{"title": "A Probabilistic Algorithm Integrating Source Localization and Noise Suppression of MEG and EEG data", "book": "Advances in Neural Information Processing Systems", "page_first": 1625, "page_last": 1632, "abstract": null, "full_text": "A Probabilistic Algorithm Integrating Source\n\nLocalization and Noise Suppression of MEG and\n\nEEG Data\n\nJohanna M. Zumer\n\nBiomagnetic Imaging Lab\nDepartment of Radiology\n\nJoint Graduate Group in Bioengineering\nUniversity of California, San Francisco\n\nSan Francisco, CA 94143-0628\njohannaz@mrsc.ucsf.edu\n\nHagai T. Attias\n\nGolden Metallic, Inc.\nSan Francisco, CA\n\nhtattias@goldenmetallic.com\n\nKensuke Sekihara\n\nDept. of Systems Design and Engineering\n\nTokyo Metropolitan, University\n\nTokyo, 191-0065 Japan\n\nksekiha@cc.tmit.ac.jp\n\nSrikantan S. Nagarajan\nBiomagnetic Imaging Lab\nDepartment of Radiology\n\nJoint Graduate Group in Bioengineering\nUniversity of California, San Francisco\n\nSan Francisco, CA 94143-0628\n\nsri@mrsc.ucsf.edu\n\nAbstract\n\nWe have developed a novel algorithm for integrating source localization and\nnoise suppression based on a probabilistic graphical model of stimulus-evoked\nMEG/EEG data. Our algorithm localizes multiple dipoles while suppressing noise\nsources with the computational complexity equivalent to a single dipole scan,\nand is therefore more ef(cid:2)cient than traditional multidipole (cid:2)tting procedures. In\nsimulation, the algorithm can accurately localize and estimate the time course of\nseveral simultaneously-active dipoles, with rotating or (cid:2)xed orientation, at noise\nlevels typical for averaged MEG data. Furthermore, the algorithm is superior to\nbeamforming techniques, which we show to be an approximation to our graphical\nmodel, in estimation of temporally correlated sources. Success of this algorithm\nfor localizing auditory cortex in a tumor patient and for localizing an epileptic\nspike source are also demonstrated.\n\n1 Introduction\n\nMapping functional brain activity is an important problem in basic neuroscience research as well as\nclinical use. Clinically, such brain mapping procedures are useful to guide neurosurgical planning,\nnavigation, and tumor and epileptic spike removal, as well as guiding the surgeon as to which areas\nof the brain are still relevant for cognitive and motor function in each patient.\nMany non-invasive techniques have emerged for functional brain mapping, such as functional mag-\nnetic resonance imaging (fMRI) and electromagnetic source imaging (ESI). Although fMRI is the\nmost popular method for functional brain imaging with high spatial resolution, it suffers from poor\ntemporal resolution since it measures blood oxygenation level signals with (cid:3)uctuations in the order\nof seconds. However, dynamic neuronal activity has (cid:3)uctuations in the sub-millisecond time-scale\nthat can only be directly measured with electromagnetic source imaging (ESI). ESI refers to imag-\ning of neuronal activity using magnetoencephalography (MEG) and electroencephalography (EEG)\n\n\fdata. MEG refers to measurement of tiny magnetic (cid:2)elds surrounding the head and EEG refers to\nmeasurement of voltage potentials using an electrode array placed on the scalp.\nThe past decade has shown rapid development of whole-head MEG/EEG sensor arrays and of al-\ngorithms for reconstruction of brain source activity from MEG and EEG data. Source localization\nalgorithms, which can be broadly classi(cid:2)ed as parametric or tomographic, make assumptions to\novercome the ill-posed inverse problem. Parametric methods, including equivalent current dipole\n(ECD) (cid:2)tting techniques, assume knowledge about the number of sources and their approximate lo-\ncations. A single dipolar source can be localized well, but ECD techniques poorly describe multiple\nsources or sources with large spatial extent. Alternatively, tomographic methods reconstruct an esti-\nmate of source activity at every grid point across the whole brain. Of many tomographic algorithms,\nthe adaptive beamformer has been shown to have the best spatial resolution and zero localization\nbias [1, 2].