NeuroImage 17, 573–582 (2002) doi:10.1006/nimg.2002.1193

Effects of Verbal Working Memory Load on Corticocortical Connectivity Modeled by Path Analysis of Functional Magnetic Resonance Imaging Data G. D. Honey,* C. H. Y. Fu,† J. Kim,† M. J. Brammer,† T. J. Croudace,* J. Suckling,† E. M. Pich,‡ S. C. R. Williams,† and E. T. Bullmore* ,1 *Department of Psychiatry, University of Cambridge, Cambridge CB2 2QQ, United Kingdom; †Institute of Psychiatry (King’s College), De Crespigny Park, London SE5 8AF, United Kingdom; and ‡Investigative Medicine, Psychiatry CEDD, GlaxoSmithKline SpA, Verona, Italy Received January 14, 2002

We investigated the hypothesis that there are load-related changes in the integrated function of frontoparietal working memory networks. Functional magnetic resonance imaging time-series data from 10 healthy volunteers performing a graded n-back verbal working memory task were modeled using path analysis. Seven generically activated regions were included in the model: left/right middle frontal gyri (L/R MFG), left/right inferior frontal gyri (L/R IFG), left/right posterior parietal cortex (L/R PPC), and supplementary motor area (SMA). The model provided a good fit to the 1-back (␹2 ⴝ 7.04, df ⴝ 8, P ⴝ 0.53) and 2-back conditions (␹2 ⴝ 9.35, df ⴝ 8, P ⴝ 0.31) but not for the 3-back condition (␹2 ⴝ 20.60, df ⴝ 8, P ⴝ 0.008). Model parameter estimates were compared overall among conditions: there was a significant difference overall between 1-back and 2 2-back conditions (␹diff ⴝ 74.77, df ⴝ 20, P < 0.001) and also 2 between 2-back and 3-back conditions (␹diff ⴝ 96.28, df ⴝ 20, P < 0.001). Path coefficients between LIFG and LPPC were significantly different from zero in both 1-back and 2-back conditions; in the 2-back condition, additional paths from LIFG to LPPC via SMA and to RMFG from LMFG and LPPC were also nonzero. This study demonstrated a significant change in functional integration of a neurocognitive network for working memory as a correlate of increased load. Enhanced inferior frontoparietal and prefrontoprefrontal connectivity was observed as a correlate of increasing memory load, which may reflect greater demand for maintenance and executive processes, respectively. © 2002 Elsevier Science (USA)

INTRODUCTION Working memory involves the temporary storage and manipulation of information by an attentionbased, limited-capacity system (Baddeley, 1986, 1992) 1 To whom correspondence should be addressed at Department of Psychiatry, University of Cambridge, Addenbrooke’s Hospital, Cambridge CB2 2QQ, UK. Fax: ⫹44 (0)1223 336581. E-mail: etb23@ cam.ac.uk.

and thus underpins virtually all conscious cognitive processes (Jonides, 1995). Numerous electrophysiological studies in nonhuman primates (Goldman-Rakic, 1987, 1990) and functional imaging studies in humans have consistently identified a neurocognitive network for working memory, the cortical components of which comprise the middle and inferior frontal gyri, anterior cingulate and medial premotor cortex, and posterior parietal cortex (for review, see Fletcher and Henson, 2001). These cortical regions are known to be richly and reciprocally interconnected by white matter tracts in monkeys and humans (Mesulam, 1990). Functional integration of working memory networks in humans has previously been investigated by various methods of multivariate data analysis including structural equation modeling or path analysis (McIntosh, 1998; DellaMaggiore et al., 2000; Krause et al., 2000). One interesting property of working memory networks highlighted by several recent neuroimaging studies is that they are load-responsive. Various experimental designs have been used to manipulate the load on memory systems following the first demonstration of this approach (Grasby et al., 1993a,b). The most widely used paradigm to date has been the n-back experiment, in which a series of stimuli is presented at regular intervals and the subject is instructed to indicate when the current stimulus is the same as that presented n places previously in the series. As a correlate of increased task difficulty, there is generally increased functional activation of prefrontal and parietal cortical epicenters (Barch et al., 1997; Braver et al., 1997; Cohen et al., 1997; Jonides et al., 1997; Klingberg et al., 1997; Manoach et al., 1997; Callicott et al., 1999; Rypma and D’Esposito, 1999; Rypma et al., 1999) although the load–response curve may be nonlinear (Cohen et al., 1997; Jonides et al., 1997), and response at the highest loads may be limited by a finite capacity for activation (Just et al., 1996; Callicott et al., 1999). Increased power of activation of the posterior parietal cortex has also been demonstrated as a positive correlate of increased latency of response to the n-back task

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1053-8119/02 $35.00 2002 Elsevier Science (USA) All rights reserved.

