−**18, k** = **35, Z** = **2.9), in (C) right inferior frontal gyrus (orbitalis; MNI co-ordinates: 42, 40,** −**14, k** = **428, Z** = **3.91), and in right superior parietal lobe (not shown) (see Table 2 in Supplementary Material)**. Graphs show size of effect (beta) with 5% confidence interval.

**FIGURE 5 | Neural activation associated with the negative reasoning time window that is not shared with the positive reasoning time window occurs in (A) left caudate nucleus (MNI co-ordinates:** −**10, 2, 20, k** = **594, Z** = **3.39) extending into left inferior frontal gyrus (opercularis; MNI co-ordinates:** −**38,** −**8, 26, Z** = **3.35), in (B) right**

occipital lobe, left inferior frontal gyrus (opercularis), and right precentral gyrus, as well as relative deactivation in right middle temporal gyrus (see **Figure 5**).

# **DISCUSSION**

The above-chance reasoning accuracy levels indicate that participants were engaged in the task. The emotion manipulations were also successful, as indicated by the variation in participants' ratings of picture valence.

## **EMOTION INDUCTION**

Patterns of neural responses during picture viewing/rating were consistent with those reported in the literature. As positive intensity increased, activation was noted in the left inferior frontal cortex. Likewise, Dolcos et al. (2004) reported neural activation in frontal cortex, left hemisphere only, in association with the rating of positive pictures. Furthermore, there is a trend in the neuroimaging literature (Wager et al., 2003) for left-lateralization in the frontal lobe associated with approach-related emotions1 .

**middle temporal gyrus (relative deactivation; MNI co-ordinates: 44,** −**62, 20, k** = **39, Z** = **2.86), in (C) right precentral gyrus (area 6; MNI co-ordinates: 48, 0, 50, k** = **38, Z** = **2.85), as well as in left occipital lobe (not shown) (See Table 2 in Supplementary Material)**. Graphs show size of effect (beta) with 5% confidence interval.

During negative picture viewing/rating, activations in the contrast (negative picture–neutral picture) included right amygdala and right inferior frontal gyrus. Activations in the contrast (negative picture–positive picture) included left amygdala and inferior frontal gyrus bilaterally. As negative intensity increased, activations were in right occipital, right amygdala, and right inferior frontal gyrus. In Dolcos et al. (2004), rating of negative pictures was associated with neural activation in bilateral frontal regions. In Taylor et al. (2000), ratings of aversiveness of negative pictures were associated with neural activation in amygdala, uncus, and anterior parahippocampus. Neuroimaging studies of emotion perception (including studies using the IAPS) often report activation in amygdala, parahippocampal cortex, pregenual anterior cingulate, dorsal inferior frontal gyrus, inferior temporal and occipital cortex, and lateral cerebellum (Wager et al., 2008); withdrawal-related emotions2 are generally correlated with bilateral frontal activation (Murphy et al., 2003) and with amygdala activation (Wager et al., 2003).

1Approach emotions include anger but are otherwise positive; none of our stimuli were designed to induce anger.

2Withdrawal emotions are negative in valence.

### **REASONING**

Based on existing literature, we had hypothesized that both positive and negative emotion would be detrimental to subsequent reasoning. We did not find a significant difference in either reasoning accuracy or mean reaction time among the positive, neutral, and negative conditions. The Congruence\*Emotion manipulation check indicated that reasoning was impaired when beliefs and logic were incongruent; however, we did not have the power to explore this at the neural level, because of design choices we made at the outset. Further study of this issue may be warranted (see Supplementary Material).

There have been other studies showing that emotion does not necessarily impair reasoning. Specifically, negative emotions have not invariably been associated in the literature with impaired reasoning. Goel and Vartanian (2011) conducted a behavioral study in which they manipulated the conflict between argument logic and beliefs about the conclusion by introducing politically incorrect material; on incongruent trials (a valid argument with an unbelievable conclusion, or an invalid argument with a believable conclusion), reasoning performance was better when the statement was politically incorrect than when otherwise. Blanchette et al. (2007) found that reasoning in the negative condition (compared to neutral) improved only when the reasoning material was related to participants'actual exposure to terrorist activity, whereas reasoning about other negative material was impaired.

Blanchette and Leese (2011) found no relation between reasoning performance and participant ratings of the intensity of negative and neutral stimuli. It is intriguing to note a similarity between their study and ours; Blanchette and Leese's study may be the first to link deductive reasoning with physiological arousal (measured with transient skin conductance response) underlying negative emotion induction, and ours may be the first study using pictures from the IAPS to link deductive reasoning with neural activation (measured using fMRI) underlying positive and negative emotion induction. Blanchette and Leese found no relation between reasoning performance and participant ratings of the intensity of negative and neutral stimuli, whereas our study found no effect on reasoning performance of positive or negative emotion induction in a design that included participant ratings.

Our main interest, reflected in our hypotheses, was to show that the neural systems underlying reasoning in each of the positive and negative conditions would differ from those in the neutral condition. These hypotheses were supported.

First, results indicated a crossover interaction, or double dissociation, between the positive and neutral reasoning time windows at the neural level. Not only did the interaction contrast [(positive reasoning–positive baseline) − (neutral reasoning–neutral baseline)] reveal activations but so also did the reverse interaction contrast [(neutral reasoning–neutral baseline) − (positive reasoning– positive baseline)]. Thus, although reasoning after positive emotion induction is not impaired, it is implemented at the neural level differently than is neutral reasoning. The neural pattern associated with the positive reasoning time window involves increased activation in left middle cingulate, occipital lobes bilaterally, left inferior parietal (angular gyrus), left intraparietal sulcus, right postcentral gyrus, left precentral gyrus, and right supplementary motor area.

A double dissociation indicates those neural regions implicated in condition A but not in condition B, and simultaneously, those neural regions implicated in condition B but not in condition A. Therefore, it indicates that conditions A and B involve separable systems.

Activation in the left inferior parietal lobe has been associated with abstract reasoning (Goel et al., 2000; Goel, 2009; Kuo et al., 2009; Watson and Chatterjee, 2012). Activation in the left angular gyrus has been associated with semantic meaning (Seghier et al., 2010; Sharp et al., 2010), more so when there is a conflict involving implausible sentences (Ye and Zhou, 2009) or when the stimulus is emotional (Hervé et al., 2012); it is implicated also in problem identification (Dandan et al., 2013b), in problem solving (Dandan et al., 2013a; Grabner et al., 2013), and in cognitive flexibility (Jacobson et al., 2011). Activation in intraparietal sulcus has been associated with item-specific processing but not with relations among items (Ackerman and Courtney, 2012), with symbolic number processing (Bugden et al., 2012), with attention to items presented in the periphery (Gillebert et al., 2013), and with temporal orienting (that is, attention toward a specific moment in time; Davranche et al., 2011). Left frontal precentral gyrus has been associated with the interaction of attention and language comprehension (Kristensen et al., 2013), with syntax complexity and *post hoc* reanalysis of sentence comprehension (Meltzer et al., 2010), and with successful inhibitory control (Padmala and Pessoa, 2010). Activation in postcentral gyrus has been associated with the illusory perception of motion (Planetta and Servos, 2012), and with visceral stimulation (Hojo et al., 2012; Kaplan and Meyer, 2012). The right frontal supplementary motor area has been associated with speeded decision-making (Wenzlaff et al., 2011), with attention maintenance (Kristensen et al., 2013), and is considered to be part of a ventral attention network that mediates bottom-up capture of attention by memory (Burianová et al., 2012).

Secondly, results indicated a crossover interaction, or double dissociation, between the negative and neutral reasoning time windows at the neural level. Not only did the interaction contrast [(negative reasoning–negative baseline) − (neutral reasoning–neutral baseline)] reveal activations but so also did the reverse interaction contrast [(neutral reasoning–neutral baseline) − (negative reasoning–negative baseline)]. Thus, although reasoning after negative emotion induction is not impaired, it is implemented at the neural level differently than is neutral reasoning. The neural pattern associated with the negative reasoning time window involves left postcentral gyrus, left inferior parietal (supramarginal gyrus), left superior parietal lobe, inferior parietal (angular gyrus) bilaterally, left inferior frontal gyrus, and right supplementary motor area.

As mentioned above, activation in postcentral gyrus has been associated with the illusory perception of motion and with visceral stimulation. Left supramarginal gyrus is considered to be part of a ventral attention network (Corbetta et al., 2008) that mediates bottom-up capture of attention by memory (Burianová et al., 2012). Superior parietal lobe is involved in the interaction between language processing and the control of movement (Segal and Petrides, 2012); activation has been associated with syllogistic reasoning involving abstract or incongruent materials (Tsujii et al., 2011). As mentioned above, activation in the left inferior parietal lobe has been associated with abstract reasoning; activation in the left angular gyrus has been associated with semantic meaning, more so when there is a conflict involving implausible sentences or when the stimulus is emotional, with problem identification and problem solving, and with cognitive flexibility. Activation in the left inferior frontal region has been associated with semantic integration (Yu et al., 2011; Huang et al., 2012) and with categorization (Lupyan et al., 2012; Philipp et al., 2013). As mentioned above, activation in the right supplementary motor area has been associated with speeded decision-making and with attention maintenance, and is considered to be part of a ventral attention network that mediates bottom-up capture of attention by memory.

The positive and negative reasoning time windows yielded similar activation in left superior parietal, left inferior parietal (angular gyrus, intraparietal sulcus, and supramarginal gyrus), left postcentral gyrus, and right supplementary motor area. This finding emerged from a conjunction analysis of two interaction contrasts: [(positive reasoning–positive baseline) − (neutral reasoning–neutral baseline)] and [(negative reasoning–negative baseline) − (neutral reasoning–neutral baseline)].

Beyond these similarities, however, results indicated a crossover interaction, or double dissociation, between the positive and negative reasoning time windows at the neural level. Not only did the interaction contrast [(positive reasoning–positive baseline) − (negative reasoning–negative baseline)] reveal activations but so also did the reverse interaction contrast [(negative reasoning–negative baseline) − (positive reasoning–positive baseline)].

The interaction favoring the positive reasoning time window revealed activation in right inferior frontal (orbitalis, or BA 47), right superior parietal, cerebellar vermis, and left fusiform. In the literature, activation in right frontal (BA 47) has been noted in unconstrained hypothesis generation (Vartanian and Goel, 2005). As mentioned above, superior parietal lobe is involved in the interaction between language processing and the control of movement. The cerebellar vermis is involved in autonomic and motor responses to an emotional state (Strata et al., 2011). Activation in left fusiform has been involved in lexico-semantic processing (Tsapkini and Rapp, 2010; Thesen et al., 2012).

The interaction favoring the negative reasoning time window revealed activation in left caudate nucleus, left inferior frontal (opercularis, or BA 44), left occipital lobe, and right precentral gyrus, as well as relative deactivation in right middle temporal gyrus. In the literature, caudate nucleus has been shown to have a crucial role in reasoning (Melrose et al., 2007) unless insufficient processing time has been allotted for reasoning (Kalbfleisch et al., 2007). Activation in left inferior frontal (BA 44) is associated more with phonological than with semantic fluency (Katzev et al., 2013). Right precentral gyrus is implicated in the representation of coordinated hand–mouth movements (Desmurget et al., 2014) and the neural coding of oculomotor and somatomotor space (Iacoboni et al., 1997). Activation in right middle temporal lobe has been associated with verbal fluency (Krug et al., 2011) and with semantic priming (Laufer et al., 2011).

Goel and Dolan (2003b) had manipulated emotion using the content of the syllogism such that content was either emotionally provocative or neutral; they found that reasoning with negatively charged material was associated with activation in ventromedial prefrontal cortex, whereas reasoning with neutral material was associated with activation in left dorsolateral prefrontal cortex. We have extended their findings by manipulating emotion separately from the material itself. Our emotion manipulation provides an emotional context in which to reason about neutral material, rather than providing emotional content. Therefore, it is not surprising that our findings differ from those in Goel and Dolan (2003b). Reasoning in an emotional but unrelated context involves a different neural underpinning than does reasoning about emotional content.

The fact that we found neural level differences in reasoning, despite a lack of behavioral difference, suggests that the neural systems underlying reasoning are sensitive to neural systems previously recruited by emotional context, and can to some extent compensate for these effects of emotions. It is possible that the behavioral manifestations (that is, impairment of reasoning) emerge only when the system is stressed.

In summary, we had predicted that both positive and negative emotion would be detrimental to reasoning, and that the neural systems underlying reasoning under those two conditions would differ from that in the neutral condition. We found that, although neither positive nor negative emotional context significantly impaired reasoning performance, positive and negative context did have dissociable effects on the underlying neural mechanisms involved in reasoning.

## **ACKNOWLEDGMENTS**

This study was funded by a Wellcome Trust Grant (ABH00 FA032YBH064) to Vinod Goel.

