Working memory is a complex psychological construct referring to the temporary storage and active processing of information. We used functional connectivity brain network metrics quantifying local and global efficiency of information transfer for predicting individual variability in working memory performance on an n-back task in both young (n = 14) and older (n = 15) adults. Individual differences in both local and global efficiency during the working memory task were significant predictors of working memory performance in addition to age (and an interaction between age and global efficiency). Decreases in local efficiency during the working memory task were associated with better working memory performance in both age cohorts. In contrast, increases in global efficiency were associated with much better working performance for young participants; however, increases in global efficiency were associated with a slight decrease in working memory performance for older participants. Individual differences in local and global efficiency during resting-state sessions were not significant predictors of working memory performance. Significant group whole-brain functional network decreases in local efficiency also were observed during the working memory task compared to rest, whereas no significant differences were observed in network global efficiency. These results are discussed in relation to recently developed models of age-related differences in working memory.
Citation: Stanley ML, Simpson SL, Dagenbach D, Lyday RG, Burdette JH, Laurienti PJ (2015) Changes in Brain Network Efficiency and Working Memory Performance in Aging. PLoS ONE 10(4): e0123950. https://doi.org/10.1371/journal.pone.0123950
Academic Editor: Yong He, Beijing Normal University,Beijing, CHINA
Received: December 20, 2014; Accepted: March 9, 2015; Published: April 13, 2015
Copyright: © 2015 Stanley et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Data Availability: Anonymized data are available through the Laboratory for Complex Brain Networks in the Department of Radiology at Wake Forest School of Medicine. Due to the requirements of the local Ethics Committee, these data are available to researchers after sending a request to Dr. Paul Laurienti at email@example.com.
Funding: This work was partially supported by the Wake Forest Older Americans Independence Center (P3021332), the Sticht Center on Aging at Wake Forest School of Medicine, and the Translational Science Center at Wake Forest University. Sean Simpson was supported by NIBIB K25 EB012236-01A1. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
Substantial progress has recently been made in the neurosciences by investigating the structure and function of the brain as a large-scale complex network [1–2]. All complex networks fundamentally consist of two basic components: differentiable elements of the system and the pairwise relationships between those elements. Formally, these elements are represented as nodes, and the pairwise relationships between elements are represented as edges. In human functional brain networks, nodes represent a predefined collection of brain tissue, and edges represent measured functional connectivity between pairs of nodes. Graph theory measures allow for the quantitative characterization of complex patterns of organization within and between large-scale brain networks. The ability to analyze these networks with graph theory measures affords a biologically meaningful research program capable of identifying critical changes in certain network properties in both normal and disordered cognitive function across the life span. The primary purpose of this paper is to explore the utility of functional brain network measures of information transfer in accounting for individual variability in working memory performance on an n-back task in both young and older adults.
Working memory broadly refers to the simultaneous temporary storage and active processing of information in the service of goal-directed behaviors . Numerous studies have measured working memory performance across the adult life span, consistently and reliably reporting that working memory performance exhibits a gradual and regular decline from early to late adulthood [4–8], presumably due to widespread decreases in neural and metabolic efficiency resulting from molecular, cellular, and structural changes in the aging brain . Studies using fMRI to investigate the effects of aging on patterns of functional activation associated with working memory have primarily focused on localizing and functionally characterizing changes in certain brain regions that facilitate different components of the working memory construct [10–15]. However, approaching the study of the brain as an adaptive system with various interdependent, interacting components that give rise to complex behaviors may confer additional insights not obtainable from measuring anatomically localized and encapsulated activations . In fact, rapidly accumulating evidence using multivariate methodologies to explore functional connectivity patterns has suggested that integrative processes and dynamic, complex interactions across numerous, distributed brain regions subserve visual recognition , language functions , cognitive control and executive functioning , emotion-cognition interactions , decision making processes , and social cognition . Despite this recent emphasis on integrative processes and complex interactions between distributed brain regions for the study of cognition, no studies have been conducted to investigate age-related differences in complex patterns of functional connectivity associated with working memory performance.
Most published work investigating the topology of complex brain networks has examined differences in resting state functional connectivity (rs-fcMRI) across certain groups of interest as opposed to patterns of complex network topology during cognitive tasks. rs-fcMRI analyses measure correlations in spontaneous low-frequency fluctuations in blood oxygen level dependent (BOLD) signal in participants while participants are engaged in internally oriented mental activities in the absence of externally focused goal-directed tasks [23–24]. This contrasts with task-evoked fMRI analyses that capture transient activations or deactivations over several seconds when a participant is presented with an external stimulus or engaged in some cognitive task. The temporal coherence in neural activity measured in rs-fcMRI data is taken to reflect underlying, intrinsic patterns of neural activity and has provided evidence of both functional homogeneity in adjacent brain areas and functional connectivity between distant, noncontiguous brain areas [23, 25–29]. A considerable quantity of work has focused on these patterns of intrinsic functional connectivity in rs-fcMRI data, which appear to be strongest within and between functionally related brain areas [30–31]. That is, these patterns are strongest among brain areas that are similarly modulated by various task paradigms [32–33].
Results from recent graph theoretic functional brain network analyses have demonstrated that differences in certain topological properties of intrinsic resting-state connectivity patterns are predictive of intelligence , working memory capacity , verbal learning and visual recall , normal aging [37–40], and certain neurological disorders including Alzheimer’s disease [41–42], Parkinson’s disease  and schizophrenia [44–45]. Although less is known about functional network topology during active experimental task performance, it is important to examine functional brain network properties during diverse tasks because certain topological properties present during rest may change during tasks. In fact, non-trivial differences in functional brain network topology have recently been identified during auditory and visual stimulation , odor recognition memory tasks , motor learning [48–49], decision making processes , emotional face processing , and changes in working memory load .
Of particular relevance to the current study, Rzucidlo et al. (2013) recently demonstrated that mean group values of whole-brain network local efficiency tend to decrease from resting-state to a commonly used working memory task, the n-back task. However, the same study reported that mean group values of whole-brain network global efficiency were not significantly different across conditions . The topological organization of a network is directly related to its local and global efficiency, which jointly determine the network’s capability of integrating information effectively [1–2, 53]. Local efficiency provides an indication of how effectively information is integrated between the immediate neighbors of a given network node, whereas global efficiency provides an indication of how effectively information is integrated across the entirety of the network. In the current study, we extend those analyses conducted by Rzucidlo et al. (2013) by determining whether the change in mean group values of whole-brain network local and global efficiency from rest to the n-back task differ between young and older adults. We further extend the work of Rzucidlo et al. (2013) by exploring the utility of local and global efficiency in accounting for individual variability in working memory performance across age groups.
