Proceedngs of the 005 IEEE Engneerng n Medcne and Bology 7th Annual Conference Shangha, Chna, September -4, 005 ICA Denosng for Event-Related fmri Studes Martn J. McKeown -3, Yong-e Hu, and Z. Jane Wang 4 Pacfc Parknson s Research Centre, Bran Research Centre, 3 Dept. of Medcne (Neurology), 4 Department of Electrcal and Computer Engneerng, Unversty of Brtsh Columba, Canada. Department of Oral and maxllofcal surgery, Afflated 9th People s Hosptal of Shangha Second Medcal Unversty, Chna. Abstract The poor SNR of fmri data requres that many repettve trals be performed durng an event-related experment to obtan statstcally sgnfcant levels of nferred bran actvty. Ths s costly n terms of scanner tme, necesstates that subects perform the behavoural task(s) for long duratons whch may nduce fatque, and vastly ncreases the amount of data generated. In ths paper, we present a method to enhance the statstcal effect sze usng ICA, so that the same level of sgnfcance can be obtaned wth shorter scannng tmes. We perform ICA on fmri data from a smple event-related motor task by proectng the orgnal data onto the lnear subspace defned by the task-related ICA components. Ths essentally denoses the sgnal and results n sgnfcant mprovement n the effect sze. Usng smulatons we demonstrate that the proposed ICA-denosng procedure s robust to a varety of realstc nose models and enhances the performance of Least Squares estmates of the evoked hemodynamc response. I. INTRODUCTION Snce t was frst ntroduced to fmri n 998 [], Independent Component Analyss (ICA) has proved to be a powerful method for exploratory analyss of fmri data. Of partcular nterest here s to employ ICA for the extracton of the event-related sgnal from the complcated fmri data under a poor SNR. FMRI experments are typcally performed n a Block desgns [8] or Event-related Desgns [9,0]. In the former, the task s performed repeatedly n order actvate bran regons and saturate the hemodynamc response. In the later, subect s nstructed to respond sngly to ntermttently presented stmul, so that the shape of the evoked hemodynamc response can be nferred. When event-related studes are analyzed, the fmri data are dvded nto epochs tme-locked to stmulaton presentaton, whch are then averaged to obtan a mean response to the stmul []. Ths method of analyss mplctly assumes that the data can be accurately modeled as a determnstc sgnal that s precsely tme-locked to stmulus presentaton and s corrupted wth random nose that wll tend to zero when averaged over many trals.e. all sgnals not precsely tme-locked to stmulus presentaton, ncludng other bran sgnals and decayng responses from prevous stmul are assumed to be nose. However, f underlyng components of the data are not completely random wth respect to stmulus presentaton, they may tend to average to values other than zero thus ntroducng bases n the estmates of stmulus locked sgnals. ICA has proved useful n explorng the valdty of some assumptons underlyng event-related fmri analyss. Analyss of fmri data wth ICA has suggested that there can be consderable tral-to-tral varablty n the fmri BOLD response []. Moreover, other components besdes the domnant task-related component may stll be sgnfcantly task-related, but wth dfferent latences and varablty n latences [3]. As the evoked hemodynamc response (HDR) s typcally small n fmri data, numerous stmul must be presented to acheve a gven level of statstcal sgnfcance. Accurate estmaton of the form of possbly overlappng, often mnscule stmulus-evoked HDR n the face of underlyng nose s challengng. A lnear model has been proposed to solate the stmulus-nduced fmri BOLD response []. In the lnear approach, a stmulus convoluton matrx based on the tmng of stmul presentaton s derved and the HDR s estmated by multvarate regresson usng ordnary least squares [3]. By estmatng the nose covarance, the maxmum lkelhood (ML) estmate of the HDR was studed n [3]. Further, by explotng the pror knowledge of the antcpated HDR shape, hemodynamc bass functons can be ncorporated nto the estmaton process to mprove the estmator effcency [4]. The choce of a sutable nose model may enhance the senstvty and the accuracy of estmatng the evoked