\nAll existing methods for brain source localization are hampered by the many types of noise present\nin MEG/EEG data. The magnitude of the stimulus-evoked neural sources are on the order of noise on\na single trial, and so typically 50-200 trials are needed to average in order to distinguish the sources\nabove noise. This can be time-consuming and dif(cid:2)cult for a subject or patient to hold still or pay\nattention through the duration of the experiment. Gaussian thermal noise is present at the sensors\nthemselves. Background room interference such as from powerlines and electronic equipment can\nbe problematic. Biological noise such as heartbeat, eyeblink or other muscle artifact can also be\npresent. Ongoing brain activity itself, including the drowsy-state alpha ((cid:24)10Hz) rhythm can drown\nout evoked brain sources. Finally, most localization algorithms have dif(cid:2)culty in separating neural\nsources of interest that have temporally overlapping activity.\nNoise in MEG and EEG data is typically reduced by a variety of preprocessing algorithms before\nbeing used by source localization algorithms. Simple forms of preprocessing include (cid:2)ltering out\nfrequency bands not containing a brain signal of interest. Additionally and more recently, ICA\nalgorithms have been used to remove artefactual components, such as eyeblinks. More sophisticated\ntechniques have also recently been developed using graphical models for preprocessing prior to\nsource localization [3, 4].\nThis paper presents a probabilistic modeling framework for MEG/EEG source localization that is\nrobust to interference and noise. The framework uses a probabilistic hidden variable model that de-\nscribes the observed sensor data in terms of activity from unobserved brain and interference sources.\nThe unobserved source activities and model parameters are inferred from the data by a Variational-\nBayes Expectation-Maximization algorithm. The algorithm then creates a spatiotemporal image of\nbrain activity by scanning the brain, inferring the model parameters and variables from sensor data,\nand using them to compute the likelihood of a dipole at each grid location in the brain. We also\nshow that an established source localization method, the minimum variance adaptive beamformer\n(MVAB), is an approximation of our framework.\n\n2 Probabilistic model integrating source localization and noise suppression\n\nThis section describes the generative model for the data. We assume that the MEG/EEG data has\nbeen collected such that stimulus onset or some other experimental marker indicated the \u2019zero\u2019 time\npoint. Ongoing brain activity, biological noise, background environmental noise, and sensor noise\nare present in both pre-stimulus and post-stimulus periods; however, the evoked neural sources of\ninterest are only present in the post-stimulus time period. We therefore assume that the sensor data\ncan be described as coming from four types of sources: (1) evoked source at a particular voxel (grid\npoint), (2) all other evoked sources not at that voxel, (3) all background noise sources with spatial\ncovariance at the sensors (including brain, biological, or environmental sources), and (4) sensor\nnoise. We (cid:2)rst infer the model describing source types (3) and (4) from the pre-stimulus data, then\n(cid:2)x certain quantities (described in section 2.2) and infer the full model describing the remaining\nsource types (1) and (2) from the post-stimulus data (described in section 2.1). After inference of\nthe model, a map of the source activity is created as well as a map of the likelihood of activity across\nvoxels.