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Modules and brain mappingKarl J. Fristona; Cathy J. Pricea

a The Wellcome Trust Centre for Neuroimaging, University College London, London, UK

First published on: 16 March 2011

To cite this Article Friston, Karl J. and Price, Cathy J.(2011) 'Modules and brain mapping', Cognitive Neuropsychology,,First published on: 16 March 2011 (iFirst)To link to this Article: DOI: 10.1080/02643294.2011.558835URL: http://dx.doi.org/10.1080/02643294.2011.558835

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Modules and brain mapping

Karl J. Friston and Cathy J. Price

The Wellcome Trust Centre for Neuroimaging, University College London, London, UK

This review highlights the key role of modularity and the additive factors method in functionalneuroimaging. Our focus is on structure–function mappings in the human brain and how these aredisclosed by brain mapping. We describe how modularity of processing (and possibly processes)was a key point of reference for establishing functional segregation as a principle of brain organization.Furthermore, modularity plays a crucial role when trying to characterize distributed brain responses interms of functional integration or coupling among brain areas. We consider additive factors logic andhow it helped to shape the design and interpretation of studies at the inception of brain mapping, witha special focus on factorial designs. We look at factorial designs in activation experiments and in thecontext of lesion–deficit mapping. In both cases, the presence or absence of interactions amongvarious experimental factors has proven essential in understanding the context-sensitive nature ofdistributed but modular processing and discerning the nature of (potentially degenerate) structure–function relationships in cognitive neuroscience.

Keywords: Additive factors; Modularity; Factorial; Connectivity; Degeneracy.

This review is essentially a narrative about howsome of the fundaments of experimental designand interpretation of human brain mappingstudies have developed over the past two decades.Its focus is on the role of modularity and additivefactors logic in guiding these developments. Thisis a somewhat self-referential account, whichallows us to describe how our earlier misconcep-tions gave way to more enduring perspectives—perspectives that help guide our current researchinto structure–function relationships in the brain.

This review comprises four sections. The firstconsiders, briefly, the rationale for modularityand its place within distributed neuronal proces-sing architectures. We consider evolutionary

imperatives for modularity and then a slightlymore abstract treatment that underpins the analy-sis of functional and effective connectivity. Thesecond section is a short historical perspectivethat covers the rise and fall of cognitive subtractionand the emergence of factorial designs in neuroi-maging. Our focus here is on the role of additivefactors logic and the connection to conjunctionanalyses in neuroimaging. The third sectionpursues the importance of interactions in factorialdesigns—specifically, their role in disclosingcontext-sensitive interactions or coupling amongmodular brain areas. We illustrate this using thenotion of dynamic diaschisis and psychophysiolo-gical interactions. The final section turns to

Correspondence should be addressed to Karl J. Friston The Wellcome Trust Centre for Neuroimaging, Institute of Neurology,

Queen Square, London WC1N 3BG, UK (E-mail: [email protected]).

This work was funded by the Wellcome Trust. We would like to thank Marcia Bennett for help preparing this manuscript.

# 2011 Psychology Press, an imprint of the Taylor & Francis Group, an Informa business 1http://www.psypress.com/cogneuropsychology DOI:10.1080/02643294.2011.558835

COGNITIVE NEUROPSYCHOLOGY, iFirst, 1–10

Downloaded By: [Friston, Karl][UCL University College London] At: 12:51 24 March 2011

lesion–deficit mapping and neuropsychology (inthe sense of using lesions to infer functional archi-tectures). Here, we review the concept of necessaryand sufficient brain systems for a given task andhow these led to the appreciation of degeneratestructure–function mappings. Additive factorslogic again plays a key role but, in this instance,the combination rule (Sternberg, 2011 this issue)becomes probabilistic and acquires a multiplicativeaspect. We rehearse the importance of degeneratemappings in the context of multilesion–deficitanalysis and conclude with some comments onthe role of cognitive ontologies in making themost of neuroimaging data.

