11 Estimation of Human Cortical Connectivity with Multimodal Integration of fMRI and HighResolution EEG Laura Astolfi, Febo Cincotti, Donatella Mattia, Serenella Salinari, and Fabio Babiloni CONTENTS 11.1 Introduction 11.2 Methods 11.2.1 Monitoring the Cerebral Hemodynamic Response by fMRI 11.2.2 Structural Equation Modeling 11.2.3 Directed Transfer Function 11.2.4 Computer Simulation 11.2.4.1 The Simulation Study 11.2.4.2 Signal Generation for the SEM Methodology 11.2.4.3 Signal Generation for the DTF Methodology 11.2.4.4 Performance Evaluation 11.2.4.5 Statistical Analysis 11.2.5 Application to MovementRelated Potentials 11.2.5.1 Subject and Experimental Design 11.2.5.2 Head and Cortical Models 11.2.5.3 EEG Recordings 11.2.5.4 Statistical Evaluation of Connectivity Measurements by SEM and DTF 11.2.5.5 Estimation of Cortical Source Current Density 11.2.5.6 Regions of Interest (ROIs) 11.2.5.7 Cortical Current Waveforms 11.3 Results 11.3.1 Computer Simulations for SEM 11.3.2 Computer Simulations for DTF Copyright 2005 by Taylor Francis Group, LLC 396 Medical Image Analysis 11.3.3 Application to HighResolution EventRelated Potential Recordings 11.3.4 Application of the Multimodal EEGfMRI Integration Techniques to the Estimation of Sources of SelfPaced Movements 11.4 Discussion 11.4.1 Simulation Results for SEM 11.4.2 Simulation Results for DTF 11.4.3 Application of Connectivity Estimation Methods to Real EEG Data 11.4.4 Application of Connectivity Estimation Methods to Real EEG Data 11.5 Conclusions Acknowledgment References 11.1 INTRODUCTION Human neocortical processes involve temporal and spatial scales spanning several orders of magnitude, from the rapidly shifting somatosensory processes characterized by a temporal scale of milliseconds and a spatial scale of a few square millimeters to the memory processes, involving time periods of seconds and a spatial scale of square centimeters. Information about the brain activity can be obtained by measuring different physical variables arising from the brain processes, such as the increase in consumption of oxygen by the neural tissues or a variation of the electric potential over the scalp surface. All these variables are connected in direct or indirect way to the ongoing neural processes, and each variable has its own spatial and temporal resolution. The different neuroimaging techniques are then confined to the spatiotemporal resolution offered by the monitored variables. For instance, it is known from physiology that the temporal resolution of the hemodynamic deoxyhemoglobin increasedecrease lies in the range of 1 to 2 sec, while its spatial resolution is generally observable with the current imaging techniques at the scale of a few millimeters. Today, no neuroimaging method allows a spatial resolution on a millimeter scale and a temporal resolution on a millisecond scale. Hence, it is of interest to study the possibility of integrating the information offered by the different physiological variables in a unique mathematical context. This operation is called the “multimodal integration” of variable X and Y, where the X variable typically has a particularly appealing spatial resolution property (millimeter scale), and the Y variable has particularly attractive temporal properties (on a millisecond scale). Nevertheless, the issue of several temporal and spatial domains is critical in the study of the brain functions, because different properties could become observable, depending on the spatiotemporal scales at which the brain processes are measured. Electroencephalography (EEG) and magnetoencephalography (MEG) are two interesting techniques that present a high temporal resolution, on the millisecond scale, adequate to follow brain activity. However, both techniques have a relatively Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 397 modest spatial resolution, beyond the centimeter. Spatial resolution for these techniques is fundamentally limited by the intersensor distances and by the fundamental laws of electromagnetism 1. On the other hand, the use of a priori information from other neuroimaging techniques like functional magnetic resonance imaging (fMRI) with high spatial resolution could improve the localization of sources from EEGMEG data. The initial part of this chapter then deals with the multimodal integration of electrical, magnetic, and hemodynamic data to locate neural sources responsible for the recorded EEGMEG activity. The rationale of the multimodal approach based on fMRI, MEG, and EEG data to locate brain activity is that neural activity generating EEG potentials or MEG fields increases glucose and oxygen demands 