\nLet yn denote the K (cid:2) 1 vector of sensor data for time point n, where K is the number of sensors\n(typically 200). Time ranges from (cid:0)Npre : 0 : Npost (cid:0) 1 where Npre (Npost) indicates the number\n\n\fF\n\ns\n\nu\n\nB\n\nx\n\ny\n\nFigure 1: (Left) Graphical model for proposed algorithm. Variables are inside dotted box, param-\neters outside dotted box. Values in circles unknown and learned from the model, and values in\nsquares known. (Right) Representation of factors in(cid:3)uencing the data recorded at the sensors. In\norange, a post-stimulus source at the voxel of interest, focused on by the lead (cid:2)eld F. In red, other\npost-stimulus sources not at that particular voxel. In green, all background sources, including on-\ngoing brain activity, eyeblinks, heartbeat, and electrical noise. In blue, thermal noise present in each\nsensor.\n\nof time samples in the pre-(post-)stimulus period. The generative model for data yn is\n\nyn =(cid:26) Bun + vn\n\nF rsr\n\nn + Arxr\n\nn + Bun + vn\n\nn = (cid:0)Npre; : : : ; (cid:0)1\nn = 0; : : : ; Npost (cid:0) 1\n\n(1)\n\nThe K (cid:2) 3 forward lead (cid:2)eld matrix F r represents the physical (and linear) relationship between\na dipole source at voxel r for each orientation, and its in(cid:3)uence on sensor k = 1 : K [5]. The\nlead (cid:2)eld F r is calculated from knowing the geometry of the source location to the sensor location,\nas well as the conducting medium in which the source lies: the human head is most commonly\napproximated as a single-shell sphere volume conductor. The source activity sr\nn is a 3 (cid:2) 1 vector\nof dipole strength in each of the three orientations at time n for the voxel r. The K (cid:2) L matrix A\nand the L (cid:2) 1 vector xn represent the post-stimulus mixing matrix and evoked non-localized factors,\nrespectively, corresponding to source type (2) discussed above. The K (cid:2) M matrix B and the M (cid:2) 1\nvector un represent the background mixing matrix and background factors, respectively. The K (cid:2) 1\nvector vn represents the sensor-level noise. All quantities depend on r in the post-stimulus period\nexcept for B; un and (cid:21) (the sensor precision), which will be learned from the pre-stimulus data and\n(cid:2)xed as the other quantities are learned for each voxel. Note however the posterior update for (cid:22)un\ndoes depend on the voxel r. The graphical model is shown in Fig. 1. This generative model becomes\na probabilistic model when we specify prior distributions, as described in the next two sections.\n\n2.1 Localization of evoked sources learned from post-stimulus data\n\nIn the stimulus-evoked paradigm, the source strength at each voxel is learned from the post-stimulus\ndata. The background mixing matrix B and sensor noise precision (cid:21) are (cid:2)xed, after having been\nlearned from the pre-stimulus data, described in section 2.2. We assume those quantities remain con-\nstant through the post-stimulus period and are independent of source location. We assume Gaussian\nprior distributions on the source factors and interference factors. We further make the assumption\nthat the signals are independent and identically distributed (i.i.d.) across time. The source factors\nhave prior precision given by the 3 (cid:2) 3 matrix (cid:8), which relates to the strength of the dipole in each\nof 3 orientations. All Normal distributions speci(cid:2)ed in this paper are de(cid:2)ned by their mean and\nprecision (inverse covariance).\n\n3\n\np(sn);\n\np(sn) =\n\np(sjn) = N (0; (cid:8))\n\n(2)\n\np(s) =Yn\n\nYj=1\n\nThe interference and background factors are assumed to have identity precision. To complete spec-\ni(cid:2)cation of this model, we need to specify prior distributions on the model parameters. We use a\n\nb\na\nA\nl\n\fconjugate prior for the interference mixing matrix A, where the (cid:11)j is a hyperparameter over the jth\ncolumn of A and (cid:21)i is the precision of the ith sensor. The hyperparameter (cid:11) (a diagonal matrix)\nprovides a robust mechanism for automatic model order selection, so that the optimal size of A is\ninferred from the data through (cid:11).