Frequency Domain Connectivity Identification: An Application of Partial Directed Coherence in fmri

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1 Human Bain Mapping 30: (2009) Fequency Domain Connectivity Identification: An Application of Patial Diected Coheence in fmri João R. Sato, 1,2 * Daniel Y. Takahashi, 2,3 Silvia M. Acui, 4 Koichi Sameshima, 2,3 Pedo A. Moettin, 1 and Luiz A. Baccalá 3,5 1 Depatment of Statistics, Institute of Mathematics and Statistics, Univesity of São Paulo, Bazil 2 NIF/LIM44-Depatment of Radiology, School of Medicine, Univesity of São Paulo, Bazil 3 Bioinfomatics Gaduate Pogam, Univesity of São Paulo, Bazil 4 Neuoimaging Section, Institute of Psychiaty, Kings College London, United Kingdom 5 Depatment of Telecommunications and Contol Engineeing, Escola Politécnica, Univesity of São Paulo, Bazil Abstact: Functional magnetic esonance imaging (fmri) has become an impotant tool in Neuoscience due to its noninvasive and high spatial esolution popeties compaed to othe methods like PET o EEG. Chaacteization of the neual connectivity has been the aim of seveal cognitive eseaches, as the inteactions among cotical aeas lie at the heat of many bain dysfunctions and mental disodes. Seveal methods like coelation analysis, stuctual equation modeling, and dynamic causal models have been poposed to quantify connectivity stength. An impotant concept elated to connectivity modeling is Gange causality, which is one of the most popula definitions fo the measue of diectional dependence between time seies. In this aticle, we popose the application of the patial diected coheence (PDC) fo the connectivity analysis of multisubject fmri data using multivaiate bootstap. PDC is a fequency domain countepat of Gange causality and has become a vey pominent tool in EEG studies. The achieved fequency decomposition of connectivity is useful in sepaating inteactions fom neual modules fom those oiginating in scanne noise, beath, and heat beating. Real fmri dataset of six subjects executing a language pocessing potocol was used fo the analysis of connectivity. Hum Bain Mapp 30: , VC 2007 Wiley-Liss, Inc. Key wods: fmri; connectivity; Gange causality; fequency domain; multisubject; bootstap INTRODUCTION Functional magnetic esonance imaging (fmri) has become one of the most pominent techniques in Neuoscience. It was fist intoduced by Ogawa [1990], who studied the popeties of BOLD signal (blood oxygenation level Contact gant sponsos: FAPESP (05/ , 03/ ), CAPES, CNPq, Bazil. *Coespondence to: J.R. Sato. jsatob@gmail.com Received fo publication 30 August 2007; Revised 10 Octobe 2007; Accepted 15 Octobe 2007 DOI: /hbm Published online 6 Decembe 2007 in Wiley InteScience (www. intescience.wiley.com). dependent), based on paamagnetic popeties of deoxyhemoglobin (T2* weighted acquisition). Because of its noninvasive and high spatial esolution popeties, the numbe of studies based on fmri has been gowing consideably. The main focus of most fmri studies is the localization of neual activation, fo which identification and modeling methods ae well established [Fackowiak et al., 1997]. Actually, most of them ely on geneal linea model (GLM), measuing the association of obseved BOLD signal and an expected haemodynamic esponse function (HRF). By contast, connectivity modeling and identification emain open questions. Seveal studies [Biswal et al. 1995; Codes et al. 2000; Peltie and Noll, 2001] ae based on BOLD coelation analysis (BCA), which can be intepeted as a measue of concuence between the signals of two bain aeas. Despite being useful as an exploatoy VC 2007 Wiley-Liss, Inc.