### **SUPPLEMENTARY MATERIAL**

The Supplementary Material for this article can be found online at http://www.frontiersin.org/Journal/10.3389/fnhum.2014.00736/ abstract

#### **REFERENCES**

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

*Received: 16 May 2014; accepted: 02 September 2014; published online: 23 September 2014.*

*Citation: Smith KW,Vartanian O and Goel V (2014) Dissociable neural systems underwrite logical reasoning in the context of induced emotions with positive and negative valence. Front. Hum. Neurosci. 8:736. doi: 10.3389/fnhum.2014.00736*

*This article was submitted to the journal Frontiers in Human Neuroscience. Copyright © 2014 Smith, Vartanian and Goel. This is an open-access article distributed*

*under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

# Analyzing the association between functional connectivity of the brain and intellectual performance

#### *Gustavo S. P. Pamplona1 \*, Gérson S. Santos Neto2, Sara R. E. Rosset 2, Baxter P. Rogers 3 and Carlos E. G. Salmon1*

*1 InBrain Lab, Department of Physics, Faculty of Philosophy, Sciences and Letters of Ribeirão Preto, University of São Paulo, São Paulo, Brazil*

*2 Faculty of Medicine of Ribeirão Preto, University of São Paulo, São Paulo, Brazil*

*3 Department of Radiology and Radiological Sciences, Department of Biomedical Engineering, Institute of Imaging Science, Vanderbilt University, Nashville, TN, USA*

#### *Edited by:*

*Gorka Navarrete, Universidad Diego Portales, Chile*

#### *Reviewed by:*

*Lucas Sedeño, Institute of Cognitive Neurology (INECO), Argentina Roberto Colom, Universidad Autonoma de Madrid, Spain*

#### *\*Correspondence:*

*Gustavo S. P. Pamplona, InBrain Lab, Department of Physics, Faculty of Philosophy, Sciences and Letters of Ribeirão Preto, University of São Paulo, Av. Bandeirantes 3900, Ribeirão Preto, São Paulo, 14040-900, Brazil e-mail<EMAIL_ADDRESS>
Measurements of functional connectivity support the hypothesis that the brain is composed of distinct networks with anatomically separated nodes but common functionality. A few studies have suggested that intellectual performance may be associated with greater functional connectivity in the fronto-parietal network and enhanced global efficiency. In this fMRI study, we performed an exploratory analysis of the relationship between the brain's functional connectivity and intelligence scores derived from the Portuguese language version of the Wechsler Adult Intelligence Scale (WAIS-III) in a sample of 29 people, born and raised in Brazil. We examined functional connectivity between 82 regions, including graph theoretic properties of the overall network. Some previous findings were extended to the Portuguese-speaking population, specifically the presence of small-world organization of the brain and relationships of intelligence with connectivity of frontal, pre-central, parietal, occipital, fusiform and supramarginal gyrus, and caudate nucleus. Verbal comprehension was associated with global network efficiency, a new finding.

**Keywords: functional connectivity, fMRI, network parameters, intelligence, Wechsler intelligence scales, exploratory data analysis**

# **INTRODUCTION**

Functional connectivity is expressed as correlations between the blood oxygenation level dependent signals in different regions of the brain (Friston et al., 1993; Biswal et al., 1995; Van den Heuvel and Hulshoff Pol, 2010). Consistent spatial patterns of functional connectivity are found for individuals at rest and are presumed to reflect information processing networks (Lowe et al., 1998; Raichle et al., 2001; Beckmann et al., 2005; Damoiseaux et al., 2006). Recent advances in neuroimaging have provided new tools to measure and analyze interactions between brain regions, catalyzing the study of functional connectivity of the brain (Van den Heuvel and Hulshoff Pol, 2010). An important recent expansion of functional connectivity studies was the use of the principles of graph theory (Watts and Strogatz, 1998) to depict the brain as an efficient complex network, with brain regions as the nodes and functional connectivity as the edge weights (Sporns and Zwi, 2004; Bullmore and Sporns, 2009). The functional brain network shows a highly efficient small-world organization, with a high level of local clustering and short effective lengths between brain regions. This leads to high global efficiency of information flow in the network (Sporns and Zwi, 2004; Van den Heuvel et al., 2008).

An important tool to measure the intelligence in adults is the Wechsler Adult Intelligence Scale (WAIS), based on the "global capacity of the individual to act purposefully, to think rationally and to deal effectively with his environment" (Wechsler, 1939).  A previous study found that higher IQ scores are associated with greater functional connectivity within a fronto-parietal network, suggesting that the coordination of these regions is an important neural basis of individual intelligence (Song et al., 2008). A region-specific analysis of the lateral prefrontal cortex, part of the fronto-parietal network, found that its global connectivity predicted working memory performance and fluid intelligence (Cole et al., 2012). Two studies have reported an association between efficiency of global communication and intellectual performance, suggesting that individuals with higher intelligence have a more organized brain network overall (Van den Heuvel et al., 2008; Song et al., 2009).

However, the relationships between brain functional connectivity and psychological measures such as intelligence are not fully defined. In the present exploratory study, we pursued this line of research further by considering how the several indices of intelligence measured by the Wechsler Adult Intelligence Scale (WAIS-III) related to connection strengths and network properties in a brain network defined by a set of 82 a priori cortical and subcortical regions derived from an atlas (Tzourio-Mazoyer et al., 2002). The use of a smaller set of regions of interest preserves structural and physiological similarities, while simplifying the analysis and easing the interpretation of the findings relative to the commonly used voxel-wise approach. In contrast to some studies that considered a priori regions known to be related to intelligence (Song et al., 2008; Cole et al., 2012), the present study explored the brain as a whole, with no region-specific or networkspecific hypotheses. This analysis could help to elucidate how the human brain supports particular intellectual processes, extending previous work and providing background to future studies.

# **MATERIALS AND METHODS**

# **PARTICIPANTS**

Thirty one healthy people were recruited from the academic community and the local population living in the state of São Paulo, Brazil. They were right-handed, had no history of neurological or psychological illnesses, and were native speakers of Brazilian Portuguese. People with a range of educational levels were recruited to provide a greater range of intelligence scores (**Table 1**). Thirty of these participants made up Dataset 1. Volunteers participated in this study after responding to the standard screening interview of the Hospital of Clinics in Ribeirão Preto, and providing written consent as approved by the Research Ethics Committee of University of São Paulo.

## **MEASURES OF INDIVIDUAL INTELLIGENCE**

The level of intellectual performance was measured (Gérson S. Santos Neto and Sara R. E. Rosset) using the WAIS III test (Wechsler Adult Intelligence Scale) as modified for the Portuguese-speaking population of Brazil (Nascimento, 1998). WAIS-III is a widely used instrument that assesses several cognitive domains contributing to intelligence. It has high test-retest reliability and a large database for comparison and standardization (Gläscher et al., 2009). Measurements originating from the third version of the test are the four fundamental indices Verbal Comprehension Index, Perceptual Organization Index, Working Memory Index, and Processing Speed Index; and the overall score, Full-Scale IQ. The test took 1 h 30 min on average and was given at a separate time from the image acquisition (less than 2 months apart, except for one participant with a 3-month difference).

# **DATA ACQUISITION**

Resting-state functional magnetic resonance images (eyes open, no fixation) from each participant were acquired in a Phillips 3 Tesla scanner with a Quasar Dual gradient system (80 mT/m, 200 mT/m/ms), using an eight channel head coil and SENSE encoding. An EPI sequence was performed with the following parameters: 2000 ms repetition time, 30 ms echo time, 240 × 240 mm field of view, 3 × 3 mm in-plane voxel size, 4.0 mm slice thickness, 0.5 mm slice gap, 32 slices, 80◦ flip angle, 200 volumes, 25.2 Hz bandwidth per pixel. Overall functional acquisition time was 6:48, including four initial volumes that were discarded prior to analysis.

High-resolution anatomical images were also acquired using a 3D T1 weighted turbo-field-echo gradient sequence with the following parameters: 2500 ms repetition time, 3.2 ms echo time, 7.0 ms time echo spacing, 900 ms inversion time, 1 mm isotropic voxel size, 8◦ flip angle, 240 × 240 × 160 mm3 field of view, and overall time 5:19. Diffusion and other functional images were also acquired, but not used in the present analysis.

A separate set of resting-state functional magnetic resonance images (open eyes, with fixation) from 30 subjects (13M/17F, age: 26.5 ± 5.5, age range: 20–42, right-handed) was included in the analysis to provide a baseline for the small-worldness measurement, and classified as Dataset 2. These images were from the 1000 Functional Connectomes Project (Biswal et al., 2010), specifically the data acquired in Leipzig, Germany, in a 3 Tesla scanner with the following parameters: 2300 ms repetition time, 34 slices, 195 volumes.

# **PRE-PROCESSING**

Functional MRI data were processed using the SPM8 software (http://www*.*fil*.*ion*.*ucl*.*ac*.*uk/spm/software/spm8) and the CONN functional connectivity toolbox (14), both implemented in MatLab (R2013a, The MathWorks, Natick, MA, USA). For each individual's functional images, rigid body movement was measured and corrected using a two-step procedure in which the first of the specified functional images was used as a reference to which all subsequent images were realigned, then the functional images were re-registered to the mean image. Participants who moved more than 2 mm in translation or 1 degree in rotation were excluded from analysis. Functional images were then spatially smoothed using a Gaussian filter of 5 mm full width at half maximum.

Anatomical images from each volunteer were registered to the mean functional image created in the previous step. The anatomical volumes were segmented into gray matter, white matter and cerebrospinal fluid compartments and non-linearly registered to the MNI standard space. The resulting masks were eroded once at an isotropic voxel size of 2 mm to minimize partial volume effects. This step produced spatial normalization parameters that were used to apply the transformations to the functional images.

Voxel time series were additionally processed to reduce noise. Signals from the white matter and CSF compartments (5 principal components each) and the estimated head motion time series and first differences were removed by regression. A temporal band-pass filter was applied to remove signals outside the range 0.008–0.09 Hz (Whitfield-Gabrieli and Nieto-Castanon, 2012).

Average signals were extracted from a set of 116 regions defined by the Automated Anatomical Labeling (AAL) atlas, which is a macroanatomical parcellation of the single subject MNI-space template brain (Tzourio-Mazoyer et al., 2002). Eight of the AAL regions were excluded from the analysis due to their small size (less than 300 voxels), which increased the likelihood that partial volume effects would contaminate signals from those regions. Cerebellum and cerebellar vermis regions were also excluded because they were not fully covered by the fMRI. Therefore, 82 cortical and subcortical regions were included in total, all of them shown in the Supplemental Material (Table S1) with their AAL abbreviations and the locations of their centers, in x, y, and z.

# **ANALYSIS OF FUNCTIONAL CONNECTIVITY AND INTELLIGENCE**

Weighted association matrices were created (**Figure 1**) using the Pearson correlations between the time series of each pair of brain regions. Functional connectivity of each path was compared with the four fundamental intelligence indices and the Full-Scale IQ using the Pearson correlation coefficient (**Table 3**, **Figure 2**). Negative values of the matrices were included to consider also the functional anticorrelations. Functional connectivity values were

the Fisher Z scores computed between the time series of each pair of regions. Each list of 3321 *p*-values (all pairs of 82 regions) was adjusted to maintain a false discovery rate of 0.05, separately for each IQ index.

# **GRAPH ANALYSIS**

We examined small-worldness, characteristic path length, clustering coefficient, and global and local efficiency. Characteristic path length is the shortest path length between all pairs of nodes. Clustering coefficient is the number of connections in the neighborhood of a certain node divided by the maximum number of possible connections between the neighbors of this node. Global efficiency is inversely related to the characteristic path length and measures how efficiently information is communicated between nodes. Local efficiency of a given node is the inverse of the average shortest path connecting all neighbors of that node and evaluates the influence of different paths based on the connection weights of the node's neighbors, i.e., a path made of strong connections contributes to the local efficiency more than a path made of weak connections. Therefore, local efficiency of a node is related to its clustering coefficient, since more connections or stronger ones between neighbors directly affect both measures.

All the network parameters were computed using the Brain Connectivity Toolbox (BCT) (Rubinov and Sporns, 2010). Negative correlations in association matrices were not included in any analysis of network measures, since they need to be removed prior to BCT computations (Rubinov and Sporns, 2010, 2011). Different network measures require different pre-processing of the association matrix.

### *Small-worldness analysis*

Characteristic path length (L) and clustering coefficient (C) were computed to study the small-worldness of our data (Dataset 1, **Figure 3**) and of an independent set of resting-state fMRI (Dataset 2, **Figure 4**) to verify the small-worldness of the network in our sample and to provide a baseline for our measurements. These calculations used binary matrices obtained by thresholding the correlation matrices (**Figure 1**) at a range of values. The same analysis was applied to 20 random matrices with the same number of connections and similar distribution of connections (Sporns and Zwi, 2004), to obtain a random-matrix characteristic path length (Lrandom) and clustering coefficient (Crandom). The networks are said to have small-world organization for correlation thresholds in which L = Lrandom and C *>* Crandom; this was calculated using a 2-sample *t*-test for *p* ≤ 0*.*01.