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presented at a single level of difficulty (Honey et al., 2000). These observations indicate that functional activation of frontal and parietal regions, estimated by a univariate analysis of the functional magnetic resonance imaging (fMRI) time series at each voxel, is dynamically modulated by changes in working memory load. Here we address the related hypothesis that there are load-related changes in integrated function of working memory networks, which may be modeled by multivariate analysis of the covariance structure of fMRI data acquired at different levels of difficulty in the n-back paradigm. A more specific hypothesis, based on a previously published path analysis of a different but comparable data set (Bullmore et al., 2000), is that effective connections from the frontal to parietal cortex may be important in mediating articulatory rehearsal in working memory or self-monitoring tasks. Path coefficients modeling frontoparietal connections in particular were therefore expected a priori to be modulated under conditions of relatively increased working memory load. METHODS Sample and fMRI Data Acquisition Functional MRI data were acquired from N ⫽ 10 right-handed volunteers (seven males), with no history of psychiatric or neurological history. Group mean age was 25.7 years (range: 20 –31; standard deviation: 3.4). Written informed consent was provided by all participants. The study was approved by the Bethlem Royal and Maudsley NHS Trust Ethics (Research) Committee. Gradient-echo echo planar T2*-weighted images depicting blood oxygen level dependent (BOLD) contrast were acquired from 16 noncontiguous near axial planes: TE ⫽ 40 ms, TR ⫽ 2 s, flip angle ⫽ 70°, slice thickness ⫽ 7 mm, slice skip ⫽ 0.7 mm, in-plane resolution ⫽ 3.75 mm. Experimental Design We used a blocked periodic ABCD design to activate brain regions specialized for executive and active maintenance components of verbal working memory, as originally described by Cohen et al. (1994). Stimuli were visually presented in 30-s epochs to subjects via a prismatic mirror as they lay in the scanner. During each epoch of the baseline condition (A), subjects viewed a series of 14 letters, which appeared consecutively, with an interstimulus interval of 2 s, and were required to press a button with their right index finger when the letter “X” appeared. During each epoch of the working memory conditions, subjects viewed a series of 14 letters and were required to indicate with the same

index finger if the currently presented letter was the same as that presented n trials previously (n ⫽ 1 (condition B), n ⫽ 2 (condition C), or n ⫽ 3 (condition D)). All conditions were matched for number of target letters presented per epoch (2 or 3). Cycles of alternation between conditions were pseudorandomized in the course of the 9-min experiment in the following order: ABACADACABADACADAB. Subject performance during scanning was monitored in terms of reaction time to target letters and accuracy (number of target letters correctly identified). All subjects received identical training in task performance prior to scanning. Activation Mapping After correction of temporal offsets due to multislice acquisition and head-movement-related effects in the fMRI time series at each voxel (Bullmore et al., 1999), a linear regression model was fitted by least squares to estimate experimentally induced signal changes in the context of residual autocorrelation with 1/f-like or longmemory structure (Bullmore et al., 2001). This yielded maps of the amplitude of response to each activation condition at each voxel, which were coregistered by an affine transformation in standard space (Talairach and Toumoux, 1988). In a random-effects analysis, the median amplitude of response to each condition over all 10 subjects was tested against its null distribution by a permutation test (Brammer et al., 1997) to construct a generic brain activation map for each level of difficulty in the n-back paradigm. We adopted a stringent level of statistical significance, with a one-tailed voxelwise probability of type I error P ⬍ 0.0001. At this size of test we expect less than one false-positive test over all the voxels tested in each map. Regional Time Series Analysis Inspection of the three generic activation maps and consideration of the prior literature identified the following cortical regions as important components of the neurocognitive system for working memory, active in all difficulty levels: left middle frontal gyrus (LMFG) (Talairach coordinates (x, y, z): ⫺39, 24, 28; Brodmann area (BA) 9/46); right middle frontal gyrus (RMFG) (28, 34, 28; BA 9/46), left inferior frontal gyrus (LIFG) (⫺40, 14, 24; BA 44), right inferior frontal gyrus (RIFG) (46, 8, 24; BA 44), left posterior parietal cortex (LPPC) (⫺46, ⫺53, 40; BA 40), right posterior parietal cortex (42, ⫺50, 40; BA 40), and medial premotor cortex corresponding to the supplementary motor area (SMA) (⫺2, 1 50; BA 6). Functional MRI time series were extracted from each individual data set at coordinates corresponding to all generically activated voxels in each of these seven regions. For each individual, a mean time series for each region was estimated by averaging a random sample of 9 time series from the