2 Fequency Domain Connectivity Identification: An application of PDC tool, BCA is unsuited fo connectivity chaacteization because it is based solely on the bivaiate analysis of elationships and the identified connections ae undiected, i.e., BCA neithe povides infomation about the multivaiate influences among time seies no about the diection of infomation flow. Advanced statistical appoaches have been poposed to ovecome these weaknesses. The most popula techniques to addess connectivity in fmri ae: the stuctual equation modeling (SEM), poposed fo fmri data analysis by McIntosh [1998] and dynamic causal models (DCM), intoduced by Fiston et al. [2003]. Howeve, both techniques ely on a pioi specification of the connectivity linkages, i.e., the stuctual gaph must be peviously known. These appoaches ae suited to test the statistical significance of the covaiance stuctue between neual aeas with known effective connectivity. Fo this eason, they cannot be consideed exploatoy tools, but athe just confimatoy methods fo some hypothesis. Recently, Gange causality identification using vecto autoegessive (VAR) models has been a useful tool fo undestanding cotical inteactions. Gange [1969] defined causality in tems of pedictability and tempoal pecedence. This concept was fist applied in econometics to identify tempoal elationships among financial time seies. Gange causality identification using VAR methods can be consideed both an exploatoy and also a modeling tool. In contast to SEM and DCM, VAR modeling does not equie any pe-specification o a pioi knowledge about the connectivity stuctue, even though a pioi infomation can also be included in the model as constaints in the paametic space. Futhemoe, consideing some gaph theoetical ideas, Eichle [2005] intoduced connectivity identification based on Gange causality and gaphical modelling. Goebel et al. [2003], Roeboeck et al. [2005] and Able et al. [2006] intoduced the Gange causality mapping in the context of fmri expeiments. They also showed the epoducibility and eliability of the connectivity identification via Gange causality fo BOLD signals. Valdes-Sosa et al. [2005] applied VAR models to fmri datasets consideing estimation in cases of ovepaametization and spase models using penalized egession. Consideing the case of nonstationay signals, Sato et al. [2006a, 2006b] intoduced intevention VAR and time vaying VAR models to infe the connectivity in fmri datasets. Fequency domain multivaiate modelling is also the aim of inteest of many eseaches, as Paseval s elationship allows decomposing signal vaiance into its fequency components. BOLD signal vaiance is composed of unobseved haemodynamic esponse, scanne noise, heat beating, habituation effect, and othe factos. Sun et al. [2004] suggested the use of spectal coheence and patial coheence to attain fequency domain connectivity identification in fmri and illustated thei application in moto expeiments. Salvado et al. [2005] intoduced an appoach based on patial coheence named nomalized patial mutual infomation, and have shown that functional connectivity lay mainly in low fequencies (0.0004, Hz). In spite of being a useful exploatoy tool, like BCA, spectal coheence does not allow infeing diectionality in the connectivity stuctue. In this aticle, we employ patial diected coheence (PDC) to identify neuonal connectivity using fmri data. This appoach does not equie stuctual pe-specification and is vey well defined in multivaiate cases. The viability and usefulness of this method is illustated though a language-pocessing paadigm. METHODS Gange Causality Gange [1969] defined the concept of causality by focusing on the desciption of tempoal elationships between time seies. The bases of the Gange causality concept ae the eduction in pediction eo and the fact that the effect cannot pecede its cause. Fo two scala time seies x t and y t, thee is Gange causality fom seies x t to y t if the past values of x t incease the foecast powe of pesent and value of y t. It fomalizes the notion of amount of infomation flow fom the aea of the signal x t to the aea of y t. It is impotant to emak that the Gange causality elationship is not ecipocal, that is, existence of Gange causality fom x t to y t does not imply the existence of Gange causality fom y t to x t and vice-vesa. Futhemoe, Gange causality does not imply physical and biological causality, but only pedictability impovement (functional connectivity). VAR modeling is the most common appoach used fo Gange causality identification. Let Y t a multidimensional time seies composed by k signals, i.e. 2 3 y 1t y 2t Y t ¼ 6. 7; t ¼ 1; 2;...T ð1þ 4. 5 y kt whee by the VAR model is defined as Y t ¼ v þ Xp l¼1 A l Y t l þ e t and v is a vecto of constants and e t is a vecto of andom distubances. The matices A l (l 5 1,...,p) ae given by 2 A l ¼ k k 22 2k 32 3k k2 kk and the element ij ði ¼ 1; :::; k; j ¼ 1; :::; kþ is the causality coefficient fom the seies y jt to the seies y it. The vecto of innovations e t has a covaiance matix given by ð2þ ð3þ 453