The primary purpose of the current study is to investigate the utility of whole brain network metrics across age groups (young and older adults) in accounting for individual differences in working memory performance. More specifically, we sought to determine (1) whether local and global efficiency are predictive of working memory performance; (2) whether local and global efficiency predict working memory performance differentially in young and older participants; and (3) whether local and global efficiency are differentially predictive of working memory performance at rest and during task. Secondarily, we sought to investigate potential differences between mean group measures of local and global efficiency from resting-state to the working memory condition and between age groups.
Materials and Methods
The research protocol was reviewed and approved by the Wake Forest School of Medicine Institutional Review Board (IRB). Informed consent was obtained in writing from each participant following the protocol approved by the IRB.
Fifteen older adults (11 females, Mage = 72.07 years, SD = 3.47, age range: 66–79 years) and 14 younger adults (9 females, Mage = 27.21 years, SD = 4.00, age range: 22–34 years) participated in this study. All participants were recruited via locally placed advertisements followed by a telephone screening. Participants were included only after fulfilling several criteria on batteries for cognition, including the Center for Epidemiological Studies Depression Scale (CES-D; ) and the Modified Mini-Mental State Examination [55–56]. Participants scoring greater than or equal to 25 of the CES-D were excluded from the study. Additionally, only right-handed participants with functional color vision , no history of alcoholism (AUDIT; ), corrected visual acuity, and no more than moderate hearing loss were included in these analyses. Participants were originally recruited as controls in three separate Body Mass Index (BMI) groups—normal weight (BMI from 18.5 to <25), overweight (BMI from 25 to <30), and obese (BMI from 30 to <40)—as part of a larger parent study investigating the effects of aging and obesity on the brain. No systematic effects of BMI group were observed within or between age groups or conditions. As such, we combined all BMI groups for the analyses herein.
During each scanning session, fMRI data were acquired during rest and the n-back task with n = 2. All participants were provided with fMRI compatible goggles, ear plugs, and a hand-held button box custom-made to be MRI compatible and interfaced with the e-prime  response box (for the 2-back task) for the entirety of each session. Participants were instructed to keep their eyes open, not fall asleep, and fixate on a black cross on the computer screen interfaced with their goggles during rest. During the 2-back condition, a sequence of 100 letters was presented on the screen in the goggles. The order of the letters presented in the sequence differed between participants in order to minimize a potential systematic effect of the presentation sequence. Letters appeared for 0.3 seconds followed by a 2.7 second blank slide during which participants were asked to respond; as such, individual trials lasted for three seconds. The entire 2-back task lasted for a total of five minutes and 20 seconds. For every letter that appeared after the second letter, participants were required to determine whether the current letter was the same as the one presented two letters back in the sequence. The 2-back task requires the maintenance and continual updating of the contents of working memory as well as an executive component for keeping instructions and goals online while inhibiting incorrect, competing responses [60–61]. Participants were instructed to press one button on the hand-held box when the current letter was the same as the one presented two letters back in the sequence. Participants were instructed to press a different button on the hand-held box when the current letter was not the same as the one presented two letters back in the sequence. Before beginning the task, participants were instructed to respond as quickly and accurately as possible with their right hands using their index and middle fingers to differentiate responses.
Data Acquisition and Pre-processing
For each participant, a multi-slice spoiled gradient inversion recovery (3DSPGR-IR) was used to collect high-resolution T1-weighted images on a 1.5T GE scanner. A GE 8 channel neurovascular headcoil was used. The protocol parameters were as follows: phase/frequency = 256/256; 156 contiguous slices, 1.0 mm thick; in-plane resolution of 0.938 mm x 0.938 mm; TE = 4.74 ms; TR = 4.68 ms; T1 = 600 ms. BOLD contrast was measured using a whole-brain gradient echo echo-planar imaging (EPI) sequence with the following parameters: phase/frequency = 64/64; 159 volumes with 28 contiguous slices per volume; slice thickness = 5.0 mm; in-plane resolution of 3.75 mm x 3.75 mm; TR/TE = 2000/40 ms.
Image preprocessing was performed using SPM8 software (http://www.fil.ion.ucl.ac.uk/spm/). All functional data were realigned, slice-time corrected, and co-registered to a skull-stripped version of the accompanying structural data. Coregistration was checked visually for each participant. Structural data were parcellated into gray matter, white matter, and cerebrospinal maps using the unified segmentation function in SPM8. As part of an integrated processing procedure, structural images were warped to MNI template space (Montreal Neurological Institute, http://www.mni.mcgill.ca/). The normalization parameters derived from the structural image warping were then applied to all functional data. A band-pass filter (0.009–0.08 Hz) was applied to remove physiological noise and low-frequency drift. Six rigid-body transformation parameters generated during the realignment process and three mean signals (whole-brain, white matter, and cerebrospinal fluid) were then regressed out of the functional data. Additionally, sinus midline and sinus occipital ROIs were regressed out of the functional data. All functional data were motion corrected to eliminate scan volumes with excessive frame-wise displacement and BOLD signal change . Values of 0.5 for frame-wise displacement and 0.5% ΔBOLD for DVARS were chosen to represent values well above the norm found in still subjects. An average of 1.2 volumes were removed for young participants at rest; an average of 1.8 were removed for older participants at rest; an average of 0.5 were removed for young participants during 2-back; and an average of 2.1 were removed for older participants during 2-back. There were no significant differences in the number of volumes removed between age groups or within subjects from rest to the 2-back task (all p’s > .11). The number of volumes removed due to motion were also included in all regression analyses (see below) as a control.
Generating Whole-Brain Networks
Pre-processed functional data were masked such that only gray matter voxels were included within areas specified by the Automated Anatomical Labeling (AAL) atlas . We constructed brain networks by assigning a node to each voxel and then measuring correlations in activity computed from pairs of simultaneously recorded time series. Two separate networks were constructed for each participant: one network for resting state and another for the 2-back task. Using a voxel-wise approach to define nodes generates high resolution networks, unbiased and unconstrained by a priori assumptions that limit the potential for making new discoveries .
