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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 2011 Nov 21;108(51):20760–20765. doi: 10.1073/pnas.1109038108

Brain network local interconnectivity loss in aging APOE-4 allele carriers

Jesse A Brown a,b, Kevin H Terashima a,b, Alison C Burggren a,b, Linda M Ercoli b, Karen J Miller b, Gary W Small b,c, Susan Y Bookheimer a,b,d,1
PMCID: PMC3251140  PMID: 22106308

Abstract

Old age and possession of the APOE-4 allele are the two main risk factors for developing later onset Alzheimer's Disease (AD). Carriers of the APOE-4 allele have known differences in intrinsic functional brain network activity across the life span. These individuals also demonstrate specific regional differences in gray and white matter gross structure. However, the relationship of these variations to whole brain structural network connectivity remains unclear. We performed diffusion tensor imaging (DTI), T1 structural imaging, and cognitive testing on aging APOE-4 noncarriers (n = 30; mean age = 63.8±8.3) and APOE-4 carriers (n = 25; mean age = 60.8 ±9.7). Fiber tractography was used to derive whole brain structural graphs, and graph theory was applied to assess structural network properties. Network communication efficiency was determined for each network by quantifying local interconnectivity, global integration, and the balance between these, the small worldness. Relative to noncarriers, APOE-4 carriers demonstrated an accelerated age-related loss of mean local interconnectivity (r = −0.64, P ≤ 0.01) and regional local interconnectivity decreases in the precuneus (r = −0.64), medial orbitofrontal cortex (r = −0.5), and lateral parietal cortex (r = −0.54). APOE-4 carriers also showed significant age-related loss in mean cortical thickness (r = −0.52, P < 0.05). Cognitively, APOE-4 carriers had significant negative correlations of age and performance on two episodic memory tasks (P < 0.05). This genotype-specific pattern of structural connectivity change with age thus appears related to changes in gross cortical structure and cognition, potentially affecting the rate and/or spatial distribution of AD-related pathology.

Keywords: complex network, genetics

Although increasing age is the primary risk factor for developing Alzheimer's disease (AD), the disease also has known genetic risk factors. The sole confirmed genetic variant is the apolipoprotein E epsilon 4 allele (APOE-4) (1) of which 15–20% of the Caucasian population carries at least one copy. Individuals in this group are three to four times more likely to develop AD and have a younger mean age at onset than APOE-4 noncarriers (2). The APOE protein functions as the principal cholesterol transporter in the brain and affects diverse cellular processes including development, plasticity, and repair in both gray and white matter (3). Neuroimaging studies of APOE-4 carriers and APOE-4 noncarriers (APOE-4 NCs) have revealed numerous structural and functional brain differences across the life span (4). Whereas APOE-4 carriers have been shown to exhibit earlier signs of cognitive decline with aging (5), some genotype-specific brain differences appear before cognitive decline (6–9). APOE-4 carriers aged ≥60 y are at elevated risk for developing AD (2) and are thus a critical target for identifying neuroimaging biomarkers of AD risk that accompany cognitive decline associated with disease risk.

Neuronal atrophy is known to follow a characteristic trajectory in AD, originating in temporal, parietal, and limbic cortices and eventually spreading to frontal regions (10). A growing body of recent research has demonstrated that disconnection between regions is a major component of AD, resulting in specific cognitive deficits such as episodic memory loss (11). White matter degradation is concomitant with gray matter loss in AD, typically originating in regions that undergo myelination late in development (12, 13). This loss of axonal myelination reduces the fidelity of communication between brain regions (14), adversely affecting neuronal synchrony (15). This process makes AD and AD genetic risk particularly amenable to study with complex brain network analysis, a methodology for quantifying the brain's communication integration, efficiency, and robustness (16).

Diffusion tensor imaging (DTI) tractography quantifies the density of white matter-insulated axonal bundles that connect different regions of the brain. It is a primary method for characterizing the brain's white matter or “structural” network (17). Structural brain networks inferred from DTI tractography can be reduced to connectivity matrices or “graphs” that describe the strength of connection between any pair of brain regions. These matrices are typically analyzed using graph theory, a branch of mathematics with methods to formally analyze a pattern of connections (“edges”) between different entities (“nodes”). Specific regional and global metrics measure the local and global efficiency of information processing by quantifying the density of connections between regions and the distance over which information must transfer (18). Network-based measures of structural and functional brain connectivity can be more sensitive to alterations that are not apparent in gross structure (e.g., cortical thickness or white matter integrity) because they consider each region's integration into the global unit rather than as an independent entity. The brain appears to exhibit small worldness, a balance of two properties: high local clustering, a dense interconnectivity among physically adjacent regions, and high global efficiency, a relatively short distance information must travel between any two nodes in the network (19, 20).