3 Most fmri studies ae based on multiple subject analysis fo infeence about the population. Because of its obustness against outlies (which ae common in medical studies), the median GPDC coefficient acoss subjects is an attactive goup statistic. Howeve, the distibution of the median GPDC s acoss subjects unde the null hypothesis of zeo GPDC in specific fequencies is difficult to obtain mainly because magnetic esonance noise is non-gaussian [Wink and Roedink, 2006] and the numbe of subjects in fmri expeiments is usually small. In this case, esults about asymptotic distibution of quantiles ae not adequate. Thus, we suggest the following bootstap algo Sato et al k k R ¼ k k1 k2 k3 Note that assuming the expectation of e t to be zeo, the pediction of Y t given all the infomation available until the time (t 2 1) is given by ^Y t ¼ v þ Xp l¼1 A l Y t l Hence, consideing the VAR model, y jt is said to Gange-cause y it if the coefficient ij is non zeo fo some value of l. This can be intepeted as existence of infomation flow fom the bain aea j to bain aea i. In pactice, infeences about the connectivity stuctue can be achieved by fitting a VAR model to the obseved BOLD signal and by testing the statistical significance of the causality coefficients. Futhe desciption, discussion and estimation algoithms can be found in Lütkepohl [1993]. Patial Diected Coheence Although conceptually inteesting, in its oiginal fom Gange causality is a time domain concept, and does not pemit discening the fequency domain chaacteistics of the signals involved and which play impotant oles in data intepetation. Fo instance, atifacts o non-neuonal physiological signals like cadiac and espiatoy signals can be distinguished using thei fequency chaacteistics. This is an impotant advantage ove common time domain analysis whee these non-neuonal signals have to be eliminated somehow most often by ad hoc methods, when that comes to be done at all. Wheeas defining Gange causality is staightfowad in the case of pais of time seies, multivaiate genealizations ae less obvious [Geweke, 1984; Hosoya, 2001]. To ovecome these difficulties, patial diected coheence (PDC) was intoduced [Sameshima and Baccalá, 1999; Baccalá and Sameshima, 2001], developed [Schelte et al., 2006; Baccalá and Sameshima, 2001] and a consideable amount of successful applications in neuophysiology have been done [Fanselow et al., 2001; Yang et al., 2005; Supp et al., 2005; Schlogl and Supp, 2006]. A useful fom of PDC called genealized PDC (GPDC) is achieved by suitable nomalization [Baccalá et al., 2006, Baccalá et al., 2007] so that fequency domain causality fom the j-th time seies to the i-th time seies at fequency k is defined as: a ij ðkþ 1 p ij ðkþ ¼sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i ð6þ P k a ij ðkþ 2 1 i¼1 2 i ð4þ ð5þ whee a ij ðkþ ¼d ij Xp l¼1 p ij expð 2plk ffiffi 1 Þ fo d ij 5 1ifi 5 j and 0 othewise. It is clea that null GPDC in all fequencies indicates absence of Gange causality and vice vesa. The main advantage of GPDC emains in its intepetability as a measue of stength of connectivity between neual stuctues. The squae modulus of GPDC value fom j-th time seies by i-th seies can be undestood intuitively as the popotion of the powe specta of the j-th time seies, which is sent to the i-th seies consideing the effects of the othe seies. Futhemoe, it can be shown to be a facto in the decomposition of the coheence in the bivaiate case and of patial coheence in the multivaiate case. Hence, zeo GPDC (p ij (k) 5 0) can be intepeted as absence of functional connectivity fom the j-th stuctue to the i-th stuctue at fequency k and high GPDC, nea one, indicates stong connectivity between the stuctues. In the liteatue thee ae also othe measues of neual connectivity in the fequency domain. Fo instance, diected tansfe function (DTF) and elative powe contibution (RPC) have been used fo the analysis of EEG [Kaminski et al., 2001] and fmri [Yamashita et al., 2005], espectively. Howeve, in the bivaiate case, GPDC, DTF, and RPC ae all equivalent in the sense that when one of them is zeo the othes ae also zeo. The diffeence becomes evident in the multivaiate case when PDC is the fequency domain countepat of Gange causality in time domain [Lütkepohl, 1993; Baccalá and Sameshima, 2001]. Actually, DTF and RPC ae not able to distinguish between diect and indiect pathways linking diffeent stuctues; thus they do not povide the multivaiate elationships fom a patial pespective. To povide a common compaative pictue PDC s popeties ae contasted to those of othe connectivity methods in Table I. Multisubject Hypothesis Testing Using Bootstap ð7þ 454