Voxel-wise functional brain networks were generated from a correlation matrix of time series data from each voxel pair using the Pearson correlation coefficient. Negative connections were not included in these analyses (for reasons noted in [16,39]). Edge density across subjects was matched using the formula N = KS, with N equal to the number of nodes, K equal to the average degree, and S set at 2.0, 2.5, and 3.0 to assess any potential threshold effects. The same analyses were run at each threshold, and no results presented herein are threshold specific. Because prior work has demonstrated that brain networks tend to fragment when S is greater than three  and the reproducibility of brain networks is highest at thresholds between two and three , we present data using a threshold of S = 2.5. A correlation coefficient cut-off that meets this density threshold was determined and only those correlations above the threshold were considered as functional edges in the analyses presented herein. Those edges between any two given voxels that met the threshold requirement were given a value of one, and all other edges were given a value of zero. As such, undirected, unweighted adjacency matrices were generated for each participant representing whole-brain functional connectivity. Thresholding the network in this way ensures that comparisons are made between networks of comparable density relative to the total number of network nodes. Young and older participants had approximately the same number of nodes in all conditions, indicating that network measures between age cohorts were comparable.
Global efficiency is a measure of the efficiency of distant information transfer in a network and is defined as the inverse of the average characteristic path length between all nodes in the network . Beginning with each voxel representing a node and the similarity in the measured time series between any two voxels providing the basis for the existence of a functional connection, the shortest number of steps required to go from node i to every other network node was computed. This was done separately for each and every node in the network, and the average number of shortest steps to all other network nodes was computed separately for each node. The inverse of the average number of shortest steps for each node was then summed across all network nodes and this summed quantity is normalized by taking into account the total possible number of connections that could exist in the network. Formally, global efficiency is calculated as where N is the set of all nodes in the network and Lj,k is the average distance (number of steps) between nodes i and j in the network. Global efficiency is a scaled measure ranging from 0–1, with a value of 1 indicating maximum global efficiency in the network. In functional brain networks, global efficiency provides a measure of the overall capacity for parallel information transfer and integrated processing among distributed components of the system . Importantly, higher order cognitive functions, such as working memory, may require the integration of information from several disparate sources, benefiting from global efficiency across the entirety of the network .
Local efficiency is a measure of the average efficiency of information transfer within local subgraphs or neighborhoods and is defined as the inverse of the shortest average path length of all neighbors of a given node among themselves . Local efficiency was first computed for each individual node i in the network by identifying the set nodes, or subgraph, to which node i is directly connected. After removing node i from the identified subgraph, the shortest path between all nodes in the subgraph was calculated. The inverse of the shortest path from each node formerly connected to node i to every other node formerly connected to node i was then summed across all nodes formerly connected to node i, and this summed quantity is normalized by taking into account the total possible number of connections that could exist among all nodes formerly connected to node i. Formally, local efficiency is calculated as where represents the number of nodes in the subgraph Gi. Local efficiency is a scaled measure ranging from 0–1, with a value of 1 indicating maximum local efficiency in the network. In functional brain networks, high local efficiency suggests a topological organization indicative of segregated neural processing . The local efficiency of the network reveals how effectively information is transferred among the first neighbors of node i when node i is removed from the network. Nodes in networks with high local efficiency tend to effectively share information within their immediate local communities, which provides a basis for effective segregated information processing in the network.
d’ Measure of Working Memory Performance
Based on work in signal detection theory , the best available method for quantifying performance on the n-back task is a total score (d’) that takes into account the range for hits and false alarms by calculating the normalized proportion of correct hits minus the normalized proportion of false alarms. This measure of working memory performance is the dependent variable in all statistical modeling analyses herein. d’ is calculated from the hit (H) rate and false-alarm (FA) rate using the formula d' = ZH − ZFA, where Z represents a transformation of the two distributions to generate z-scores of the rate of hits and the rate of false alarms . The better an individual maximizes hits (and thus minimizes misses) and minimizes false alarms (and thus maximizes correct rejections), the higher the individual’s d’ score. Higher scores on the d’ measure indicate better performance on the n-back task (for review of the d’ measure, see ).
Older adults tend to be substantially slower than young adults during most tasks that emphasize rapid responding (e.g., [71–72]). Two explanations for this age-related slowing in response times have gained traction in the literature. One explanation is that age-related increases in neural noise resulting from molecular, cellular, and structural alterations slow down all processes related to evidence accumulation and response selection at the same rate [73–77]. The second explanation is that older adults are simply more reluctant to commit errors and tend to attach a greater importance to responding accurately than to responding quickly [72, 78–80]. Thus, in order to avoid mistakes and achieve better performance, older adults are more likely to strategically balance the opposing demands of accuracy and speed, which is commonly referred to as the speed-accuracy trade-off . In order to avoid this potential confound, we controlled for the possibility that older adults cautiously and strategically chose to accumulate more evidence before making a decision on the n-back task. Because the distributions of average response times (RT) on correct trials overlapped between young and older adults, exclusively including an age group variable was insufficient as a control. So, after excluding those responses +/- 3 SDs from the mean for each participant, the average RT on correct trials for each participant was recorded to serve as a control in regression analyses.
Age-related group differences in local and global efficiency were computed using independent samples t-tests, while paired-samples t-tests were used to identify potential differences in local and global efficiency between resting state and the 2-back task within subjects.
In order to determine whether differences in local and global efficiency account for a substantial proportion of individual variability in working memory performance across age groups, backward/forward stepwise linear regression analyses were conducted with Akaike’s information criterion (AIC; [82–83]) and Adjusted R2 as criteria to uncover the model that accounts for substantial individual variability in working memory performance. AIC provides a measure of the quality of a statistical model by simultaneously maximizing the goodness of fit of the model (amount of variance explained) while minimizing the number of parameters included in the model. With AIC and Adjusted R2 as criteria, backward/forward stepwise linear regression is a semi-automated process of successively removing or adding variables to identify the model that simultaneously ensures that the goodness of fit of the model is maximized while minimizing the complexity of the model. Age was included as an independent variable and coded as a binary, categorical variable (0 = young, 1 = old). d’ was used as the dependent variable in all regression analyses. We sought to quantify the relationship between working memory performance and each of the covariates, all possible interactions between those covariates, and all possible quadratic terms after controlling for the variability in working memory performance explained by the speed of responding (measured in milliseconds) and the number of volumes removed per participant due to excessive motion.
The mean d’ score for younger participants was 3.44 (SD = 1.01), and scores ranged from 1.69 to 4.61; the mean d’ score for older participants was 2.15 (SD = .72), and scores ranged from. 84 to 3.35. Working memory performance (measured by d’) on the 2-back task was significantly worse among older participants than younger participants, t(27) = 4.00, p < .001, Cohen’s d = .74.
Whole Brain Mean Differences in Local and Global Efficiency
For each participant, whole-brain network measures of local and global efficiency were computed during resting-state and the working memory task for each participant. These values were then averaged within each age group to obtain group means, and standard deviations of the means across subjects were computed (Table 1).