HDR. Much pror work has assumed a whte Gaussan nose model (e.g., [6]), though t has been suggested that nosy MRI data may follow non-gaussan dstrbutons, such as a Rcan [4]. Methods suggested for nose reducton n fmri data nclude wavelets [6], spectrum subtracton [5] and component analyss [7]. However, the extent to whch evoked bran estmates are based by the choce of nose models has yet to be fully explored. In ths paper, we present work whch elucdates the above concepts. We perform ICA on fmri data from a smple event-related motor task, and show that naïve applcaton of Infomax ICA may overft the data as several spatally-ndependent components appear task-related. However, we demonstrate that proectng the orgnal data onto the lnear subspace defned by these task-related components essentally denoses the sgnal and results n sgnfcant mprovement n the effect sze. We then perform smulatons, usng a number of dfferent nose models. We demonstrate that the ICA-denosng procedure compares favorably to prevously descrbed regresson methods for determnng HDR and s robust to a varety of nose models. 0-7803-8740-6/05/$0.00 005 IEEE. 57
II. METHODS A. Lnear model for overlappng hemodynamc responses We start wth a lnear model for the observed fmri eventrelated response [3]. For smplcty, we consder the case of sngle type of event, rather than multple nterleaved stmul, each evokng a dfferent response. For each voxel, =,, N, the fmri observaton y (t) s modeled as: y ( t) = x( t) h ( t) + n ( t), () where the event sequence x(t) s a sum of tme-shfted delta functons determned by the stmulus ntervals, h (t) s the evoked hemodynamc response of each voxel, whch s to be estmated, n (t) represents addtve nose and * represents the lnear convoluton operator. In a dscrete verson, we defne the correspondng vectors y, h and n, thus the model becomes: y = Xh + n, () where X s the so-called stmulus convoluton matrx determned by the event sequence x(t). We plan to estmate the HDRs {h } based on the fmri observatons {y }. B. Proposed scheme to estmate the evoked HDRs The basc dea of the proposed scheme s to frst denose the observatons by ICA analyss. In bref, the data are frst analyzed by ICA and the event-related components are dentfed. The orgnal data s then proected nto the lnear subspace spanned by the components of nterest. The proposed scheme s summarzed as follows: Step-: Apply Prncple Component Analyss (PCA) to acheve dmenson reducton [7]. PCA seeks to acheve dmenson reducton by proectng the orgnal data nto a few orthogonal lnear combnatons (the PCs), thus t provdes the best lnear dmenson reducton performance n the sense of mean-square error. Step-: Apply ICA, and choose the most related components. In the current stuaton, the frst 50 prncple components were subsequently used as nput to ICA. Infomax ICA [5] was then used to separate the egenmages nto spatally ndependent components []. The assocated tme courses were then estmated. Step-3: Select components deemed task-related by modelfttng. Denote the -th component by the vector f.. If f s event-related, accordng to the sgnal model (), we expect that f follows a smlar formulaton n the form f = Xe + n, where e s the orgnal event-related sgnal. Therefore, we propose to select components deemed task-related by fttng each component vector to the above model to estmate e n the least square sense ( e ˆ ), and usng the correspondng relatve fttng error, defned as f ˆ Xe d =, as a crteron to determne whether a f component f s task-related or not. Step-4: Denose the observaton by proectng the orgnal data onto the selected ndependent components. Wthout loss of generalty, suppose the components f, for =,..M, are determned as task-related n Step-3. One smple way s to denose the orgnal voxel vector y s to proect t onto the sgnal subspace spanned by the components f, =,..M. Therefore, we defne S = [ f, f,..., f M ], and the voxel vector y after denosng s then expressed as T T yˆ = S( S S) S y. (3) Step-5: For each voxel, estmate the mpulse (HDR) h, based on the denosed vector ŷ. We apply the least-square approach to estmate the HDRs, expressed as ˆ T T h ˆ = X X X y. (4) Suppose that the nose after the denosng