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TABLE 1 Interregional Associations Summarized as Observed Correlation (Lower Diagonal Entries) and Covariance (Upper Diagonal Entries in Italics) Matrices for Each of Three Levels of Difficulty in the n-Back Working Memory Paradigm (1-Back, 2-Back, and 3-Back)

1-BACK L MFG R MFG L IFG R IFG L PPC R PPC SMA Residual variances 2-BACK L MFG R MFG L IFG R IFG L PPC R PPC SMA Residual variances 3-BACK L MFG R MFG L IFG R IFG L PPC R PPC SMA Residual variances

L MFG

R MFG

L IFG

R IFG

L PPC

R PPC

SMA

2.21 0.236 0.581 ⫺0.029 0.754 0.515 0.218 0.779

.51 2.15 0.002 ⫺0.541 0.345 0.238 ⫺0.456 0.785

1.23 .00 2.04 0.094 0.53 0.534 0.258 0.796

⫺.06 ⫺1.10 .19 1.94 ⫺0.08 0.083 0.507 0.806

1.58 .71 1.06 ⫺.16 1.98 0.588 0.124 0.802

1.19 .54 1.18 .18 1.29 2.42 0.423 0.758

.45 ⫺.93 .51 .98 .24 .92 1.94 0.806

2.02 0.558 0.473 ⫺0.304 0.43 ⫺0.27 0.467 0.798

1.12 1.98 0.589 ⫺0.471 0.313 ⫺0.318 0.671 0.802

1.03 1.26 2.32 ⫺0.52 0.471 ⫺0.078 0.614 0.768

⫺.63 ⫺.97 ⫺1.16 2.12 ⫺0.224 0.191 ⫺0.459 0.788

.64 .61 .99 ⫺.45 1.87 ⫺0.366 0.493 0.811

⫺.55 ⫺.64 ⫺.17 .40 ⫺.72 2.06 ⫺0.181 0.794

.94 1.34 1.33 ⫺.95 .96 ⫺.37 2.01 0.799

2.41 0.014 0.706 0.435 0.523 0.317 ⫺0.645 0.759

.03 1.84 0.219 0.252 ⫺0.153 0.094 ⫺0.018 0.816

1.67 .45 2.31 0.448 0.338 0.225 ⫺0.712 0.769

.96 .49 .97 2.02 ⫺0.125 ⫺0.038 ⫺0.261 0.798

1.22 ⫺.31 .77 ⫺.27 2.26 0.714 ⫺0.491 0.774

.74 .19 .51 ⫺.08 1.62 2.27 ⫺0.432 0.773

⫺1.47 ⫺.04 ⫺1.59 ⫺.54 ⫺1.08 ⫺.95 2.15 0.785

Note. (L/R) MFG, (left/right) middle frontal gyrus; PPC, posterior parietal cortex; IFG, inferior frontal gyrus; SMA, supplementary motor area.

set of time series of generically activated voxels. The segments of each regional mean time series corresponding to presentation of the different activation conditions were then extracted. To do this, we assumed a mean hemodynamic delay of 4 s, i.e., 2TR, between the onset and offset of each activation condition and the corresponding onset and offset of related physiological response. The segments of signal corresponding to the presentation of each of the three activation conditions were concatenated, resulting in a set of three task-specific or within-task time series for each individual in each region (Horwitz et al., 2000). For the 2and 3-back conditions, there were T ⫽ 45 time points comprising each regional within-task series; for the 1-back condition, there were T ⫽ 43 time points per series, because one of the epochs of the 1-back task was presented last in the experimental sequence of conditions and therefore truncated by (4 s ⫽ 2TR) correction for hemodynamic delay (see Fig. 1). For each of seven regions, the (N ⫻ T) data matrix for each level of task difficulty was decomposed by principal components analysis (Bullmore et al., 1996; Bu¨ chel and Friston, 1997; Fletcher et al., 1999). The

first eigenvector resulting from this analysis provides a measure of the main component of variance common to all subjects in a given region and is therefore likely to be determined by experimental design. The first eigenvalue divided by the sum of eigenvalues is an estimator of the proportion of total variance due to experimental design. Likewise, the sum of eigenvalues (total variance) minus the first eigenvalue, divided by the sum of eigenvalues, provides an estimate of the proportion of variance not due to experimental design, i.e., the residual variance ␺ in each region (Bullmore et al., 2000). The number of independent observations or effective degrees of freedom m in each region was estimated by the nominal degrees of freedom (number of time points, T) multiplied by the residual variance. The average number of independent observations over all regions was 34 for 1-back, 36 for 2-back, and 35 for 3-back working memory conditions; grand mean m ⫽ 35. For each level of task difficulty, interregional associations were summarized as a (7 ⫻ 7) covariance matrix (see Table 1) which was constructed pairwise from the values of the first eigenvector extracted by PCA from each of the regional data matrices.