\n\nL\n\np(x) =Yn\np(u) =Yn\n\np(xn); p(xn) =\n\np(un); p(un) =\n\nM\n\nYj=1\nYj=1\n\np(xjn) = N (0; I);\n\np(ujn) = N (0; I)\n\nN (Aijj0; (cid:21)i(cid:11)j)\n\n(3)\n\nWe now specify the full model:\n\np(A) =Yij\np(yjs; x; u; A; B) =Yn\n\np(ynjsn; xn; un; A; B);\n\np(ynjsn; xn; un; A; B; (cid:21)) = N (ynjF sn + Axn + Bun; (cid:21))\n\n(4)\nExact inference on this model is intractable using the joint posterior over the interference factors and\ninterference mixing matrix; thus the following variational-Bayesian approximation for the posteriors\nis used:\n\np(s; x; Ajy) (cid:25) q(s; x; Ajy) = q(s; xjy)q(Ajy)\n\n(5)\nWe learn the hidden variables and parameters from the post-stimulus data, iterating through each\nvoxel in the brain, using a variational-Bayesian Expectation-Maximization (EM) algorithm. All\nvariables, parameters and hyperparameters are hidden and are learned from the data. In place of\nmaximizing the logp(y), which would be mathematically intractable, we maximize a lower bound\nto logp(y) de(cid:2)ned by F in the following equation\n\nF =Z dx ds dA q(s; x; Ajy) [logp(y; s; x; A) (cid:0) logq(s; x; Ajy)]\n\n= log p(y) (cid:0) KL[q(s; x; Ajy)jjp(s; x; Ajy)]\n\n(6)\nwhere KL(qjjp) is the Kullback-Leibler divergence between distributions q and p. F is equal to\nlogp(y) when the approximation in Eq. 5 is true, thus making the KL-distance zero. We use a\nvariational-Bayesian EM algorithm which alternately maximizes the function F with respect to the\nposteriors q(s; xjy) and q(Ajy). In the E-step, F is maximized w.r.t. q(s; xjy), keeping q(Ajy)\nconstant, and the suf(cid:2)cient statistics of the hidden variables are computed.\nIn the M-step, F is\nmaximized w.r.t. q(Ajy), keeping q(s; xjy) constant, and the MAP estimate of the parameters and\nhyperparameters are computed. In the E-step, the posterior distribution of the background factors\ngiven the data is computed:\n\nwhere we de(cid:2)ne:\n\nn = (cid:0)(cid:0)1 (cid:22)A0T (cid:21)yn;\n(cid:22)x0\n\n(cid:0) = (cid:22)A0T (cid:21) (cid:22)A0 + K(cid:9) + I 0\n\n(7)\n\nq(x0\n\nnjyn) = N ((cid:22)x0\n\nn; (cid:0));\n\n(cid:22)x0\n\nn = (cid:22)sn\n\n(cid:22)un ! ;\n\n(cid:22)xn\n\n(cid:22)A0 =(cid:0) F (cid:22)A (cid:22)B (cid:1) ; I 0 = (cid:8) 0\n\n0\n0\n\nI\n0\n\n0\n0\n\nI ! ; (cid:9) = 0\n\n0\n0 (cid:9)AA 0\n0\n\n0 ! (8)\n\n0\n\n0\n\nIn the M-step, we maximize the function F w.r.t. q(Ajy) holding q(s; xjy) (cid:2)xed. We update the\nposterior distribution of the interference mixing matrix A including its precision (cid:9)AA. Note that the\nlead (cid:2)eld F is (cid:2)xed based on the geometry of the sensors relative to the head, and (cid:22)B was learned\nand (cid:2)xed from the pre-stimulus data. The sensor noise precision (cid:21) is also kept (cid:2)xed from the pre-\nstimulus period. The MAP values of the hyperparameter (cid:11) and source factor precision (cid:8) are learned\nhere from the post-stimulus data.\n\n(cid:22)A = (Ryx (cid:0) F Rsx (cid:0) (cid:22)BRux)(cid:9)AA; (cid:9)AA = (Rxx + (cid:11))(cid:0)1;\n\n(cid:8)(cid:0)1 =\n\n1\nN\n\nRss;\n\n(cid:11)(cid:0)1 = diag(\n\n1\nK\n\n(cid:22)AT(cid:21) (cid:22)A + (cid:9)AA)\n\n(9)\n\n\fThe matrices, such as Ryx, represent the posterior covariance between the two subscripts and explicit\nde(cid:2)nitions are omitted for space.\nIn each iteration of EM, the marginal likelihood is increased.\nThe variational likelihood function (the lower bound on the exact marginal likelihood) is given as\nfollows:\n\nLr =\n\nN\n2\n\nlog\n\nj(cid:21)jj(cid:8)rj\n\nj(cid:0)rj\n\n(cid:0)\n\n1\n2\n\nN\n\nXn=1(cid:16)yT\n\nn (cid:21)yn (cid:0) (cid:22)x\n\n0T r\nn (cid:0)r (cid:22)x\n\n0r\n\nn(cid:17) +\n\nK\n2\n\nlogj(cid:11)rjj(cid:9)rj\n\n(10)\n\nThis likelihood function is dependent on the source voxel r and thus a map of the likelihood across\nthe brain can be displayed. Furthermore, we can also plot an image of the source power estimates\nand the time course of activity at each voxel.