In defence of modularity

Most neurobiologists who are sensitive to the dis-tributed and self-organized nature of neuronaldynamics tend to distance themselves from func-tionalist accounts of modularity. However, thereis a growing appreciation of the importance ofmodularity in network theory (e.g., Bullmore &Sporns, 2009; He & Evans, 2010; Valencia et al.,2009) and the study of complex systems ingeneral. The importance of modularity is usuallycast in terms of robustness and evolvability in anevolutionary setting (e.g., Calabretta, 2007;Redies & Puelles, 2001). At first glance, robust-ness might appear to limit the evolvability ofbiological networks, because it reduces thenumber of genetic variations that are expressedphenotypically (and upon which natural selectioncan act; Sporns, 2010). However, neutralmutations, which are expressed in a phenotypicallyneutral way, can promote evolution by creatingsystems that are genetically varied but functionequally well (i.e., degenerate, many-to-one map-pings between genotype and functional pheno-type). In brief, “robustness implies that manymutations are neutral and such neutrality fostersinnovation” (Wagner, 2005 p. 1773). Both robust-ness and evolvability are enhanced by the modularorganization of biological systems—from gene andprotein networks to complex processes in develop-ment (e.g., Duffau, 2006). The dissociability ordecomposability afforded by modularity is

characteristic of the brain’s small world connec-tivity architecture, a feature that has receivedincreasing empirical support from analyses of ana-tomical and functional connectivity (Bullmore &Sporns, 2009). In short, modularity may be anemergent characteristic of any biological networkthat has been optimized by selective pressure (irre-spective of the particular constraints on adaptivefitness). Interestingly, these arguments aboutmodularity have emerged in a field one mightleast expect—namely, network theory.

The role of network theory (and graph theory)is also central to the way that imaging neurosciencetries to assess functional brain architectures. Inbrief, the brain appears to adhere to two principlesof organization: functional segregation and inte-gration. Functional segregation refers to thespecialization of brain regions for a particular cog-nitive or sensorimotor function, where that func-tion is anatomically segregated within a corticalarea or system. Functional integration refers tothe coupling and interactions (message passing)among these areas (Friston, Frith, Liddle, &Frackowiak, 1993). The mathematical descriptionof networks like the brain often appeals to graphtheory, where the interactions among regions(nodes) are encoded by connections (edges).These connections imply a conditional depen-dency between the (usually hidden) states of eachregion. In the brain, these hidden states corre-spond to population or ensemble neuronal activityperforming computations. The key point here isthat, to understand the network, one has to ident-ify where there are no connections. This maysound paradoxical but emphasizes the importanceof conditional independencies. Conditional inde-pendence means that knowing the activity of onearea tells you nothing about the activity of asecond area, given the activity in all other areas.If this can be shown statistically, one can inferthe absence of a connection between the twoareas in question. This absence endows the graphwith a sparsity structure and a specific sort of archi-tecture. The very existence of conditional indepen-dencies induces modularity and becomes theultimate aim of network and effective connectivityanalyses in neuroimaging.

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The importance of conditional independence isreflected in the first sentence of Sternberg (2011this issue, p. xxx): “The first step in one approachto understanding a complex process is to attemptto divide into modules; parts that are independentin some sense.” Mathematically, this “sense” is aconditional independence.

A key example of a connectivity analysis isdynamic causal modelling (DCM), in which oneis trying to explain observed neuronal responsesin terms of an underlying Bayesian dependencygraph (Friston, Harrison, & Penny, 2003). InDCM, the dependencies are modelled in termsof the effective connectivity between hidden neur-onal states in each brain area. Model selection isthen used to identify the architecture that best

explains the systems response, using Bayesianmodel selection. The very fact that one character-izes distributed responses in terms of a set of con-nected regions (nodes) speaks to the implicitmodularity of processing within each node. SeeFigure 1 (and Seghier & Price, 2010) for anexample of dynamic causal modelling in addres-sing the modular but distributed architecturesunderlying reading and object naming. It shouldbe noted, however, that the dependencies canthemselves be context sensitive. In other words,being modular does not mean responding to thesame inputs in the same way all the time.Understanding this context sensitivity is one ofthe most important aspects of network andcausal modelling, especially in cognitive

Figure 1. An example of how dynamic causal modelling (DCM) can address modular and distributed architectures. This DCM includes five

regions that are commonly activated during reading and picture naming. The results of the DCM analysis show that the connection from

visual recognition areas (pOT/aOT) to articulatory areas (PrC), via the putamen, is stronger for reading than for object naming

(Seghier & Price, 2010).