Several independent lines of evidence implicate reduced network connectivity in AD. A recent network-based DTI tractography analysis of AD patients by Lo and colleagues (21) assessed characteristic path length, a measure of the average distance information must transfer between brain regions. In general, a network in which there is a shorter average distance for information to transfer is considered more efficient, given that there is a greater metabolic and structural cost required to transmit information over a longer distance. Lo et al. found that AD patients had significantly higher characteristic path length than control individuals, indicating reduced global efficiency. Resting state fMRI connectivity studies of AD patients have also consistently revealed network deficits. Reduced functional connectivity in the brain's default mode network (DMN) is a hallmark of AD (22). This network is composed of the posterior cingulate, medial prefrontal cortex, lateral inferior parietal cortex, lateral inferior temporal cortex, anterior cingulate, medial temporal lobe, and precuneus (23, 24). The DMN is highly metabolically active, particularly when an individual has internally focused attention, such as during episodic memory retrieval (25, 26). Importantly, DMN hubs in the posterior cingulate, precuneus, and medial prefrontal cortex have also been shown to exhibit a striking overlap with the sites of greatest Aβ deposition in AD (27).

In cognitively normal APOE-4 carriers, structural brain connectivity has primarily been assessed by looking at gross measures of white matter integrity such as fractional anisotropy (FA) and apparent diffusion coefficient (ADC). In older APOE-4 carriers, age-related decreases in myelination (28) and FA (29) have been observed that are more rapid than those in noncarriers, particularly in the frontal and temporal lobes. There is also substantial evidence that older APOE-4 carriers perform worse than noncarriers on episodic memory tests (30). It remains unclear which structural and functional brain changes drive these declines in cognitive performance.

Here we used DTI and a hybrid probabilistic/deterministic tractography approach to characterize fiber network topology in aging subjects with genetic risk for AD. We analyzed the fiber networks of APOE-4 noncarriers and APOE-4 carriers for path length, clustering, and small worldness to assess local and global variations in network topology that may be associated with cognitive decline and precede the conversion to AD.

Results

Cognitive Performance.

Cognitive scores on all neuropsychological tests were compared for APOE-4 carriers and noncarriers, using two-sample two-tailed t tests (Table 1). No significant between-group differences were found with the exception of the mini-mental state examination (MMSE). However, when MMSE was included as a covariate in subsequent statistical analyses, it did not affect any statistical results. Relationships between age and cognitive performance were tested in two ways. First, within genotype group, partial correlations were calculated between age and each neuropsychological measure, controlling for sex, years of education, and family history of dementia. Second, a stepwise regression was run, starting with a model of APOE status (carrier or noncarrier), sex, age, and APOE × age interaction. In all cases reported here, the model with APOE status, sex, and APOE × age interaction yielded the most accurate predictions (Methods). APOE-4 carriers exhibited significant negative partial correlations with age on the Rey–Osterrith Complex Figure (ROF), delayed recall (delay ROF; r = −0.57, P = 0.005), and Wechsler memory scale (WMS), logical memory (LM) delayed recall portion (delay total LM; r = −0.44, P = 0.04) (Fig. S1). APOE-4 noncarriers had no significant age-related reduction in score on these tests. The partial correlation values were significantly different for Rey–Osterrith (Rey-O) delay (P = 0.01) and there was a trend toward difference for the WMS LM delay (P = 0.08). The regression model found the APOE × age interaction to be significant for both the delay total LM (P = 0.02) and delay ROF (P = 0.001) tests.

Table 1.