\nWe note that the computational complexity of the proposed\nalgorithm is on the order O(KLN S), roughly equivalent to\na single dipole scan, which is of order O(N (K 2 +S)). These\nare much smaller than the complexity of a multi-dipole scan\nwhich is order O(N S P ) where P is the number of dipoles,\nand if S represents roughly several thousand voxels. We fur-\nther note that the number of hidden variables to be estimated\nis less than the number of data points observed, thus not pos-\ning signi(cid:2)cant problems for estimation accuracy.\n\nAlgortihm, sim. interference\nAlgorithm, real brain noise\nMVAB, sim. inteference\nMVAB, real brain noise\n\nrelative to beamforming (green)\n\nLocalization error of proposed model (blue) \n\n(\n \nr\no\nr\nr\nE\n\nm\nm\n\n20\n20\n\n15\n15\n\n10\n10\n\n5\n5\n\n)\n\n2.2 Separation\nof background sources learned from pre-stimulus data\n\n0\n0\n\n-10\n-10\n\n-5\n-5\n\n0\n0\n\n5\n5\n\nSNIR (dB)\n\nWe learn the background mixing matrix and sensor noise pre-\ncision from the pre-stimulus data using a variational-Bayes\nfactor analysis model. We assume Gaussian prior distribu-\ntions on the background factors and sensor noise, with zero\nmean and identity precision; we assume a (cid:3)at prior on the\nsensor precision. We again use a conjugate prior for the back-\nground mixing matrix B, where (cid:12)j is a hyperparameter, similar to the expression for the interference\nmixing matrix. All variables, parameters and hyperparameters are hidden and are learned from the\npre-stimulus data. We make the variational-Bayesian approximation for the background mixing ma-\ntrix and background factors p(u; Bjy) (cid:25) q(u; Bjy) = q(ujy)q(Bjy). In the E-step, we maximize\nthe function F w.r.t. q(ujy) holding q(Bjy) (cid:2)xed. We update the posterior distribution of the factors:\n\nFigure 2: Performance of algorithm\nrelative to beamforming for simu-\nlated datasets. See text for details.\n\nq(ujy) =Yn\n\nq(unjyn); q(unjyn) = N ((cid:22)un; (cid:13))\n\n(cid:22)un = (cid:13)(cid:0)1BT (cid:21)yn; (cid:13) = (cid:22)BT (cid:21) (cid:22)B + K (cid:0)1 + I\n\nIn the M-step, we compute the full posterior distribution of the background mixing matrix B, includ-\ning its precision matrix , and the MAP estimates of the noise precision (cid:21) and the hyperparameter\n(cid:12). We assume the noise precision is diagonal.\n(cid:22)B = Ryu ;\n1\nK\n\ndiag(Ryy (cid:0) (cid:22)BRT\n\n = (Ruu + (cid:12))(cid:0)1\n\n(cid:22)BT(cid:21) (cid:22)B + );\n\n(cid:12)(cid:0)1 = diag(\n\n(cid:21)(cid:0)1 =\n\n(11)\n\n1\nN\n\nyu)\n\n2.3 Relationship to minimum-variance adaptive beamforming\n\nMinimum variance adaptive beamforming (MVAB) is one of the best performing source local-\nization techniques. MVAB estimates the dipole source time series by ^sn = WM V AByn, where\nyy and Ryy is the measured data covariance matrix. Thus, MVAB\nWM V AB = (F T R(cid:0)1\nalso has computational complexity equivalent to a single-dipole scan, on the order O(K 2 + S).\nMVAB attempts to suppress interference, but recent studies have shown the MVAB is ineffective in\ncancellation of interference from other brain sources, especially if there are many such sources. In\nthis section, we derive that MVAB is an approximation to inference on our model.\n\nyy F )(cid:0)1F T R(cid:0)1\n\n\f)\n\nm\nm\n\n(\n \nz\n\n40\n\n20\n\n0\n\n-20\n\n)\n\nm\nm\n\n(\n \nz\n\n40\n\n20\n\n0\n\n-20\n\n-50\n\n0\nx (mm)\n\n50\n\n-50\n\n0\nx (mm)\n\n50\n\n1\n\n0\n\n-1\n-600\n1\n0.5\n\n-0.5\n\n-600\n1\n\n0\n\n-1\n-600\n\n-200\n\n200\n\n600\n\n1000\n\n-200\n\n200\n\n600\n\n1000\n\n-200\n\n200\n\n600\n\n1000\n\nFigure 3: Example of algorithm and MVAB for correlated source simulation. See text for details\n\nWe start by rewriting Eq. (1) as yn = F sn + zn, where zn is termed the total noise and is given\nby zn = Axn + Bun + vn. It has mean zero and precision matrix (cid:7) = (AAT + BBT + (cid:21)(cid:0)1)(cid:0)1.\nAssuming we have estimated the model parameters A; B; (cid:21); (cid:8), the MAP estimate of the dipole\nsource time series is (cid:22)sn = W yn, where W = (cid:0)(cid:0)1F T (cid:7) and (cid:0) = F T (cid:7)F + (cid:8). It can be shown that\nthis expression is equivalent to Eq. 8.