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neuroimaging (cf. McIntosh, 2004). We return tothis later but first consider how the key regions(nodes) in casual modelling are identified in thefirst place.

Additive factors logic and context sensitivity

Prior to the inception of modern brain mapping,the principle of functional segregation was ahypothesis, based upon decades of careful electro-physiological and anatomical research (Zeki &Shipp, 1988). Within months of the introductionof whole-brain activation studies, the selectiveactivation of functionally segregated brain areaswas evident, and the hypothesis became a principle(e.g., Zeki et al., 1991). It is interesting to lookback at how these activation maps were obtainedexperimentally: Most early brain mapping studiesused an elaboration of Donder’s subtractivemethod (e.g., Petersen, Fox, Posner, Mintun, &Raichle, 1988). Put simply, this entailed adding aprocess to a task and subtracting the evokedbrain activity to reveal the activation due to theextra processing. Our first misconception wasthat one could associate the brain activation withthe added process.

This interpretation of an activation rests uponthe assumption of pure insertion—namely, thatthe extra process can be inserted purely withoutchanging existing processes or eliciting new pro-cesses (or processing). The pure insertion assump-tion is very similar to the additivity assumption inthe combination of factors in the additive factorsmethod (Sternberg, 2011, this issue). In otherwords, it is necessary to exclude interactionsbetween the old and new task factors before associ-ating any brain activation with the new task com-ponent. To address this empirically, one needs afactorial design in which one can test for the inter-actions (Friston et al., 1996). The adoption of fac-torial designs—and the ability to assessinteractions in neuroimaging experiments—wasincredibly important and allowed people toexamine the context-sensitive nature of the acti-vations, in the sense of quantifying the dependencyof the activation due to one factor on that ofanother. Factorial designs are now the mainstay

of experimental design in neuroimaging.Certainly, in our unit, it has been nearly a decadesince we have used a design that had fewer thantwo factors. Indeed, at the time of writing, asearch on PubMed.gov for “interaction ANDbrain AND (fMRI OR PET)” yielded 1,854results, while a search for “subtraction ANDbrain AND (fMRI OR PET)” gave only 1,615.Figure 2a shows a simple example of a factorialdesign and a test for a regionally specific inter-action, again focusing on the processes underlyingreading and object naming.

Cognitive subtraction and processdecomposition

As described carefully by Sternberg (2011, thisissue), there is a key distinction between cognitivesubtraction and process decomposition. In cogni-tive subtraction, one changes the task in a qualitat-ive way to induce a new putative processingcomponent. Conversely, in process decomposition,the task remains the same but the stimuli orcontext is changed in a multifactorial way. Thiscircumvents the assumption of pure insertion,while affording the opportunity to test for inter-actions. As noted in Sternberg (2011 this issue,p. xxx) “with a composite measure factorial exper-iments are essential, to assess how the effects of thefactors combine”. Neuronal responses are, by theirnature, composite, in the sense that they reflect theprocessing of multiple processing elements. Figure2b provides an example of a factorial design wherestimulus factors were varied parametrically toreveal an interaction or dependency betweenname frequency and stimulus modality (picturesor written names). Much of the additive factorsmethod rests upon excluding an interaction tomake inferences about the decomposition of theunderlying processes: If two processes do notinteract, they can be decomposed functionally.Exactly the same logic underpins cognitive con-junctions in neuroimaging (Price & Friston,1997). In cognitive conjunction analyses, onetests for colocalized activation attributable to twoor more factors in the absence of an interaction.Figure 2 provides a simple example of this


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method, which has become popular—with 195PubMed.gov results for (cognitive AND conjunc-tion) AND (fMRI OR PET OR neuroimaging).However, in the context of brain mapping, inter-actions can be extremely informative about neur-onal processing and are usually used to infer theintegration of inputs from two or more modules(brain regions). This can be essential in under-standing the coupling among brain regions and

the nature of hierarchical and recursive messagepassing among and within levels of sensory proces-sing hierarchies. We pursue this theme in thecontext of changes in coupling below.

