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Identification and Localization of Human Brain Activity Patterns Using Particle

Swarm Optimization

Malin Bjrnsdotter & Johan WessbergInstitute of Neuroscience and Physiology

University of GothenburgGothenburg, Sweden

e-mail: malin.bjornsdotter@neuro.gu.se

Abstract Classifier-based multivariate pattern recognition

techniques have in recent years enabled highly sensitive

mapping of brain regions where mind states can be decoded

from functional magnetic resonance imaging (fMRI) data. The

searchlight mapping approach, where the brain volume is

exhaustively scanned with a fixed-size search volume, is highly

appealing in terms of sensitivity but also exceedingly time

consuming [1]. We therefore propose an efficient, easily-

implemented particle swarm optimization (PSO) brain

mapping method, where fixed-size, fixed-shape (spherical)

particles search the brain volume for informative regions

where a classifier can decode the mind states. Particle positions

and velocities are encoded in Cartesian coordinates, and

niching techniques are used to identify multiple informative

brain regions. We demonstrate the versatility of the algorithm

in combination with linear discriminant analysis (LDA) and

linear and non-linear support vector machines (SVMs) to

decode brain states on simulated as well as authentic fMRI

data. The PSO method outperformed the conventional general

linear model (GLM) method in terms of mapping sensitivity,

and compared favorably with the searchlight algorithm fora dramatic reduction in time requirements (e.g. 6.7 min

compared to 9 h for a minute reduction in mapping sensitivity).

On the authentic fMRI dataset, expected brain regions were

identified. The PSO algorithm is a promising highly efficient

multivariate alternative for functional brain mapping and

brain state decoding.

Keywords-Particle swarm optimization; functional magnetic

resonance imaging; support vector machines; machine learning;

data mining; brain, neuroscience.

I. INTRODUCTIONHuman brain activity can be non-invasively assessed by

functional magnetic resonance imaging (fMRI), where local blood flow changes are estimated in measuring points(termed voxels) evenly distributed across the brain volume.Identification of brain regions which are activated by a givencondition is typically achieved using a voxelwise generallinear model (GLM; [2]) approach. Multivoxel patternanalysis (MVPA) has, however, recently emerged as a highlyappealing alternative (see [3] or [4] for reviews). As opposedto univariate GLM mapping, MVPA methods utilize thecombined effect of numerous voxels in a multivariatefashion, allowing identification of brain regions containingspatially distributed patterns related to the experimentalconditions under investigation. Such multivariate approachesallow highly sensitive differentiation of signal changes

encoded across voxels that conventional univariate statisticsfail to capture [1, 5-7]. In addition, MVPA approaches allowfor decoding of single-trial brain states, effectively providingtools for observing brain state changes in real time(somewhat equivocally termed mind reading; [8]).

Pattern recognition analysis is typically performed bytraining a classifier to recognize and decode subtle intrinsicsignal patterns correlated to given brain states, such as theindistinct fMRI pattern, consisting of tens of thousands ofvoxels, produced by a single touch stimulus [9]. Trainedmodels can be applied in mental state tracking [8], liedetection [10], the decoding of single visual stimuli visible[11-13], as well as invisible [14] biofeedback [15-16], andvarious types of real-time fMRI analysis [17-18]. A majorchallenge in such pattern recognition studies is to identifywhich voxels, out of the hundreds of thousands that aresampled, contain information about the brain states ofinterest. To this end, we propose a particle swarmoptimization (PSO) approach which allows for fast yet

highly sensitive identification and localization of humanbrain activity patterns [19].

II. RELATED WORKInformative brain regions may be localized by region-of-

interest (ROI) based methods where classifiers are applied tovoxels in anatomically or functionally predefined areas [12-14]. ROI selection methods based on univariate functionalranking include estimates of activation magnitude due to anycondition (activation-based voxel selection) or the ability todifferentiate the conditions, as quantified by e.g. the standardGLM (discrimination-based voxel selection; [14, 20-21]).Such univariate measures can also be used as an initialranking scheme for improved speed or accuracy in

subsequent multivariate voxel selection [6, 22]. Coarse brainmaps can be obtained by assessing the classification performance in a number of ROIs. However, univariatefeature selection disregards any distributed brain activityeffects and provides little additional information regardingthe localization of brain response patterns compared to theunivariate measure on its own.