Subject characteristics

Characteristic (mean ± SD) APOE-4 NC APOE-4 P APOE-4 NC partial correlation with age APOE-4 partial correlation with age
Age, y 63.8 ± 8.3 60.8 ± 9.7 0.22
Age range 45–76 43–78
No. (males/females) 30 (10/20) 25 (12/13)
Education, y 16.7 ± 1.8 17.5 ± 3.3 0.33
Family history, yes/no 21/9 16/9
MMSE, score range 0–30 29.4 ± 0.9 28.6 ± 1.2 0.01* r = −0.41, P = 0.07 r = −0.14, P = 0.55
WMS LM delay, 0–50 29.1 ± 7.1 27.1 ± 9.2 0.45 r = −0.09, P = 0.66 r = −0.45, P = 0.038*
Buschke CLTR, 0–144 56.7 ± 39.7 57.8 ± 34.2 0.92 r = −0.16, P = 0.44 r = −0.36, P = 0.1
Rey-O delay, 0–36 12.9 ± 7.2 13.8 ± 7.1 0.68 r = −0.03, P = 0.87 r = −0.57, P = 0.005*
WMS VP, 0–32 22.3 ± 7.4 20.6 ± 8.2 0.49 r = −0.17, P = 0.38 r = 0.05, P = 0.8
WAIS digit span 17.7 ± 3.6 18.1 ± 3.1 0.65 r = 0.21, P = 0.29 r = 0.1, P = 0.65
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Partial correlations with age were controlled for sex, years of education, and family history of dementia. Buschke CLTR, Buschke–Fuld selective reminding test, consistent long-term retrieval section; MMSE, mini-mental state examination; NC, noncarriers; Rey-O delay, Rey–Osterrith Complex Figure, delayed recall; WAIS digit span, Wechsler Adult Intelligence Scale 3, digit span; WMS LM delay, Wechsler memory scale, logical memory delayed recall portion; WMS VP, Wechsler memory scale, verbal paired associations II. *P < 0.05.

Age Effects on Global Network Connectivity.

Structural connectivity matrices were analyzed for each subject to determine global structural network measures of global integration (characteristic path length), local interconnectivity (mean clustering coefficient), the balance of integration and interconnectivity (small worldness), and the total amount of fiber constituting the network (total network cost). These metrics were then assessed for genotype-specific age-related changes. The partial correlation was calculated between all structural network metrics and age, controlling for sex, scanner, and total network cost. The inclusion of total network cost ensured that differences in clustering coefficient between APOE-4 carriers and APOE-4 noncarriers were not driven by differences in the total amount of axonal fibers between groups. The partial correlation of clustering coefficient and age was strongly negative for APOE-4 carriers (r = −0.64, P = 0.002) and nonsignificant for APOE-4 noncarriers (r = −0.21 P = 0.28) (Fig. 1A). These partial correlation values were significantly different (P = 0.03) and the regression model found that the APOE × age interaction was significant (P = 0.0005).

Fig. 1.

Fig. 1.

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(A and B) Mean clustering coefficient (MCC) and mean cortical thickness (MCT) residuals based on partial correlations with age plotted for APOE-4 noncarriers (APOE-4 NC, open circles, dashed line) and APOE-4 carriers (solid circles, solid line). Partial correlations controlled for sex, scanner, and, in the MCC case only, total network cost. Both MCC and MCT had a significant interaction between APOE and genotype (P < 0.05).

The partial correlation between characteristic path length and age trended toward significance for APOE-4 noncarriers (r = 0.36, P = 0.08) but was nonsignificant for APOE-4 carriers (r = 0.21, P = 0.37). The correlation values were not significantly different and the regression found no significant APOE × age interaction for characteristic path length.

To look at the combined effect of clustering coefficient and characteristic path length, small worldness (σ) was assessed separately for the two groups. APOE-4 carriers exhibited a strong negative correlation between age and small worldness (r = −0.52, P = 0.01) whereas APOE-4 noncarriers showed no significant relationship (r = −0.26, P = 0.2). However, partial correlation coefficients did not significantly differ and regression did not find a significant APOE × age interaction for small worldness.

Finally, measurements of total network cost were compared with age. The partial correlation of age and total cost was significantly negative for APOE-4 carriers (r = −0.44, P = 0.02) but not for APOE-4 noncarriers (r = −0.31, P = 0.18). However, partial correlation coefficients were not significantly different, and regression did not find a significant APOE × age interaction.

Age Effects on Regional Network Connectivity.