Context-sensitive coupling

In the same way that factorial designs discloseinteractions in terms of regional processing, they

Figure 2. Factorial designs in brain activation experiments. (a) An example of a simple factorial design that uses the interaction to identify

regions where differences between naming and semantic categorization are greater for pictures of objects than for their written names. (b)

Regions identified by the interaction and conjunction (unpublished data). (c) An example of a factorial parametric design that uses the

interaction to identify regions where the effect of a parametric factor (e.g., word frequency) is stronger for naming than for reading. (d)

Hypothetical data illustrating an interaction. To view a colour version of this figure, please see the online issue of the Journal.




can also inform the context-sensitive nature ofcoupling between brain areas. Interactions simplymean a difference in a difference (e.g., how aresponse to one factor depends upon the responseto another). If we replace one (psychological)factor with the (physiological) activity in a seedor reference brain area, then the ensuing inter-action becomes a psychophysiological interaction(PPI; Friston et al., 1997). Roughly speaking,this PPI reports a significant change in the(linear) influence of the seed region on any signifi-cant target region, with different levels of thepsychological factor. Although a simple analysis,this has been exploited in a large number of neu-roimaging studies to look at how couplingbetween brain areas can change with brain stateor set—with 222 PubMed.gov results for (psycho-physiological interaction OR PPI) AND (fMRIOR PET OR imaging). The notion that connec-tivity (and implicit modularity) is itself state andactivity dependent is crucial for understandingthe dynamic repertoire of real brain networks.Furthermore, it reiterates the importance of think-ing about modular function in a context-sensitiveway.

This becomes important in a pragmatic sensewhen one tries to understand the remote effectof brain lesions on brain activity and responses.This is usually referred to in terms of diaschisis(from Greek, meaning “shocked throughout”). Aparticular form of diaschisis can emerge whenthe remote effect of a lesion is itself context depen-dent—in other words, where there is an abnormal-ity of evoked responses, due to a remote lesion thatis revealed in, and only in, some specific tasks orbrain states. This has been referred to as“dynamic diaschisis” (Price, Warburton, Moore,Frackowiak, & Friston, 2001) and underscoresthe subtleties in understanding highlycontext-dependent and nonlinear exchangesbetween modular brain regions. An example ofdynamic diaschisis is shown in Figure 3. In thefinal section, we pursue the effect of brainlesions on evoked responses and look moreclosely at the notion of modularity and segre-gation, in the context of structure–functionrelationships.

Modularity, structure, and function

For many people, the goal of neuroimaging is tounderstand the functional architecture of thebrain in relation to particular tasks or cognitiveprocessing. This understanding entails knowledgeof the mapping between the brain’s structure andits function. An important complement to brainactivation studies are lesion–deficit studies. Herebrain imaging is used to define a regionally specificbrain insult, and its implicit functional specializ-ation is inferred from the associated behaviouraldeficit. Many people in neuroimaging have notedthe importance of the complimentary contri-butions of functional and structural imaging. Forexample, identifying a regionally specific lesion,in the context of a behavioural deficit, suggeststhat this region was necessary for performance.Initially, it was hoped that a combination oflesion–deficit mapping and functional activationstudies would identify necessary and sufficientbrain regions for a particular task or process(Price, Mummery, Moore, Frackowiak, &Friston, 1999). However, this ambition quicklyturned out to be misguided: This is because itoverlooked the ubiquitous many-to-one (degener-ate) mapping between structure and function inbiological networks (Edelman & Gally, 2001).Put simply, this means that two or more areascould fulfil the same task requirements.Extending this notion to high-order combinato-rics means that there may be no necessary brainarea for any particular process and therefore no“necessary and sufficient brain area”. This was afundamental insight, which mandated arevision of (our) approaches to lesion–deficitmapping and activation studies (Price & Friston,2002).