2. This results in an increase in the local hemodynamic response that can be measured by fMRI 3, 4. On the whole, such a correlation between electrical and hemodynamic concomitants provides the basis for a spatial correspondence between fMRI responses and EEGMEG source activity. However, static images of brain regions activated during particular tasks do not convey the information of how these regions communicate with each other. The concept of brain connectivity is viewed as central for the understanding of the organized behavior of cortical regions beyond the simple mapping of their activity 5, 6. This organization is thought to be based on the interaction between different and differently specialized cortical sites. Corticalconnectivity estimation aims at describing these interactions as connectivity patterns that hold the direction and strength of the information flow between cortical areas. To achieve this, several methods have already been applied on data gathered from both hemodynamic and electromagnetic techniques 7–11. Two main definitions of brain connectivity have been proposed over the years: functional and effective connectivity 12. While functional connectivity is defined as temporal correlation between spatially remote neurophysiologic events, the effective connectivity is defined as the simplest brain circuit that would produce the same temporal relationship as observed experimentally between cortical sites. As for the functional connectivity, the several computational methods proposed to estimate how different brain areas are working together typically involve the estimation of some covariance properties between the different time series measured from the different spatial sites during motor and cognitive tasks studied by EEG and fMRI techniques 13–16. In contrast, structural equation modeling (SEM) is a different technique that has been used for a decade to assess effective connectivity between cortical areas in humans by using hemodynamic and metabolic measurements 7, 17–19. The basic idea of SEM differs from the usual statistical approach of modeling individual observations, because SEM considers the covariance structure of the data 17. However, the estimation of cortical effective connectivity obtained with the application of the SEM technique on fMRI data has a low temporal resolution (on the order of 10 sec), which is far from the time scale at which the brain operates normally. Hence, it becomes of interest to understand whether the SEM technique could be applied to cortical activity estimated by applying the linearinverse techniques to the highresolution EEG (HREEG) data 20–23. In this way, it would be possible to study timevarying patterns of brain connectivity linked to the different parts of the experimental task studied. Copyright 2005 by Taylor Francis Group, LLC 398 Medical Image Analysis So far, the estimation of functional connectivity on EEG signals has been addressed by applying either linear or nonlinear methods, both of which can track the direct flow of information between scalp electrodes in the time domain, although with different computational demands 21, 24–31. In addition, given the evidence that important information in the EEG signals is often coded in the frequency rather than time domain (reviewed in 32), research attention has been focused on detecting frequencyspecific interactions in EEG or MEG signals by analyzing the coherence between the activity of pairs of structures 33–35. However, coherence analysis does not have a directional nature (i.e., it just examines whether a link exists between two neural structures by describing instances when they are in synchronous activity), and it does not directly provide the direction of the information flow. In this respect, a multivariate spectral technique called directed transfer function (DTF) was proposed 36 to determine the directional influences between any given pair of channels in a multivariate data set. This estimator can simultaneously characterize both the directional and spectral properties of the brain signals, requiring only one multivariate autoregressive (MVAR) model that is estimated from all of the EEG channel recordings. The DTF technique has recently been demonstrated 37 to rely on the key concept of Granger causality between time series 38, according to which an observed time series x(n) generates another series y(n) if knowledge of x(n)’s past significantly improves the prediction of y(n). This relation between time series is not reciprocal, i.e., x(n) may cause y(n) without y(n) necessarily causing x(n). This lack of reciprocity is what allows the evaluation of the