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FIG. 1. Generation of fMRI time series segments corresponding to each level of working memory load. The experimental design used a blocked periodic presentation in which a 30-s working memory condition was periodically alternated with a 30-s baseline condition. The level of difficulty of the working memory condition was presented in pseudorandomized order among 1-back, 2-back, and 3-back difficulty levels. fMRI time series were temporally shifted to reflect a 4-s (2TR) hemodynamic delay. The three segments corresponding to each of the three levels of difficulty were then concatenated to produce a within-task or load-specific series for 1-back, 2-back, and 3-back working memory conditions at each cortical region.

Path Analysis Path analysis is a form of covariance structure analysis which can be applied to multivariate data that are ideally summarized by a variance– covariance or correlation matrix. A structural model is posited which specifies the number and direction of connections between the observed (manifest) variables. The aim of the analysis is to reproduce the key elements of the association structure among observed measures using the minimum (a parsimoniously small) number of parameters. The elements of the structural model are mathematically defined in terms of a set of simultaneous regression equations relating each observed variable to the others. The values for the path coefficients can then be estimated through the solution of the set of simultaneous regression equations. This is usually achieved by maximum-likelihood methods (Horwitz et al., 2000) which generate log-likelihood and ␹ 2 values for each model (from which goodness of fit criteria can be calculated; see below) and standard errors of estimated path coefficients. The set of connections in the structural model can also be summarized graphically by a path diagram in which variables are represented as circles and associations between variables are indicated by connecting the circles by directional arrows. In such diagrams the results of a path analysis can be summarized by labeling the directed arrows with estimates of the path coefficients. (For a general introduction to path analysis see (Loehlin, 1987; Glymour et al., 1987; or Bollen, 1988; for prior applications to functional neuroimaging, see McIntosh et al., 1994; Bu¨ chel and Friston, 1997; Horwitz et al., 2000; Bu¨ chel and Friston, 2000; and Bullmore et al., 2000). Details of model identifica-

tion for nonrecursive models (those with bidirectional paths/connections) are described by Bollen (1998). The maximum likelihood approach to model estimation finds the minimum discrepancy F between the observed covariance matrix C and the matrix predicted by the path model ⌺(q), i.e., F ⫽ min{f(C, ⌺(q))}. If the size of the covariance matrix is (p ⫻ p) then the number of quantities to be estimated, q, must be less than or equal to k ⫽ 21 p(p ⫹ 1). Since we use prior estimates of the residual variances obtained by PCA of the regional data matrices (see above), q denotes simply the number of path coefficients to be estimated in the model. Under

FIG. 2. Path diagram or structural model for corticocortical connections in a working memory network. Regional variables are shown by circles and directional connections between them by arrowheaded lines: (R/L)MFG, (right/left) middle frontal gyrus; PPC, posterior parietal cortex; IFG, inferior frontal gyrus; SMA, supplementary motor area.

EFFECTIVE CONNECTIVITY AND VERBAL WORKING MEMORY LOAD

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FIG. 3. Generic brain activation maps for different levels of difficulty in the n-back working memory paradigm. Highlighted voxels indicate areas of significant response across subjects for each level of difficulty. Frontoparietal regions are shown to be activated robustly across conditions, consistent with previous imaging studies of working memory, with some evidence of a load-dependent increase in response to the 2-back and 3-back conditions. The distance of each map above the intercommissural line in the standard space of Talairach and Tournoux (1988) is given in millimeters; the red crosshair locates the origin of the x and y coordinates in each slice. In accordance with radiological convention, the right side of the brain is shown on the left side of each map. FIG. 4. Path coefficients significantly different from zero under the 1-back and 2-back conditions. Positive path coefficients are denoted by green arrows and negative path coefficients by red arrows. The right side of the brain is shown on the left side of each map in accordance with radiological convention. The positive connection between the left inferior frontal gyrus (IFG) and the left posterior parietal cortex (PPC) is consistent across load conditions. At higher load, there is additionally a significant connection from the left MFG to the left PPC via the supplementary motor area (SMA) and enhanced connectivity between the right middle frontal gyrus (MFG) and the left hemispheric frontoparietal regions.