#### *Analysis of global network properties and intelligence*

Global network parameters (characteristic path length, clustering coefficient, and efficiency), obtained using weighted networks, were related to the intelligence indices using the Pearson correlation coefficient (**Table 4**). The Z-transformed correlation matrix was used for the association matrix, except for global efficiency, which used the Pearson correlations due to the need to restrict the range to [0,1]. Negative values were set to zero. Some form of normalization is necessary to obtain measures that are independent of the network size, dividing parameters obtained from brain networks by those obtained from random networks. For normalization of weighted networks, a recently approach purposes to compute the average value from an ensemble of surrogate graphs (Stam et al., 2009). In our study, 100 surrogate random weighted networks were constructed, derived from the original networks by randomly permuting the edge weights. The parameters of these random weighted networks were averaged

and used in normalization. For this analysis, *p*-values were not adjusted.

An additional analysis of global characteristic path length and global clustering coefficient associated to intelligence indices was performed using a binarized association matrix (thresholded at *r* = 0*.*45) to facilitate comparisons with Van den Heuvel et al. (2009) (**Figure 5**). Both metrics were normalized using the same 20 equivalent random binary matrices, specified in Section Small-Worldness Analysis, averaged for each brain network. Pearson correlations were also transformed using the Fisher Z in this analysis.

### *Analysis of local network properties and intelligence*

Finally, local efficiency, which is related to clustering coefficient, was related to the intelligence indices using the Pearson correlation coefficient (**Table 5**, **Figure 6**). Local efficiency calculations used the untransformed Pearson correlation matrix for the association matrix, except that negative weights were replaced with 0. For this analysis, false discovery rates were computed per node (over the list of the 81 other regions).

# **RESULTS**

Of the 31 volunteers, one did not perform the intelligence test and exhibited excessive movement during imaging acquisition; thus 30 participants (Dataset 1) were included in the small-world organization study (ages: mean 27 years, standard deviation 6, range: 19–38; 15 women) and 29 participants were included in the intellectual performance study (ages: mean 27 years, standard deviation 6, range: 19–38; 14 women). Demographic data for the intellectual performance study (29 participants) are in **Table 1**.

We have included a table of correlations between the intelligence indices in our sample (**Table 2**). Verbal IQ (VIQ) was strongly correlated with Verbal Comprehension Index (VCI) and Working Memory Index (WMI). Performance IQ (PIQ) was correlated strongly with Perceptual Organization Index (POI) and moderately with Processing Speed Index (PSI). This was expected because VIQ and PIQ are derived from the fundamental indices, and so these indices were not used in the analysis of this study. Full scale IQ (FSIQ) was strongly correlated with Perceptual Organization and Working Memory indices and moderately correlated with Verbal Comprehension and Processing Speed Indices, also expected.

# **ASSOCIATIONS BETWEEN FUNCTIONAL CONNECTIVITY AND INTELLIGENCE**

Possible correlations of functional connectivity with FSIQ and perceptual organization are shown in **Table 3** and **Figure 2**. **Table 3** shows all correlations with FDR*<*0.05; Tables S2–S6 in the Supplemental Material show complete results for the 15 most significant associations for each IQ index. The most prevalent regions were pre-central, parietal, and occipital.

#### **SMALL-WORLDNESS ANALYSIS**

To establish the baseline validity of the network analysis, we computed small-worldness for our data and compared the results to an independent data set. Brain networks showed a clear smallworld organization over a range of thresholds. **Figure 3** (left) and **Figure 4** (left) show normalized characteristic path length from binary networks as a function of threshold for participants for Dataset 1 and Dataset 2, respectively. Mean values for 20 matched random networks are also shown for comparison. **Figure 3** (right) and **Figure 4** (right) shows the same for the normalized clustering coefficient. In both datasets, networks showed a clear small-world organization for correlation thresholds between 0.05 and 0.20, characterized by L ≈ Lrandom for thresholds lower than 0.20 and C Crandom for thresholds higher than 0.05 (2-sample *t*-test, all *p <* α = 0*.*01, Bonferroni corrected for multiple thresholds).

# **ASSOCIATIONS BETWEEN GLOBAL NETWORK PROPERTIES AND INTELLIGENCE**

We observed a negative, though statistically weak (*p* = 0*.*14), correlation between FSIQ and normalized characteristic path length (lambda) (**Figure 5**, left). This was computed using correlation matrices binarized at a threshold of 0.45, the same threshold applied by Van den Heuvel et al. (2009), for the purpose of direct comparison.

Verbal comprehension was associated with normalized global efficiency (*r* = 0*.*43, *p* = 0*.*02, uncorrected *p*-value). Also, global efficiency was weakly correlated with FSIQ (*r* = 0*.*24, *p* = 0*.*22, uncorrected *p*-value). These results along with a complete list of correlations between intelligence scores and global network parameters are shown in **Table 4**.

# **ASSOCATIONS BETWEEN LOCAL NETWORK PROPERTIES AND INTELLIGENCE**

We observed also possible relationships between local efficiency and measures of intelligence (**Table 5**, **Figure 6**). Prominent regions were pre-central gyrus, associated with FSIQ; caudate nucleus, associated with verbal comprehension and processing speed; bilateral inferior occipital gyrus, associated with verbal comprehension; and bilateral rolandic operculum, associated with working memory and processing speed. However, in all cases the false discovery rate was *>*0.05; uncorrected *p*-values are reported here.

# **DISCUSSION**

We have extended a number of previous observations concerning brain functional connectivity and intelligence to the Portuguesespeaking population. These include the presence of small-world organization and correlations of intelligence with global and local characteristics of the brain's functional networks. Additionally, some novel findings in this exploratory study suggest hypotheses for future research.

The global functional brain network exhibited small-world organization at correlation thresholds between 0.05 and 0.20, α = 0*.*01, Bonferroni corrected for multiple comparisons of thresholds, and this closely matched the small-world organization that was apparent in the confirmation data set (**Figures 3**, **4**). This suggests a high level of local clustering combined with a relatively

*Age and intelligence scores are shown as mean* ± *standard deviation.*

#### **Table 2 | Correlations between intelligence scores.**

*Bold numbers represent significant values for* α *< 0.01.*

small number of long-distance connections (Watts and Strogatz, 1998). This threshold range is smaller than the thresholds of 0.3–0.5 reported in previous observations of small-worldness in whole-brain networks (Van den Heuvel et al., 2008, 2009). However, node definitions differed substantially between the studies as well. Small-world networks are an attractive model for the connected human brain, because of their ability to transfer information with high efficiency for low wiring cost (Watts and Strogatz, 1998), and seem ubiquitous in the organization of anatomical connectivity, affected in a variety of diseases (Bassett and Bullmore, 2009). Moreover, Sporns and Zwi, in 2004, stated that information integration and even mental awareness depend on the small-world structure. Our replication of this effect supports the validity and the reliability of the network measures in this sample.

Globally, FSIQ showed a weak negative correlation with characteristic path length (**Figure 5**, left; *r* = −0*.*28, 95% CI = −0*.*59, 0.10), although with no statistical significance. Additionally, global efficiency (inversely correlated with path length) showed a weak positive correlation with FSIQ (**Table 4**; *r* = 0*.*24 95% CI = −0.14, 0.56), not statistically significant also. These same correlations were weaker when the full (weighted) association matrix was used (**Table 4**) instead of a binarized matrix (**Figure 5**). It is not known whether the thresholding step increases or decreases the reliability of the resulting measurements; however, possibly of note, correlations were observed to be the same sign in our results and in previous literature regardless of method or statistical significance. The consistent finding of a negative correlation between characteristic path length and FSIQ could be an extension to Portuguese speakers of the previous finding in Dutch speakers (Van den Heuvel et al., 2009): for characteristic path length, *r* = −0*.*54, 95% CI −0.80,−0.11. The negative correlation is consistent with the previously proposed idea that human intelligence is related to how efficiently different brain regions are organized and integrated (Van den Heuvel et al., 2009). It also suggests that functional brain networks are optimized in computational efficiency to promote higher

**Table 3 | Associations between functional connectivity and intelligence indices (Full-Scale IQ—FSIQ, Perceptual Organization Index—POI) for specific nodes (center coordinates in x, y, and z) in the overall network, and with (uncorrected) 95% confidence intervals.**

*Functional connectivity was measured as the Fisher transformed correlation between the two regions' time series. Only region pairs whose connectivity was correlated with IQ index at FDR < 0.05 are shown. Tables S2–S6 in the Supplemental Material show further results.*

processing speed (Van den Heuvel et al., 2009) with minimal wiring cost (Chklovskii et al., 2002).

The network parameters studied here were measurements of functional segregation (clustering coefficient and local efficiency), that describe the processing occurring within densely interconnected networks of brain regions; and functional integration (characteristic path length, and its inverse, global efficiency), that is related to how information from distributed brain regions is combined (Rubinov and Sporns, 2010). Global efficiency was associated with verbal comprehension (*r* = 0*.*43; 95% CI = 0.08, 0.69) (**Table 4**), a novel suggestive finding worthy of further study. This finding, combined with associations between VCI and local efficiency found in several brain regions (**Table 5**, **Figure 6B** and further discussed below) suggests that linguistic and verbal abilities are linked with a higher brain efficiency, at both global and local levels.

No other associations were found between global network parameters and intellectual performance (**Table 4**). Because of the relatively small sample size of this study, we are not able to make strong conclusions from this and it does not necessarily conflict with prior findings, as our estimated 95% confidence intervals included the statistically significant correlation values found by others (Song et al., 2009; Van den Heuvel et al., 2009). However, it is possible that relationships between functional connectivity and intelligence could be limited to sub-networks of the brain, rather than being present at a global level, so we proceeded to examine network characteristics at a regional level also.

Local efficiency in the caudate nuclei was associated with VCI (**Table 5**). Some studies show that this region is important for language and verbal abilities, revealing that a smaller shortest path between the caudate and neighbor regions would be related to a higher verbal intelligence. This was not the only feature involving the caudate that was related with verbal abilities. Caudate function has also been related to verbal fluency during a working memory task (Gruber and von Cramon, 2003), and has shown activity during speech contrasted with a non-speech rest baseline condition (Simmonds et al., 2011). Significant associations with verbal fluency performance have also been found for caudate nuclei volume, suggesting that this region is implicated in the circuitry mediating this ability (Hannan et al., 2010). Left caudate plays an important role in language selection in both monolingual and multilingual people (Crinion et al., 2006), and some studies propose that the caudate would act to finetune interactions between automatic and more complex language processing (Friederici, 2006) or in the resolution of word ambiguity (Ketteler et al., 2008).

Local efficiency in the parietal gyrus was correlated with Verbal Comprehension and Processing Speed indices (**Table 5**), and connection strengths to the parietal lobe correlated with Perceptual

**Table 5 | Associations between non-normalized weighted-network local efficiency and intelligence indices (Full-Scale IQ—FSIQ, Verbal Comprehension Index—VCI, Working Memory Index—WMI, Processing Speed Index—PSI) for specific nodes in the overall network, with 95% confidence intervals and** *p***-values (uncorrected for multiple comparisons).**

*Only the subset with correlations at p < 0.05 are shown (uncorrected for multiple comparisons).*

**Table 4 | Pearson correlations between normalized weighted-network global parameters (characteristic path length, global efficiency, and global clustering coefficient) and intelligence indices (Full-Scale IQ—FSIQ, Verbal Comprehension Index—VCI, Perceptual Organization Index—POI, Working Memory Index—WMI, Processing Speed Index—PSI) with 95% confidence intervals and** *p***-values (uncorrected for multiple comparisons).**

Organization and Working Memory indices (Tables S4, S5 in Supplemental Material).

Local efficiency and connection strength in occipital lobe regions were associated with higher general intelligence scores and other indices (**Tables 3**, **5**). This suggests an impact of early perceptual processing on WAIS scores, especially Perceptual Organization. Although we did not observe correlations between the POI and segregational network properties (**Table 5**), there were some correlations with individual connections (**Table 3**). This may mean that this index is more related to individual connections than to network organization, possibly because of the necessity of rapid transfer of information of this region to others. It may reflect the same phenomenon observed in a recent study where higher IQ was correlated with shorter inspection time measured by EEG (which tells how fast the system extracts information from a given stimulus) because recurrent signals those that are transmitted from a higher-tier sensory region to a lower one and that cognitive functions rely on—reach visual areas faster (Jolij et al., 2007).

Local efficiency of bilateral rolandic operculum correlated with WMI (**Table 5**, **Figure 6C**). This region encompasses part of the pre-central gyrus. This is consistent with a number of other findings relating pre-central areas to working memory, in terms of both activity (Gruber and von Cramon, 2003; Colom et al., 2010) and functional connectivity (Newton et al., 2011; Cole et al., 2012). We also observed a correlation between left precentral regions and occipital ones with measures of general and fluid intelligence (**Table 3**, **Figure 2A**). Although other findings reported that pre-central activity and connectivity properties are related to fluid intelligence (Cole et al., 2012) as well as general intelligence (Gray et al., 2003), the specific role of the pre-centraloccipital connection to the general intelligence is not known. Since these relationships are not described yet in the literature, this study may be a starting point for this question.