\nIn the in(cid:2)nite data limit, the data covariance satis(cid:2)es Ryy = F (cid:8)(cid:0)1F T + (cid:7)(cid:0)1. Its inverse is found,\nusing the matrix inversion lemma, to be R(cid:0)1\n\nyy = (cid:7) (cid:0) (cid:7)F (cid:0)(cid:0)1F T (cid:7). Hence, we obtain\n\nF T R(cid:0)1\n\nyy = (I (cid:0) F T (cid:7)F (cid:0)(cid:0)1)F T (cid:7) = (cid:8)(cid:0)(cid:0)1F T (cid:7)\n\n(12)\nwhere the last step used the expression for (cid:0). Next, we approximate (cid:0) (cid:25) F T (cid:7)F . We then use Eq.\n(12) to obtain:\nW (cid:25) (F T (cid:7)F )(cid:0)1F T (cid:7) = (F T (cid:7)F )(cid:0)1(cid:0)(cid:8)(cid:0)1(cid:8)(cid:0)(cid:0)1F T (cid:7) = (F T R(cid:0)1\n\nyy F )(cid:0)1F T R(cid:0)1\n\nyy = WM V AB\n\n3 Results\n\n3.1 Simulations\n\nPerformance of SAKETINI (blue) relative to \n\nbeamforming (green) in ability to estimate source time course \n\nNA\n\n1\n\nIN\n\n1\n\nRE\n\n1\n\n0.8\n\n0.6\n\n0.8\n\n0.6\n\n0.4\n\n0.2\n\n0.4\n\n0.2\n\n0.8\n\n0.6\n\n0.4\n\n0.2\n\n \n\nw\nd\ne\nt\na\nm\n\n \n\ni\nt\ns\ne\n \nf\no\nn\no\ni\nt\na\nl\ne\nr\nr\no\nC\n\ne\nc\nr\nu\no\ns\n \ne\nu\nr\nt\n \nh\nt\ni\n\nThe proposed method was tested in a variety of real-\nistic source con(cid:2)gurations reconstructed on a 5mm\nvoxel grid. A single-shell spherical volume conduc-\ntor model was used to calculate the forward lead\n(cid:2)eld [5]. Simulated datasets were constructed by\nplacing Gaussian-damped sinusoidal time courses at\nspeci(cid:2)c locations inside a voxel grid based on real-\nistic head geometry. Sources were assumed to be\npresent in the post-stimulus period with 437 samples\nalong with a pre-stimulus period of 263 samples.\nIn the (cid:148)noise-alone (NA)(cid:148) cases, Gaussian noise\nonly was added to all time points at the sensors. In\nthe (cid:148)interference (IN)(cid:148) cases, Gaussian noise time\ncourses occurring in both pre- and post-stimulus\nperiods, representing simulated (cid:148)ongoing(cid:148) activity,\nwere placed at 50 random locations throughout the\nbrain voxel grid, and their activity was projected\nonto the sensors and added to both the sensor noise\nand source activity. Finally, in the (cid:148)real (RE)(cid:148) cases,\n700 samples of real MEG sensor data averaged over\n100 trials collected while a human subject was alert but not performing tasks or receiving stimuli.\nThis real background data thus includes real sensor noise plus real (cid:148)ongoing(cid:148) brain activity that\ncould interfere with evoked sources and adds spatial correlation to the sensor data. We varied the\nSignal-to-Noise Ratio (SNR) and the corresponding Signal to Noise-plus-Interference Ratio (SNIR).\nSNIR is calculated from the ratio of the sensor data resulting from sources only to sensor data from\nnoise plus interference. The (cid:2)rst performance (cid:2)gure (Fig. 2) shows the localization error of the\nproposed method relative to the MVAB. For this data, a single dipole was placed randomly within\n\nFigure 4: Performance of algorithm relative\nto beamforming for simulated datasets. See\ntext for details.\n\nAlgorithm, uncorrelated sources\nMVAB, uncorrelated sources\nAlgorithm, correlated sources\nMVAB, correlated sources\n\n5\nSNIR (dB)\n\n5\nSNIR (dB)\n\nSNIR (dB)\n\n0\n\n5\n\n0\n-5\n\n0\n-5\n\n0\n\n0\n\n0\n-5\n\n\f)\n0\n0\n0\n 1\no\nt\n \n0\n0\n0\n1\n-\n (\ny\nt\nsi\nn\ne\nt\nn\n\nI\n \n\nd\ne\nz\ni\nal\nm\nr\no\nN\n\n1000\n\n500\n\n0\n\n-500\n\n-1000\n\n-100\n\n0\n\n100\n\n200\n\nTime (ms)\n\n300\n\n400\n\nFigure 5: Algorithm applied to auditory MEG dataset in patient with temporal lobe tumor.\n\nthe voxel grid space. The largest peak in the likelihood map was found and the distance from this\npoint to the true source was recorded. Each datapoint is an average of 20 realizations of the source\ncon(cid:2)guration, with error bars showing standard error. This simulation was performed for a variety\nof SNIR\u2019s and for all three cases of noise described above. The results from NA were omitted since\nboth the proposed method and MVAB performed perfectly (zero error). This (cid:2)gure clearly shows\nthat the error in localization is smaller for the proposed method (black) than for MVAB (green).