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the null hypothesis that the population covariance matrix ⌺ ⫽ ⌺(q), the minimum value of the discrepancy function, multiplied by the number of independent observations on each variable m, is distributed approximately as ␹ 2 on k– q degrees of freedom, i.e., mF ⬃ ␹ 2 k– q. Path models which provide a good account of the observed data will be associated with small minima of the discrepancy function F and correspondingly large probabilities (P ⬎ 0.1) under the null hypothesis. Model performance can be evaluated by various indices: good models will generally have low values for the root mean square error of approximation (RMSEA), and high values for Bollen’s (parsimonious) fit index (0 ⬍ BFI ⬍ 1). Automated search procedures have been developed to find the set of path coefficients which minimize RMSEA or maximize BFI (Bullmore et al., 2000). Nested models for the same set of data may also be compared in terms of their ␹ 2 statistics and difference in degrees of freedom. If model A has ␹ a2 on k– q a df and model B has ␹ b2 on k– q b df, then under the null hypothesis that both models fit the data equally well, 2 the difference between the two merit functions ␹ diff ⫽ ␹ a2 2 2 ⫺ ␹ b is distributed as ␹ on (k– q a)–(k– q b) df. If the same structural model is fitted to two different groups of data, the values of all coefficients simultaneously may be compared in a similar fashion (since restricted models are, by definition, a subset of an unrestricted model). Among nested models “better fitting” models are also likely to have lower values for various information criteria, for example, RMSEA. Path model specification. To define a path model that would account for the pattern of corticocortical associations during our working memory task, we initially used an automated search procedure (Bullmore et al., 2000). This approach set out to find the set of paths (directed connections) and their coefficient values (path coefficients) which best accounted for the left hemispheric interregional associations captured by the correlations in the 1-back task. This procedure identified the following structure as the best model : LPPC 3 LMFG; LMFG 3 LIFG; LIFG 3 LPPC; and LIFG 3 SMA. (Three of four of these paths, i.e., all but LPPC 3 LMFG, were also included in the best fitting path model for data acquired previously in an experiment demanding semantic categorization and subvocal rehearsal (Bullmore et al., 2000.) We then assumed that the same set of paths accounted for intrahemispheric correlations among RPPC, RMFG, RIFG, and SMA and that there were reciprocal interhemispheric connections among homologous regions of the dorsolateral frontal and parietal cortex and between the dorsolateral prefrontal cortex and contralateral parietal cortex. All of these functional connections are permissible in the context of known monosynaptic anatomical connections between homologous regions of monkey cortex (McGuire et al.,

1991; Mesulam, 1990; Young, 1993). This structural model is summarized by the path diagram in Fig. 2. All models were estimated using maximum likelihood methods implemented in LISREL software (version 8) (Jo¨ reskog and So¨ rbom, 1996). RESULTS Behavioral Data Subjects performed the baseline and working memory conditions with a high degree of accuracy, correctly identifying 99.6% of the targets in the baseline condition and 97.5, 93.5, and 80% of targets in the 1-back, 2-back, and 3-back working memory conditions, respectively. The reduction in accuracy as memory load increased was significant (repeated-measures ANOVA: F ⫽ 6.715, df ⫽ 2, 27, P ⫽ 0.006); post hoc comparisons with Bonferroni adjustment for multiple comparisons showed that accuracy under the 3-back condition was significantly reduced compared to the 1-back condition (P ⫽ 0.034). Mean reaction time for correct responses was 0.48 (⫾0.06) s for the baseline condition and 0.49 (⫾0.11), 0.58 (⫾0.12), and 0.55 (⫾0.16) s for the 1-back, 2-back, and 3-back working memory conditions, respectively. There were no significant differences in reaction time between conditions (repeated-measures one-way ANOVA: F ⫽ 1.87, df ⫽ 2, 27, P ⫽ 0.15). Accuracy was significantly positively correlated with reaction time under the 3-back condition (r 2 ⫽ 0.876, F ⫽ 29.77, df ⫽ 1, 8, P ⬍ 0.0001), but not in the other conditions. Generic Brain Activation Maps A significant response was observed in several cortical regions across working memory loads, consistent with numerous previous imaging studies of verbal working memory, including bilateral posterior parietal cortex (Brodmann areas 7, 40, and 39), bilateral inferior frontal gyrus (BA 44 and 45), bilateral middle frontal gyrus (BA 46 and 9), and supplementary motor area (BA 6); see Fig. 3. Correlational and Path Analysis The interregional associations captured from the fMRI data are summarized as covariance/correlation matrices in Table 1 for each level of difficulty in the n-back working memory task. Simply by inspection of these data, there is some evidence for modulation of connectivity by load. For example, increasing load from 1- to 2-back is associated with increased correlation between right and left MFG and between left IFG and SMA. Also shown here is the estimated residual variance ␺ for each region. The path coefficients estimated by fitting the same model of path connections separately to each of these