4 Fequency Domain Connectivity Identification: An application of PDC TABLE I. Compaison between connectivity models Fequency specification Intensity intepetation Diectionality Patial elationship Peason coelation No Yes No No Gange causality test No No Yes Yes Coheence Yes Yes No No Patial coheence Yes Yes No Yes PDC Yes Yes Yes Yes DTF Yes Yes Yes No RPC Yes Yes Yes No ithm to obtain the statistical significance of the goup GPDC statistic: Step 1: Fit VAR models fo the BOLD time seies of each subject sepaately. Step 2: Obtain the VAR coefficient estimates and esiduals fo each subject. Step 3: Fo each fequency, calculate the GPDC estimates [see Eq. (7)]. Step 4: Obtain the median GPDC acoss subjects at each fequency (obseved GPDC). Step 5: Fo each subject, esample the esiduals (andom sampling with eplacement) obtained in Step 2. Step 6: To test each influence fom time seies j to i, assume a model whee the VAR coefficients a (l) ij, l 5 1,...,p (i.e., all coefficients elated to time seies j causing i) ae 0. The othe VAR coefficients emain as oiginally estimated by least squaes in Step 2. Basically, this step consists of assuming a model unde the assumption of no Gange causality fom time seies j to i, and thus can be used to geneate bootstap samples unde the null hypothesis. Step 7: By using the esampled esiduals obtained in Step 5, and the model specified in Step 6, simulate a bootstap multivaiate time seies (note that this pocedue geneates time seies unde the null hypothesis of no causality fom time seies j to i). Step 8: Obtain the median GPDC fo this bootstap sample. Step 9: Go to step 5 until the desied numbe of bootstap samples is achieved. Step 10: Estimate the citical value fo each fequency using the espective median GPDC bootstap samples. The citical value is defined as the (1 2a) quantile of bootstap samples, whee a is the expected Type I Eo. Step 11: Compae the obseved median GPDC with the estimated citical value. A diagam of the pevious steps is pesented in Figue 1. This is a geneal algoithm that may be applied to any statistic obtained by using any function of GPDC coefficients. This is a useful popety, as any hypothesis on moments o quantiles can be tested analogously and independently on the distibution of the data. Data Acquisition and Expeiment In this study, six healthy subjects executed a languageelated task. Incomplete sentences with a missing wod wee visually (text) pesented to them. The missing wod was eveled only afte a shot time inteval, allowing the subjects to pocess the sentence. Illustative examples of this task ae the sentences: He posted the lette without a... o The leaves ae aleady falling fom the.... The stems wee pesented fo 2,500 ms, followed by a blank sceen. Afte an inteval of 700 ms the taget wod appeaed (e.g., stamp ). The subjects wee asked to espond if the taget wod adequately complete o not the sentence by using a yes/no button box. Afte the esponse, an asteisk eplaced the taget wod until the beginning of the next tial. Eighty sentences wee pesented to the subjects (in five uns of 16 tials) in fixed intevals of 20.4 s, coesponding to 12 time points pe sentence. In othe wods, the subjects wee asked to complete diffeent sentences peiodically in a cycle of 12 points. The aim of this expeiment was to identify the aeas activated when subjects did these tasks to study sentence pocessing in healthy contols. Gadient echo-plana images wee acquied in a 1.5 Tesla magnetic esonance GE system (Geneal Electic, Figue 1. Diagam of bootstap GPDC testing. 455

5 Sato et al. Figue 2. Language task activation maps (cluste wise P-value <0.01). [Colo figue can be viewed in the online issue, which is available at Milwaukee, WS) at the Maudsley Hospital, Institute of Psychiaty, King s College London. The total numbe of volumes was 960, acquied using T2* weighted MR images depicting BOLD contast (paallel to intecomissual plane, TE 5 40 ms, TR s, in plane esolution mm, thickness mm, gap mm, flip angle 5 908) [Acui et al., 2000]. Images Pocessing The fmri data was pepocessed by using head motion ealignment (igid body tansfomation), slice time coection, spatial smoothing (Gaussian kenel with size of five voxels) and nomalization to the space of Talaiach and Tounoux [1988]. The goup activation maps wee obtained using the GLM assuming an HRF function com- Figue 3. Illustative ROIs time seies of a subject. 456