direction of information flow between structures. In this study, we propose to estimate the patterns of cortical connectivity by exploiting the SEM and DTF techniques applied on highresolution EEG signals, which exhibit a higher spatial resolution than conventional cerebral electromagnetic measures. Indeed, this EEG technique includes the use of a large number of scalp electrodes, realistic models of the head derived from structural magnetic resonance images (MRIs), and advanced processing methodologies related to the solution of the linearinverse problem. These methodologies facilitate the estimation of cortical current density from sensor measurements 39–41. To pursue the aim of this study, we first explored the behavior of the SEM and DTF methods in a simulation context under various conditions that affect the EEG recordings, mainly the signaltonoise ratio (factor SNR) and the length of the recordings (factor LENGTH). In particular, the following questions were addressed: What is the influence of a variable SNR level (imposed on the highresolution EEG data) on the accuracy of the estimation of pattern connectivity obtained by SEM and DTF? What amount of highresolution EEG data is needed to accurately estimate the accuracy of the connectivity between cortical areas? To answer these questions, a simulation study was performed on the basis of a predefined connectivity scheme that linked several modeled cortical areas. Cortical connections between these areas were retrieved by the estimation process under different experimental SNR and LENGTH conditions. Indexes of the errors in the estimation of the connection strength were defined, and statistical multivariate analyses Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 399 were performed by ANOVA (analysis of variance) and Duncan post hoc tests, with these error indexes as dependent variables. Subsequently, both SEM and DTF methods were applied to the cortical estimates obtained from highresolution EEG data related to a simple fingertapping experiment in humans to underline the capability of the proposed methodology to draw patterns of cortical connectivity between brain areas during a simple motor task. Finally, we also present both the mathematical principle and the practical applications of the multimodal integration of highresolution EEG and fMRI for the localization of sources responsible for intentional movements. 11.2 METHODS 11.2.1 MONITORING THECEREBRALHEMODYNAMICRESPONSE BY FMRI A brainimaging method, known as functional magnetic resonance imaging (fMRI), has gained favor among neuroscientists over the last few years. Functional MRI reflects oxygen consumption, and because oxygen consumption is tied to processing or neural activation, it can give a map of functional activity. When neurons fire, they consume oxygen, and this causes the local oxygen levels to decrease briefly and then actually increase above the resting level as nearby capillaries dilate to let more oxygenated blood flow into the active area. The most commonly used acquisition paradigm is the socalled bloodoxygen level dependence (BOLD), in which the fMRI scanner works by imaging blood oxygenation. The BOLD paradigm relies on the brain mechanisms, which overcompensate for oxygen usage (activation causes an influx of oxygenated blood in excess of that used, and therefore the local oxyhemoglobin concentration increases). Oxygen is carried to the brain in the hemoglobin molecules of blood red cells. Figure 11.1shows the physiologic principle at the base of the generation of fMRI signals. This figure shows how the hemodynamic responses elicited by increased neuronal activity (Figure 11.1(a)) reduce the deoxyhemoglobin content of the blood flow in the same neuronal district after a few seconds (Figure 11.1(b)).The magnetic properties of hemoglobin when saturated with oxygen are different than when it has given up oxygen. Technically, deoxygenated hemoglobin is paramagnetic and therefore has a short relaxation time. As the ratio of oxygenated to deoxygenated hemoglobin increases, so does the signal recorded by the MRI. Deoxyhemoglobin increases the rate of depolarization of the hydrogen nuclei creating the MR signal, thus decreasing the intensity of the T2 image. The bottom line is that image intensity increases with increasing brain activation. The problem is that at the standard intensity used for the static magnetic field (1.5 Tesla), this increase is small (usually less than 2%) and easily obscured by noise and various artifacts. By increasing the static field of the fMRI scanner, the signaltonoise ratio increases to more convenient values. Staticfield values