NeuroinformaticsNeuroinformaticsISSN 1539–2791 Volume 2 • Number 2 • 2004

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Indexed and Abstracted in:Medline/Pubmed/Index Medicus

Science Citation Index®

Indexed and Abstracted in:Medline/Pubmed/Index Medicus

Science Citation Index®

Special Issue on Functional Connectivity

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NeuroinformaticsCopyright ©Humana Press Inc.All rights of any nature whatsoever are reserved.ISSN 1539-2791/04/163–168/$25.00

Original Article

163

Fair Localization of Function Via Multi-Lesion Analysis

Alon Keinan,1 Alon Kaufman,2 Nadia Sachs,3 Claus C. Hilgetag,3 and Eytan Ruppin*,1,4

1School of Computer Science,Tel Aviv University,Tel Aviv, Israel; 2Center of Neural Computation,Hebrew University, Jerusalem, Israel; 3School of Engineering and Science, International UniversityBremen, Bremen, Germany; 4School of Medicine,Tel Aviv University,Tel Aviv, Israel. (The first twoauthors contributed equally to the paper.)

Abstract

Acknowledging that causal localization offunction in a processing network requires amulti-lesion analysis, this paper presents a rig-orous and efficient method for defining andcalculating the functional contributions of net-work elements as well as their interactions.The method’s applicability to biological net-works is demonstrated in the investigation ofspatial attention in cats via lesion andreversible deactivation experiments.

Index Entries: Localization of function;multi-lesions; Shapley value; contributionsanalysis; interactions; multi-perturbations.

Introduction

One of the fundamental challenges in under-standing neural information processing isidentifying the individual roles of a neural

*Address to which all correspondence and reprint requests should be sent. E-mail: ruppin@post.tau.ac.il

network’s elements. Localization of specifictasks in the nervous system is typically doneby recording neural activity during behaviorand correlating the elements’ activation withbehavioral and functional observables.

However, this correlation does not neces-sarily identify causality. To enable a causallocalization of function, lesion studies havebeen employed in which functional performanceis measured after disabling different elementsof the system. While lesion studies have clas-sically played an important role in functionlocalization, most of them have been singlelesion studies, in which only one element is dis-abled at a time. Such approaches are limited intheir ability to reveal the significance of inter-acting elements (Aharonov et al., 2003). Oneobvious example is provided by two elementsthat exhibit a high degree of redundancy intheir function: Lesioning either element alonewill not reveal its significance.

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Acknowledging that single lesions are insuf-ficient for localization of function in neuralsystems, a multi-lesion analysis approach isneeded. This article presents a new method,the Multi-perturbation Shapley value Analysis(MSA), which addresses the challenge of defin-ing and calculating the contributions of net-work elements from a data set of multiplelesions (or, more generally, multi-perturba-tions) and their corresponding performancescores. In this framework, we view a set of mul-tiple lesion experiments as a coalitional game,borrowing concepts and analytical approachesfrom the field of game theory. Specifically, wedefine the set of contributions to be the Shapleyvalue (Shapley, 1953), which stands for theunique fair division of the game’s worth (thenetwork’s performance score when all elementsare intact) among the different players (the net-work elements). The contribution of an elementto a function measures its importance, that is,the part it plays in the successful performanceof that function. While in traditional game the-ory the Shapley value is more a theoreticaltool that assumes full knowledge of the behav-ior of the game at all possible coalitions, wehave developed methods to compute itapproximately with high accuracy and effi-ciency from a relatively small set of multiplelesion experiments (see Keinan et al., 2004 fora more detailed account of the MSA).Specifically, in the results to follow, a predic-tor is trained using a given subset of multi-lesion experiments to predict the performancelevels of all possible multi-lesion experiments(various predictors were used, including pro-jection pursuit regression and multiple expertneural networks).