We next examined whether the relationship between age and network characteristics varied by region for APOE-4 carriers and noncarriers. The analysis was focused on regional clustering coefficients because mean clustering coefficients showed a global APOE × age interaction effect. For the model to best predict a regional clustering coefficient, the set of terms that stepwise regression found to best fit the mean clustering coefficient was used. This model included APOE, sex, APOE × age interaction, total cost, and scanner. At a false discovery rate (FDR)-corrected α of P = 0.05, several regions showed a significant interaction where APOE-4 carriers decreased more sharply than noncarriers: the right precuneus (P = 0.00006), left orbitofrontal cortex (P = 0.004), left supramarginal gyrus (P = 0.002), and right inferior temporal gyrus anteriorly (P = 0.0009) and posteriorly (P = 0.002) (Fig. 2). At an exploratory threshold of P < 0.005 (uncorrected), additional regions displaying a potential APOE × age interaction included right subcallosal cortex (part of the ventromedial prefrontal cortex, P = 0.009) and right precentral gyrus (P = 0.009) (Fig. 2). These regions all showed significant negative partial correlations with age for APOE-4 carriers, no significant correlation for APOE-4 noncarriers, and a significant difference in correlation coefficients (P < 0.05) (Table S2).

Fig. 2.

Fig. 2.

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(A) DTI average weighted network with node radius corresponding to value of negative correlation of age with clustering coefficient for APOE-4 carriers. The width of each edge in the graph corresponds to the average fiber density between those regions. Nodes colored in yellow have significant negative APOE-4 × age interactions for clustering coefficient (P < 0.05, FDR corrected), nodes colored in red indicate the same measure at an exploratory threshold (P < 0.005, uncorrected). (B) The same nodes from A displayed on an anatomical brain model. Node abbreviations: AC, anterior cingulate; FORB, frontal orbital cortex; ITGa, inferior temporal gyrus (anterior); ITGp, inferior temporal gyrus; PCNT, precentral gyrus; PCUN, precuneus (posterior); SMGp, supramarginal gyrus (posterior); and SUBC, subcallosal cortex (part of the ventromedial prefrontal cortex).

Cortical Thickness.

The mean cortical thickness values were also examined in relationship to age for APOE-4 carriers and noncarriers. APOE-4 carriers demonstrated a significant negative partial correlation between cortical thickness and age (r = −0.52, P = 0.01) whereas noncarriers displayed no relationship (r = −0.09, P = 0.66) (Fig. 1B). The partial correlation coefficients were significantly different (P = 0.047) and regression found a significant APOE × age interaction for cortical thickness (P = 0.003).

Finally, the relationship between mean cortical thickness and mean clustering coefficient was tested by examining the within-genotype partial correlation of the two measures, controlling for the effects of scanner and total cost. The relationship was strongly positive for APOE-4 carriers (r = 0.64, P = 0.001) but showed no significant trend for noncarriers (r = 0.04, P = 0.84). These partial correlation coefficients were significantly different (P = 0.02).

Discussion

This study of axonal fiber networks found that aging APOE-4 carriers showed a significantly more negative relationship between local interconnectivity and age than noncarriers. APOE-4 carriers also exhibited a significant decrease in small worldness with age, although no significant interaction between APOE and age was detected. Neither APOE-4 carriers nor noncarriers showed significant relationships between characteristic path length and age, indicating no major loss of global structural integration. Small worldness represents the balance of clustering coefficient (local interconnectivity) and characteristic path length (global integration) in a real network with respect to a random network. Here it appears that the APOE-4 carrier age-related reduction in small worldness was driven primarily by the loss of local interconnectivity whereas global integration was relatively spared.

APOE-4 carriers also showed a significant negative relationship of cortical thickness with age. This decrease paralleled the reduction in structural network local interconnectivity with age, suggesting a relationship between cortical thickness and the degree of local structural connectivity. This relationship was explicitly tested by calculating the partial correlation of mean cortical thickness and mean clustering coefficient for each genotype group. This relationship was significantly more positive for APOE-4 carriers. It is possible that the relationship between these two measures grows stronger as they decrease, which would help explain why only APOE-4 carriers showed this association. Alternatively, the APOE-4 allele may contribute to a tighter relationship between these brain structural properties. The finding of cortical thinning with age in APOE-4 carriers is not without precedence, as a previous report (31) found that aging APOE-4 carriers have (i) higher cortical thickness when controlling for age and (ii) a stronger age-related decrease in cortical thickness than noncarriers. However, it should be noted that in the current study the relationship of local interconnectivity and age was more pronounced than the decrease in cortical thickness, indicating partial independence of these measures and the utility of both in detecting age-related changes that may precede the conversion to AD.