\nThe next set of simulations examines the proposed method\u2019s ability to estimate the source time\ncourse sn. Three sources were placed in the brain voxel grid. The locations of these sources were\n(cid:2)xed, but the orientation and time courses were allowed to vary across realizations of the simula-\ntions. In half the cases, two of the three sources were forced to be perfectly correlated in time (a\nscenario where the MVAB is known to fail), while the time course of the third source was random\nrelative to the other two. An example of the likelihood map and estimated time courses are shown in\nFig. 3. The likelihood map from the proposed method (on the left) has peaks near all three sources,\nincluding the two that were perfectly correlated (depicted by squares). However, the MVAB (middle\nplot) largely misses the source on the left. On the right plot, the estimated time courses from the\nproposed method (dashes) and MVAB (dots) are plotted relative to the true time course (solid). The\ntop and middle plots correspond to the (square) correlated sources. While both methods estimate\nthe time courses well, MVAB underestimates the overall strength of the source on the top plot, and\nexhibits extra noise in the pre-stimulus period for the middle plot.\nThe performance of the proposed model on the same set of simulations of correlated sources, com-\npared to beamforming, are shown in Fig. 4. This (cid:2)gure shows the correlation of the estimated\nwith the true time course, for three cases of NA, IN, and RE, and for both correlated and uncorre-\nlated sources, as a function of SNIR. The proposed method consistently out-performs the MVAB\nwhether the simulated sources are highly correlated with each other (dashed lines), or uncorrelated\n(solid), and especially in the RE case. Each datapoint represents an average of 10 realizations of the\nsimulation, with standard errors on the order of 0.05 (not shown).\n\n3.2 Real data\n\nStimulus-evoked data was collected in a 275-channel CTF System MEG device from a patient with\ntemporal lobe tumor near auditory cortex. The stimulus was a noise burst presented binaurally in\n120 trials. A large peak is typically seen around 100ms after presentation of an auditory stimulus,\ntermed the M100 peak. Figure 5 shows the results of the proposed method applied to this dataset.\nOn the right, the likelihood map show a spatial peak in auditory cortex near the tumor. At that peak\nvoxel, the time course was extracted and plotted on the left, showing the clear M100 peak. This\ninformation can be useful to the neurosurgical team for guiding the location of surgical lesion and\nfor providing knowledge of the patient\u2019s auditory processing abilities.\nWe next tested the proposed method on its ability to localize interictal spikes obtained from a patient\nwith epilepsy. No sensory stimuli were presented to this patient in this dataset, which was collected\nin the same MEG device described above. A Registered EEG/Evoked Potential Technologist marked\nsegments of the continuously-collected dataset which contained spontaneous spikes, as well as seg-\nments that clearly contained no spikes. One segment of data with a spike marked at 400ms was used\nhere as the (cid:148)post-stimulus(cid:148) period and a separate, spike-free, segment of equal length was used as\nthe (cid:148)pre-stimulus(cid:148) period. Figure 6 shows the proposed method\u2019s performance on this dataset. The\ntop left subplot shows the raw sensor data for the segment containing the marked spike. The bottom\nleft shows the location of the equivalent-current dipole (ECD) (cid:2)t to several spikes from this patient;\nthis location from the ECD (cid:2)t would normally be used clinically. The middle bottom (cid:2)gure shows\nthe likelihood map from the proposed model; the peak is in clear agreement with the standard ECD\nlocalization. The middle top (cid:2)gure shows the time course estimated for the likelihood spatial peak.