At the level of single paths, the strongest correlations we observed between FSIQ and functional connectivity (**Table 3**, **Figure 2A**) are consistent with the parieto-frontal integration theory (P-FIT) of Jung and Haier (2007), which was based on an extensive review of the literature relating measures of intelligence to brain structure and function. Individual differences of the described connections in this model are predicted to correlate with differences in intellectual performance. That is what we have partially observed in the patterns of functional connectivity, with higher functional connectivity predicting greater FSIQ and perceptual organization capacity. The model proposes information flow from basic sensory/perceptual processing regions to areas where structural abstraction and elaboration are involved. This is represented in our results by the connection between fusiform gyrus—a region involved in recognition of visual input and visual imagery—and parietal gyrus; and the connection between occipital and parietal cortex (**Table 3**). Then, a parieto-frontal network is responsible for information processing and abstraction, and finally the anterior cingulate selects the response (Jung and Haier, 2007), although no associations could be detected in our study to corroborate these two parts of the model. Nevertheless, direct connections between occipital regions and pre-central ones were associated with FSIQ (**Table 3**, Table S2 in Supplementary Material), which is not in accordance with the P-FIT and thus suggests a need for further study. Of note, as not all of the relationships predicted by this model were present, more experiments would be needed to robustly confirm or reject all aspects of the model.

Our selection of 82 pre-defined atlas regions as network nodes offers reduced complexity of the networks and higher data processing speed compared to a voxel-wise approach, and possibly easier interpretability of the findings in terms of known properties of the relatively large regions. The finding of small-world organization bolsters the comparability of our results to those of other studies that used different node definitions. However, it is also true that results of this study are partially dependent on the node definitions, and the node definitions used here may not coincide with others. Example of correspondences include an association between local efficiency in the left pre-central gyrus and the Full-Scale IQ for a weighted anatomical network made of 90 AAL atlas regions (Li et al., 2009) (*r* = 0*.*25; 0.03, 0.45), endorsing our result in **Table 5** (*r* = 0*.*37; 0.010, 0.65). In addition, we observed a weak correlation (*r* = 0*.*24; *p* = 0*.*22) between global efficiency and Full-Scale IQ (**Table 4**), just as Song et al. (2009) did for the default mode network (*r* = 0*.*24; *p* = 0*.*072). Findings we did not observe include those involving local efficiency of a number of cortical and subcortical regions (Li et al., 2009) and the associations between intelligence and functional connectivity reported by Song et al. (2008, 2009). Direct comparisons are reported in the Supplement Material (Tables S7, S8).

In an exploratory study such as this one, the possibility of chance findings must be clearly communicated. Failing to acknowledge multiple tests would lead to many false positive associations. On the other hand, strictly controlling type I error is likely to eliminate interesting leads in a sample of this size. Therefore, in associations between path connectivity values and intelligence scores, we compromised by controlling the false discovery rate (estimated fraction of positive findings that were false) at 5% for each path (3321 values). As the associations with global and local network parameters showed high *p*-values, FDR control was not performed in these cases to conserve a few of the most relevant associations. Our findings that certain regions were important in more than one context, and that some regions showed symmetric bilateral effects, do lend some apparent validity to the results. We have provided complete information about the statistical reliability of all findings to facilitate hypothesis development and comparisons with other studies.

Further study of the relationships between brain network organization and intelligence would be necessary to complement and extend the findings shown here. This study considered a Portuguese-speaking population, but further data from different populations should be analyzed to allow the results to be generalized, in particular the relationship between global efficiency and verbal intelligence that was strongly apparent in our work. More detailed templates could be used in the definition of the network nodes for a finer-grained investigation of the brain's connectivity. It is also noteworthy that we considered only positive correlations between nodes; anticorrelations may provide complementary data once methods to quantify them arise (Rubinov and Sporns, 2010).

The findings shown here replicate and extend the negative association between characteristic path length of the functional brain network and cognitive general intelligence for a Portuguesespeaking population. The small-world organization model was verified as a feature of brain networks, suggesting an ability to transfer information with high efficiency and low wiring cost. Global efficiency was weakly associated with general intelligence but strongly associated with VCI, a novel finding. Combined with the observed relationship between verbal comprehension and local efficiency in several regions, this suggests that a possible link between language ability and organizational and integrational properties of the brain network warrants further study. Additionally, an exploratory analysis suggested associations between intelligence and network properties of frontal, parietal, and occipital cortices; and fusiform, supramarginal, pre-central gyrus, and caudate nuclei.

# **SUPPLEMENTARY MATERIAL**

The Supplementary Material for this article can be found online at: http://www*.*frontiersin*.*org/journal/10*.*3389/fnhum*.* 2015*.*00061/abstract

# **REFERENCES**

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

*Received: 10 October 2014; accepted: 23 January 2015; published online: 10 February 2015.*

*Citation: Pamplona GSP, Santos Neto GS, Rosset SRE, Rogers BP and Salmon CEG (2015) Analyzing the association between functional connectivity of the brain and intellectual performance. Front. Hum. Neurosci. 9:61. doi: 10.3389/fnhum.2015.00061 This article was submitted to the journal Frontiers in Human Neuroscience.*

*Copyright © 2015 Pamplona, Santos Neto, Rosset, Rogers and Salmon. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

# HUMAN NEUROSCIENCE

# Planning following stroke: a relational complexity approach using the Tower of London

#### **Glenda Andrews 1\*, Graeme S. Halford2 , Mark Chappell 2 , Annick Maujean3 and David H. K. Shum2**

1 Behavioural Basis of Health Program, Griffith Health Institute, School of Applied Psychology, Griffith University, Gold Coast, QLD, Australia

2 Behavioural Basis of Health Program, Griffith Health Institute, School of Applied Psychology, Griffith University, Brisbane, QLD, Australia

3 Centre for National Research on Disability and Rehabilitation Medicine (CONROD), Griffith Health Institute, Griffith University, Meadowbrook, QLD, Australia

#### **Edited by:**

Vinod Goel, York University, Canada

#### **Reviewed by:**

Hasan Ayaz, Drexel University, USA Sharlene D. Newman, Indiana University, USA Sashank Varma, University of Minnesota, USA

#### **\*Correspondence:**

Glenda Andrews, School of Applied Psychology, Griffith University, Parklands Drive, Southport, Gold Coast, QLD 4222, Australia e-mail<EMAIL_ADDRESS>
Planning on the 4-disk version of the Tower of London (TOL4) was examined in stroke patients and unimpaired controls. Overall TOL4 solution scores indicated impaired planning in the frontal stroke but not non-frontal stroke patients. Consistent with the claim that processing the relations between current states, intermediate states, and goal states is a key process in planning, the domain-general relational complexity metric was a good indicator of the experienced difficulty of TOL4 problems. The relational complexity metric shared variance with task-specific metrics of moves to solution and search depth. Frontal stroke patients showed impaired planning compared to controls on problems at all three complexity levels, but at only two of the three levels of moves to solution, search depth and goal ambiguity. Non-frontal stroke patients showed impaired planning only on the most difficult quaternary-relational and high search depth problems. An independent measure of relational processing (viz., Latin square task) predicted TOL4 solution scores after controlling for stroke status and location, and executive processing (Trail Making Test). The findings suggest that planning involves a domain-general capacity for relational processing that depends on the frontal brain regions.

**Keywords: Tower of London, planning, moves to solution, search depth, goal ambiguity, relational complexity, stroke, frontal lobes**

# **INTRODUCTION**

Planning is important in many areas of life and impairments in this capacity have adverse implications for independent living (Jefferson et al., 2006). Planning involves cognitive processes that depend on frontal regions of the brain (Shum et al., 2000, 2009; Unterrainer and Owen, 2006). In the current research, we examined the extent to which planning assessed using a 4-disk version of the Tower of London (TOL) is impaired in people who have suffered a stroke. A further issue relates to the nature of the cognitive processes that planning involves. More specifically, the research investigated the claim that processing the relations between current states, intermediate states, and goal states is a key process in planning (Halford et al., 1998) and that the complexity of these relations is a good indicator of the experienced difficulty of the TOL problems.

Planning in tower tasks such as the Tower of Hanoi and the TOL involves devising a sequence of moves in order to transform an initial state into a specified goal state. In the original 3-disk version of the TOL (viz., TOL3) developed by Shallice (1982), three colored disks are presented on three poles that differ in height. Respondents are required to rearrange the disks to match a target configuration (goal state) and to do so in a specified number of moves.

The results of several studies that employed the TOL3 to assess planning following traumatic brain injury (e.g., Cockburn, 1995; Rasmussen et al., 2006), suggested the need to increase the sensitivity of the TOL3 by including more difficult items. To address this issue, Tunstall (1999) developed the 4-disk version (TOL4) that includes ten items that require as many as nine moves. Shum et al. (2009) used the TOL4 to examine impairments in planning following traumatic brain injury. The patients performed more poorly than matched controls, but the impairment was specific to patients with frontal damage and to the items that required a greater number (i.e., six to nine) of moves. No planning impairment was observed on items that required fewer (i.e., two to five) moves. Planning performance in patients with no frontal damage was comparable to matched controls. The findings of Shum et al. (2009) demonstrated the importance of employing sensitive measures of planning. In that study, sensitivity was achieved by including simpler as well as more difficult problems that required fewer moves or more moves, respectively.

Moves to solution is widely used as a metric of TOL problem difficulty that has been employed in brain imaging studies and computational approaches to planning and problem solving in the TOL (e.g., Dehaene and Changeux, 1997; Newman et al., 2003). However, the number of moves to solution has been criticized as a complexity metric on the grounds that it does not sufficiently capture the cognitive processes underlying performance. Such criticisms have prompted researchers to consider alternate complexity metrics that tap different structural parameters of the tower tasks (Ward and Allport, 1997; Kaller et al., 2011, 2012; Köstering et al., 2014).

Köstering et al. (2014) examined two such factors (search depth and goal hierarchy) in the 3-disk TOL. Search depth refers to the number of intermediate moves that must be considered before the first goal move is made. When search depth is higher a longer series of intermediate moves and their interdependencies must be considered. Goal hierarchy (goal ambiguity) refers to the extent to which the correct sequential ordering of the goal moves is obvious from the specified goal state. When the goal state is vertical (i.e., all disks on the same pole), it is clear that the disk in the lowest position on the pole has to be placed before the disks in higher positions, so the sequential ordering of the moves is relatively unambiguous. When the goal state is flat (i.e., a disk on each of three poles), the sequential ordering of the moves is more ambiguous. Köstering et al. (2014) examined the effects of these two factors in a sample of normally aging adults. Adults aged from 60 to 76 years performed comparably on problems with low search depth, but performance declined significantly from 60 to 76 years on problems with high search depth. Adults over 76 years performed poorly irrespective of search depth. The effect of goal ambiguity was significant in that problems with less ambiguous goals were performed better than those with goals that were more ambiguous. However, this effect did not vary with age. The findings were interpreted as consistent with the frontal lobe theory of cognitive aging. Greater search depth imposes a higher demand on working memory, which is subserved by frontal regions, whereas increased goal ambiguity is thought to involve the striatum.

The search depth metric used by Köstering et al. (2014) to estimate the complexity of items on the 3-disk TOL is similar in some respects to the metric proposed in relational complexity theory (Halford et al., 1998). In this theory, complexity is defined in a domain-general way. It corresponds to the number of variables that are related in a cognitive representation, or the number of slots that must be filled. The simplest (unary) relations have a single slot. An example is class membership. The fact that Fido is a dog can be expressed as *dog* (Fido). Binary relations have two slots. An example is *larger-than*(elephant, mouse). Ternary relations have three slots as in *arithmetic addition*(2,3,5). Quaternary relations have four slots, as in *proportion*(2,3,6,9). More complex relations are predicted to impose higher processing loads than less complex relations.  On average, young adults can process four interacting variables in the same decision (Halford et al., 2005) consistent with a quaternary-relational limit.

The Method for Analysis of Relational Complexity (MARC) incorporates a set of principles for estimating the complexity of cognitive tasks (in terms of the metric) and the processing loads they impose (Halford et al., 2007b, 2010; Andrews and Halford, 2011). The estimates must be based on sound knowledge of how people perform the task and opportunities to reduce complexity and processing load through the use of segmentation and chunking must be taken into account. Segmentation involves decomposing (segmenting) complex tasks into less complex components that do not overload capacity and that can be processed in succession. Conceptual chunking involves recoding concepts into fewer variables. For example, the ternary-relational concept velocity, defined as *velocity* = *distance/time*, can be recoded into a unary-relational concept as when speed is indicated by the position of a pointer on a dial. However, the reduction in processing load occasioned by conceptual chunking comes at the cost of temporary loss of access to the relationships that make up the concept. For example, a unary-relational representation of velocity would not be sufficient to determine how velocity changes as a function of time or of distance, but it would be adequate if current velocity is the only variable of interest. By the principle of cognitive economy, humans will employ the least complex representation available to complete the task. More complex representations will be constructed only when less complex representations prove inadequate.