Crucially, the possibility of degeneratestructure–function mappings brings us back tofactorial designs and additive factors logic. Onecan see this simply by considering the differencebetween two structure–function relationships: Inthe first mapping, processing is distributed overtwo regions (nodes). This means that damage tothe first or the second will produce a deficit.Now consider the degenerate case, where either


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Figure 3. An example of dynamic diaschisis (unpublished data). Following a lesion to the left putamen (see Figure 1), activation in the left

precentral cortex (PrC in Figure 1) is abnormally low during successful reading but normally activated during successful object naming. This is

consistent with the dynamic causal modelling (DCM) results reported in Figure 1 and suggests that PrC activation is driven by left putamen

activation during reading but not naming. See Figure 2a for details of Conditions A, B, C, and D. To view a colour version of this figure,

please see the online issue of the Journal.




node can support the function. Here, only a lesionto the first and second area will cause a deficit. Ifwe assume that the deficit is a pure measure ofthe assumed process in question, then we havetwo fundamentally different (multiplicative) com-bination rules within additive factors logic. In thefirst situation (deficit following lesions to first orsecond area), the probability of a deficit p(D|L) isequal to one minus the probability that they areboth undamaged, which is the product of the

probability that neither are lesioned.

p(D|L) = 1− [1 − p(L1 = 1)][1 − p(L2 = 1)] 1a

Conversely, under the degenerate mapping, theprobability of a deficit becomes the probability ofa lesion in either area, leading to a very differentcombination rule:

p(D|L) = p(L1 = 1)p(L2 = 1) 1b

Figure 4. An example of degeneracy. Reading is impaired following lesions that damage the left putamen, left insula, and left parietal cortex

inclusively (Patient 3). However, damage to only one of these regions does not impair reading (Patients 1 and 2). The results suggest that

reading can be supported either by a pathway that involves the parietal cortex or by a pathway that involves the putamen/insula. When one

pathway is damaged, the other pathway can support reading. When both pathways are damaged, reading is impaired. This previously

unpublished result is consistent with a study of reading aloud in healthy subjects (Seghier, Lee, Schofield, Ellis, & Price, 2008) that

showed an inverse relationship (across participants) between activation in the left putamen and parietal cortex. Together, the results from

patient studies (above) and healthy subjects (Seghier et al., 2008) suggest that the putamen and parietal cortex are components of

different reading pathways and that either one or the other is needed for successful reading.


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Crucially, in order to disambiguate between thesetwo scenarios we need a factorial design, in whichwe can lesion (or obtain access to patients withlesions in) one area L1 = 1 and the other areaL2 = 1. In short, we need a multilesion analysis.This provides an important and principled motiv-ation for studying patients with different brainlesions (and has implications for traditionalsingle-case studies in neuropsychology). Figure 4shows an example of degeneracy inferred usingthis Boolean logic associated with degenerate struc-ture–function mappings. Interestingly, a classicalone-to-one structure–function mapping impliesthat p(Di|L) = p(Li = 1) ⇒ p(Di|L) = p(Di|Li),which means the deficit is conditionally indepen-dent of lesion Lk [ {0, 1} : ∀k = i in all otherareas.

There are many interesting issues that attendthe analysis of multilesions studies. However, weclose by noting that a truly inclusive approach tomodularity and structure–function mappings inthe human brain will account for both lesion–deficit data and functional activation studies. Inshort, our empirical and conceptual models ofbrain architecture have to explain both evokedresponses due to experimental manipulations inactivation studies and the behavioural deficits eli-cited by selective lesions. Clearly, these modelsentail a precise specification of the mappingbetween neuronal activity and cognitive function.This mapping is itself a holy grail of cognitiveneuroscience, which has been referred to as a cog-nitive ontology (Poldrack, 2006; Price & Friston,2005). Indeed, cognitive ontologies are nowbecoming a major focus of the brain imaging andcognitive neuroscience community, particularlywith the advent of new neuroinformatics tools(Poldrack, Halchenko, & Hanson, 2009). Onecan see how the combination of data from differ-ent modalities and different patients acquires aprincipled motivation from the arguments above.

In conclusion, the arguments and developmentsdiscussed in this review rest explicitly on thenotion of modular but coupled brain regions andthe additive factors method (with linear ornonlinear combination rules), introduced bySternberg (2011 this issue).

Original manuscript received 10 October 2010

Revised manuscript received 14 December 2010

Revised manuscript accepted 14 December 2010

First published online day month year

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Cognitive Neuropsychology Modules and brain mappingkarl/Modules and brain mapping.pdf · context of lesion–deﬁcit mapping. In both cases, the presence or absence of interactions