In contrast, the attractively simple and intuitivesearchlight algorithm introduced by Kriegeskorte andcolleagues has proved useful in numerous studies [28-33].Whole-volume maps are produced by computingmultivariate brain response measures across fixed-size(typically spherical) search volumes sequentially centered oneach voxel in the brain volume. As opposed to region-of-

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interest approaches, the searchlight requires no a priorispatial hypotheses with the drawback that an excessivenumber of information computations (one per voxel, that is,in the order of tens to hundreds of thousands or higher) isrequired.

As a solution to the computational requirement problem,we propose the PSO as an intelligent and efficient way ofidentifying regions where brain states can be decoded. Akinto the searchlight, we utilize spherical, fixed-size searchclusters for the PSO method to evaluate regional informationcontent, but in an intelligent fashion as opposed to using rawcomputational power. Comparing with the searchlight, weevaluated the performance on simulated data at differentcontrast-to-noise ratios, as well as on authentic fMRIdatasets exploring brain processing of gentle touch.

III. METHODSA. Particle swarm optimization

Particle swarm optimization (PSO) is a stochasticoptimization method based on the behavior of swarminganimals such as insects and birds. Virtual particlesrepresenting potential solutions to the problem at hand flythrough problem space with given velocity, exchangingtopology-related information in search for the optimalsolution [19]. The algorithm was implemented as follows:

1. Initialize random positions and velocities for particles,xi, vi, i = 1...n

2. Evaluate each particle in the swarm,xi f(xi)3. Update the best position for each particle and the

global best position.- iff(xi) > f(pi ) => pi = xi- iff(xi) > f(pg) => pg= xi

4. Update velocity and position for each particle.5. Return to step 2 unless the termination criterion

has been met.

The movement of each particle i is governed by a set ofrules describing how the position x and velocity v changeover time:

vi = vi + c1 r1 (pi -xi) + c2 r2 (pg-xi)xid=xid+vid

where c1 is a cognitive parameter, determining the degree ofacceleration towards the particles personal best position pid,and c2 is a social parameter, determining the accelerationtowards the global best positionpgd. The stochastic nature ofthe velocity equation is represented by r1 and r2, which arerandom numbers in the range [0,1].

Since multiple brain regions are likely to be involved incognitive processing, we adapted the NichePSO algorithmfrom Brits and colleagues utilizing subswarms in order toidentify more than one optima as follows [34]:

1. Initialize main particle swarm.

2. Train main swarm using the cognition only model.3. Update fitness of each main swarm particle.4. For each subswarm:(a) Train subswarm particles using the standard

algorithm.(b) Update each particles fitness.(c) Update the swarm radius.

5. If possible, merge subswarms.6. Absorb any intersecting main swarm particles

into the subswarms.7. Search main swarm for particles that meet partitioning

criteria.- If any found, create new subswarm.

8. Repeat from 2 until stopping criteria are met.

A main swarm is thus trained using the cognition onlymodel (c2 set to 0) allowing each particle to perform a localsearch. Subswarms are formed from particles whose fitnessshow a small change over a small number of iterations andtheir one closest topological neighbor. Particles are absorbedinto a swarm when they move into it, and subswarms aremerged when they intersect (see [34] for further details onrules for subswarm behavior). In the current implementation,the search space corresponds to the three-dimensional brainvolume whereas each particle represents a fixed-size,spherical cluster of voxels. Positions are encoded inCartesian coordinates, and velocities correspond to simpleEuclidean movements. The goodness (fitness) of a

particles position can be evaluated using any arbitrarymeasure, and we compared the performance of threedifferent classifier schemes (see below) in terms of mappingsensitivity as well as ability to classify between the brainstates. To prevent overfitting, a hold-out validation schemewhere 60% of the data samples were used as training dataand the remaining as testing data, repeated twice, was used tocompute the fitness. The number of swarm update iterationswas fixed to 10. The algorithm was implemented in Matlab(The Mathworks, Massachusetts, USA) on a standarddesktop computer (3 GHz, 2 GB RAM).