When tasks have multiple steps, task complexity corresponds to the most complex step. The processing load imposed will depend on the number of interacting variables that must be represented in parallel to perform the most complex step of the task, using the least demanding strategy available. Thus, demand corresponds to the peak load imposed during performance of the task, rather than to the total amount of processing involved. Complexity and number of steps can be manipulated independently as shown by Birney et al. (2006).

The relational complexity metric has been applied to tasks in many different content domains including transitive inference (Halford, 1984; Andrews and Halford, 1998; Andrews, 2010; Andrews and Mihelic, 2014), suppositional reasoning (Birney and Halford, 2002), categorical syllogisms (Zielinski et al., 2010), conditional reasoning (Cocchi et al., 2014), class inclusion (Halford and Leitch, 1989), inferences based on classification hierarchies (Halford et al., 2002b), card sorting (Halford et al., 2007a), balance scale reasoning (Halford et al., 2002a; Andrews et al., 2009), numerical reasoning (English and Halford, 1995; Andrews and Halford, 2002; Knox et al., 2010), and theory of mind (Andrews et al., 2003; Halford and Andrews, 2014), as well as decision making in gambling tasks (Bunch et al., 2007; Andrews et al., 2008), delay of gratification (Bunch and Andrews, 2012), reversal learning and conditional discrimination (Andrews et al., 2012), and comprehension of relative clause sentence (Andrews et al., 2006). The breadth with which the relational complexity metric has been (can be) applied contrasts with other metrics that apply to specific content domains or tasks with a specific structure.

Studies such as those cited above show that the complexity of relations that humans can process increases with age during childhood (Andrews and Halford, 2002, 2011; Bunch and Andrews, 2012), reaching quaternary relations in adulthood (Halford et al., 2005) before declining in later adulthood (Viskontas et al., 2005; Andrews and Todd, 2008).

In the current research, we tested the hypothesis that the difficulty of TOL4 problems stems from their complexity. A relational complexity analysis of the 10 TOL4 items was conducted. The complexity analysis of three of the problems will be illustrated. The initial configuration of disks on poles was the same for all problems and it is shown in **Figure 1A**. The yellow (Y) and white (W) disks were on the leftmost pole (1), the blue (Bu) and black (Bk) disks were on the rightmost pole (3), while the middle pole (2) was unoccupied.

A move is coded as the binary relation, shift(color, pole). In the first problem, the goal is to transform the initial configuration (**Figure 1A**) into the target configuration (**Figure 1B**) in which yellow and white are on pole 1 and black and blue disks are on

pole 2. This requires two moves. First, blue must be moved to pole 2. This is expressed as shift(Bu, 2). Second, black must be moved to pole 2. This can be expressed as shift(Bk, 2). Each move can be performed without taking any other move into account so complexity depends solely on two slots, the disk to be moved and the location to which it is moved. Therefore both moves are binaryrelational, so the maximum complexity during this problem is binary-relational.

In a more complex problem, the goal is to transform the initial configuration (**Figure 1A**) into the target configuration (**Figure 1C**) in which all four disks are on pole 3 in the top-down order yellow, white, blue, and black. This problem involves nested moves. Before white can be moved to pole 3, yellow must be moved to pole 2. Nested moves such as this are coded as the higher-order relation:

prior(shift(color, pole), shift(color, pole)).

For the problem described, this sequence can be expressed as:

$$\text{prior}(\text{shift}(\mathsf{W}, \mathsf{3}), \text{shift}(\mathsf{Y}, \mathsf{2})).$$

Here, there are four slots to be filled, so *prima facie* a relation between four variables is being represented. However, conceptual chunking can be employed to reduce the task to ternary-relational. In the preceding example, Y, 2 can be chunked as a single entity corresponding to "obstructing disk" (Y2) that has to be removed to enable shift(W, 3). Thus the operative variables are: disk to be shifted (W), the goal for that disk (3), and the goal for the obstructing disk (2). The principle is that the color of the obstructing disk (Y) does not need to be processed independently of the need to find a pole to shift it to, so as to remove the obstruction of shifting white to pole 3. Planning these nested moves involves ternaryrelational processing. The final move involves shifting the yellow disk to pole 3, shift(Y, 3),which is binary-relational, as in the previous example. Thus the maximum complexity during this problem is ternary-relational.

In an even more complex problem, the goal is to transform the initial configuration (**Figure 1A**) into the target configuration (**Figure 1D**) in which yellow is on pole 1, black is above white on pole 2, and blue is on pole 3. This problem involves multiple nestings and conceptual chunking. Before yellow can be placed at the base of pole 1, yellow must first be moved to pole 3 so that white can be moved to pole 2. Such situations can be expressed as the higher-order relation,

> prior(shift(colour, pole), prior(shift(colour, pole)), shift(colour, pole)).

These expressions can be read most easily starting at the rightmost move. Thus, in the example immediately below, Y, 3 is moved first, followed by W, 2, followed by Y, 1. For the problem described (**Figure 1D**), this move can be expressed as:

prior(shift(Y, 1), prior(shift(W, 2), shift(Y, 3))).

This can be chunked to quaternary-relational representation as;

prior(shift(Y, 1), prior(shift(W/Y, 2/3)))

The chunked portion can then be unpacked as;

prior(shift(W, 2), shift(Y, 3))

This yields the move to shift Y to 3 before shifting W to 2, then Y can be shifted to 1. The goal of the next move is to have blue on pole 3 and black on pole 2. To achieve this goal, blue must be first be moved to pole 1 so that black can be moved to pole 2 before blue is moved back to pole 3. This move can be expressed as,

prior(shift(Bu, 3), prior(shift(Bk, 2), shift(Bu, 1))).

As with the previous problem, chunks Bu/Bk and 2/1 can be formed, reducing the move to quaternary-relational complexity. The chunked representation can be unpacked yielding Bk on 2 and Bu on 1. Finally, Bu can be moved to 3. As in the ternaryrelational problem described above, some chunking is possible. However, planning the sequence of moves will be more demanding in problems with multiple nestings because each nesting adds a new variable. By applying chunking according to the MARC principles the task can be performed with representations no more complex than quaternary-relational.

Our complexity analysis showed that the 10-item TOL4 (Shum et al., 2000, 2009) consists of two binary-relational, five ternaryrelational, and three quaternary-relational problems. To ensure there were sufficient items at each complexity level, five additional items were generated, resulting in a 15-item test with three, six, and six problems at the binary-, ternary-, and quaternary-relational levels of complexity, for use in the current study.

We predicted that problems with lower estimated complexity would be easier than those with higher estimated complexity. Based on previous research demonstrating a quaternary-relational limit in young to middle adulthood (Halford et al., 2005) and age-related declines in relational processing in later adulthood (Viskontas et al., 2005;Andrews and Todd, 2008), we expected that quaternary-relational problems would be very difficultfor our participants whose mean age was 66.3 years. Problem difficulty was also examined in relation to three metrics that are specific to tower tasks; namely moves to solution, goal ambiguity, and search depth.

We predicted that frontal lobe lesions would particularly impair TOL4 performance. This prediction is based on two lines of evidence. First, planning as assessed by the TOL3 has been shown to depend on the frontal regions (Newman et al., 2003; Unterrainer and Owen, 2006; Köstering et al., 2014). Second, evidence from lesion (Waltz et al., 1999, 2004; Andrews et al., 2013) and imaging studies (Kroger et al., 2002; Crone et al., 2009) has demonstrated an important role for the frontal lobes in relational processing. Therefore, if participants who have suffered a stroke affecting the frontal brain regions should show greater impairment on the TOL4 problems than those who have suffered a stroke affecting nonfrontal regions or those who have not suffered a stroke, this would be consistent with the relational processing interpretation. Group differences will be examined on TOL4 problems at each level of relational complexity and at each level of moves to solution, goal ambiguity, and search depth.

A further prediction based on relational complexity theory was that an independent measure of relational processing [viz., Latin square task (LST)] would predict TOL4 solution scores after controlling for stroke status and location. This prediction was based on research demonstrating the domain-general nature of capacity to process complex relations (Halford et al., 2002a,b; Andrews et al., 2006, 2013; Birney et al., 2006, 2012; Bunch and Andrews, 2012). The predictive ability of the LST which includes items at binary, ternary, and quaternary levels of complexity was compared to the Trail Making Test (TMT), which is widely used to assess executive processes and frontal functioning. TMT was expected to account for variance in TOL4 due to the tasks' common reliance on frontal regions (Müller et al., 2014). If the LST accounts for variance in TOL4 performance over and above the TMT this would further support the view that TOL4 involves complex relational processing.

# **MATERIALS AND METHODS PARTICIPANTS**

The sample consisted of 83 individuals who were all native speakers of English and who were living independently in the community. Forty-three participants had brain lesions due to stroke and 40 had no known brain injury. The unimpaired individuals were recruited through sporting and social clubs. The stroke sufferers were recruited through stroke support groups in the Brisbane and Gold Coast areas in QLD,Australia. They were assigned to a frontal stroke group (*n* = 14) or a non-frontal stroke group (*n* = 29) based on neurologists' reports and MRI/CT scan findings. Demographic details for the three groups are reported in **Table 1**.

The three groups did not differ significantly in terms of gender balance, χ 2 (2, *N* = 83) = 0.95, *p* = 0.963, age, *F* (2, 80) = 0.94, *p* = 0.394, nor years of education, *F* (2, 80) = 0.04, *p* = 0.96. Time since stroke was significantly longer for the frontal stroke group

**Table 1 | Demographic details for participants in the unimpaired, non-frontal stroke, and frontal stroke groups.**

N = 83.

**Table 2 | Lesion location in the non-frontal and frontal stroke groups**.

Entries are frequencies.

than for the non-frontal stroke group, *t* (41) = 2.59, *p* = 0.013. To the extent that there is some recovery of function over time, this longer time since stroke would advantage the frontal stroke group over the non-frontal stroke group, thus providing a counterconfound to predicted differences between this and the other groups.

**Table 2** summarizes lesion location as a function of stroke group. There was no significant association between stroke group and damage to left, right, or both hemispheres, χ 2 (1, *N* = 43) = 3.48, *p* = 0.09, damage to temporal lobes, χ 2 (1, *N* = 43) = 0.30, *p* = 0.73, occipital lobes, χ 2 (1, *N* = 43) = 0.12, *p* = 0.74, sub-cortical regions,χ 2 (1, *N* = 43) = 3.40, *p* = 0.10, nor parietal regions, χ 2 (1, *N* = 43) = 3.85, *p* = 0.08 (exact tests).

The Mini-Mental State Examination (MMSE; Folstein et al., 1975) was administered to all participants in the standard manner. The test consists of items assessing orientation to time and place, concentration, language, constructional ability, and immediate and delayed recall. The score was the number of correct responses

(max. = 30). Mean MMSE scores are shown in **Table 1**. Analysis of variance (ANOVA) revealed a significant effect of group, *F* (2, 80) = 7.59, *p* = 0.001, partial η 2 = 0.159. *Post hoc* Scheffe tests showed that the unimpaired group had significantly higher MMSE scores than the non-frontal stroke group (*p* = 0.019) and the frontal stroke group (*p* = 0.004). MMSE was therefore used as a covariate in all analyses that compared the groups.

#### **MEASURES AND PROCEDURES**

Ethical approval for the research was granted by the Griffith University Human Research Ethics Committee (GU Ref No: APY/82/04/HREC). Participants were tested individually at their residences by two female research assistants with postgraduate training in psychology and experience working with brain-injured individuals. The tests described below were administered as part of a larger battery. Testing was spread over two to four sessions, each 1–2 h in duration. Breaks were offered between tasks. Instructions were repeated or elaborated as required to ensure that participants understood the task requirements.

#### **Tower of London**

The task was an expanded 15-item version of the 4-disk TOL task of Shum et al. (2000, 2009). The apparatus consisted of four colored disks and a base with three vertical poles that differed in height and accommodated a maximum of two, three, or four disks. On all problems the apparatus was presented with the disks in the same initial configuration, which is shown in **Figure 1A** and **Table 3**. The goal states for the 15 problems are also shown in **Table 3** as are the moves to solution, estimated search depth, goal ambiguity, and relational complexity for each problem.

Participants were instructed to rearrange the disks into the target configuration (shown pictorially), and to do so in a specified number of moves. Only one disk could be moved at a time. Scores of three, two, or one were awarded for correct solutions on the first-, second-, and third-attempts, respectively, and zero for no solution after three attempts. All participants received the problems in the order shown in **Table 3** in which the problems with higher expected difficulty were concentrated later in the sequence. A stopping rule was implemented such that if participants failed to solve two consecutive problems after three attempts at each problem, no further problems were presented. The maximum score was 45 (based on 15 items). The mean number of TOL problems presented was 13.53 (SD = 2.11, range 5–15). Planning times were measured for the first attempt of each problem. Timing began at the commencement of each trial and ended when the first disk was moved. Instances of rule breaking (e.g., placing more than the allowed number of disks on a pole, moving two disks at a time) were also recorded. Rule breaks were not immediately corrected because doing so might have unduly influenced participants' subsequent attempts on the problem.