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TABLE 2 95% Confidence Intervals (CI) for the Estimated Path Coefficients for Each of Three Levels of Difficulty in the n-Back Working Memory Paradigm (1-Back, 2-Back, and 3-Back) 1-Back

2-Back

3-Back

Path Connections

Path coefficient

95% CI

Path coefficient

95% CI

Path coefficient

95% CI

R MFG ➜ L MFG L PPC ➜ L MFG R PPC ➜ L MFG L MFG ➜ R MFG L PPC ➜ R MFG R PPC ➜ R MFG L MFG ➜ L IFG R MFG ➜ R IFG R MFG ➜ L PPC L IFG ➜ L PPC R PPC ➜ L PPC SMA ➜ L PPC L MFG ➜ R PPC R IFG ➜ R PPC L PPC ➜ R PPC SMA ➜ R PPC L MFG ➜ SMA R MFG ➜ SMA L IFG ➜ SMA R IFG ➜ SMA

0.04 1.24** ⴚ0.55** ⫺0.35 0.18 0.23 0.28 ⴚ0.53** 0.44 0.6** ⴚ0.46* 0.21 0.55 ⫺0.14 0.34 0.76** 0.54 ⴚ0.54* ⫺0.05 0.3

⫺1.58, 1.66 0.68, 1.8 ⴚ0.91, ⴚ0.19 ⫺1.81, 1.11 ⫺1.72, 2.08 ⫺0.81, 1.27 ⫺0.1, 0.66 ⴚ0.89, ⴚ0.17 ⫺0.26, 1.14 0.2, 1.0 ⴚ0.9, ⴚ0.02 ⫺0.39, 0.81 ⫺0.07, 1.17 ⫺0.56, 0.28 ⫺0.48, 1.16 0.18, 1.34 ⫺0.02, 1.1 ⴚ1.1, 0.02 ⫺0.45, 0.35 ⫺0.06, 0.66

0.07 0.65 ⫺0.07 0.6* 0.54* ⫺0.03 0.18 ⴚ0.49** ⴚ1.07** 0.48* ⫺0.44 0.78** 0.03 0.02 ⫺0.17 ⫺0.1 ⫺0.09 0.02 0.56** 0.0

⫺0.39, 0.53 ⫺0.43, 1.73 ⫺4.01, 3.87 0.02, 1.18 0.08, 1 ⫺1.03, 0.97 ⫺0.24, 0.6 ⴚ0.87, ⴚ0.11 ⴚ1.49, ⴚ0.65 0.08, 0.88 ⫺1.14, 0.26 0.32, 1.24 ⫺3.51, 3.57 ⫺0.34, 0.38 ⫺3.73, 3.39 ⫺0.82, 0.62 ⫺0.59, 0.41 ⫺0.48, 0.52 0.12, 1 ⫺0.38, 0.38

0.23 0.03 0.68 0.12 ⫺0.39 0.66 0.53* 0.09 ⫺0.21 0.35 0.01 ⴚ0.78** ⴚ1.06** ⴚ0.47* 1.28** ⴚ0.51* 0.33 0.44 ⴚ0.75** ⫺0.15

⫺2.61, 3.07 ⫺1.13, 1.19 ⫺0.94, 2.3 ⫺2.16, 2.4 ⫺1.31, 0.53 ⫺0.9, 2.22 0.05, 1.01 ⫺0.35, 0.53 ⫺1.33, 0.91 ⫺0.15, 0.85 ⫺0.39, 0.41 ⴚ1.28, ⴚ0.28 ⴚ1.58, ⴚ0.54 ⴚ0.87, ⴚ0.07 0.78, 1.78 ⴚ0.93, ⴚ0.09 ⫺0.27, 0.93 ⫺0.42, 1.3 ⴚ1.17, ⴚ0.33 ⫺0.55, 0.25

Note. Values in bold indicate confidence intervals which exclude zero. (L/R) MFG, (left/right) middle frontal gyrus; PPC, posterior parietal cortex; IFG, inferior frontal gyrus; SMA, supplementary motor area. * P ⬍ 0.05. ** P ⬍ 0.01.