The age-related reduction in local interconnectivity among APOE-4 carriers in this study appeared to be especially driven by the younger subjects, who had the highest measurements of clustering coefficient. The relationship between high structural local connectivity and brain health in general is not entirely clear. The first study of DTI structural network properties and intelligence found a positive relationship between intelligence quotient and clustering coefficient (32). The APOE-4 carriers in the present study had significant negative relationships of performance and age on two different episodic memory tasks, supporting the notion that decreasing interconnectivity has negative cognitive consequences. Importantly, previous evidence does suggest higher connectivity in young APOE-4 carriers. A study of resting state fMRI patterns found healthy APOE-4 carriers in young adulthood exhibited greater DMN connectivity than noncarriers (33). Similar studies in older APOE-4 carriers have shown a complex pattern of increased and decreased functional connectivity with respect to noncarriers (34, 35). Overall, there appears to be a unique age-related trajectory of connectivity change across the life span for APOE-4 carriers. Specifically, there is an apparent higher degree of connectivity early in life that declines more steeply across the age span. Interestingly, a similar pattern appears to hold for cognitive abilities associated with APOE-4. Several cognitive studies in healthy APOE-4 carriers and noncarriers have found better cognitive performance for young APOE-4 carriers (36, 37), a trend that reverses for APOE-4 carriers in their 50s with declines in memory occurring the earliest (38). This developmental trajectory has been hypothesized as a case of antagonistic pleiotropy, in which the APOE-4 allele offers benefits during development and early adulthood at the expense of more rapid decline with aging (30). Alternatively, local connectivity has been shown to reduce during development in the years when pruning is the dominant structural process (39, 40), which may indicate that APOE-4 carriers undergo less pruning. Regardless of the potential benefit that higher local interconnectivity may provide, it is tempting to speculate that APOE-4 carrier-specific increases in metabolic activity within the default mode network may reflect higher structural local connectivity. Elevated metabolic activity could conceivably contribute to increased amyloid production and aggregation over time (27, 41). Although the underlying causes of these different developmental trajectories are currently unknown, it is clear that the APOE-4 allele does not simply cause reduced anatomical connectivity and cognitive performance across the life span (42). Future structural network studies in developing and young individuals should shed light on the possibility of increased local interconnectivity in APOE-4 carriers.

Many regions that are part of the default mode network showed a negative correlation between age and local interconnectivity for APOE-4 carriers in this study; specifically, the right precuneus, left inferior parietal lobule (supramarginal gyrus), ventromedial and orbital prefrontal cortex, and anterior cingulate gyrus have all been cited as components of the DMN (24, 43, 44) although there is some heterogeneity in the precise definition of the DMN. The majority of the regions that exhibited significant negative correlations of age and clustering are connected to one another. Because clustering coefficient is a measure of connectivity among a region's first-degree neighbors, the implication is that there is less total connectivity within this network of regions with aging in APOE-4 carriers. These findings are consistent with prior studies showing decreased resting fMRI correlation between the medial prefrontal cortex, lateral parietal cortex, and posterior cingulate in older individuals harboring high amyloid burden (45). In older individuals with subjective memory complaints, amyloid levels have also been associated with cortical thinning of the medial orbital frontal cortex, anterior cingulate, and precuneus (46). In the current study, the combined impact of aging and genetic risk contributes to lower connectivity and cortical thickness within the DMN and other structural hubs as age increases. Furthermore, this decreased interconnectivity appears to have behavioral consequences, as APOE-4 carriers exhibited significant age-related reduction in episodic memory performance. This DMN-memory relationship is consistent with the putative role of the DMN in episodic memory retrieval (26) and suggests a potential link between anatomical and behavioral phenotypes.

The use of DTI to construct a whole brain fiber network has known limitations. DTI is not ideal for detecting crossing fibers. However, we used a hybrid probabilistic–deterministic tractography method to improve sensitivity to the detection of crossing fibers. Furthermore, network hubs were observed in expected regions including the precuneus, posterior cingulate, and insula (Table S2). Because four of the APOE-4 carriers were 4/4 homozygotes, local interconnectivity, cortical thickness, and two episodic memory tests showing negative correlation with age (WMS LM delay and Rey-O delay) were tested in the same regression model after excluding the four homozygotes. All properites remained significantly negatively related to age. This result indicates no significant additive effect of an additional e4 allele.