The Shapley value stands for the averagemarginal importance of an element in the per-formance of an investigated function. Forcomplex networks where the importance maydepend on the state (lesioned or intact) of otherelements, a higher order description isrequired to capture the characteristics of the

function’s performance. Focusing here on atwo-dimensional analysis, we define the inter-action between a pair of elements as how muchlarger (or smaller) the average marginal impor-tance of the two combined elements is, comparedwith the sum of the average marginal impor-tance of each of them separately when the otherone is lesioned. Intuitively, the interaction stateshow much “the whole is greater than the sumof its parts” (synergism) or vice versa (antag-onism), where the whole is the pair of elements.Furthermore, the MSA classifies the type ofinteraction between each pair based on com-parison of the average marginal importance ofan element when its pair is always intact (γi,j)and when its pair is always lesioned (γi,j

−): Apositive value of both measures denotes thatelement i’s contribution is always positive, irre-spective of whether element j is lesioned orintact. When both are negative, element ialways hinders the performance, irrespectiveof the state of element j. In cases where the twomeasures have inverted signs, we define thecontribution of element i as j-modulated. Theinteraction is defined as positive modulatedwhen γi,j is positive while γi,j

− is negative, caus-ing a “paradoxical” effect. We define the inter-action as negative modulated when the formermeasure is negative and the latter is positive.The interaction of j with respect to i may be cat-egorized in a similar way, yielding a fulldescription of the type of interaction betweenthe pair.

To demonstrate the applicability of ourapproach to the analysis of biological data, weinvestigated the localization of spatial atten-tion to auditory and visual stimuli, usingbehavioral data from deactivation and lesionexperiments of different brain regions in cats.The experiments tested auditory and visualstimuli detection and orientation responses,as a measure of spatial attentional behavior, inthe left hemifield of the cat. While attentionalmechanisms proceed efficiently and incon-spicuously in the intact brain, perturbation of

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these mechanisms can lead to severe behavioralimpairments. From the perspective of systemsneuroscience, attentional mechanisms are par-ticularly interesting because this function isknown to be widely distributed in the brain.Moreover, lesions in the attentional networkresult in “paradoxical” effects, in which thedeactivation of some regions results in a better-than-normal performance (Hilgetag et al.,2001), or reverses behavioral deficits resultingfrom earlier lesions (Sprague, 1966). Sucheffects challenge traditional approaches forlesion analysis and provide a testbed for novelformal analysis approaches such as the MSA.

Auditory Spatial Attention

The elements studied in the auditory exper-iments were left and right Superior Colliculus(SC) and left and right posterior MiddleSuprasylvian (pMS) cortex. These structureswere further subdivided into superficial anddeep laminar compartments, so that there werealtogether eight regions in the system’s descrip-tion. Figure 1Apresents the MSAcontributionsof the different regions, calculated using pre-diction based on 33 available lesion experi-ments. The analysis revealed that only regions

SCL-deep and SCR-deep play a role in deter-mining auditory attentional performance in theleft hemifield, which is in line with previousfunctional characterizations of the collicularsystem (Lomber et al., 2001). The contralateraldeep layer of the SC has a positive contribu-tion, suggesting that lesioning this region hin-ders performance. In contrast, the negativecontribution of the ipsilateral SC indicates thatlesioning of this region tends to improve theperformance. Because of the restricted experi-mental access to deeper brain structures, whena deep layer of the SC was lesioned, the super-ficial one was lesioned as well. Nevertheless, theMSAframework successfully revealed that onlythe deep SC regions are the ones of significance.

We further performed a two-dimensionalMSA to quantify the interactions betweeneach pair of regions, finding only one signif-icant interaction, between SCL-deep and SCR-deep. Observing that SCL-deep has nocontribution when SCR-deep is intact, whileit has an average negative contribution whenSCR-deep is lesioned, the MSA concluded thatSCL-deep exhibits a positive-modulated inter-action with respect to SCR-deep, uncoveringthe type of interaction assumed to take placein this function (Hilgetag et al., 2000; Lomber

Fig. 1. MSA contributions of the different regions to auditory (A) and visual (B) spatial attention, in the lefthemifield of the cat.