process s temporally uncorrelated, then the maxmum lkelhood estmator for our problem reduces to the above ordnary least-square estmate. It s worth mentonng that, n Step-4 we denose the sgnal by proectng the raw data nto a sgnal subspace derved from ICA (Equaton 3). Ths s dfferent from prevous methods of removng artfacts wthn the ICA components by smply settng those components to zero [7]. If we consder the data Y, we are modelng the ICA data as: Cs Y = [ S N] C, where Y s the observaton matrx, S n s the sgnal subspace and N s the nose subspace. We propose ˆ T T Y = S S S S Y, as opposed to ^ = C s [ S N ] Y suggested n [7]. 0 For comparson, we compared the HDR estmate calculated from the orgnal ~ data: T T h = X X X y. (5) To determne f any of the tme ponts contaned n h has statstcal sgnfcance, a null dstrbuton for each voxel was determned by computng averages from randomly placed 6-sec wndows contanng the same number of stmul as n the orgnal case. One thousand draws were used to calculate the null dstrbuton. C. Smulatons ncorporatng several nose models To test the robustness of the proposed denosng procedure to nose, we consder the addton of several types of nose to dealzed underlyng sgnal. The nose parameters 58
are chosen to yeld an SNR of around -5dB n order to emulate the low SNR observed n real fmri data. The smulaton of deal error-free fmri observatons s performed as follows. Frst, the unbased ML HDR estmator descrbed n [3] was appled to a real eventrelated fmri data. Then, usng the convoluton matrx X and such estmated HDRs, the voxel event-related tme courses were reconstructed to create a true underlyng sgnal that was then corrupted wth dfferent types of nose. As we base our smulatons on our collected data, the data sze settngs are as follows: the number of total voxels of nterest s 7846, the number of stmulus s 6 wth duratons randomly dstrbuted between 3 to 7, the temporal length of the observaton s 60, and the duraton of HDR s assumed to be captured n a 6sec wndow. The choces of nose models are as follows: Case-: Spatally and temporally whte Gaussan nose. In other words, the nose covarance matrx s assumed as R σ n = I. The SNR was chosen to be around -5dB. Case : Temporally correlated Gaussan nose wth 0-mean and covarance matrx R n. R n was estmated from the real fmri data, and the SNR was around -3dB. Case 3: d Raylegh nose. The nose s assumed to follow a Raylegh dstrbuton (.e. specal case of Rcan, wth the parameter A=0). The SNR was around -db. Case 4: d Rcan nose. The nose s assumed to follow a dstrbuton Rcan(A, ), where A and are the dstrbuton parameters. The SNR was around -db, and the parameter A/ was set to 0.4. Case 5: Rcan nose wth tme-varyng parameter A. The nose at tme follows a Rcan dstrbuton Rcan(A, ), wth the tme-varyng parameter A / randomly chosen from 0.3 to 0.9. In all cases, the estmaton performance of the proposed scheme was compared wth that of the LS approach (5) when no denosng process was performed. D. Estmaton effcency Due to the complex nature of ICA and the unknown nose model of the event-related fmri data, t s mpossble to characterze the estmaton performance of the proposed scheme analytcally. Hence, performance demonstratons are based on smulatons. In ths study, we am to estmate HDRs as effcently as possble. To evaluate the estmaton performance wth regard to ths obectve, we may examne varous statstcal crtera, such as the estmator effcency E defned n [3, 8]. Let h and ĥ be the true and estmated HDR wth length n, respectvely. To evaluate the estmaton performance, we calculate the correlaton coeffcent (CC) between the estmated HDRs and the true ones. We also study the relatve estmaton resdual power (.e. the ˆ h h estmator varance) defned as r = E, snce t h s desrable for an estmator to ft the real HDR curve n a least-square sense, where E(.) denotes the expectaton operaton. Note that ths estmaton crtera r s closely related to the estmaton effcency E n [3] whch s defned as the recprocal of estmator varance. Assumng the HDRs are normalzed, r defned here s the recprocal of E defned n [3]. The reason why we chose to study the crtera r nstead of the crtera E s due to that r s generally