interregional correlation matrices are shown in Table 2. Overall, the model provided a good fit to the interregional correlation matrix observed during the 1-back condition (␹ 2 ⫽ 7.04, df ⫽ 8, P ⫽ 0.53; root mean square error of approximation ⫽ 0.0 (90% confidence interval (CI) [0.0, 0.19]; Bollen’s parsimonious fit index, BFI ⫽ 0.79). The model also provided a reasonable fit to the interregional correlation matrix observed during the 2-back condition (␹ 2 ⫽ 9.35, df ⫽ 8, P ⫽ 0.31; RMSEA ⫽ 0.061 (90% CI [0.0, 0.22]); BFI ⫽ 0.69). However, the model did not provide an adequate account of the interregional correlation matrix observed during the 3-back condition (␹ 2 ⫽ 20.60, df ⫽ 8, P ⫽ 0.008; RMSEA ⫽ 0.25 (90% CI [0.14, 0.35]); BFI ⫽ 0.45). Model parameter estimates were compared overall between 1-back and 2-back data sets by fitting the same structural model to the covariance matrices from each task, once under the constraint that the path coefficients had equal parameter estimates, i.e., were equal under both conditions, and once with path coefficients allowed to take different values between con2 ditions: ␹ diff ⫽ 74.36, df ⫽ 20, P ⬍ 0.001 (note: both models specified the same paths). This indicates that although the same structural model can provide an adequate fit to data acquired under both 1-back and 2-back conditions, the estimated parameters for the

coefficients differed significantly overall between these conditions. Similarly, there was a significant difference overall between 2-back and 3-back conditions in esti2 mated path coefficients: ␹ diff ⫽ 95.85, df ⫽ 20, P ⬍ 0.001. Since the structural model did not provide a satisfactory fit overall to the 3-back data, we restricted subsequent evaluation of the estimates for the path coefficients to the parameter estimates for the 1-back and 2-back data analysis. As shown in Table 2 and Fig. 4, path coefficients that were significantly different from zero under the 1-back condition included the backward connection from the left inferior frontal gyrus to the left posterior parietal cortex and the forward connection from the left posterior parietal cortex to the left middle frontal gyrus; there were also significant connections to and from the right posterior parietal cortex and between the right middle frontal and inferior frontal gyrus. Under the 2-back condition, the backward projection from the left inferior frontal gyrus to the left posterior parietal cortex remained significant and there was a second significant projection from the left inferior frontal gyrus to the left posterior parietal cortex via SMA. There were also two significant positive connections to the right prefrontal cortex, from the left prefrontal cortex and

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left posterior parietal cortex, and a significant negative connection from the right prefrontal cortex to the left posterior parietal cortex. Under the 1-back condition, there was also a significant negative connection from the right prefrontal cortex to the right inferior frontal gyrus. DISCUSSION Using path analysis of fMRI time series data, the current study demonstrates for the first time that manipulation of cognitive demand in a verbal working memory task is associated with concomitant changes in corticocortical connections. The main results of this study are compatible with our motivating hypotheses. Our more general hypothesis was that an experimental manipulation of working memory load in the n-back paradigm would cause changes in the integrated function of a large-scale neurocognitive network. We used path analysis to model a set of directional or effective connections between frontal and parietal cortical areas and found clear evidence for load-related modulation of path model parameters. Although the same path model could provide an acceptable fit to data acquired under both 1-back and 2-back conditions, the null hypothesis that the estimated path coefficients were identical for the two conditions was decisively refuted. A closer inspection of the most significant path coefficients estimated under each condition identified some interesting commonalities and differences in task-specific patterns of corticocortical connectivity. Under both 1-back and 2-back conditions, there was a significant connection from the left inferior frontal gyrus to the left posterior parietal cortex. A similar frontoparietal connection was found to be important in our previous path analysis of a different data set acquired during a semantic categorization task demanding articulatory rehearsal (Bullmore et al., 2000). The n-back paradigm also entails articulatory rehearsal at all levels of difficulty and we suggest that frontoparietal connectivity, specifically a projection from the left inferior frontal gyrus to the left posterior parietal cortex, may be generally important in mediating this function. This suggestion is strengthened by the fact that these two studies were conducted on different subjects, performing two different tasks, in which the common cognitive component was the articulatory rehearsal of verbal information. Taken together these multivariate results provide direct support for a frontoparietal model of the phonological loop or articulatory rehearsal circuit, as proposed on the basis of previous univariate analyses of functional imaging data (Zatorre et al., 1992; Paulesu et al., 1993; Awh et al., 1996). Our more specific hypothesis, explicitly formulated a priori (Bullmore et al., 2000, p. 300), was that task manipulations which increased load on articulatory rehearsal would modulate connections between the in-