For classification, we used a linear as well as a non-linear(radial basis function, RBF, kernel) support vector machine(SVM), in addition to linear discriminant analysis (LDA;linear diagonal covariance matrix estimate). The matlabSVM package LS-SVMlab (SCD/sista, ESAT, KULeuven,Belgium) was used [35], and the parameters were fixedempirically

B. Simulated dataThe performance of the algorithm was evaluated on

realistic data modeled according to De Martino andcolleagues with a two-condition block-design [6]. Therepetition time (TR) was set to 3.5 s and the functional voxelresolution to 333 mm. The voxels were distributed withina cortex mask extracted from a human subject (containing 28502 voxels) for realistic spatial brain activity arrangement.80 stimulations (equal number of each condition), lasting10.5 s, were simulated. Six discriminative regions ofdifferent size and degree of discriminative informationcontent were added three large regions (142 voxels) and

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three small (38 voxels), each with a contrast-to-noise ratio(CNR; the difference between responses compared to thestandard deviation of the noise) of 0.2, 0.5 or 0.8. Thevariability of the BOLD response to the condition trials(percent of variability compared to the maximum response)was set to 10%, and The signal-to-noise ratio (SNR; theamplitude of the response compared to the standarddeviation of the noise) was fixed to 0.8.

C. Real dataThe Regional Ethical Review Board at University of

Gothenburg approved the study, and the experiments wereperformed in accordance with the Declaration of Helsinki. A1.5 T fMRI scanner (Philips Intera, Eindhoven, Netherlands)was used to collect anatomical and, subsequently, functionalscans using a BOLD (blood oxygenation level dependent)

protocol and a T2*-weighted gradient echo-planar imagingsequence (flip angle 90, TR=3.5s, TE=51ms). The scanning

planes were oriented parallel to the line between the anteriorand posterior commissure and covered the brain from the topof the cortex to the base of the cerebellum. In five healthysubjects (all female and right-handed), 480 volumes (28minutes) of alternating three-volume gentle brushing on theleft thigh and three volumes of rest (total of 80 stimulation

blocks per condition) were obtained. Each scan volumecontained 25 slices at a grid resolution of 128 128 voxels.The data was pre-processed with the BrainVoyager software

package (developed at the Maastricht Brain Imaging Center).All fMRI data was motion corrected and resampled to 333mm voxels. A stereotactic normalization of individual data tofit the Talairach standard space was performed [36]. Voxelsnot containing brain matter were removed. The resultingdataset contained 160 samples (half stimulation, half rest)and a subject mean of 34 374 (range 33 331 - 34 982) voxels.

D. Single trial response estimationWe estimated the brain activity responses (for both real

and simulated data) on the single trial level as De Martinoand colleagues [6] by fitting a general linear model (GLM)with one predictor representing the trial response (obtained

by convolution of a boxcar with a double-gammahemodynamic response function; [2]) and one linear

predictor accounting for a within-trial linear trend. Theregressor coefficients were subsequently obtained as anestimation of each trial response.

E. Performance evaluationFor each voxel, the mean classification performance of

all final iteration particles including that voxel was computedto form a brain map. On the simulated data the mappingsensitivity of the algorithm in detecting the discriminativevoxels was then measured using receiver operativecharacteristics (ROCs) curves (a plot of the sensitivity versus1- specificity for varying thresholds), and the area under thecurve (AUC) was computed. On the real data, on the otherhand, the maximum classification rate was used as anindication of mapping success.

IV. RESULTSA. Simulated data

The PSO outperformed the GLM in localizing thediscriminative voxels (figure 1B). Where the GLM achieveda mapping sensitivity of 0.54, the PSO algorithm producedresults of well above 0.75 for all classifiers and radii of 5voxels and larger. Increased radii had higher impact up to 5voxels, after which there was no improvement (figure 1A).For the best search sphere radius (5.2 voxels), maximalmapping sensitivity and classification scores were obtainedwith the non-linear (RBF kernel) SVM classifier, whereasthe LDA achieved the lowest scores on both measures(figure 1B). The difference between methods was notsubstantial, however, and inconsistent across radii (figure1A).