restrcted to the range 0 to. The larger the CC and the smaller the relatve resdual power r, the better the estmaton performance. III. RESULTS Fgure 4 shows the true HDRs and the HDRs estmated by the proposed scheme under the presumed realstc Rcan nose model [4] (Case-4) for 6 typcal voxels. The proposed scheme, LS-D, more closely followed the underlyng sgnal compared to the LS-R estmate, wth LS-R and LS-D representng LS approach descrbed n (5) and (4), respectvely. Unlke the estmate from the proposed LS-D, the LS-R estmate occasonally demonstrated more than peak n the estmate. To further evaluate the estmaton performance statstcally, we study the performance measures n terms of correlaton between the true HDR and the estmated HDR (CC) and the statstcal effcency (r) dscussed above. Table shows the statstcal results of estmatng the HDRs, where the emprcal means and standard devatons of these two performance measures are reported. The proposed ICAbased scheme provded consstently superor estmate performance over the LS-R approach wthout ICA denosng. Both methods demonstrated sgnfcantly degraded performance wth the temporally correlated Gaussan nose model (Case ), although the LS-R method was more severely affected. fmri data results Fgure 5 s a scatterplot comparng the z-score of the 4 th tme pont (.e. 4sec after stmulus presentaton) for each voxel for the LS-D and LS-R cases. The 4 th tme pont was chosen because each tme pont wthn the estmated HDR had an assocated z-score, and the peak was typcally at tme ponts 4-6. The other scatter plots for tme ponts 5 and 6 (not shown) were qualtatvely the same. Almost all (93%) voxels had greater z-scores usng the LS-D estmate compared to the LS-R case, as evdenced by the poston of the pont above the 45 lne. The dstrbuton of the z-scores across all actve voxels was z = 4.4 z =.3 for LS-R and z = 8.90, z = 3.8 of LS-D. The spatal dstrbutons of actvated voxels usng the orgnal and denosed data were qualtatvely smlar (F.g 6, 59
Performance crtera vs. Nose Model Case- whte Gaussan Case- Temporally correlated Gaussan Case-3 Raylegh nose Case-4 Statonary Rcan nose Case-5 Non- Statonary Rcan nose LS-R: CC (0.900, 0.059) (0.856, 0.76) (0.95, 0.09) (0.946, 0.03) (0.936, 0.037) LS-D: CC (0.960, 0.036) (0.934, 0.64) (0.98, 0.04) (0.980, 0.06) (0.979, 0.07) LS-R: r (0.69, 0.60) (0.36, 0.356) (0.4, 0.067) (0.9, 0.073) (0.53, 0.090) LS-D: r (0.6, 0.085) (0.54, 0.50) (0.067, 0.036) (0.068, 0.040) (0.078, 0.045) Table : Estmaton effcency of the proposed scheme n estmatng HDRs, n terms of the emprcal mean and standard devaton of CC and r. top panel). Both methods relably demonstrated actvaton n the left prmary motor (rght sde of mage -- sold arrow) and supplementary motor cortces (open arrow). The LS-D estmator detected addtonal sgnfcant actvaton n the contralateral prmary motor cortex. To ensure that any spatal dfferences between the estmates based on the raw and denosed data were not the result of arbtrarly chosen threshold levels, we plotted actvated voxels under a range of dfferent thresholds (Fgure 6, lower panels). Agan the spatal dstrbuton of actvaton was qualtatvely smlar across the two data sets. From Fg. 6, we can see that the proposed scheme resulted n areas of sgnfcant actvaton that were qualtatvely smlar to the denosed case. However, the effect sze, or sgnfcance of actvaton, was much hgher n the denosed case (Fgure 5). As scanner costs are consderable, ths suggests that the same level of statstcal sgnfcance could be obtaned wth substantally fewer stmul presentatons, resultng n less scanner tme, or fewer subects beng scanned n order to obtan a desred level of statstcal sgnfcance. To take nto consderaton of the over-fttng ssue, we denose the sgnal by proectng the raw data nto a sgnal subspace derved from ICA (Equaton 3). Ths s n contrast to prevous methods of removng artfacts wthn the ICA components by smply settng those components to zero, as suggested n [7]. III. CONCLUSION & DISCUSSION We propose a scheme employng ICA denosng and LS estmaton of the evoked HDR. Smulatons suggest that the method s more robust to dfferent nose models compared to naïve applcaton of LS. The result s a