6 Fequency Domain Connectivity Identification: An application of PDC posed of two Poisson functions with peeks in 9.1 (activation) and 13.1 s (undeshoot) afte the pesentation of sentences. The events modeled by GLM efe mainly to the time when the taget wod appeas and thee is a cognitive pocessing about the adequacy of the pesented sentence and this wod, coected by the haemodynamic delay. These steps wee caied out using the fmri XBAM softwae [Bamme et al., 1997], feely available at RESULTS AND DISCUSSION Figue 2 shows the bain activation maps. Significant activations (cluste wise P-values <0.01) wee found in ceebellum (Tal: 7, 278, 224), pimay visual cotex (V1; Tal: 0, 285, 9), left supeio tempoal gyus (STG; Tal: 251, 4, 22), left Insula (Tal: 247, 4, 9) and Thalamus (Tal: 11, 28, 0). The pimay visual cotex, supeio tempoal gyus and Insula wee selected as egions of inteest (ROI) fo the connectivity analysis. The infomation flow chaacteization between these thee aeas was then assessed using GPDC. Because of low fequency atifacts, which lead to nonstationaity chaacteistics to the signals, the diffeence opeato was applied to ROI s aveage time seies. The seies wee then nomalized to zeo mean and unit vaiance. Figues 3 and 4 illustate the ROI s time seies fo one subject and the aveage peiodogam acoss subjects, espectively. Language undestanding and sentences pocessing ae extemely complex pocesses. Fist, the auditoy (o visual) stimuli must be tanslated into meaningful subjective concepts, the undelying message must be undestood, and agumentation must be pocessed. BA-17 is a sensoy cotical aea located in the calcaine sulcus (occipital lobe) and coesponds to the pimay visual cotex (o stiate cotex). In this expeiment, incomplete sentences wee pesented visually, and thus, visual cotex activation was expected. Boadman aea 22 (BA-22) in the lateal aspect of the supeio tempoal gyus is classically involved in pocessing auditoy signals and language eception being a majo component of Wenicke s aea, the main neuonal module in language compehension. Hence, sentence compehension involves activity in this aea. Futhe, BA-72 in Insula is involved in language undestanding and pocessing. In this expeiment, subjects wee asked to decide if the taget wod complete the sentences pesented, implying that the paadigm involves not only language undestanding but also the analysis of semantic meaning. It is impotant to highlight that these thee aeas do not wok independently, but fom an integated netwok. Sonty et al. [2007] studied the changes in the effective connectivity of language netwoks in cases of pimay pogessive aphasia. Oblese et al. [2007] have shown that function integation of bain egions impoves speech peception. Kaunanayaka et al. [2007] identified that lan- Figue 4. ROIs aveage peiodogam acoss subjects. 457

7 Sato et al. Figue 5. ROIs multisubject median patial diected coheence. The dotted line shows the 95% confidence uppe bound unde the hypothesis of no connectivity between the nodes. guage connectivity stuctue when childen listen to histoies is age-elated. Note that the ROI s peiodogams in Figue 4 show significant powe at Hz (and Hz, a hamonic), which is exactly the stimulation fequency in this paadigm. This esult is expected as the ROI s wee identified as egions which espond to the stimulus. In addition, hamonic peaks ae expected, since the haemodynamic esponse diffes significantly fom sinusoidal functions. Using multisubject GPDC analysis (Figs. 5 and 7), we found evidence of a connectivity netwok involving the ROIs concentated mostly at and Hz. A diagam epesenting the connectivity gaph obtained using the median PDC only at Hz is shown in Figue 6. The elationship between these aeas diectly elated to the execution of the task is expected to occu at this fequency. Panel STG to Insula (see Fig. 5) shows that thee ae significant enegies at othe fequencies (e.g., fequencies less than 0.03, at 0.07 Hz o 0.13 Hz), indicating the existence of elationships between these aeas, as mioed by the BOLD time seies, but which ae unelated to pocessing the task. Low fequency acquisition atifacts ae fequent in long scanning fmri sessions. PDC is useful to disciminate between stimulus-induced functional connectivity fom othe souces. Howeve, the physiological oigin (cadiac, beath, etc.) of the connectivity geneated by these othe souces may be difficult to disciminate, since aliasing is pesent