\n\n\fT)\n(\n \n\nl\n\ni\n\nd\ne\nF\n \nc\ni\nt\n\ne\nn\ng\na\nM\n\n \n\nx 10 12\n\nRMS = 311.2 fT\n\n1\n\n0.8\n\n0.6\n\n0.4\n\n0.2\n\n0\n\n0. 2\n\n0. 4\n\n0. 6\n\n0. 8\n\n1\n\n0\n\n100\n\n200\n\n300\n\n400\n\n500\n\n600\n\n700\n\nTime (ms)\n\n)\n0\n0\n0\n 1\no\nt\n \n0\n0\n0\n1\n-\n (\ny\nt\nsi\nn\ne\nt\nn\n\nI\n \n\nd\ne\nz\ni\nal\nm\nr\no\nN\n\n1000\n\n500\n\n0\n\n-500\n\n-1000\n0\n\n200\n\n400\n\nTime (ms)\n\n600\n\n)\n0\n0\n0\n 1\no\nt\n \n0\n0\n0\n1\n-\n (\ny\nt\nsi\nn\ne\nt\nn\n\nI\n \n\nd\ne\nz\ni\nal\nm\nr\no\nN\n\n1000\n\n500\n\n0\n\n-500\n\n-1000\n0\n\n200\n\n400\n\nTime (ms)\n\n600\n\n1000\n\n900\n\n800\n\n700\n\n600\n\n500\n\n400\n\n300\n\n200\n\n100\n\n0\n\n1000\n\n800\n\n600\n\n400\n\n200\n\n0\n\n200\n\n400\n\n600\n\n800\n\n1000\n\nFigure 6: Performance of algorithm applied to data from an epileptic patient. See text for details.\n\nThe spike at 400ms is clearly seen; this cleaned waveform could be of use to the clinician in ana-\nlyzing peak shape. Finally, the top right plot shows a source time course from a randomly selected\nlocation far from the epileptic spike source (shown with cross-hairs on bottom right plot), in order\nto show the low noise level and to show lack of cross-talk onto source estimates elsewhere.\n\n4 Extensions\n\nWe have described a novel probabilistic algorithm which performs source localization while robust\nto interference and demonstrated its superior performance over a standard method in a variety of\nsimulations and real datasets. The model takes advantage of knowledge of when sources of interest\nare not occurring (such as in the pre-stimulus period of a evoked response paradigm). This model\ncurrently assumes averaged data from an evoked response paradigm, but could be extended to exam-\nine variations from the average in individual trials, only involving a few extra parameters to estimate.\nFurthermore, the model could be extended to take advantage of temporal smoothness in the data as\nwell as frequency content. Additionally, spatial smoothness or spatial priors from other modalities,\nsuch as structural or functional MRI, could be incorporated. Furthermore, one is not limited to sn\nin a single voxel; the above formulation holds for any P arbitrarily chosen dipole components, no\nmatter which voxels they belong to, and for any value of P . Of course, as P increases the inferred\nvalue of (cid:8) becomes less accurate, and one might choose to restrict it to a diagonal or block-diagonal\nform.\n\nReferences\n[1] K. Sekihara, M. Sahani, and S.S. Nagarajan, (cid:147)Localization bias and spatial resolution of adaptive\nand non-adaptive spatial (cid:2)lters for MEG source reconstruction,(cid:148) NeuroImage, vol. 25, pp. 1056(cid:150)\n1067, 2005.\n\n[2] K. Sekihara, S.S. Nagarajan, D. Poeppel, and A. Marantz, (cid:147)Performance of an MEG adaptive-\nbeamformer technique in the presence of correlated neural activities: Effects on signal intensity\nand time-course estimates,(cid:148) IEEE Trans Biomed Eng, vol. 49, pp. 1534(cid:150)1546, 2002.\n\n[3] Srikantan S. Nagarajan, Hagai T. Attias, Kenneth E. Hild, and Kensuke Sekihara, (cid:147)A graphical\nmodel for estimating stimulus-evoked brain responses from magnetoencephalography data with\nlarge background brain activity,(cid:148) Neuroimage, vol. 30, pp. 400(cid:150)416, 2006.\n\n[4] S.S. Nagarajan, H.T. Attias, K.E. Hild, and K. Sekihara, (cid:147)Stimulus evoked independent factor\n\nanalysis of MEG data with large background activity,(cid:148) in Adv. Neur. Info. Proc. Sys., 2005.\n\n[5] J. Sarvas, (cid:147)Basic mathematical and electromagnetic concepts of the biomagnetic inverse prob-\n\nlem,(cid:148) Phys Med Biol, vol. 32, pp. 11(cid:150)22, 1987.\n\n\f", "award": [], "sourceid": 3061, "authors": [{"given_name": "Johanna", "family_name": "Zumer", "institution": null}, {"given_name": "Hagai", "family_name": "Attias", "institution": null}, {"given_name": "Kensuke", "family_name": "Sekihara", "institution": null}, {"given_name": "Srikantan", "family_name": "Nagarajan", "institution": null}]}