No significant differences were obtained between age groups during rest for local efficiency t(27) = .88, p = .39, or global efficiency t(27) = .03, p = .98. No significant differences were obtained between age groups during the 2-back task for local efficiency, t(27) = .15, p = .88, or global efficiency, t(27) = 1.22, p = .23. However, there was a significant difference in the change in local efficiency from rest to 2-back with the groups combined, t(28) = 4.00, p < .001, Cohen’s d = .74. Post-hoc paired-samples t-tests for each age group indicated that there was a significant difference in local efficiency from rest to 2-back for young participants, t(13) = 4.22, p = .001, Cohen’s d = 1.13, and a marginally significant difference for older participants, t(14) = 1.96, p = .070, Cohen’s d = 0.51. No significant differences in global efficiency were obtained across conditions in either age group.
Working Memory Performance and Brain Network Efficiency
The primary purpose of this study is to determine whether differences in local and global efficiency account for a substantial proportion of individual variability in working memory performance across age groups. In order to approach this research question, we conducted backward/forward stepwise linear regression analyses with Akaike’s information criterion (AIC; [82–83]) and Adjusted R2 as criteria to discover (1) whether individual differences in local and global efficiency are significantly predictive of working memory performance, and (2) whether local and global efficiency are dependent upon age-related differences in predicting working memory performance. Age was included as an independent variable and coded as a binary, categorical variable (0 = young, 1 = old). d’ was used as the dependent variable in all regression analyses. We sought to quantify the relationship between working memory performance and each of the covariates, all possible interactions between those covariates, and all possible quadratic terms while controlling for the variability in working memory performance explained by the speed of responding (measured in milliseconds) and the number of volumes removed per participant due to excessive motion.
Local efficiency during task, global efficiency during task, average response time, number of volumes removed due to motion, participant age group, and all possible interactions and quadratic terms were assessed in identifying the most efficient model for predicting working memory performance. After completing backward/forward stepwise regression with AIC and Adjusted R2 as criteria, the most efficient model that emerged accounted for 73% of the variance in working memory performance as measured by d’ scores. The predictors in the final model were: local efficiency (b = -9.46, p = .038), global efficiency (b = 20.29, p = .005), average response time (b = -.004, p < .001), age (b = 5.53, p = .011) and an interaction between global efficiency and age (b = -23.04, p = .008). The Adjusted R2 value was. 671, the model was significant (F(5,23) = 12.42, p < .001), and the model produced an effect size of 2.704 (Cohen’s f2), collectively indicating that the model is highly effective in explaining individual variability in working memory performance across age groups. Evaluation of condition indices and variance inflation factors showed no issues with multicolinearity. Evaluation of residual plots showed that the conditions of linearity, normality, and constant variance were satisfied. Thus, all conditions were satisfied for the linear model. Importantly, the number of volumes removed due to motion did not significantly predict working memory performance. Table 2 provides a summary of the final model.
Although the predictive utility of local efficiency remained the same for both age groups, both the magnitude and direction of the global efficiency variable differed between young and older adults for predicting working memory performance. This demonstrates that slight increases in global efficiency among young adults produce substantial improvements in working memory performance, whereas the same magnitude increases in global efficiency among older adults produce slight decreases in working memory performance. Fig 1 provides a graphical summary of the results from the final regression model.
The predicted d’ values from the final model (the model containing local efficiency during task, global efficiency during task, age group, average RT, and an interaction between global efficiency during task and age group as parameters) are plotted against observed local efficiency (A) and global efficiency (B) values during the 2-back task, respectively, and split by age group.
In a second model, local efficiency during resting-state, global efficiency during resting-state, average response time, number of volumes removed due to motion, participant age group, and all possible interactions and quadratic terms were assessed in identifying the most efficient model for predicting working memory performance. After completing backward/forward stepwise regression with AIC and Adjusted R2 as criteria, neither local nor global efficiency at rest were significant predictors of working memory performance, and thus, will not be discussed further in this section.
The primary purpose of this study was to analyze the relationship between the efficiency of information transfer in the brain and working memory performance in both young and older adults. We have demonstrated that these biologically meaningful whole-brain measures account for a considerable proportion of the variance in working memory performance. Both local and global efficiency during the n-back task were significant predictors of working memory performance in addition to age (and an interaction between age and global efficiency), even after controlling for potential age-related and within group differences in the speed-accuracy trade-off. After identifying the best model using AIC and Adjusted R2 as criteria, the results indicated that decreases in local efficiency during task were associated with better working memory performance in both age cohorts. In contrast, the results also indicated that increases in global efficiency during task were associated with much better working performance for young participants; however, increases in global efficiency during task were associated with a slight decrease in working memory performance for older participants. Thus, changes in global efficiency during the n-back task were differentially important in accounting for individual variability in working memory performance between age groups. However, neither local nor global efficiency at rest were significant predictors of working memory performance.
Furthermore, we found that mean whole-brain measures of local efficiency decreased significantly in young adults during 2-back compared to rest, akin to what was observed by Rzucidlo et al. (2013), and marginally significantly in older adults. There was also a substantial difference in the magnitude of the effect size between young and older participants from rest to 2-back for the local efficiency measure. Whereas the change in local efficiency from rest to 2-back among the younger adults was quite substantial, the older adults only displayed a moderate shift. No whole-brain mean differences in global efficiency were observed for either age group between rest and 2-back. No age-related differences in local or global efficiency were observed within conditions either.
Lower local efficiency during the working memory task was significantly associated with better working memory performance within both age groups. The local efficiency measure has traditionally served as an indication of the degree to which segregated (or specialized) information processing persists in the brain. The idea that localized brain regions are functionally specialized information processing units and make specific contributions to cognitive processes is supported by a substantial body of evidence from activation studies. However, localized functional specialization alone cannot fully account for most aspects of brain function . Integrated (or distributed) processes (e.g., executive functions commonly included in the working memory construct) may instead benefit from high global efficiency of information transfer across the brain as a whole, especially for more demanding tasks that require more complex operations for successful performance . For example, van den Heuvel et al. (2009) demonstrated that higher IQ scores are associated with greater global efficiency in functional brain networks. In line with van den Heuvel et al. (2009), our results demonstrate that while local functional specialization does not facilitate better behavioral performance, greater integration of information across the network, measured with global efficiency, is associated with better working memory performance at least for young adults.