Classificationaccura

cy(%)

Mappingsensitivity

(AUC)

0.85

0.75

0.65

0.55

AUC%

LDALin SVM

RBF SVM

2 3 4 5 6 7Search sphere radius (voxels)

Mappingsensitivity(AU

C)

0.55

0.65

0.75

0.85

LDALin SVMRBF SVM

A

B

GLM

Figure 1. A) The mapping sensitivity performance (measured

in area under the receiver operative characteristics curve, AUC) as afunction of the search sphere size for all classification methods. B) The best

mapping sensitivity performance and classification accuracy for a searchsphere radius of 5.2 voxels.

The number of particles included in the search also has afundamental impact on the performance, although on thecurrent dataset more than 200 particles did not improve the

performance substantially (figure 2A). The PSO approach proved highly efficient in identifying the discriminativevoxels compared to the conventional exhaustive searchlightapproach [1]: as shown in figure 2A, the mapping sensitivityapproached that of the exhaustive search at 300 particles andhigher, for a dramatic reduction in time requirements (e.g.6.7 min compared to 9 h, figure 2B).

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0.85

0.55

0.75

0.65

Searchlight

0 100 200 300 400Number of particles

Time(h)

10

2

8

4

6

6.7 minutes

0 100 200 300 400Number of particles

Mappingperformance

(AUC)

PSO

A

B

Figure 2. Comparison between the exhaustive search

(searchlight) approach [1] and the proposed PSO mapping algorithm as afunction of the number of included particles, using LDA for classification,

in terms of sensitivity (A) and time requirements (B).

B. Real dataGiven the results obtained on the simulated data, the PSO

algorithm was applied on the real data using a search sphere

radius of 5.2 voxels and 300 particles using the LDAclassifier. In all subjects, high classification scores wereobtained (subject mean 89%, range 81-98% correctclassification; figure 3A), whereas the subject average timeto obtain the maps was low at 3.13 (range 3.00- 3.26)minutes (figure 3B). The algorithm was successful indetecting the expected somatosensory (primary andsecondary) cortices (as shown in figure 3C [37]), in additionto a number of visual areas which have been reported

previously in relation to tactile stimulation [38-39].

V. DISCUSSIONOur proposed niching PSO approach is a promising

multivariate alternative for functional brain mapping,superior in sensitivity to the univariate GLM andsubstantially faster than the searchlight algorithm [1].

The utility of multivariate functional brain-mapping,focusing on subtle spatial patterns contained in fMRI data,has been demonstrated numerous times in recent years (e.g[7], [40]). However, the often staggering time requirementsfor whole brain mapping (without a priori assumptions, incontrast to fast but heavily restricted regions-of-interestanalysis) renders the existing methods of little utility foreveryday use. Moreover, fast multivariate methods are

becoming increasingly acute as the functional resolutionimproves [41], and the number of required subject increases.

S2

S1

708090

100

2.5

3.5

Minutes

%

3.0

CA

1 2 3 4 5Subject

B

Figure 3. The maximum map value (classification score, A)and time required to generate each individual map (B) are also shown. C)Subject mean particle swarm maps obtained on the authentic fMRI tactiledataset, showing in gray the contralateral (left) primary (S1) and bilateral

secondary (S2) somatosensory cortices in which are involved in the

processing of touch.

The non-linear SVM kernel was found to produce moresensitive maps than the linear kernel, although the differencewas not substantial. Despite the theoretical superiority ofnonlinear classifiers, linear classifiers have by far been most

popular in fMRI multivoxel research (e.g. [21], [24], [6], [7]).Although LDA and linear SVMs have dominated the field,there appears to be little practical difference between linearclassifiers [42].

In the present implementation, a static, fixed-size spherewas used for performance evaluation. A highly feasibleextension of the current algorithm where the size and shapeof the search sphere is also optimized would, however, be of

great utility. Such fixed-size, fixed-shape methods rely onthe assumption that response patterns are contained withinthe locality of the search volume, and may fail to detectdiscriminative patterns encoded across regions of differentshape and size.

VI. CONCLUSIONThe proposed particle swarm mapping approach is a

promising multivariate alternative for functional brain-mapping, superior in sensitivity to the univariate GLM andsubstantially faster than state-of-the-art locally-multivariatemethods.

ACKNOWLEDGEMENT

This study was supported by the Swedish ResearchCouncil (grant 3548) and the Sahlgrenska UniversityHospital (grant ALFGBG 3161). We are grateful to Dr.Federico De Martino for data simulation scripts and to KarinRylander for the tactile fMRI data.

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