In this study we examined axonal fiber networks in healthy aging APOE-4 carriers and noncarriers and found APOE-4 carriers exhibited a negative correlation of local structural connectivity with age that was tightly coupled to reductions in cortical thickness. Additionally, they demonstrated accelerated decrease of small worldness with age, suggesting a more rapid loss in the balance between global integration and local modularity of information processing. At the regional level, APOE-4 carriers were found to have age-related loss of interconnectivity among regions composing the default mode network. APOE-4 carriers also demonstrated significant decreases in performance with age on two different episodic memory tasks that are known to engage the affected regions. Genetic variations in the structure and function of these networks may contribute to differential rates of amyloid production with age and eventual impairment of brain communication efficiency.

Methods

Subject Inclusion and Imaging.

Fifty-five subjects participated in this study. Subjects are summarized in Table 1 with additional details in SI Methods. Any subject who possessed at least one APOE-4 allele was categorized as an “APOE-4 carrier”; subjects homozygous for the APOE-3 allele were designated as “noncarriers” or equivalently, “APOE-4 noncarriers.” All e2 carriers were excluded. All subjects in these groups were without dementia, based on (i) MMSE score ≥26; (ii) a composite neuropsychological test score including immediate memory, delayed memory, and nonmemory components; and (iii) subjective memory scores from the Memory Functioning Questionnaire (47) (Table 1). All subjects collectively scored within 1 SD of the age-adjusted average on the tests listed in Table 1.

All subjects received T1 structural and 30-direction DTI scans. Forty subjects were scanned on a 3T Siemens Allegra and 25 subjects were scanned on a Siemens 3T Trio. DTI was run with single-shot echo-planar sequences with the following parameters (Trio differences in parentheses): 30 diffusion weighted volumes with gradient vectors taken from the International Consortium for Brain Mapping protocol (48), 5 B0 volumes (1 B0), b = 800 s/mm2 (1,000 s/mm2), axial slicing, repetition time (TR) = 7,300 ms (7,000 ms), echo time (TE) = 95 ms (86 ms), k-space matrix = 96 × 96, slice thickness = 2.5 mm, 55 slices with no gap, field of view = 240 mm2, and voxel size = 2.5 mm3. Subjects also received T1-weighted magnetization-prepared rapid gradient echo (MP-RAGE) scans with the following parameters: sagittal slicing, TR = 2,300 ms (1,900 ms), TE = 2.93 ms (2.26 ms), matrix = 192 × 192 (256 × 224), 160 slices with no gap (176), field of view = 256 mm2 (218 × 250 mm), flip angle = 8° (9°), and voxel size = 1 mm3. To control for scanner-specific differences, scanner was included as a dummy covariate in all subsequent statistical analyses.

DTI Processing and Tractography.

DTI tractography was performed using the first and second dyad vectors calculated by FMRIB Software Library (FSL)'s BEDPOSTX program as the input to Diffusion Toolkit's (http://trackvis.org/dtk) fiber assignment by continuous tracking (FACT) algorithm (SI Methods) (49). To obtain each subject's connectivity matrix, the brain was partitioned into 110 regions using the Harvard–Oxford subcortical and cortical probabilistic atlases distributed with FSL. Regions included 7 subcortical regions from each hemisphere (excluding the midbrain) and 47 cortical regions from each hemisphere. Next, the set of fibers connecting each pair of regions was counted to derive a 110 × 110 whole brain connectivity matrix, using custom software written for this purpose [University of California (Los Angeles) Multimodal Connectivity Package, http://www.ccn.ucla.edu/wiki/index.php/UCLA_Multimodal_Connectivity_Package].

Network Construction and Analysis.

Fiber density matrices were obtained by scaling the raw fiber count between region–region pairs by the summed volume of the two regions, to control for the unequal number of voxels in each region (SI Methods). We sought to compare subject networks at their intrinsic densities rather than artificially removing connections to force equivalent density (50) and therefore did not perform thresholding. To control for individual differences in density, total network cost was included as a covariate in all statistical analyses. To account for the white matter “fidelity”, each connection weight was scaled by the averaged FA for all fibers composing that connection.

Network metrics for each subject were quantified using the Brain Connectivity Toolbox (http://sites.google.com/a/brain-connectivity-toolbox.net/bct/metrics). All analyses used weighted networks to calculate the node strengths, clustering coefficients, characteristic path lengths, betweenness centrality, and small worldness. The formulas used to quantify all metrics are described in detail elsewhere (16) and implementations of these from the Brain Connectivity Toolbox were used (SI Methods).