Functional brain networks tend to exhibit small-world properties traditionally characterized by high clustering and low path length, which jointly support the efficient transfer of parallel information at a relatively low cost [85–89]. High clustering supports the functional specialization of local collections of densely interconnected nodes. Shorter path lengths ensure that information easily spreads throughout the network, making parallel and distributed information processing possible. Extensive research has established that short path length is a characteristic of random networks, whereas high clustering is a property of lattice networks . Small-world networks possess clustering comparable to a regular lattice and path length comparable to a random network. Because local efficiency closely corresponds to clustering and global efficiency is computed as the inverse of path length, recent work has explored small-world properties using local and global efficiency [37, 67, 91]. However, little work has explored whether small-world properties in functional brain networks facilitate better behavioral performance on cognitive tasks. For it remains possible that more clustered than distributed brain networks during tasks facilitate better behavioral performance or that more distributed than clustered brain networks during tasks facilitate better behavioral performance. Among young adults, increases in global efficiency accompanied decreases in local efficiency for predicting better working memory performance. This suggests that a more distributed than tightly clustered network facilitates better working memory performance.
Furthermore, several previous studies have demonstrated that average group whole-brain local efficiency during resting-state decreases from early to late adulthood [37, 39–40]. However, we observed no significant differences in local efficiency between age groups. This difference between our study and previous work could be due to differences in nodal definition, which can dramatically impact network metrics [65, 92]. These three previous studies utilized a more macroscopic nodal partitioning scheme, whereas we implemented a mesoscopic voxel-wise partitioning scheme. Because these networks were fundamentally constructed in such different ways, those results obtained from our study and these previous studies should not be considered inconsistent or contradictory.
There are mixed results in the literature regarding differences in global efficiency from early to late adulthood during resting state. Some have reported that global efficiency decreases with aging , while others have reported no significant changes in global efficiency with aging [39–40]. In the current study, while there were no significant average group differences in global efficiency during rest or the 2-back task, there was a significant interaction between age and global efficiency during the 2-back task for predicting individual variability in working memory performance. This interaction between global efficiency and age indicates that the predictive value of network global efficiency is dependent upon the age of the individual. For young participants, slight increases in the global efficiency of the network produce substantial improvements in working memory performance. The ability of the network to effectively integrate information across disparate brain regions facilitates effective working memory performance in young adults. Taking the global efficiency results together, these suggest that there is consistency in the average group global efficiency from rest to task, but the global efficiency scores of individual participants do vary considerably around that mean between rest and 2-back; and critically, the manner in which those individual scores tend to vary around that mean from one condition to the other is systematically related to working memory performance. Our results are consistent with recent work from Stanley et al. (2014), who have shown that a less defined modular structure (and therefore a more globally integrated system) in the entire brain network is associated with improvements in working memory performance even when the number of items that must be held “on line” during the working memory task increases. Thus, the degree of integration in the entire brain seems to be closely related to how well individuals perform on working memory tasks, at least among young adults. Importantly, however, the same magnitude changes in global efficiency among older participants in the current study failed to produce improvements in working memory performance. In fact, increases in global efficiency among older participants were actually associated with slight decreases in predicted working memory performance.
This age-related difference in the predictive utility of global efficiency complements and extends a recently developed model of age-related differences in working memory using a different paradigm. Developed from prior work examining brain activation as opposed to functional connectivity, the Compensation-Related Utilization of Neural Circuits Hypothesis (CRUNCH) maintains that older adults demonstrate comparable working memory performance to young adults during minimally demanding tasks, but that older adults must recruit more brain areas to achieve similar levels of accuracy [93–94]. However, at higher task demands, these mechanisms fail in older adults, resulting in poorer performance and the recruitment of fewer cortical resources in frontal and parietal brain areas; this reflects working memory overload. In the current study, older adults performed considerably worse than younger adults on the 2-back task, suggesting that the task was highly demanding for the older cohort. If the 2-back task were excessively cognitively demanding for the older cohort, then the accompanying recruitment of fewer cortical resources during the task could be associated with the mitigated importance for high global network efficiency to effectively interconnect the relatively fewer cortical areas involved for performing the task. Future work should seek to empirically determine whether the relationship between global network efficiency and the amount of cortical activity observed during working memory tasks changes in accordance with age.
Complex network analyses of neuroimaging data have become increasingly popular, but the meaning of such analyses relative to behavior remains unclear. Is greater global efficiency related to better or worse performance on cognitive tasks? Is greater local efficiency related to better or worse performance on cognitive tasks? Do these relationships change with normal aging? Mapping out these age-related differences in the relationship between whole brain network properties and behavioral performance is especially relevant because decline in working memory can lead to difficulties performing a multitude of everyday activities, and working memory deficits have been associated with both Alzheimer’s disease and Parkinson’s disease [95–97]. The current findings provide an important step toward identifying these relationships.
Differences in the topological properties of the entire functional network have been linked to intelligence , motor learning  working memory capacity , verbal learning and visual recall , and increasing working memory load . However, analyses of average whole-brain network metrics may not be sufficient to identify critical differences in network topology between groups because analyzing group averages tends to dilute regional changes and leave localized spatial shifts in network organization undetected . Future work should seek to determine (1) whether localized spatial shifts in network measures can account for individual variability in behavioral performance, and (2) whether whole brain or regional network properties better account for individual variability in behavioral performance
This work was partially supported by the Wake Forest Older Americans Independence Center (P3021332), the Sticht Center on Aging at Wake Forest School of Medicine, and the Translational Science Center at Wake Forest University. Sean Simpson was supported by NIBIB K25 EB012236-01A1. We would like to thank Ms. Crystal Blair for assistance with data collection.
Conceived and designed the experiments: PJL JHB. Performed the experiments: PJL JHB. Analyzed the data: MLS RGL SLS. Contributed reagents/materials/analysis tools: PJL RGL JHB. Wrote the paper: MLS SLS DD RGL PJL.
- 1. Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience 10: 186–198. pmid:19190637
- 2. Rubinov M, Sporns O (2010) Complex network measures of brain connectivity: Uses and interpretations. NeuroImage 52: 1059–1069. pmid:19819337
- 3. Baddeley A (1996) The fractionation of working memory. Proceedings of the National Academy of Sciences of the United States of America 93: 13468–13472. pmid:8942958
- 4. Salthouse TA, Babcock RL (1991) Decomposing adult age differences in working memory. Developmental Psychology 27: 763–776.
- 5. Kidder DP, Park DC, Hertzog C, Morrell RW (1997) Prospective memory and aging: The effects of working memory and prospective memory task load. Aging, Neuropsychology, and Cognition 4: 93–112.