#### **Latin square task**

On each problem on the LST task, a 4 × 4 matrix was presented on the left side of the computer screen (Birney et al., 2006, 2012; Perret et al., 2011;Andrews and Maurer, 2012). Colored geometric objects filled some cells, while other cells were empty, as shown in **Figure 2**. The participants' task was to select one of four objects to fill a target cell (indicated by "?"). The response options were shown to the right of the matrix. The rule was that each of the four objects could occur only once in each row and column of the matrix. Consistent with the principles described previously, the complexity estimates reflect the most complex step within each problem.

For binary-relational problems, the most complex step required consideration of information from a single row or column. For example, the first step of the binary-relational problem shown in **Figure 2A**, involves working out that the empty cell in column 2 must be filled with a green square. This can be accomplished by considering the contents of a single column, column 2 in this example. On the next step, the object to be placed in the target cell can be identified by considering the contents of a single row, row 1 in this example. Row 1 now includes blue diamond, green square, and red circle, so it is clear that the pink cross must be placed in target cell. According to the analysis of Birney et al. (2006, 2012) considering the contents of a single row or a single column is binary-relational.

For ternary-relational problems, the most complex step required integration of information from a row and column. These two sources of variation must be integrated to determine the cell content. For the problem in **Figure 2B**, the first step is to identify the object to be placed in the cell at the intersection of column 3 and row 3 (blue square) by considering the objects already present in row 3 and column 3. Once this object is identified, the content of the target cell (pink cross) can be determined by considering the contents of row 3. The first (most complex) step is ternary-relational, whereas the second step is binary-relational.

For quaternary-relational problems, the most complex step required integration of information across multiple rows and columns. For the problem in **Figure 2C**, the first step is to identify the object to be placed in the cell at the intersection of column 1 and row 3 (light blue diamond) by considering the objects already present in this row and column. This step is ternary-relational. The next step requires consideration of the information in three columns (1, 2, and 4) to determine that light blue diamond should be placed in the target cell. According to the analysis provided by Birney et al. (2006, 2012) the second step is quaternary-relational.

There were four problems at each complexity level. Participants worked through the problems as quickly as possible doing all working in their heads. The score was number correct (max = 12).

#### **Trail making test**

In TMT Part A, numbers (1–25) were arranged randomly on a page. Participants drew lines connecting the numbers in ascending order as quickly as possible (Reitan and Wolfson, 1995). In TMT Part B, the stimuli were numbers (1–13) and letters (A– L). Participants drew lines connecting the numbers and letters in alternating order (1, A, 2, B, . . .). Part B required integration of two sequences (one numerical and one alphabetic) into a single alternating sequence. The two dependent measures corresponded to the times taken to complete Part A and Part B.

### **RESULTS**

#### **DIFFICULTY OF TOL PROBLEMS**

Item-based correlations were computed to examine the extent of overlap among the four metrics and the extent to which each

**Table 3 | Initial statea , goal states, moves to solution, relational complexity, goal ambiguity, and search depth for the 15 Tower of London problems**.

aThe initial state was the same in all problems.

b Indicates an empty peg. metric was associated with performance on the fifteen TOL problems. As shown in **Table 4**, moves to solution, search depth and relational complexity were significantly and positively intercorrelated, but the correlations with goal ambiguity did not reach significance.

Moves to solution, search depth and relational complexity were significantly negatively correlated with solution accuracy on the TOL problems. Solution accuracy was lower for problems that required more moves, had greater search depth and higher relational complexity. Moves to solution, search depth and relational complexity were significantly positively correlated with planning times on problems correctly solved on the first attempt. Planning times were longer for problems that required more moves, had greater search depth and higher relational complexity. Goal ambiguity was not significantly associated with solution accuracy or planning times, therefore it was not included in subsequent regression analyses.

Item-based multiple regression analyses were conducted to determine which of three metrics accounted for independent variance in solution accuracy and planning times. Given the small sample size (*N* = 15) the findings should be interpreted with caution. In the first analysis, moves to solution, search depth and relational complexity together accounted for 88% variance in solution accuracy, *F* (3, 11) = 26.85, *p* < 0.001. Moves to solution (8.29%, *p* = 0.019) and search depth (6.6%, *p* = 0.032) each accounted for unique variance. The remaining variance (73%) was shared by the predictors. In the second analysis, moves to solution, search depth, and relational complexity together accounted for 76.3% variance in planning times, *F* (3, 11) = 11.79, *p* = 0.001. Search depth accounted for unique variance (10.96%, *p* = 0.046). The remaining variance (65%) was shared by the predictors.

#### **TOL4 SOLUTION ACCURACY IN STROKE GROUPS**

Mini-mental state examination was included as a covariate in all analyses examining group differences. The means reported for the group based analyses have been adjusted for the covariate.

A preliminary analysis of covariance (ANCOVA) was conducted with group (unimpaired, non-frontal stroke, and frontal stroke) as the between subjects variable, and MMSE as the covariate. The dependent variable was the total score (max = 45) for the 15 TOL4 problems. The analysis yielded a significant effect of Group, *F* (2, 79) = 5.12, *p* = 0.008, partial η 2 = 0.115. Contrast analyses showed that the difference between unimpaired group (*M* = 32.29; SE = 0.99) and the non-frontal stroke groups (*M* = 30.72; SE = 1.13) was not significant (*p* = 0.31). However,

\*\*p < 0.01; \*p < 0.05.

the frontal stroke group (*M* = 25.91; SE = 1.66) had significantly lower scores than the non-frontal stroke group (*p* = 0.017) and the unimpaired control group (*p* = 0.002). An analysis based on the original ten TOL4 problems yielded the same pattern of group differences.

### **SENSITIVITY OF THE DIFFICULTY METRICS TO STROKE DAMAGE**

Four mixed ANCOVAs were conducted to examine group differences as a function of problem difficulty operationalized as moves, goal ambiguity, search depth, and relational complexity.

For the first analysis, the problems were categorized according to number of moves. The five low move problems required 2, 3, or 4 moves to solution, the six moderate move problems required 5 or 6 moves, and the four high move problems required 7 or 9 moves. Solution accuracy scores were converted to percentages and subjected to a mixed 3 × 3 ANCOVA in which Moves (low, moderate, and high) was a within-subject variable, Group was a between groups variable, and MMSE was the covariate. Consistent with the preceding ANCOVA and the correlations (**Table 4**), there were significant effects of Group, *F* (2, 79) = 4.86, *p* = 0.01, partial η 2 = 0.11, and of Moves, *F* (2, 158) = 4.49, *p* = 0.013, partial η 2 = 0.054. Percentage solution scores were higher for low move problems (*M* = 94.09; SE = 1.00) than for both the moderate move problems (*M* = 70.67; SE = 2.38) (*p* = 0.007) and the high move problems (*M* = 23.37; SE = 2.84) (*p* = 0.012). The Group × Moves interaction, *F* (4, 158) = 1.37, *p* = 0.25 was not significant. To facilitate comparison with other metrics, group differences were examined at each level of moves. The adjusted means are presented in **Table 5**.

For low move problems, there was a significant effect of group, *F* (2, 79) = 7.78, *p* = 0.001, partial η 2 = 0.165. Solution accuracy in the unimpaired group and non-frontal stroke did not differ significantly (*p* = 0.84). Solution accuracy in the frontal stroke group was significantly lower than the unimpaired (*p* < 0.001) and non-frontal stroke group (*p* = 0.001). For the moderate moves problems there were significant effects of the covariate, *F* (1, 79) = 4.33, *p* = 0.041, partial η 2 = 0.052 and of group, *F* (2, 79) = 3.90, *p* = 0.024, partial η 2 = 0.09. Solution accuracy in the unimpaired group and non-frontal stroke did not differ significantly (*p* = 0.76). Solution accuracy in the frontal stroke group was significantly lower than the unimpaired (*p* = 0.009) and nonfrontal stroke group (*p* = 0.016). For the high moves problems

there was no significant effect of group, *F* (2, 79) = 2.31, *p* = 0.11, partial η 2 = 0.055.

A similar approach was used to examine goal ambiguity. There were two problems with low goal ambiguity, nine with moderate goal ambiguity, and four with high goal ambiguity. There were significant effects of Group, *F* (2, 79) = 5.40, *p* = 0.006, partial η 2 = 0.12, and Goal Ambiguity, *F* (2, 158) = 4.32, *p* = 0.015, partial η 2 = 0.052. Percentage solution scores were significantly higher for low goal ambiguity (*M* = 89.28; *SE* = 2.05) than high ambiguity (*M* = 53.82; *SE* = 2.97) problems, *F* (1, 79) = 6.13, *p* = 0.015, η 2 = 0.072, and marginally higher than for problems with the moderate goal ambiguity (*M* = 66.01; SE = 1.44), *F* (1, 79) = 3.60, *p* = 0.061, η 2 = 0.044. The Group × Goal Ambiguity interaction, *F* (4, 158) < 1, *p* = 0.55, did not approach significance. Group differences for problems with low,moderate, and high goal ambiguity were examined. The adjusted means are presented in **Table 6**.

For problems with low goal ambiguity, there was a significant effect of group, *F* (2, 79) = 5.44, *p* = 0.006, partial η 2 = 0.121. Solution accuracy in the unimpaired group and non-frontal stroke did not differ significantly (*p* = 0.68). Solution accuracy in the frontal stroke group was significantly lower than the unimpaired (*p* = 0.002) and non-frontal stroke group (*p* = 0.005). For problems with moderate goal ambiguity there was a significant effect of group,*F* (2, 79) = 4.92, *p* = 0.01, partial η 2 = 0.111. Solution accuracy in the unimpaired group and non-frontal stroke did not differ significantly (*p* = 0.56). Solution accuracy in the frontal stroke group was significantly lower than the unimpaired (*p* = 0.003) and non-frontal stroke group (*p* = 0.01). For problems with high goal ambiguity there was no significant effect of group, *F* (2, 79) = 2.40, *p* = 0.097, partial η 2 = 0.057.

Search depth was examined in the same way. The five low search depth problems had a depth of zero, the six medium depth problems had depths of 1 or 2, and the four high search depth problems had depths of 3 or 5. There were significant effects of Group, *F* (2, 79) = 5.36, *p* = 0.007, partial η 2 = 0.12, and Search Depth, *F* (2, 158) = 4.55, *p* = 0.012, partial η 2 = 0.054. Percentage solution scores were significantly higher for low depth (*M* = 92.55; SE = 1.14) than high depth (*M* = 16.33; SE = 2.38) problems, *F* (1, 79) = 8.30, *p* = 0.005, η 2 = 0.095. Solution accuracy for the moderate depth (*M* = 75.74; SE = 2.43) problems did not differ significantly from low (*p* = 0.11) or high depth problems (*p* = 0.15). The Group × Search Depth interaction, *F*

**Table 6 | Solution accuracy for TOL4 problems with low, medium, and high goal ambiguity by group**.

**Relational complexity Binary Ternary Quaternary** Unimpaired M 98.18 83.55 46.73 SE 1.16 2.78 3.18 Non-frontal stroke M 99.32 83.90 37.09 SE 1.32 3.17 3.63 Frontal stroke M 90.75 68.43 30.14 SE 1.94 4.66 5.32

(4, 158) = 2.27, *p* = 0.065, partial η 2 = 0.054, approached significance. Group differences were examined at each level of search depth. The adjusted means are shown in **Table 7**.

For low depth problems, there were significant effects of the covariate (MMSE), *F* (1, 79) = 4.47, *p* < 0.038, η 2 = 0.053, and Group, *F* (2, 79) = 10.90, *p* < 0.001, η 2 = 0.216. Solution accuracy in the unimpaired and non-frontal stroke groups did not differ significantly (*p* = 0.56). Solution accuracy in the frontal stroke group was significantly lower than in the non-frontal stroke group (*p* < 0.001) and the unimpaired group (*p* < 0.001). For the moderate depth problems, solution accuracy in the unimpaired, non-frontal, and frontal stroke groups did not differ significantly, *F* (2, 79) = 2.37, *p* = 0.10, η 2 = 0.057. For high depth problems, there was a significant effect of Group, *F* (2, 79) = 4.19, *p* = 0.019, η 2 = 0.096. Solution accuracy in the unimpaired group was significantly higher than in the non-frontal stroke group (*p* = 0.018) and significantly higher than in the frontal stroke group (*p* = 0.018) but the two stroke groups did not differ significantly (*p* = 0.577).

Relational complexity was examined in the same way. There were three, six, and six problems, respectively at the binary, ternary, and quaternary-relational levels of complexity. The analysis yielded significant effects of Group, *F* (2, 79) = 5.65, *p* = 0.005, partial η 2 = 0.125 and Complexity, *F* (2, 158) = 5.23, *p* = 0.006, η 2 = 0.062. Solution accuracy was significantly higher for binary- (*M* = 96.08; SE = 0.86) than ternary-relational problems (*M* = 78.63; SE = 2.05), *F* (1, 79) = 4.07, *p* = 0.047, η 2 = 0.049, and for binary- than quaternary-relational problems (*M* = 37.99; SE = 2.35), *F* (1, 79) = 8.85, *p* = 0.004, η 2 = 0.101. There was also a significant Group × Complexity interaction, *F* (4, 158) = 2.43, *p* = 0.05, η 2 = 0.058. Group differences were examined at each complexity level. The adjusted means are shown in **Table 8**.