in the data and oscillatoy components of BOLD signal and atifacts ae still not completely identified o established. Thus, additional cae must be to taken when designing the expeiment, because aliasing poblems may ovelap the stimulation fequency. Figue 7 indicates stong infomation flow fom the Insula to STG, whee 33% of the spectum enegy of Insula at Hz (see Fig. 5) is sent to STG. Futhemoe, PDC analysis shows significant amount of infomation fom the visual cotex (11% of the enegy) to the Insula, which is easonable, as the sentences wee pesented visually. The othe connections ae maginally significant (nea statistical theshold) and show low powe (less than 5%), indicating no elevant infomation flow. In summay, multisubject GPDC analysis suggests that paticipants ead the sentences; the infomation migates fom the pimay visual cotex to the Insula and then to STG. Figues 6 and 7 show the estimated coheence function between the ROI aeas which show pattens simila to GPDC, but is unable 458

8 Fequency Domain Connectivity Identification: An application of PDC Figue 6. ROIs multisubject median coheence function. The dotted line shows the 95% confidence uppe bound unde the hypothesis of no connectivity between the nodes (citical egion). to pinpoint link diectionality hindeing its intepetation (see Table I). The statistical powe of VAR model-based connectivity estimatos like PDC is a compomise between the numbe of ROIs, numbe of lags consideed, and signal duation. Lags incease the paametes that need to be estimated in a linea fashion, wheeas the numbe of consideed ROIs does so quadatically. Hence including egions that do not signifi- Figue 7. Multisubject median patial diected coheence at 0.049Hz, simple coheence at 0.049Hz (using the same bootstap algoithm). The fequency of stimulation in the language paadigm was 0.049Hz. The thick solid lines descibe the links with elevant intensity of infomation flow. The citical egions at 5% of significance ae values geate than the shown in paentheses. 459

9 Sato et al. cantly paticipate in the connectivity netwok implies a shap decease in the powe to identify links. One may ty to cicumvent this poblem by constaining the numbe of paametes in the model, i.e., by specifying the linkages a pioi, even though this limits the PDC s usefulness as an exploatoy tool. In fmri expeiments, ou expeience with typical signal duations, suggests selecting a maximum of five o six aeas fo inclusion in the analysis. A second limitation involving fmri expeiments with the execution of multiple tasks is that they do not povide infomation about what is being pocessed no whee each cognitive component of the task is pocessed and much less how this infomation is pocessed to poduce behavio. In the pesent case, GPDC may help infe the inteactions between the aeas activated in the task, suggesting the existence of connectivity netwoks, with a peiodic infomation flow at the fequency of stimulation, besides being able to pinpoint the diection of this flow. Note, howeve that the infeed infomation pathway is not enough to assess whethe semantic intepetation o sentence completion happen at the Insula, the STG o both. The answe to this question is conceivably only possible by compaing the pesent esults to othe studies, as one cannot daw such conclusions fom the pesent data/expeimental paadigm alone. In view of these limitations, futue woks will equie elaboating paadigms and sequences of stimulation to sepaate the cognitive components, using state subtactions o simila techniques [Amao and Bake, 2006]. Howeve, the discimination between task-elated and othe components povided by GPDC epesents a stating point in addessing these questions. CONCLUSION In this aticle, we intoduced a method fo connectivity infeence between neual stuctues which: (1) is based on Gange causality concept, (2) is able to disciminate physiological and nonphysiological components based on thei fequency chaacteistics, (3) is multivaiate, i.e., it consides the patial/diect elationships between all pais of time seies. Also a bootstap pocedue fo the median nomalized GPDC analysis of fmri data is poposed. ACKNOWLEDGMENTS The fmri expeiment was pat of SMA s PhD studies supevised and patially suppoted by Pof. Philip K. McGuie, to whom we ae gateful. REFERENCES Able B, Roeboeck A, Goebel R, Hose A, Schonfeldt-Lecuona C, Hole G, Walte H (2006): Investigating diected influences between activated bain aeas in a moto-esponse task using fmri. Magn Reson Imaging 24: Amao E J, Bake GJ (2006): Study design in fmri: Basic pinciples. Bain Cogn 60: Review. 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