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et al., 2001). One should emphasize that a singlelesioning analysis of the same data would nothave revealed this “paradoxical” effect, andwould have concluded that SCR-deep is theonly important region in this task.

Visual Spatial AttentionWe turn to analyzing data from similar

lesion experiments studying the localizationof spatial attention to moving visual stimuli.The analyzed data set was collected from var-ious lesion and reversible deactivation exper-iments of striate and parastriate visual cortex(VC), SC and deep and superficial layers ofthe pMS cortex in the cat (e.g., Sprague, [1966];Lomber and Payne, [1996]; Lomber et al.,[2001]; Lomber et al., [2002]). The MSA con-tributions were calculated using predictionbased on 21 available lesion experiments outof the 28 multi-lesion space. This small num-ber of lesion experiments is not sufficient topredict precisely the full multiple lesion setand hence, the results might be inaccurate.However, any additional experimental results,as they become available, can be added in astraightforward manner to refine the predic-tion. Figure 1B shows the contributions of thedifferent regions involved in the experiments.The analysis yielded opposite contributionsof left- and right-hemispheric structures, withthe structures on the ipsilateral side to thetested (left) field having negative contribu-tions and the structures on the contralateralside having positive ones. The largest posi-tive contribution made by SCR is in line withthe presumed central role of the SC in visualspatial attention in cats. Conversely, the largestnegative contribution is made by the superfi-cial layers of the ipsilateral pMS owing to theirpowerful role in reversing the impact of con-tralateral lesions. For example, deactivationof the ipsilateral superficial pMS is sufficientto reverse the impact of a complete deactiva-tion (superficial and deep) of contralateralpMS (Lomber and Payne, 1996), or even a

lesion of the entire contralateral VC includingthe pMS (Lomber et al., 2002). The role of cor-tical regions in visual spatial attention in thecat has been previously investigated in greatdetail for pMS. Our analysis also suggestsimportant contributions of other corticalregions (VC). It remains a challenge for futuredeactivation experiments to test this predic-tion and identify additional regions within thecat visual cortex that specifically contributeto attentional behavior.

Detailed two-dimensional MSA reveals thefunctional interactions between the regions.Figure 2A illustrates the type of the most sig-nificant interactions. Figure 2B quantifies thecontributions of lesioning various regions,with respect to a given lesion in the network.The contribution of lesioning region i whileregion j is already lesioned (−γi,j

−) is based onthe average marginal contribution of suchlesioning, taking into consideration other pos-sible unknown lesions to other regions in thenetwork. The figure clearly shows the signif-icant reverse impact of the ipsilateral super-ficial layers of pMS. This graph is just oneexample of displaying the causal effects thatcan be revealed by the MSA, testifying to itsusefulness in deducing the functionallyimportant regions, as well as their significantinteractions.

MSA is a novel method for causal localiza-tion of function, with a wide range of poten-tial applications, not only for the analysis oflesion and reversible deactivation experiments,but also for the analysis of laser ablation stud-ies of neurons and TMS-induced “virtuallesions.” It can also serve in the analysis ofexisting neural models of biological systems,ranging from detailed models of organisms tolarge-scale integrated models of imaging andactivation dynamics in different tasks.

AcknowledgmentsWe acknowledge the valuable contributions

and suggestions made by Ranit Aharonov,

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Dudi Deutscher, Ehud Lehrer, and IsaacMeilijson. This research has been supported bythe Adams Super Center for Brain Studies inTel Aviv University and by the Israel ScienceFoundation founded by the Israel Academy ofSciences and Humanities.

References

Aharonov, R., Segev, L., Meilijson, I., and Ruppin, E.(2003) Localization of function via lesion analy-sis. Neural Comput. 15 (4), 885–913.

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Fig. 2. Significant interactions in the visual experiments. (A) The type, in both directions, of the twelve mostsignificant two-dimensional interactions. (B) The positive contributions of lesioning a region knowing a spe-cific other region is lesioned (−γi,j

−).The figure shows the significant values, arrows representing the contribu-tion of lesioning the arrow’s base region (i), given that the arrow’s end region (j) is already lesioned.

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