For binary-relational problems, there were significant effects of the covariate (MMSE), *F* (1, 79) = 4.57, *p* < 0.036, η 2 = 0.055, and Group, *F* (2, 79) = 7.30, *p* = 0.001, η 2 = 0.156. Solution accuracy in the unimpaired and the non-frontal stroke groups did not differ significantly (*p* = 0.53). Solution accuracy was significantly lower in the frontal stroke group than the non-frontal stroke group (*p* < 0.001) and the unimpaired group (*p* = 0.002). For the ternary-relational problems, there was a significant effect of Group, *F* (2, 79) = 4.47, *p* = 0.015, η 2 = 0.102. Solution accuracy in the unimpaired and the non-frontal stroke groups did not

differ significantly (*p* = 0.94). Solution accuracy was significantly lower in the frontal stroke group than the non-frontal stroke group (*p* = 0.006) and the unimpaired group (*p* = 0.008). For quaternary-relational problems, there was a significant effect of Group, *F* (2, 79) = 3.85, *p* = 0.025, partial η 2 = 0.089. Solution accuracy was marginally higher in the unimpaired group than the non-frontal stroke group (*p* = 0.054) and significantly higher than in the frontal stroke group (*p* = 0.011). The two stroke groups did not differ significantly (*p* = 0.274).

In summary, the foregoing analyses show that patterns of group differences on problems at low, intermediate, and high difficulty levels differ according to how problem difficulty is measured. On the easiest problems, the frontal stroke group performed more poorly than the unimpaired group irrespective of whether problem difficulty was expressed in terms of moves to solution, goal ambiguity, search depth, or relational complexity. The frontal stroke group also performed more poorly than the non-frontal stroke group on the easiest problems.

On problems with an intermediate level of difficulty, the frontal stroke group performed more poorly than the unimpaired group and the non-frontal stroke group when problem difficulty was expressed in terms of moves to solution, goal ambiguity, and relational complexity, but not when difficulty was expressed in terms of search depth. No significant group differences were observed on moderate depth problems.

On problems at the highest level of difficulty, the frontal stroke group performed more poorly than the unimpaired group when problem difficulty was expressed in terms of search depth and relational complexity. The frontal and non-frontal stroke groups performed poorly on high search depth and quaternary-relational problems and there were no significant differences between these two groups. No significant differences were observed between unimpaired, non-frontal stroke, and frontal stroke groups on high move problems and problems with high goal ambiguity.

Thus the pattern of significance for the group effects shows that TOL4 problems at all three levels of the domain-general relational complexity metric were sensitive to frontal lobe damage whereas TOL4 problems at two levels of the task-specific metrics (moves, goal ambiguity, and search depth) were sensitive to frontal lobe damage. Inspection of the effect sizes reported above indicates a similar pattern in that effect sizes were <0.058 for the moderate search depth, high moves, high goal ambiguity problems for which

the group effect was not significant, whereas effects sizes exceeded 0.088 in all other conditions.

#### **PLANNING TIMES FOR TOL PROBLEMS SOLVED ON FIRST ATTEMPT**

Participants with no first attempt solutions for any problems at a particular difficulty level were excluded from these analyses. This meant that the overall sample sizes were reduced to 39 (*n* = 22 unimpaired; *n* = 12 non-frontal stroke; *n* = 5 frontal stroke) for the analysis examining moves to solution, to 72 (*n* = 35 unimpaired; *n* = 27 non-frontal stroke; *n* = 10 frontal stroke) for the analysis examining goal ambiguity, to 28 (*n* = 22 unimpaired; *n* = 4 non-frontal stroke; *n* = 2 frontal stroke) for the analysis examining search depth and to 75 (*n* = 38 unimpaired; *n* = 27 non-frontal stroke; *n* = 10 frontal stroke) for the analysis examining relational complexity. The losses were due mainly to the more difficult problems, where participants were more likely to require multiple attempts.

Four separate ANOVAs were conducted with moves, goal ambiguity, search depth, or relational complexity as the within-subject factor. There was a significant effect of Moves, *F* (2, 76) = 20.72, *p* < 0.001, partial η 2 = 0.353. Planning times (seconds) were significantly shorter for low move problems (*M* = 8.22; SE = 0.52) than for moderate move problems (*M* = 15.27; SE = 1.56), *F* (1, 38) = 19.87, *p* < 0.001, partial η 2 = 0.343, which were significantly shorter than for high move problems (*M* = 30.71; SE = 4.71), *F* (1, 38) = 17.17, *p* < 0.001, partial η 2 = 0.311.

There was a significant effect of Goal Ambiguity, *F* (2, 142) = 21.36, *p* < 0.001, partial η 2 = 0.231. Planning times (seconds) for problems with low (*M* = 10.73; SE = 1.06) and moderate goal ambiguity (*M* = 11.93; SE = 0.76) did not differ significantly, *F* (1, 71) = 1.18, *p* = 0.282. Planning tomes for problems with low ambiguity were significantly shorter than for problems with high goal ambiguity (*M* = 19.69; SE = 1.91), *F* (1, 71) = 28.897, *p* < 0.001, partial η 2 = 0.289.

There was a significant effect of Search Depth,*F* (2, 54) = 23.48, *p* < 0.001, partial η 2 = 0.465. Planning times were significantly shorter for low depth problems (*M* = 7.81; SE = 0.60) than for medium depth problems (*M* = 13.90; SE = 1.30), *F* (1, 27) = 22.68, *p* < 0.001, partial η 2 = 0.467, which were significantly shorter than for high depth problems (*M* = 34.76; SE = 5.43), *F* (1, 27) = 20.87, *p* < 0.001, partial η 2 = 0.436.

These findings are generally consistent with the item-based correlations. However, when Group was included as an independent variable along with MMSE as the covariate, the ANCOVAs yielded no significant effects of Group, MMSE, Moves, Goal Ambiguity, Depth or Relational Complexity, and no significant interactions. These null results likely reflect inclusion of the covariate, the small and unequal sizes of the unimpaired, non-frontal stroke and frontal stroke groups, and high within-group variability in planning times.

#### **TOL RULE BREAKS**

Analysis of covariance was applied to the number of rule breaks. The analysis yielded a significant effect of Group, *F* (2, 79) = 5.03, *p* = 0.009, partial η 2 = 0.113. Contrast analyses showed that the difference between the unimpaired group (*M* = 0.35; SE = 0.21) and the non-frontal stroke group (*M* = 0.38; SE = 0.23) was not significant (*p* = 0.938). The frontal stroke group (*M* = 1.56; SE = 0.34) committed significantly more rule breaks than the nonfrontal stroke group (*p* = 0.005), however it should be noted that the absolute number of rule breaks was quite low (*M* = 0.77; SE = 0.15; *N* = 83).

#### **PREDICTING TOL SOLUTION ACCURACY**

**Table 9** shows the zero-order correlations among the TOL4, LST scores (max = 12) and TMT-Parts A and B. Stroke status (0 = unimpaired; 1 = stroke) and frontal location (0 = no frontal injury; 1 = frontal injury) were dummy variables that together capture the grouping variable used in the ANCOVAs. The TOL4 measure is the average of the binary-, ternary-, and quaternaryrelational percentages scores. The results are very similar when the total score (max 45) is used. The negative correlations occur because TMT-A and TMT-B are measures of response times rather than accuracy.

**Table 9 | Zero-order correlations (N** = **83)**.

TOL, Tower of London; TMT-A, trail making test part A completion times; TMT-B, trail making test part B completion times; LST, Latin square task. \*\*p < 0.01; \*\*\*p < 0.001.

#### **Table 10 | Multiple regression analyses predicting TOL4 solution accuracy**.

A multiple regression analysis with TOL4 as the criterion variable was conducted. On step 1, the dummy variables stroke status and frontal-non-frontal were entered, along with MMSE. These variables together accounted for significant variance in TOL4 performance. On step 2, TMT-A and TMT-B accounted for an additional 18.6% variance (*p* < 0.001). On step 3, LST accounted for a further 4.41% variance (*p* = 0.016). The unique contribution of TMT-B was reduced from 8.47% at step 2 to 5.38% at step 3, indicating that TMT-B and LST accounted for shared variance in TOL performance. This analysis is summarized in **Table 10**.

# **DISCUSSION**

Our research examined planning assessed using a 4-disk version of the TOL (Shum et al., 2009) following stroke. The overall solution scores provided evidence of impairment but only in those whose strokes resulted in damage to frontal regions of the brain. The overall solution scores, which collapse over problem difficulty, provided no evidence of planning impairments following stroke affecting non-frontal brain regions. These findings are consistent with previous research using the TOL4 (Shum et al., 2009).

We also investigated the extent to which relational complexity theory (Halford et al., 1998), which has been shown to account for performance in many cognitive domains also applies to planning on the TOL4. According to relational complexity theory, integrating the relations between current states, intermediate states, and goal states is a key process in planning. Three aspects of the findings are consistent with relational complexity theory.

First, the observed difficulty of the TOL4 problems increased with the estimated relational complexity of the problems. This was also the case for other complexity metrics. The item-based correlations demonstrate that moves to solution, search depth, and relational complexity are not independent. In the regression analyses, search depth and moves to solution emerged as predictors of solution accuracy and search depth also predicted planning times on problems correctly solved on the first attempt, but in both cases the majority of the variance was shared. Search depth and moves to solution are intrinsic to the TOL4 task but unlike relational complexity they are not applicable across domains.

Search depth quantifies difficulty up to the first goal move. Köstering et al. (2014) showed that search depth is well suited to TOL3 problems. Our findings show that it also captures the difficulty of TOL4 problems that require up to nine moves to solution. The search depth metric and the relational complexity metric both focus on the relations and interdependencies within a sequence of moves and this might underpin the observed positive correlation.

That the number of moves metric predicted solution accuracy is consistent with many previous findings (e.g., Newman et al., 2003; Kaller et al., 2012). The finding is unsurprising in one sense because problems that require more moves to solution also provide more opportunities for errors. Nevertheless, the fact that number of moves was strongly correlated with search depth and relational complexity, which are less vulnerable to this criticism indicates its usefulness as a difficulty metric. One feature of the moves metric that might contribute to its prediction of performance is its scaling. For problems used in the current study, moves ranged from 2 to 9 with most intermediate values represented. The values of search depth (0, 1, 2, 3, 5), goal ambiguity (low, moderate, and high), and relational complexity (binary-, ternary-, and quaternary-relational) were more limited in range. These scaling differences between the metrics should be considered when interpreting the item-based correlations and regression analyses.

It is also likely that metrics that are specific to a task, as moves to solution and search depth are to TOL, will tend to account for more variance in that task. However, because such metrics cannot be applied to other tasks, they cannot be used to compare difficulty of TOL problems with other tasks. The relational complexity approach does allow this. For example, number of moves on the TOL4 task does not have the same meaning as number of moves (steps to solution) on the LST, whereas the relational complexity values are arguably comparable.

The second finding consistent with relational complexity theory is that as in previous studies (Unterrainer and Owen, 2006; Shum et al., 2009) impaired performance was most evident in people with frontal lobe damage. Relational processing is known to rely on the integrity of the frontal lobes (e.g., Waltz et al., 1999, 2004; Kroger et al., 2002; Crone et al., 2009; Andrews et al., 2013), so this finding is consistent with the view that TOL4 problems involve relational processing.

The frontal stroke group was impaired relative to unimpaired controls on TOL4 problems at all three levels of relational complexity. This was not the case when difficulty was expressed in terms of moves, goal ambiguity, and search depth. TOL4 problems with low and moderate numbers of moves, low and moderate goal ambiguity, and low and high search depth were sensitive to frontal lobe damage. Thus relational complexity was more sensitive to frontal lobe damage than the other metrics were.

Relative to the non-frontal stroke group, the frontal stroke group was impaired on low move and moderate move problems, problems with low and moderate goal ambiguity, and problems with low search depth and binary- and ternary-relational problems. Thus none of the metrics was successful in distinguishing patients with frontal versus non-frontal damage at all three levels of difficulty. The significant group effects that were observed on the most difficult quaternary-relational and high search depth problems reflected differences between unimpaired and stroke groups rather than between non-frontal and frontal stroke groups. That this impairment in the non-frontal group was detected only on a subset of the problems illustrates one benefit of analyzing the cognitive demands involved in planning on the TOL4.

Given the demonstrated limit for young adults (Halford et al., 2005), the poor performance of the two stroke groups on the quaternary-relational problems is not surprising. Recent brain imaging of individuals without brain damage showed that limits in relational processing during a deductive reasoning task were manifested in the brain as complexity-dependent modulations of largescale networks that involved both frontal and non-frontal (e.g., parietal, occipital) regions (Cocchi et al., 2014). If these regions are damaged in individuals in the non-frontal stroke group, their performance on the quaternary-relational TOL4 problems would be adversely affected relative to the unimpaired group. Four of the six quaternary-relational problems were classified as high search depth, and this overlap would explain the similar pattern observed on the high search depth and quaternary-relational problems.