of 3 Tesla are now commonly used for research on humans, while an fMRI scanner at 7 Tesla was recently employed to map hemodynamic responses in the human brain 42. At such a high field value, there is a possibility of detecting the initial increase of deoxyhemoglobin (after the initial “dip”). The interest in the detection of the dip is based on the fact that this hemodynamic response happens on a time scale of 500 msec (as revealed by hemodynamic optical Copyright 2005 by Taylor Francis Group, LLC 400 Medical Image Analysis measures 43) compared with 1 to 2 sec needed for the response of the vascular system to the oxygen demand. Furthermore, in the latter case, the response has a temporal extension well beyond the activation that has occurred (10 sec). As a last point, the spatial distribution of the initial dip (as described by using the optical dyes 43) is sharper than those related to the vascular response of the oxygenated hemoglobin. Recently, with highfieldstrength MR scanners at 7 or even 9.4 Tesla (on animals), a resolution down to the corticalcolumn level has been achieved 44. However, at the standard field intensity commonly used in fMRI studies (1.5 or 3 Tesla), the identification of such initial transient increase of deoxyhemoglobin is controversial. Compared with positronemitted tomography (PET) or singlephotonemitted tomography (SPECT), fMRI does not require the injection of radiolabeled substances, and its images have a higher resolution (as reviewed in the literature 45). PET, however, is still the most informative technique for directly imaging metabolic processes and neurotransmitter turnover. 11.2.2 STRUCTURALEQUATIONMODELING In structural equation modeling (SEM), the parameters are estimated by minimizing the difference between the observed covariances and those implied by a structural or path model. In terms of neural systems, a measure of covariance represents the degree to which the activities of two or more regions are related. FIGURE 11.1 (Color figure follows p. 274.)Physiologic principle at the base of the generation of fMRI signals. (a) Neurons increase their firing rates, which increases oxygen consumption. (b) Hemodynamic response in a second scale increases the diameter of the vessel close to the activated neurons. The induced increase in blood flow overcomes the need for oxygen supply. As a consequence, the percentage of deoxyhemoglobin in the blood flow decreases in the vessel with respect to (a). Hemoglobin Oxygen (a) (b) fMRI Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 401 The SEM consists of a set of linear structural equations containing observed variables and parameters defining causal relationships among the variables. Variables in the equation system can be endogenous (i.e., dependent on the other variables in the model) or exogenous (independent of the model itself). The structural equation model specifies the causal relationship among the variables, describes the causal effects, and assigns the explained and the unexplained variance. Let us consider a set of variables (expressed as deviations from their means) with N observations. In this study, these variables represent the activity estimated in each cortical region, obtained with the procedures described in the following section. The SEM for these variables is the following: y = By + Γx + ζ (11.1) where: y is a (m × 1) vector of dependent (endogenous) variables x is a (n × 1) vector of independent (exogenous) variables ζ is a (m × 1) vector of equation errors (random disturbances) B is a (m × m) matrix of coefficients of the endogenous variables Γ is a (m × n) matrix of coefficients of the exogenous variables It is assumed that ζ is uncorrelated with the exogenous variables, and B is supposed to have zeros in its diagonal (i.e., an endogenous variable does not influence itself) and to satisfy the assumption that (I − B) is nonsingular, where I is the identity matrix. The covariance matrices of this model are the following: Φ = Exx T is the (n × n) covariance matrix of the exogenous variables Ψ = Eζζ T is the (m × m) covariance matrix of the errors If z is a vector containing all the p = m + n variables, exogenous and endogenous, in the following order: z T = x1 … xn , y1 … ym (11.2) then the observed covariances can be expressed as Σobs = (1(N − 1))⋅Z⋅ZT (11.3) where Z is the p × N matrix of the p observed variables for N observations. The covariance matrix implied by the model can be obtained as follows: (11.4) Σmod == E EE EE T TT TT zz xx xy yx yy Copyright 2005 by Taylor Francis Group, LLC 402 Medical Image Analysis where Eyy T = E(I − B) −1 (Γx + ζ)(Γx + ζ) T ((I −B) −1 ) T = (I −B) −1 (ΓΦΓ + Ψ) ((I − B) −1 ) T (11.5) because the errors ζare not correlated with the x, and where Exx T = Φ (11.6) Exy T = (I − B) −1 Φ (11.7) Eyx T = ((I − B) −1 Φ) T (11.8) because Σmod is symmetric. The resulting covariance matrix, in terms of the model parameters, is the following: (11.9) Without other constraints, the problem of the minimizing the differences between the observed covariances and those implied by the model is undetermined, because the number of variables (elements of matrices B, Γ, Ψ, and Φ) is greater than the number of equations (m + n)(m + n + 1)2. For this reason, the SEM technique is based on the a priori formulation of a model on the basis of anatomical and physiological constraints. This model implies the existence of just some causal relationships among variables, represented by arcs in a “path” diagram; all the parameters related to arcs not present in the hypothesized model are forced to zero. For this reason, all the parameters to be estimated are called free parameters. If t is the number of free parameters, it must be that t ≤(m + n)(m + n + 1)2. These parameters are estimated by minimizing a function of the observed and implied covariance matrices. The most widely used objective function for SEM is the maximum likelihood (ML) function: FML = log|Σmod| + tr(Σobs ⋅Σmod −1 ) − log|Σobs | − p (11.10) where tr(·) is the trace of matrix. In the context of multivariate, normally distributed variables, the minimum of the ML function multiplied by (N − 1) follows a χ 2 distribution with p(p + 1)2 – t degrees of freedom, where t is the number of parameters to be estimated, and p is the total number of observed variables (endogenous + exogenous). The χ 2 statistic test can then be used to infer statistical significance of the structural equation model obtained. In the present study, the software package LISREL 46 was used to implement the SEM technique. Σ ΦΦΦΦ ΦΦΓΓΦ ΦΓΓΨΨ mod= − () − () ()− () + ()− ( − −− IB IB IB IB 1 11T )) () −1 T Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 403 11.2.3 DIRECTEDTRANSFERFUNCTION In this study, the DTF technique was applied to the set of cortical estimated waveforms S z(t)= z 1 (t), z 2 (t), …, z N (t) T (11.11) obtained for the N ROIs considered, as will be described in detail in the following sections. The following MVAR process is an adequate description of the data set Z. , with (0) = I (11.12) where e(t) is a vector of a multivariate zeromean uncorrelated white noise process; (1), (2), …, (q) are the N × N matrices of model coefficients, and q is the model order chosen, in our case, with the Akaike information criterion for MVAR processes 37. To investigate the spectral properties of the examined process, Equation 11.12 is transformed to the frequency domain (f) Z(f) = E(f) (11.13) where (11.14) and t is the temporal interval between two samples. Equation 11.13 can then be rewritten as Z(f) = Λ−1 (f) E(f) = H(f) E(f) (11.15) Here, H(f) is the transfer matrix of the system whose element Hij represents the connection between the jth input and the ith output of the system. With these definitions, the causal influence of the cortical waveform estimated in the jth ROI on that estimated in the ith ROI (the directed transfer function θ 2 ij (f)) is defined as (11.16) To enable comparison of the results obtained for cortical waveforms with different power spectra, a normalization was performed by dividing each estimated DTF by the squared sums of all elements of the relevant row, thus obtaining the socalled normalized DTF 36 Λktk t k q () − ()= () = ∑ ze 0 ΛΛΛΛ fkejftk k q ()= ()− = ∑ 2 0 π∆ θij ij fHf 2 2 ()= () Copyright 2005 by Taylor Francis Group, LLC 404 Medical Image Analysis (11.17) where γ ij (f) expresses the ratio of influence of the cortical waveform estimated in the jth ROI on the cortical waveform estimated on the ith ROI, with respect to the influence of all the estimated cortical waveforms. Normalized DTF values are in the interval 47, and the normalization condition (11.18) is applied. 