- 6. Park DC, Lautenschlager G, Hedden T, Davidson NS, Smith AD, Smith PK (2002) Models of visuospatial and verbal memory across the adult life span. Psychology and Aging 17: 299–320. pmid:12061414
- 7. Hedden T, Gabrieli JDE (2004) Insights into the ageing mind: A view from cognitive neuroscience. Nature Reviews Neuroscience 5: 87–96. pmid:14735112
- 8. Bopp KL, Verhaeghen P (2005) Aging and verbal memory span: A meta-analysis. The Journals of Gerontology Series B: Psychological Sciences and Social Sciences 60: 223–233.
- 9. Pradhan SN (1980) Central neurotransmitters and aging. Life Sciences 26: 1643–1656. http://dx.doi.org/10.1016/0024-3205(80)90172-1. pmid:6104765
- 10. Cabeza R, Anderson ND, Locantore JK, McIntosh AR (2002) Aging gracefully: Compensatory brain activity in high-performing older adults. NeuroImage 17: 1394–1402. pmid:12414279
- 11. Grossman M, Cooke A, DeVita C, Alsop D, Detre J, Chen W, et al. (2002) Age-related changes in working memory during sentence comprehension: an fMRI study. NeuroImage 15: 302–317. pmid:11798267
- 12. Cabeza R, Daselaar SM, Dolcos F, Prince SE, Budde M, Nyberg L (2004) Task-independent and task-specific age effects on brain activity during working memory, visual attention and episodic retrieval. Cerebral Cortex 14: 364–375. pmid:15028641
- 13. Mattay VS, Fera F, Tessitore A, Hariri AR, Berman KF, Das S, et al. (2006) Neurophysiological correlates of age-related changes in working memory capacity. Neuroscience Letters 392: 32–37. pmid:16213083
- 14. Persson J, Nyberg L, Lind J, Larsson A, Nilsson L-G, Ingvar M, et al. (2006) Structure-function correlates of cognitive decline in aging. Cerebral Cortex 16: 907–915. pmid:16162855
- 15. Jolles DD, Kleibeuker SW, Rombouts SARB, Crone EA (2011) Developmental differences in prefrontal activation during working memory maintenance and manipulation for different memory loads. Developmental Science 14: 713–724. pmid:21676092
- 16. Telesford QK, Simpson SL, Burdette JH, Hayasaka S, Laurienti PJ (2011) The brain as a complex system: Using network science as a tool for understanding the brain. Brain Connectivity 1: 295–308. pmid:22432419
- 17. Behrmann M, Plaut DC (2013) Distributed circuits, not circumscribed centers, mediate visual recognition. Trends in Cognitive Sciences 17: 210–219. pmid:23608364
- 18. Friederici AD, Gierhan SME (2013) The language network. Current Opinion in Neurobiology 23: 250–254. pmid:23146876
- 19. Power JD, Petersen SE (2013) Control-related systems in the human brain. Current Opinion in Neurobiology 23: 223–228. pmid:23347645
- 20. Pessoa L (2012) Beyond brain regions: Network perspective of cognition-emotion interactions. Behavioral and Brain Sciences 35: 158–159. pmid:22617666
- 21. Moussa MN, Wesley MJ, Porrino LJ, Hayasaka S, Bechara A, Burdette J, et al. (2014) Age-related differences in advantageous decision making are associated with distinct differences in functional community structure. Brain Connectivity 4: 193–202. pmid:24575804
- 22. Barrett LF, Satpute AB (2013) Large-scale brain networks in affective and social neuroscience: Towards an integrative functional architecture of the brain. Current Opinion in Neurobiology 23: 361–372. pmid:23352202
- 23. Biswal B, Yetkin FZ, Haughton VM, Hyde JS (1995) Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn Reson Med 34: 537–541. pmid:8524021
- 24. Biswal BB, Van Kylen J, Hyde JS (1997) Simultaneous assessment of flow and BOLD signals in resting-state functional connectivity maps. NMR Biomed 10: 165–170. pmid:9430343
- 25. Cordes D, Haughton VM, Arfanakis K, Carew JD, Turski PA, Moritz CH, et al. (2001) Frequencies contributing to functional connectivity in the cerebral cortex in “resting-state” data. American Journal of Neuroradiology 22: 1326–1333. pmid:11498421
- 26. Fox MD, Snyder AZ, Vincent JL, Corbetta M, Van Essen DC, Raichle ME (2005) The human brain is intrinsically organized into dynamic, anticorrelated functional networks. Proceedings of the National Academy of Sciences of the United States of America 102: 9673–9678. pmid:15976020
- 27. Damoiseaux JS, Rombouts SARB, Barkhof F, Scheltens P, Stam CJ, Smith SM, et al. (2006) Consistent resting-state networks across healthy subjects. Proceedings of the National Academy of Sciences of the United States of America 103: 13848–13853. pmid:16945915
- 28. de Luca M, Beckmann CF, De Stefano N, Matthews PM, Smith SM (2006) fMRI resting state networks define distinct modes of long-distance interactions in the human brain. NeuroImage 29: 1359–1367. pmid:16260155
- 29. van den Heuvel M, Mandl R, Hulshoff Pol H (2008) Normalized cut group clustering of resting-state FMRI data. PloS One 3: e2001. pmid:18431486
- 30. Fox MD, Raichle ME (2007) Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging. Nature Reviews Neuroscience 8: 700–711. pmid:17704812
- 31. Rosazza C, Minati L (2011) Resting-state brain networks: Literature review and clinical applications. Neurological Sciences: Official Journal of the Italian Neurological Society and of the Italian Society of Clinical Neurophysiology 32: 773–785. pmid:21667095
- 32. Fox MD, Corbetta M, Snyder AZ, Vincent JL, Raichle ME (2006) Spontaneous neuronal activity distinguishes human dorsal and ventral attention systems. Proceedings of the National Academy of Sciences of the United States of America 103: 10046–10051. pmid:16788060