A third finding is consistent with relational complexity theory. As noted, the relational complexity approach has been applied to tasks in many different content domains and cross-domain correspondences in performance have been demonstrated in children (Andrews and Halford, 2002; Halford et al., 2002a,b; Bunch and Andrews, 2012), and adults (Andrews et al., 2006, 2013), suggesting that relational processing is a domain-general capacity. As predicted, relational processing in the LST accounted for variance in TOL4 performance after controlling for stroke status and location, MMSE and completion times on parts A and B of the TMT. The TOL4 and the LST differ substantially in terms of their stimuli and procedural requirements. Therefore the shared variance is unlikely to reflect common surface features of the tasks. We interpret the variance shared by TOL4 and LST as evidence that a common capacity for complex relational processing underpins both tasks.

Completion times for the TMT also accounted for variance in TOL4, but this was due mainly to part B rather than part A. Whereas TMT-A and TMT-B both require nonexecutive processes involved in visual scanning and speeded motor responses, TMT-B also requires the executive processes involved in set-shifting, maintaining two response sets in working memory, and inhibitory control (Müller et al., 2014). The unique contribution of TMT-B on step 2 of the regression analysis is consistent with the involvement of executive processes in TOL4.

As well as accounting for independent variance in TOL4, TMT-B, and LST also accounted for shared variance in TOL4. This suggests that all three tasks have some common processes. We argued previously that relational processing underpins both TOL4 and LST. TMT-B can also be construed in this way. It requires integration of two well-known sequences, one numerical and the other alphabetic. Each sequence incorporates a succession relation, in that one element is succeeded by the next element, for example, *succeeded by*(3, 4) or *succeeded by*(D, E). Succession is a binary relation because it cannot be defined on fewer than two entities. TMT-B involves integrating the numerical and alphabetic sequences such that the categories (numbers, letters) alternate, for example, *alternating* (3, D, 4). Alternation is ternary-relational because it cannot be defined on fewer than three entities. Thus we propose that the variance shared by the three tasks reflects ternaryrelational processing. Some LST and TOL4 problems require quaternary-relational processing, so the unique contribution of LST might reflect this higher complexity.

The research contributes to our understanding of the processes involved in TOL4. It adds to the studies cited previously, which demonstrate that relational processing underpins performance on a wide range of cognitive tasks. Given the ubiquitous nature of relational processing, and the demonstrated effects of relational complexity on performance, relational complexity theory provides a parsimonious approach to conceptualizing human cognition.

The research also has practical implications. To the extent that planning on tower tasks can be construed as relational processing, interventions designed to improve relational processing through for example, structural alignment training (Son et al., 2011; Hribar et al., 2012), use of relational language (Gentner et al., 2011), and techniques to improve access to relational components (e.g., Andrews et al., 2012) might also have beneficial effects on planning. Thus the findings have the potential to inform cognitive rehabilitation of planning deficits following brain injury due to stroke and other factors. Impairments in planning have adverse implications for independent living (Jefferson et al., 2006). For example,without the ability to plan, a person might have problems

in achieving independent activities of daily living or their vocational goals. Thus effective interventions would imply considerable benefits for individuals as well as for society more broadly.

#### **ACKNOWLEDGMENTS**

We are grateful to the organizations that assisted with recruitment of the stroke and control groups and to participants themselves. This research was funded by an Australian Research Council Discovery Grant (DPO452547) awarded to Halford, Andrews, Birney, Chappell, and Shum.

### **REFERENCES**

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

*Received: 16 September 2014; accepted: 08 December 2014; published online: 23 December 2014.*

*Citation: Andrews G, Halford GS, Chappell M, Maujean A and Shum DHK (2014) Planning following stroke: a relational complexity approach using the Tower of London. Front. Hum. Neurosci. 8:1032. doi: 10.3389/fnhum.2014.01032*

*This article was submitted to the journal Frontiers in Human Neuroscience.*

*Copyright © 2014 Andrews, Halford, Chappell, Maujean and Shum. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

# Hemispheric differences in relational reasoning: novel insights based on an old technique

#### **Michael S. Vendetti 1\* † , Elizabeth L. Johnson1,2† , Connor J. Lemos 2 and Silvia A. Bunge1,2**

1 Helen Wills Neuroscience Institute, University of California at Berkeley, Berkeley, CA, USA

2 Department of Psychology, University of California at Berkeley, Berkeley, CA, USA

#### **Edited by:**

Jérôme Prado, Centre National de la Recherche Scientifique, France

#### **Reviewed by:**

Glenda Andrews, Griffith University, Australia James Kenneth Kroger, New Mexico State University, USA

#### **\*Correspondence:**

Michael S. Vendetti, Helen Wills Neuroscience Institute, University of California at Berkeley, 134 Barker Hall, Berkeley, CA 94720, USA e-mail<EMAIL_ADDRESS>
†Shared first authorship.

Relational reasoning, or the ability to integrate multiple mental relations to arrive at a logical conclusion, is a critical component of higher cognition. A bilateral brain network involving lateral prefrontal and parietal cortices has been consistently implicated in relational reasoning. Some data suggest a preferential role for the left hemisphere in this form of reasoning, whereas others suggest that the two hemispheres make important contributions. To test for a hemispheric asymmetry in relational reasoning, we made use of an old technique known as visual half-field stimulus presentation to manipulate whether stimuli were presented briefly to one hemisphere or the other. Across two experiments, 54 neurologically healthy young adults performed a visuospatial transitive inference task. Pairs of colored shapes were presented rapidly in either the left or right visual hemifield as participants maintained central fixation, thereby isolating initial encoding to the contralateral hemisphere. We observed a left-hemisphere advantage for encoding a series of ordered visuospatial relations, but both hemispheres contributed equally to task performance when the relations were presented out of order.To our knowledge, this is the first study to reveal hemispheric differences in relational encoding in the intact brain.We discuss these findings in the context of a rich literature on hemispheric asymmetries in cognition.

**Keywords: reasoning, hemispheric specialization, deductive, transitive inference**

# **INTRODUCTION**

Relational reasoning is a cognitive process that requires the joint consideration of relations in order to generate an inference to support a conclusion. Although there is a wide range of theoretical models for relational reasoning (for review, see Goodwin and Johnson-Laird, 2005; Knowlton et al., 2012), all of these models present relational reasoning as a unitary system. However, work from neuropsychological and neuroimaging literatures indicates that some cognitive functions may be supported by multiple, redundant systems in the brain (Roser and Gazzaniga, 2004; Marinsek et al., 2014). Here, we sought to test whether one hemisphere displays an advantage over the other during relational encoding, or whether this function can be carried out equally well by each hemisphere.

Hints of a possible left-hemisphere advantage in relational reasoning have emerged over the course of a number of neuroimaging experiments (e.g., Goel and Dolan, 2004; Green et al., 2006; Bunge et al., 2009;Wendelken et al., 2011). Importantly, similar patterns have been observed for tasks involving either verbal or non-linguistic/pictorial stimuli, suggesting that the observed differences are not entirely stimulus-driven and do not completely overlap with regions supporting language (Monti and Osherson, 2012). However, the conclusions we can draw from these fMRI studies about lateralization of function are limited in several ways. Namely, brain imaging provides correlational rather than causal evidence, and results depend on the specific contrasts used as well as the choice of statistical threshold. All of these factors can mask

whether both hemispheres are indicated as being involved in a particular task, and thus, any conclusions about localization should converge with experimental findings using multiple approaches.

The neuropsychological literature also hints at possible hemispheric differences in contributions to reasoning. Much of the early work investigating differential hemispheric contributions to cognitive function came from work on split-brain patients (e.g., Sperry et al., 1969). These studies indicated an improved ability for hypothesis testing during problem solving in the left relative to the right hemisphere (LeDoux et al., 1977) and has led to the idea of the left hemisphere being an "interpreter" of events – i.e., the hemisphere with a major role of integrating newly acquired perceived information with previously constructed theories (Gazzaniga, 2000; Marinsek et al., 2014).

Following the seminal work of Gazzaniga et al. (1962) indicating how cognitive function differed in the two hemispheres following sectioning of the commissures, hemispheric asymmetries in cognition have alternately been characterized as a dichotomy between local and global (van Kleeck, 1989), categorical and coordinate (Kosslyn, 1987; van der Ham et al., 2014), or serial and parallel (e.g., Cohen, 1973) processes (for review, see Bradshaw and Nettleton, 1981). In the present study, we did not set out to evaluate these competing accounts of hemispheric specialization; rather, we sought to characterize the contribution of each hemisphere to performance of a relational reasoning task adapted from one used in a prior fMRI study from our group (Wendelken and Bunge, 2010).

There is not a consistent pattern relating relational reasoning ability to damage in a particular hemisphere. Neuropsychological work on relational reasoning has demonstrated the necessity of prefrontal and posterior parietal regions during transitive inference (Waltz et al., 1999; Krawczyk et al., 2008; Waechter et al., 2012), analogical reasoning (Morrison et al., 2004; Krawczyk et al., 2008), and matrix reasoning (Baldo et al., 2010; Woolgar et al., 2010). Additionally, studies employing voxel-based lesion symptom mapping to investigate relationships between patterns of brain damage and resulting cognitive deficits in fluid intelligence (Barbey et al., 2014) have suggested that damage to the right hemisphere plays a more critical role. However, Baldo et al. (2010) demonstrated that patients who have incurred strokes in the left hemisphere have been shown to also have significant deficits in a visuospatial relational reasoning task; therefore, more research is needed to provide a better understanding of each hemisphere's role in relational reasoning.

We designed the current study to test the role of each hemisphere in relational encoding through the use of a visual half-field stimulus presentation procedure. This paradigm was originally developed for use in split-brain patients, who have either minimal or no connection between the two hemispheres (e.g., Gazzaniga et al., 1962). Here, our participants were healthy adults whose hemispheres are presumed to interact closely in the coordination of task performance (Weissman and Banich, 2000). Nevertheless, we sought to test for differences in response times and/or accuracy when relational information is *initially encoded* by the left or the right hemisphere. This visual half-field stimulus presentation

procedure allowed us to test whether left and right hemispheres differentially support relational encoding.

In the present study, we used a transitive inference task adapted from an fMRI task that we have used previously (Wendelken and Bunge, 2010). When reasoning using transitive inference, the logical conclusion is deduced through transferring relational inferences among terms expressed in the premises (e.g., if A > B and B > C, then A must be greater than C). On this task, shown in **Figure 1**, participants view a new set of relations on every trial and are expected to integrate them in working memory. There has been a rich literature on this form of reasoning (e.g., Halford, 1984; Cohen et al., 1997; Andrews and Halford, 1998; Greene et al., 2001). Importantly, this form of relational reasoning bears only a passing resemblance to transitive inference paradigms that involve learning paired associations over many trials (e.g., Acuna et al., 2002; Zalesak and Heckers, 2009; Koscik and Tranel, 2012; for discussion, see Wendelken and Bunge, 2010). The major difference between our transitive inference paradigm and those based on learning paired associations is that our task does not rely on remembering associations to be transferred; instead, participants must infer the spatial relationship based on the relations from the most recent trial only. Having to perform this inference anew each trial reduces any tendency to assume an object-order relationship when attempting to solve the task.

Inspired by neuropsychological research demonstrating that prefrontal patients have difficulty with transitive inference when the relations are presented out of order (e.g., "Sam is taller than Roy," "James is taller than Sam"; Waltz et al., 1999;

Participants were shown three pairs of colored shapes. Following each pair, participants were shown a visual mask overlaying the previous shapes, and then a fixation cross. After the third pair was presented in a given trial, participants had up to 10 s to decide the correct linear order of two shapes

example of a reordered trial, in which participants would presumably have to manipulate their memory of the pairs in order to deduce that the square goes on top of the pentagon. Study 1 was similar in design except for the absence of the visual mask presentations.

Krawczyk et al., 2008), we manipulated the sequence of presentation of the three relations. On half of the trials, the relations were *ordered* (A > B; B > C; C > D), and on the other half, they were *reordered* (A > B; C > D; B > C *or* C > D, A > B, B > C). We hypothesized that manipulating encoding in this manner would have an influence on the downstream integration process, and sought to test for hemispheric differences in performance on trials whose relations could be integrated readily (*ordered* trials) and those that could not (*reordered* trials).

### **MATERIALS AND METHODS**

#### **PARTICIPANTS**

*Experiment 1:* Twenty-three healthy adults (14 female, aged 18–34 years; *X*¯ ± SD age, 22 ±3.08 years). *Experiment 2:* Thirtyone healthy adults (24 female, aged 18–25 years; *X*¯ ± SD age, 20 ±1.80 years). All participants attended the University of California, Berkeley, and participated in either Experiment 1 or 2 for partial fulfillment of a course requirement. All participants had normal or corrected-to-normal vision, were right-handed, and were fluent in English. Participants had no reported history of neurological or psychiatric disorders. All participants gave their informed consent to participate in the study, which was approved by the Committee for Protection of Human Subjects at the University of California, Berkeley.

#### **DESIGN**