more connected to dissimilar node. Such characteristics are crucial for biological systems, ensuring adaptability, resilience, and robustness against various perturbations [51]. In this study, this characteristic can be clearly identified in three distinct age groups. It also suggests that the network displays disassortativity during the observed time periods.

Two other global measures that have shown significant values in statistical analysis are the global efficiency and transitivity measures. These two graph measures are consistent with the findings of previous functional connectivity study [19]. Global efficiency assesses how well information is integrated throughout all regions of the brain and is linked to the ability to quickly exchange information among different regions [38, 52]. Higher values of this characteristic indicate a higher level of efficiency. Several studies have indicated that as individuals grow older, there is a decline in global efficiency when compared to younger participants [53, 54]. However, other studies do not reference any alteration in global efficiency [52]. Additionally, studies have indicated that in healthy adults, processing speed, visual-spatial ability, and executive task performance show a positive correlation with both local and global efficiency measurements [55]. A validated biomarker for identifying dementia in patients with age-related mild cognitive impairment is a proven indicator of reduced global efficiency [56].

Transitivity serves as an indicator of segregation within the brain, with higher values reflecting a greater level of specialization [54]. The analysis revealed a correlation between age and this characteristic, showing a gradual increase as individuals grow older. These findings align with previous studies, which have shown that a decrease in transitivity is linked to improved memory performance [54].

In the majority of the local graph measures, significant differences were observed among age groups. The statistical analysis revealed that the local graph measures outperformed the global measures. Measures like betweenness centrality, local efficiency, participation coefficient, and clustering coefficient displayed significant differences among the three age groups. The study on healthy elderly has revealed a significant reduction in network topology measures such as local efficiency, global efficiency, betweenness centrality, and clustering coefficient, during various cognitive states [51]. Research has shown that as individuals age, there is a decrease in clustering coefficients, which suggests a decrease in local processing efficiency [57]. The participation coefficient in aging brain connectivity has been observed to increase, indicating a shift towards more distributed and less specialized functional network organization [2, 58].

Brain regions, including the right and left putamen ($PUT.R\&PUT.L$), left superior frontal gyrus/dorsolateral ($SFGdor.L$), left superior frontal gyrus/medial ($SFGmed.L$), right superior frontal gyrus/medial orbital ($ORBsupmed.R$), left paracentral lobule ($PCL.L$), left precuneus ($PCUN.L$), right calcarine $(CAL.R)$, vermis lobule $IV/V$ ($vermis45$), vermis lobule $\mathit{III}$ ($vermis3$), vermis lobule $\mathit{VII}$ ($vermis7$), and right cerebellum lobule $\mathit{VIIb}$ ($CRBL7b.R$) from the AAL atlas, have exhibited significant differences in most graph measures between study groups.

The putamen plays an important role in various functions, including learning, motor control, reward processing, and cognitive functioning [59]. Research has identified putaminal dysfunctions in several neurological and psychiatric disorders, such as Parkinson’s disease, Alzheimer’s disease, and depression [37, 59]. These findings suggest that the integrity and proper functioning of the putamen are essential for maintaining healthy motor, cognitive, and behavioral processes. Studies have shown age-related differences in the functioning of the putamen. In one study, putamen integration increased with age in males but not in females [60]. Another study found that older adults exhibited reduced neural activity in the right putamen compared to younger individuals. This suggests age-related differences in proprioceptive processing, and the structural differences in the right putamen may serve as a biomarker for proprioceptive sensibility [61].

The frontal lobes, especially the right frontal lobe, are crucial for working memory function. Research has indicated that a decrease in the cortical surface area of the right superior frontal gyrus, the inferior frontal gyrus (pars opercularis), and the medial orbital frontal gyrus is associated with age-related decline in working memory performance [62]. The superior frontal gyrus (SFG) is a large region of the prefrontal cortex. The medial superior frontal gyrus (SFGmed) has been shown to be affected by normal brain aging in previous studies [63, 64]. Additionally, study has shown the importance of the left dorsolateral prefrontal cortex (DLPFC) in inductive reasoning in both normal aging individuals and those with mild cognitive impairment (MCI), highlighting the role of the DLPFC in cognitive processes across the aging spectrum [65]. A recent study employing functional near-infrared spectroscopy (fNIRS) has revealed that as individuals age, there is a notable increase in functional connectivity within the frontal cortex [3]. This finding suggests that disruptions in the coordination between neural activity and vascular responses may underlie the cognitive decline often observed in older adults. The study proposes that frontal brain networks compensate for the impaired neurovascular coupling responses by recruiting additional functional connections, potentially as a means to maintain cognitive function in the face of age-related changes [3]. Similar compensatory mechanisms have been documented in other research, where increases in connectivity strength were found to offset losses in structural connectivity, enabling the preservation of healthy cognition [66].

The paracentral lobule is responsible for coordinating both sensory and motor functions. Research indicates that this brain region is also involved in executive control processes [67]. Research has shown that the precuneus is a major cortical hub that undergoes changes with normal aging, impacting verbal fluency processing [68]. Aging-related alterations in white matter integrity are associated with changes in functional connectivity density in hub regions, including the precuneus, suggesting compensatory mechanisms in neurocognitive aging [69]. The calcarine, a region located in the occipital lobe of the brain, is essential for visual processing. A study on healthy participants across various age groups indicates that functional connectivity within visual networks demonstrates changes over the lifespan. This research finds that local functional connectivity in the right calcarine decreases with aging [70].