- 33. Smith SM, Fox PT, Miller KL, Glahn DC, Fox PM, Mackay CE, et al. (2009) Correspondence of the brain’s functional architecture during activation and rest. Proceedings of the National Academy of Sciences of the United States of America 106: 13040–13045. pmid:19620724
- 34. van den Heuvel MP, Stam CJ, Kahn RS, Hulshoff Pol HE (2009) Efficiency of functional brain networks and intellectual performance. The Journal of Neuroscience 29: 7619–7624. pmid:19515930
- 35. Stevens AA, Tappon SC, Garg A, Fair DA (2012) Functional brain network modularity captures inter- and intra-individual variation in working memory capacity. PloS One 7: e30468. pmid:22276205
- 36. Sala-Llonch R, Junqué C, Arenaza-Urquijo EM, Vidal-Piñeiro D, Valls-Pedret C, Pallacios EM, et al. (2014) Changes in whole-brain functional networks and memory performance in aging. Neurobiology of Aging. https://doi.org/10.1016/j.neurobiolaging.2014.04.007
- 37. Achard S, Bullmore E (2007) Efficiency and cost of economical brain functional networks. PLoS Computational Biology 3: e17. pmid:17274684
- 38. Wu K, Taki Y, Sato K, Hashizume H, Sassa Y, Takeuchi H, et al. (2013) Topological organization of functional brain networks in healthy children: Differences in relation to age, sex, and intelligence. PloS One 8: e55347. pmid:23390528
- 39. Cao M, Wang J-H, Dai Z-J, Cao X-Y, Jiang L-L, Fan F-M, et al. (2014b) Topological organization of the human brain functional connectome across the lifespan. Developmental Cognitive Neuroscience 7: 76–93. pmid:24333927
- 40. Geerligs L, Renken RJ, Saliasi E, Maurits NM, Lorist MM (2014) A brain-wide study of age-related changes in functional connectivity. Cerebral Cortex. https://doi.org/10.1093/cercor/bhu012
- 41. Supekar K, Menon V, Rubin D, Musen M, Greicius MD (2008) Network analysis of intrinsic functional brain connectivity in Alzheimer’s disease. PLoS Computational Biology 4: e1000100. pmid:18584043
- 42. Sanz-Arigita EJ, Schoonheim MM, Damoiseaux JS, Rombouts SARB, Maris E, Barkhof F, et al. (2010) Loss of “small-world” networks in Alzheimer’s disease: Graph analysis of FMRI resting-state functional connectivity. PloS One 5: e13788. pmid:21072180
- 43. Baggio H-C, Sala-Llonch R, Segura B, Marti M-J, Valldeoriola F, Compta Y, et al. (2014) Functional brain networks and cognitive deficits in Parkinson’s disease. Human Brain Mapping. https://doi.org/10.1002/hbm.22499
- 44. Lynall M-E, Bassett DS, Kerwin R, McKenna PJ, Kitzbichler M, Muller U, et al. (2010) Functional connectivity and brain networks in schizophrenia. The Journal of Neuroscience 30: 9477–9487. pmid:20631176
- 45. Alexander-Bloch A, Lambiotte R, Roberts B, Giedd J, Gogtay N, Bullmore E (2012) The discovery of population differences in network community structure: New methods and applications to brain functional networks in schizophrenia. NeuroImage 59: 3889–3900. pmid:22119652
- 46. Moussa MN, Vechlekar CD, Burdette JH, Steen MR, Hugenschmidt CE, Laurienti PJ (2011) Changes in cognitive state alter human functional brain networks. Frontiers in Human Neuroscience. https://doi.org/10.3389/fnhum.2011.00083
- 47. Meunier D, Fonlupt P, Saive A-L, Plailly J, Ravel N, Royet JP (2014) Modular structure of functional networks in olfactory memory. NeuroImage. https://doi.org/10.1016/j.neuroimage.2014.03.041
- 48. Bassett DS, Wymbs NF, Porter MA, Mucha PJ, Carlson JM, Grafton ST (2011) Dynamic reconfiguration of human brain networks during learning. Proceedings of the National Academy of Sciences of the United States of America 108: 7641–7646. pmid:21502525
- 49. Heitger MH, Ronsse R, Dhollander T, Dupont P, Caeyenberghs K, Swinnen SP (2012) Motor learning-induced changes in functional brain connectivity as revealed by means of graph-theoretical network analysis. NeuroImage 61: 633–650. pmid:22503778
- 50. Cao H, Plichta MM, Schäfer A, Haddad L, Grimm O, Schneider M (2014) Test-retest reliability of fMRI-based graph theoretical properties during working memory, emotion processing, and resting state. NeuroImage 84: 888–900. pmid:24055506
- 51. Stanley ML, Dagenbach D, Lyday RG, Burdette JH, Laurienti PJ (2014) Changes in global and regional modularity associated with increasing working memory load. Frontiers in Human Neuroscience. https://doi.org/10.3389/fnhum.2014.00954
- 52. Rzucidlo JK, Roseman PL, Laurienti PJ, Dagenbach D (2013) Stability of whole brain and regional network topology within and between resting and cognitive states. PloS One 8: e70275. pmid:23940554
- 53. Bullmore E, Sporns O (2012) The economy of brain network organization. Nature Reviews Neuroscience 13: 336–349. pmid:22498897
- 54. Radloff LS (1977) The CES-D Scale: A self-report depression scale for research in the general population. Applied Psychological Measurement 1: 385–401.
- 55. Folstein MF, Folstein SE, McHugh PR (1975) “Mini-mental state”. A practical method for grading the cognitive state of patients for the clinician. Journal of Psychiatric Research 12: 189–198. pmid:1202204
- 56. Bravo G, Hébert R (1997) Age- and education-specific reference values for the Mini-Mental and modified Mini-Mental State Examinations derived from a non-demented elderly population. International Journal of Geriatric Psychiatry 12: 1008–1018. pmid:9395933
- 57. Ishihara S (1917) Tests for Color-Blindness. Tokyo, Japan: Kanehara and Company.