11.2.4 COMPUTERSIMULATION 11.2.4.1 The Simulation Study The experimental design we adopted was meant to analyze the recovery of the connectivity patterns obtained under the different levels of SNR and signal temporal length that were imposed during the generation of sets of test signals simulating cortical average activations. As described in the following subsections, the simulated signals were obtained from actual cortical data estimated with the highresolution EEG procedures available at the highresolution EEG Laboratory of the University of Rome. 11.2.4.2 Signal Generation for the SEM Methodology Different sets of test signals were generated to fit an imposed connectivity pattern (shown in Figure 11.2)and to respect imposed levels of temporal duration (LENGTH) and signaltonoise ratio (SNR). In the following discussion, using a more compact notation, signals have been represented with the z vector defined in Equation 11.2, containing both the endogenous and the exogenous variables. Channel z 1 is a referencesource waveform, estimated from a highresolution EEG (128 electrodes) recording in a healthy subject during the execution of unaimed selfpaced movements of the right finger. Signals z 2 , z 3 , and z 4were obtained by the contribution of signals from all other channels, with an amplitude variation plus zeromean uncorrelated white noise processes with appropriate variances, as shown in Equation 11.19 zk = Azk + Wk (11.19) where zk is the 4×1 vector of signals, Wk is the 4×1 noise vector, and A is the 4×4 parameters matrix obtained from the Γand Bmatrices in the following way: γ ij ij im m N f Hf Hf 2 2 2 1 ()= () () = ∑ γ in n N f 2 1 1 ()= = ∑ Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 405 (11.20) where βij stands for the generic (i,j) element of the B matrix, and γ i is the ith element of the vector Γ. All procedures of signal generation were repeated under the following conditions: SNR factor levels = (1, 3, 5, 10, 100) LENGTH factor levels = (60, 190, 310, 610) sec. This corresponds, for instance, to (120, 380, 620, 1220) EEG epochs, each of which is 500 msec long. It is worth noting that the levels chosen for both SNR and LENGTH factors cover the typical range for the cortical activity estimated with highresolution EEG techniques. FIGURE 11.2 Connectivity pattern imposed in the generation of simulated signals. z 1 , …, z 4 represent the average activities in four cortical areas. Values on the arcs represent the connection’s strength (a21 = 1.4, a31 = 1.1, a32 = 0.5, a42 = 0.7, a43 = 1.2). a42 Z2 Z4 Z3 Z1 a32 a31 a21 a43 A= 00 0 0 1111213 2212223 3313233 γβ β β γβ β β γβ β β = aa aa 11 14 41 44 Copyright 2005 by Taylor Francis Group, LLC 406 Medical Image Analysis 11.2.4.3 Signal Generation for the DTF Methodology Different sets of test signals were generated to fit an imposed coupling scheme involving four different cortical areas (shown in Figure 11.2)while also respecting imposed levels of signaltonoise ratio (factor SNR) and duration (factor LENGTH). Signal z 1 (t) was a reference cortical waveform estimated from a highresolution EEG (96 electrodes) recording in a healthy subject during the execution of selfpaced movements of the left finger. Subsequent signals z 2 (t) to z 4 (t) were iteratively obtained according to the imposed scheme (Figure 11.2)by adding to signal z j contributions from the other signals, delayed by intervals τ ij and amplified by factors aij plus an uncorrelated Gaussian white noise. Coefficients of the connection strengths were chosen in a range of realistic values as met in previous studies during the application of other connectivityestimation techniques, such as structural equation modeling, in several memory, motor, and sensory tasks 7. Here, the values used for the connection strength were a21 = 1.4, a31 = 1.1, a32 = 0.5, a42 = 0.7, and a43 = 1.2. The values used for the delay from the ith ROI to the jth one (τ ij) ranged from one sample up to the q − 2, where q was the order of the MVAR model used. Because the statistical analysis performed with different values of such delay samples returned the same information with respect to the variation of this parameter, in the following we particularized the results to the case τ 21 = τ 31 = τ 32 = τ 42 = τ 43 = 1 sample, which for a sampling rate of 64 Hz became a delay of 15 msec. All procedures of signal generation were repeated under the following conditions: SNR factor levels = (0.1, 1, 3, 5, 10) LENGTH factor levels = (960, 2,880, 4,800, 9,600, 19,200, 38,400) data samples, corresponding to signals length of (15, 45, 75, 150, 300, 600) sec at a sampling rate of 64 Hz, or to (7, 22, 37, 75, 150, 300) EEG trials of 2 sec each The levels chosen for both SNR and LENGTH factors cover the typical range for the cortical activity estimated with highresolution EEG techniques. The MVAR model was estimated by means of the NuttallStrand method or the multivariate Burg algorithm, which is one of the most common estimators for MVAR models and has been demonstrated to provide the most accurate results 48–50. 