ferior frontal and parietal cortex. Clearly, increasing n from 1 to 2 in the n-back working paradigm is an experimental manipulation that increases the load on articulatory rehearsal and, indeed, this manipulation was associated with the emergence of a second significant connection between the inferior frontal gyrus and posterior parietal cortex via SMA. In other words, one might say that greater articulatory load was associated with “parallelization” of frontoparietal connectivity. Another interesting consequence of greater working memory load was greater integration between contralaterally homologous areas of the middle frontal gyrus. Under the 1-back condition, the right MFG was directly connected to the ipsilateral inferior and medial frontal cortex; whereas under the 2-back condition there was additionally a significant projection from the left to right MFG. There was also a significant reciprocal connection between the right MFG and left parietal cortex under the 2-back condition uniquely. These results suggest that as verbal working memory load is increased there is enhanced connectivity between the right prefrontal cortex and both the frontal and the parietal region of the left hemisphere. Increased connectivity of bilateral functional networks has also previously been reported in response to increased retention delay periods of facial stimuli (McIntosh et al., 1996). These multivariate results are also broadly compatible with previous studies using univariate analysis to demonstrate that unilateral prefrontal cortical activation tends to become bilateral under conditions of enhanced difficulty such as dual task interference (D’Esposito et al., 1995) or increased complexity of material retrieved from episodic memory (Hunkin et al., 2000). In particular, Rypma et al., (1999) demonstrated that increased executive processing requirements of higher memory load tasks were associated with rightlateralized activation of the middle and superior frontal gyri, specifically during the encoding phase (Rypma and D’Esposito, 1999). This suggests that enhanced connectivity between homologous areas of the prefrontal cortex, which might also be conceived as increasing the parallelization of network organization, may be a common compensatory response to increased demands for executive processing. The pattern of connections that emerges at higher working memory load is arguably also consistent with a process-specific subdivision of the prefrontal cortex into dorsal and ventral regions specialized for executive and maintenance processes, respectively (D’Esposito et al., 2000; Owen, 2000; Petrides, 2000). Increasing n in the n-back paradigm increases demands on both executive and maintenance processes (Honey et al., 2000) and it is interesting to speculate that load-related changes in interhemispheric dorsal prefrontal connectivity reflect increased executive demands, whereas enhanced connectivity of the inferior frontal and posterior parietal cortex reflects increased maintenance

EFFECTIVE CONNECTIVITY AND VERBAL WORKING MEMORY LOAD

demands. This hypothesis is empirically refutable by path analysis of functional MRI data acquired under experimental conditions where the difficulty of executive and maintenance components of a working memory task can be manipulated independently. The modeled covariance structure of data acquired under the 3-back condition was significantly different overall from the structure of data acquired under the 2-back condition, providing further evidence in support of load-related modulation of functional integration, perhaps relating to changes in cognitive strategy at higher loads. However, our path model did not provide a good fit to the 3-back data so we refrain from making a more detailed comparison between 3-back and other conditions, e.g., in terms of individual path coefficients. We exercise this restraint because the failure of a path model to fit a given covariance matrix generally refutes the null hypothesis that the covariance matrix predicted by the model is the population covariance matrix. Therefore, the path coefficients and other parameters of a nonfitting model are quite unlikely to describe properties of the population covariance structure and are correspondingly unlikely to be replicated in another sample drawn from the same population. In short, it seems unhelpful to risk substantive interpretation of path coefficients which are unlikely to be replicable. If we were to consider in greater detail why our model does not fit the 3-back data, we could use modification indices and other model diagnostics to inform iterative respecification of the model until it fit. The main drawback of such data-driven respecification is that of overfitting, i.e., the model might provide an excellent fit but only to the data in hand and not necessarily to another sample drawn from the same population. Full evaluation of any alternative model specified for the 3-back data would ideally therefore include fitting it to data from a new sample. We conclude that whereas changes in integrated brain function associated with increase in working memory load from 1- to 2-back may be modeled by quantitative variation in the strength of connections between nodes in a common model, the change in functional integration induced by an increase in load from 2- to 3-back may require qualititative reconstruction of the path diagram if it is to be successfully modeled. One general implication is that the goodness of any single path model as an account of integrated brain function may be restricted to a certain dynamic range in terms of task load or difficulty and that changes in load beyond the limits of this range may require radically new models or modeling techniques. In summary, we have demonstrated a significant change in functional integration of a neurocognitive network for working memory as a correlate of increased load. We suggest that inferior frontoparietal connections may mediate articulatory rehearsal or maintenance processes and we have shown enhanced

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inferior frontoparietal connectivity as a correlate of increasing load from n ⫽ 1 to n ⫽ 2 in the n-back paradigm. Enhanced prefrontoprefrontal connectivity under the 2-back condition may reflect greater demand for executive processes. ACKNOWLEDGMENTS This work was supported by an experimental medicine research grant from GlaxoSmithKline plc to ETB, SCRW, and others. GDH was supported by a University of Cambridge Pinsent–Darwin Fellowship in Mental Pathology. CHYF was supported by the Wellcome Trust.

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