consderably ncreased level of sgnfcance of actvaton for a gven voxel, but qualtatvely smlar spatal dstrbuton of actvatons over all voxels. We suggest that the proposed method has the potental to substantally reduce total scannng tme requrements to acheve the same level of statstcally sgnfcant actvaton. We are currently nvestgatng a more general model n whch HDR of each tral could have dfferent magntude over tme. Fgure 4: HDR smulaton examples. Note the spurous multple peaks present n the LS-estmate, presumably because of the msmatch between the mplct Gaussan model wth the LS and the other nose model used n the smulaton. Denosed data effect sze (z-scores) - - 8 6 4 0 0 5 Orgnal data effect sze (z-scores) Fgure 5: Comparson of level of sgnfcance ( effect sze ) before and after denosng. Monte Carlo estmates were used to estmate the null dstrbuton of mean actvty. Note that 60
the vast maorty of voxels have ncreased levels of sgnfcance after the proposed denosng procedure, evdenced by the fact that they le above the dagonal lne (same horzontal and vertcal scales). Orgnal Denosed Fgure 6: Spatal dstrbuton of actvated voxels, before and after denosng. Although the denosed voxels have greater effect sze (Fgure 5), the spatal dstrbuton of actvated voxels s qualtatvely smlar between the denosed data and the orgnal data. Note the evdence of actvaton n the prmary motor cortex (sold arrow), the supplementary motor cortex (open arrow), although the denosed data also detected actvty n the pslateral motor cortex (patterned arrow). Voxels wth z-scores above the 70 th, 80 th, 90 th and 95 th percentles are shown. REFERENCES > 70 th > 80 th > 90 th > 95 th [] McKeown, M.J., et al., Analyss of fmri data by blnd separaton nto ndependent spatal components. Human Bran Mappng, 6(3): p. 60-88, 998. [] Duann, J.R., et al., Sngle-tral varablty n eventrelated BOLD sgnals. Neuromage, 5(4): p. 83-35, 00. [3] McKeown, M.J., et al., Determnstc and stochastc features of fmri data: mplcatons for analyss of eventrelated experments. Journal of Neuroscence Methods.,8(): p. 03-3, 00. [4] Zarahn, E., G.K. Agurre, and M. D'Esposto, Emprcal analyses of BOLD fmri statstcs. I. Spatally unsmoothed data collected under null-hypothess condtons. Neuromage, 5(3): p. 79-97, 997. [5] Bell, A.J. and T.J. Senowsk, An nformatonmaxmzaton approach to blnd separaton and blnd deconvoluton. Neural Comput, 7(6): p. 9-59, 995. [6] Beckmann, C.F. and S.M. Smth, Probablstc ndependent component analyss for functonal magnetc resonance magng. IEEE Transactons on Medcal Imagng, 3(): p. 37-5, 004. [7] Thomas, C.G., R.A. Harshman, and R.S. Menon, Nose reducton n BOLD-based fmri usng component analyss. Neuromage.,7(3): p. 5-37, 00. [8] Bandettn, P.A., et al., Tme course EPI of human bran functon durng task actvaton. Magn Reson Med, 5(): p. 390-7, 99. [9] Bandettn, P.A. and R.W. Cox, Event-related fmri contrast when usng constant nterstmulus nterval: theory and experment. Magnetc Resonance n Medcne, 43(4): p. 540-8, 000. [0] Dale, A.M. and R.L. Buckner, Selectve averagng of ndvdual trals usng fmri. Human Bran Mappng, 5: p. 39-340, 997. [] Huettel, S.A. and G. McCarthy, Regonal dfferences n the refractory perod of the hemodynamc response: an event-related fmri study. Neuromage, 4(5): p. 967-76, 00. [] Dale, A.M. and R.L. Buckner, Selectve averagng of rapdly presented ndvdual trals usng fmri. Human Bran Mappng, 5: p. 39-340, 997. [3] Dale, A.M., Optmal expermental desgn for eventrelated fmri. Human Bran Mappng, 8(-3): p. 09-4, 999. [4] Henson, R.N., M.D. Rugg, and K.J. Frston, The choce of bass functons n event-related fmri. Neuromage, 3: p. S49, 00. [5] Kadah, Y.M., S. LaConte, and X. Hu, Denosng of Event-Related fmri Data Based on a Rcan Nose Model for Robust Analyss Usng ICA. Proc. Intl. Soc. Mag. Reson. Med., 0, 00. [6] LaConte, S.M., S.C. Ngan, and X. Hu, Wavelet transform-based Wener flterng of event-related fmri data. Magnetc Resonance n Medcne, 44(5): p. 746-57, 000. [7] Center, I.F., A Survey of Dmenson Reducton Technques. 00. [8] Mechell A., Prce C., Henson R., and Frston K., Estmatng effcency a pror: a comparson of blocked and randomzed desgns, NeuroImage, 8(3):798-805, 003. 6