- 58. Bohn MJ, Babor TF, Kranzler HR (1995) The Alcohol Use Disorders Identification Test (AUDIT): Validation of a screening instrument for use in medical settings. Journal of Studies on Alcohol 56: 423–432. pmid:7674678
- 59. Schneider W, Eschman A, Zuccolotto A (2001) E-Prime User’s Guide. Pittsburgh: Psychology Software Tools, Inc. https://doi.org/10.3758/s13428-012-0302-1 pmid:23292569
- 60. McElree B (2001) Working memory and focal attention. Journal of Experimental Psychology: Learning, Memory, and Cognition 27: 817–835. pmid:11394682
- 61. Owen AM, McMillan KM, Laird AR, Bullmore E (2005) N-back working memory paradigm: A meta-analysis of normative functional neuroimaging studies. Human Brain Mapping 25: 46–59. pmid:15846822
- 62. Power JD, Barnes KA, Snyder AZ, Schlaggar BL, Petersen SE (2012) Spurious but systematic correlations in functional connectivity MRI networks arise from subject motion. NeuroImage 59: 2142–2154. pmid:22019881
- 63. Tzourio-Mazoyer N, Landeau B, Papathanassiou D, Crivello F, Etard O, Delcroix N, et al. (2002) Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage 15: 273–289. pmid:11771995
- 64. Stanley ML, Moussa MN, Paolini BM, Lyday RG, Burdette JH, Laurienti PJ (2013) Defining nodes in complex brain networks. Frontiers in Computational Neuroscience 7: 169. pmid:24319426
- 65. Hayasaka S, Laurienti PJ (2010) Comparison of characteristics between region-and voxel-based network analyses in resting-state fMRI data. NeuroImage 50: 499–508. pmid:20026219
- 66. Telesford QK, Burdette JH, Laurienti PJ (2013) An exploration of graph metric reproducibility in complex brain networks. Frontiers in Neuroscience. https://doi.org/10.3389/fnins.2013.00067
- 67. Latora V, Marchiori M (2001) Efficient behavior of small-world networks. Physical Review Letters 87: 198701. pmid:11690461
- 68. Swets J, Tanner WP, Birdsall TG (1961) Decision processes in perception. Psychological Review 68: 301–340. pmid:13774292
- 69. Macmillan NA, Creelman CD (1997) d’plus: A program to calculate accuracy and bias measures from detection and discrimination data. Spatial Vision 11: 141–143. pmid:18095396
- 70. Haatveit BC, Sundet K, Hugdahl K, Ueland T, Melle I, Andreassen OA (2010) The validity of d prime as a working memory index: Results from the “Bergen n-back task.” Journal of Clinical & Experimental Neuropsychology 32: 871–880.
- 71. Botwinick J (1973) Aging and behavior: A comprehensive integration of research findings. New York: Springer Pub. Co.
- 72. Salthouse T (1979) Adult age and the speed-accuracy trade-off. Ergonomics 22: 811–821. pmid:488072
- 73. Brinley JF (1965) Cognitive sets, speed, and accuracy of performance in the elderly. In: Welford AT editor. Behavior, aging and the nervous system. Springfield, Illinois: Thomas. pp. 114–149.
- 74. Cerella J. (1985). Information processing rates in the elderly. Psychological Bulletin 98: 67–83. pmid:4034819
- 75. Forstmann BU, Dutilh G, Brown S, Neumann J, Cramon DY von, Ridderinkhof KR, et al. (2008) Striatum and pre-SMA facilitate decision-making under time pressure. Proceedings of the National Academy of Sciences 105: 17538–17542. pmid:18981414
- 76. Bogacz R, Wagenmakers E-J, Forstmann BU, Nieuwenhuis S (2010) The neural basis of the speed-accuracy tradeoff. Trends in Neurosciences 33: 10–16. pmid:19819033
- 77. Forstmann BU, Tittgemeyer M, Wagenmakers E-J, Derrfuss J, Imperati D, Brown S (2011) The speed-accuracy tradeoff in the elderly brain: A structural model-based approach. The Journal of Neuroscience 31: 17242–17249. pmid:22114290
- 78. Rabbitt P (1979) How old and young subjects monitor and control responses for accuracy and speed. British Journal of Psychology 70: 305–311.
- 79. Smith GA, Brewer N (1985) Age and individual differences in correct and error reaction times. British Journal of Psychology 76 (Pt 2), 199–203. pmid:4027487
- 80. Starns JJ, Ratcliff R (2010) The effects of aging on the speed-accuracy compromise: Boundary optimality in the diffusion model. Psychology and Aging 25: 377–390. pmid:20545422
- 81. Ratcliff R, Thapar A, McKoon G (2007) Application of the diffusion model to two-choice tasks for adults 75–90 years old. Psychology and Aging 22: 56–66. pmid:17385983
- 82. Akaike H (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control 19: 716–723.
- 83. Hurvich CM, Tsai C-L (1989) Regression and time series model selection in small samples. Biometrika 76: 297–307.
- 84. van den Heuvel MP, Sporns O (2013) Network hubs in the human brain. Trends in Cognitive Sciences 17: 683–696. pmid:24231140
- 85. Bassett DS, Bullmore E (2006) Small-world brain networks. The Neuroscientist 12: 512–523. pmid:17079517
- 86. Bassett DS, Bullmore ET, Meyer-Lindenberg A, Apud JA, Weinberger DR, Coppola R (2009) Cognitive fitness of cost-efficient brain functional networks. Proceedings of the National Academy of Sciences 106: 11747–11752. pmid:19564605
- 87. Liu Y, Liang M, Zhou Y, He Y, Hao Y, Song M, et al. (2008) Disrupted small-world networks in schizophrenia. Brain 131: 945–961. pmid:18299296
- 88. Guye M, Bettus G, Bartolomei F, Cozzone PJ (2010) Graph theoretical analysis of structural and functional connectivity MRI in normal and pathological brain networks. Magma 23: 409–421. pmid:20349109
- 89. Telesford QK, Joyce KE, Hayasaka S, Burdette JH, Laurienti PJ (2011) The ubiquity of small-world networks. Brain Connectivity 1: 367–375. pmid:22432451
- 90. Watts DJ, Strogatz SH (1998) Collective dynamics of “small-world” networks. Nature 393: 440–442. pmid:9623998
- 91. Hsu T-W, Wu CW, Cheng Y-F, Chen H-L, Lu C-H, Cho K-H, et al. (2012) Impaired small-world network efficiency and dynamic functional distribution in patients with cirrhosis. PloS One 7: e35266. pmid:22563460
- 92. Butts CT (2009) Revisiting the foundations of network analysis. Science 325: 414–416. pmid:19628855
- 93. Reuter-Lorenz PA, Cappell KA (2008) Neurocognitive aging and the compensation hypothesis. Current Directions in Psychological Science 17: 177–182.
- 94. Reuter-Lorenz PA, Park DC (2010) Human neuroscience and the aging mind: A new look at old problems. The Journals of Gerontology Series B: Psychological Sciences and Social Sciences 65B. pmid:19515992
- 95. Kensinger EA, Shearer DK, Locascio JJ, Growdon JH, Corkin S (2003) Working memory in mild Alzheimer’s disease and early Parkinson’s disease. Neuropsychology 17: 230–239. pmid:12803428
- 96. Gilbert B, Belleville S, Bherer L, Chouinard S (2005) Study of verbal working memory in patients with Parkinson’s disease. Neuropsychology 19: 106–114. pmid:15656768
- 97. Stopford CL, Snowden JS, Thompson JC, Neary D (2007) Distinct memory profiles in Alzheimer’s disease. Cortex 43: 846–857. pmid:17941343