The cerebellum is primarily responsible for coordinating voluntary movements and maintaining balance [71–73]. As people grow older, the cerebellum undergoes structural changes, particularly a reduction in grey matter [71]. Studies have highlighted the significant role of the cerebellum in age-related brain connectivity and volumetric differences. Specifically, the right cerebellum has shown a high degree of functional connectivity change with age [72]. Additionally, the anterior lobe of the cerebellum, which is mainly concerned with motor control function, has exhibited age-related volumetric differences in lobules $\mathit{III}$, $V$, and $\mathit{IX}$ (bilaterally) and $\mathit{IV}$, $\mathit{VI}$, and $\mathit{VIIb}$ (unilaterally). The posterior part of the cerebellum also demonstrated age-related volumetric changes in Crus $\mathit{II}$ and $\mathit{VIIb}$ (bilaterally) [71]. The cerebellar vermis is associated with affective or emotional processing [73]. Previous research has also revealed distinct volumetric patterns in the anterior cerebellum/vermis and posterior cerebellum. The anterior cerebellum and vermis exhibit a logarithmic trajectory, where volumes are largest during adolescence and undergo a rapid decline in early adulthood [74].

A further goal of this research was to identify distinctions among age groups by examining relevant graph measures. We applied machine learning methods to evaluate the effectiveness of these measures in differentiating the three groups. The highest classification performance achieved was an accuracy of $86.67\text{\%}$, obtained by applying the Kruskal–Wallis feature selection and a DT classifier. This outcome suggests that this approach could prove valuable for distinguishing between age groups using graph measures. The discriminative measures for age group classification were the local graph measures of degree [4], betweenness centrality, flow coefficient, and clustering coefficient [4, 75].

The ability of each individual local measure to distinguish between the three age groups was also analyzed. This was done to explore the discriminatory potential of using a single local measure to categorize individuals into different age categories. Betweenness centrality achieved an accuracy of $86.67\%$ when the DT classifier and Kruskal–Wallis test were used for a single local measure. In a network context, a higher Betweenness centrality means that a node plays a more important role in connecting other nodes as it participates in more of the shortest paths [16]. The utilization of graph measures in investigating effective connectivity has successfully demonstrated acceptable results in distinguishing age groups and classifying them. As a result, graph theory has proven itself to be a valuable tool in comprehending and characterizing these alterations in connectivity.

Moreover, the age-related differences in the interactions between various brain regions within the brain network were explored. The study examined the dynamic effective connectivity, which investigates the interactions between distinct brain areas. The statistical analysis aimed to identify any significant variations in these interactions among the three age groups under investigation. The analysis focused on both intra-hemispheric (within-hemisphere) and inter-hemispheric (between-hemisphere) connectivity. The results indicate that the within-hemisphere connections played a significant role in distinguishing between the three age groups. Specifically, a previous study found that during motor execution, the within-hemisphere connections were stronger in the older group compared to the younger group [18].

In addition to age, gender is also an important factor to consider when investigating brain connectivity [54]. The anatomy and functioning of the human brain exhibit notable differences between males and females, which can consequently impact the observed connectivity patterns. While the primary focus of this study was not to investigate gender-related differences, a statistical analysis was conducted on the local graph measures to analyze the age-related differences, taking into account the potential effects that gender might have on these local graph measures. Table 7 presents the results for brain regions that were consistently identified as significantly important across more than half of the thresholds tested. This suggests that these brain areas demonstrate robust age-related changes in their local connectivity measures.

Limitations and future work

There were some limitations in this study. The study examined age group classifications for adolescent, adult, and middle age and senior, but the criteria used may not have accurately captured the developmental stages and unique characteristics of each group. The research had a small sample size of $30$ participants, limited by the available HCP dataset, which constrained the ability to increase the number of participants in the adolescent and senior groups. To maintain balance across the groups for better classification performance, the focus was on ensuring equal representation between the groups, rather than increasing the overall number of data points, as equal group sizes are important for effective classification and performance of the classifiers. Future research should consider refining the age group classification and increasing the sample size to overcome these limitations and enhance the validity and reliability of the findings.

There is an ongoing debate regarding the choice of atlases for defining nodes in network analyses. The AAL atlas has been utilized in various network analyses of fMRI data that are relevant to the current study. Its use allows for easier comparison with published works. However, the primary concern with the AAL atlas is that its larger regions may contain multiple functional areas, which could be addressed by using newer high-resolution functionally defined atlases [17].

Considering the results of this study, it is worth noting that the fMRI technique provides valuable insights into the functional connectivity of the brain, but it is important to consider its inherent limitations. The temporal resolution of fMRI is relatively low compared to other neuroimaging modalities, which can limit the ability to capture the dynamic nature of brain activity. To gain a more comprehensive understanding of the underlying neurophysiological and cerebral hemodynamic processes, other techniques such as electroencephalography (EEG) and fNIRS can be highly informative [3, 66].

Conclusion

In conclusion, our study demonstrates the potential of analyzing brain network measures in understanding age-related changes in the brain. By employing dynamic effective connectivity on rs-fMRI data, we constructed brain networks and extracted relevant graph measures. These measures showed significant differences between age groups and identified crucial brain regions involved in age-related changes.

Furthermore, we were able to achieve a classification accuracy of $86.67\text{\%}$ by combining a DT classifier with feature selection based on Kruskal–Wallis. These findings not only provide valuable biomarkers for detecting age-related changes but also lay the foundation for developing interventions to slow down or prevent cognitive decline in aging populations. As we continue to explore and understand the complexities of the aging brain, this research offers important insights and directions for future investigations.

Declarations

Competing interests

The authors declare no competing interests.