Cortical Thickness.

Cortical thickness values were obtained on the basis of the analysis of the MP-RAGE scans, using the Freesurfer package (http://surfer.nmr.mgh.harvard.edu) (51). Specifically, the recon-all program was used to normalize image intensities, skull strip, and automatically delineate the white matter and pial (gray matter) surfaces on the basis of the use of intensity gradients to optimally place the borders between tissue types. The distance between the surfaces was measured for ∼220,000 vertex pairs per subject. The average of these thickness measures was used as the measurement of mean cortical thickness for each subject.

Statistical Analysis.

All age-related analyses calculated Pearson's partial correlation coefficient (and the associated P value) between age and the global/regional network metric of interest, separately for APOE-4 carriers and noncarriers, after controlling for the effects of sex, scanner, and total network cost for structural network metrics. To assess between-group differences, we tested three statistical models for each cognitive and global neuroimaging measure. For all models of scanning-related measures, a dummy covariate for scanner (Allegra/Trio) was included. For all models of structural network metrics, a total network cost covariate was included to account for the individual differences in fiber volume.

The first model included only main effects of genotype, sex, and age. The second model added a genotype × age interaction to the model. The third model (model 3) was selected by a stepwise regression procedure that returned the subset of terms producing the most accurate linear regression model. This model began with genotype, sex, age, and genotype × age interaction. In the case of the Rey-O delay, WMS LM delay, cortical thickness, and mean clustering coefficient, the model unanimously offering the best predictions included genotype, sex, and the genotype × age interaction. The interpretability of this model was confirmed by performing a partial correlation of age and each measure, separately for the age-matched APOE-4 carriers and noncarriers, controlling for sex (and scanner/total network cost where appropriate). In each case, the correlation coefficient was significantly negative for APOE-4 carriers but not for noncarriers (P < 0.05) (Table 1 and Results). Model 3 was therefore used to examine the interactive effect of genotype and age on regional clustering coefficients. For all regions demonstrating a significant genotype × age interaction, the partial correlation of age and regional clustering was significantly negative for the APOE-4 carriers and significantly different from that of the noncarriers (P < 0.05) (Table S2). The overall F statistics for all three models are shown in SI Methods. For all models, we tested the effect of including covariates for years of education and family history of dementia. These variables never exhibited any significant main effect on any of the results and were excluded from the models reported on here to maximize degrees of freedom.

For behavioral measures and global network measures, a P value of 0.05 was used to determine significant difference/correlation. For regional network measures, the P values for a given measure were adjusted to correct for multiple comparisons, using a FDR procedure with a q value of 0.05. In all cases examining age relationships, one-tailed tests of P values were performed, focusing solely on significant negative APOE-4 × age interactions. The focus on negative relationships was based on the substantial body of prior findings in similar populations in the literature indicating that aging APOE-4 carriers exhibit faster rates of decline in cortical thickness (31), 1 − (apparent diffusion coefficient) (29), and memory scores (38). Consequently, we did not test effects that may increase with age. Regional network measures were predicted with a robust regression model that downweighted outlying observations.

Supplementary Material

Supporting Information
supp_108_51_20760__index.html (878B, html)

Acknowledgments

We thank Mike Jones and Brian Renner for data collection. Jeff Rudie provided valuable review of the manuscript. This work was supported by National Institutes of Health National Research Service Award 1F31AG035438-01 (to J.A.B.); by National Institutes of Health Grants P01-AG025831, AG13308, P50 AG 16570, MH/AG58156, MH52453, AG10123, and M01-RR00865; by the Department of Energy (Contract DE-FC03-87-ER60615); by the General Clinical Research Centers Program; by the Fran and Ray Stark Foundation Fund for Alzheimer's Disease Research; and by the Ahmanson Foundation.

Footnotes

Conflict of interest statement: The authors declare a conflict of interest. G.W.S. reports having served as a consultant and/or having received lecture fees from Dakim, Eisai, Forest, Medivation, Novartis, and Pfizer. G.W.S. also reports having received stock options from Dakim.

This article is a PNAS Direct Submission.

Data deposition: The connectivity matrices for each subject in this study have been uploaded to the University of California, Los Angeles (UCLA) Multimodal Connectivity Database, http://umcd.ccn.ucla.edu, where they are publicly available.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1109038108/-/DCSupplemental.

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