11.2.4.4 Performance Evaluation The quality of the performed estimation was evaluated using the Frobenius norm of the matrix, which reports the differences between the values of the estimated (via SEM) and the imposed connections (relative error). The norm was computed for the connectivity patterns obtained with the SEM methodology (11.21) E aa a ij j m ij i m ij j m i relative = − = = = ∑ ∑ ∑ ( ˆ ) () 1 2 1 1 2 == ∑ 1 m Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 407 In the case in which the DTF method was used, the statistical evaluation of DTF performances required a precise definition of an error function describing the goodness of the pattern recognition performed. This was achieved by focusing on the MVAR model structure described in Equation 11.12 and comparing it with the signalsgeneration scheme. The elements of matrices (k) of MVAR model coefficients can be put in relation with the coefficients used in the signal generation, and they are different from zero only for k = τ ij , where τ ij is the delay chosen for each pair ijof ROIs and for each direction among them. In particular, for the independent reference source waveform z 1 (t), an autoregressive model of the same order of the MVAR has been estimated, whose coefficients a11 (1), …, a11 (q) correspond to the elements Λ11 (1), …, Λ11 (q) of the MVAR coefficients matrix. Thus, with the estimation of the MVAR model parameters, we aim to recover the original coefficients aij (k) used in signal generation. In this way, reference DTF functions have been computed on the basis of the signalgeneration parameters. The error function was then computed as the difference between these reference functions and the estimated ones (both averaged in the frequency band of interest). To evaluate the performances in retrieving the connections between areas, the same index used in the case of the SEM was adopted, but with light differences of notation, i.e., the Frobenius norm of the matrix reporting the differences between the values of the estimated and the imposed connections (total relative error) (11.22) In Equation 11.22, represents the average value of the DTF function from j to i within the frequency band of interest. For both SEM and DTF, the simulations were performed by repeating each generationestimation procedure 50 times to increase the robustness of the successive statistical analysis. 11.2.4.5 Statistical Analysis The results obtained were subjected to separate ANOVA. The main factors of the ANOVAs for the DTF method were the SNR (with five levels: 0.1, 1, 3, 5, 10) and the signal LENGTH (with six levels: 960, 2,880, 4,800, 9,600, 19,200, 38,400 data samples, equivalent to 15, 45, 75, 150, 300, 600 sec at 64 Hz of sampling rate). In the case of the SEM method, the main factors were identical, but the LENGTH has only four levels (equal to 60, 190, 310, and 610 sec at 64 Hz). For all of the methodologies used, ANOVA was performed on the error index that was adopted (relative error). The correction of GreenhouseGasser for the violation of the spherical hypothesis was used. The post hoc analysis with the Duncan test at the p = 0.05 statistical significance level was then performed. E ff ij j m ij i relative band band = − = = ∑(() ˆ () ) γγ 1 2 1 mm ij j m i m f ∑ ∑ ∑ = = (() ) γ band 1 2 1 γ ij f () band Copyright 2005 by Taylor Francis Group, LLC 408 Medical Image Analysis 11.2.5 APPLICATION TOMOVEMENTRELATEDPOTENTIALS The estimation of connectivity patterns by using the DTF and SEM on highresolution EEG recordings was applied to the analysis of a simple movement task. In particular, we considered a righthand fingertapping movement that was externally paced by a visual stimulus. This task was chosen because it has been very widely studied in literature with various brainimaging techniques such as EEG or fMRI 51–53. 11.2.5.1 Subject and Experimental Design Three righthanded healthy subjects (age 23.3 ± 0.58, one male and two females) participated in the study after providing informed consent. Subjects were seated comfortably in an armchair with both arms relaxed and resting on pillows, and they were asked to perform fast, repetitive rightfinger movements. During this motor task, the subjects were instructed to avoid eye blinks, swallowing, or any movement other than the required finger movements. 11.2.5.2 Head and Cortical Models A realistic head model of the subjects, reconstructed from T1weighted MRIs, was employed in this study. Scalp, skull, and dura mater compartments were segmented from MRIs with software originally developed at the Department of Human Physiology of Rome, and such structures were triangulated with about 1,000 triangles for each surface. The source model was built with the following procedure: 1. The cortex compartment was segmented from MRIs and triangulated to obtain a fine mesh with about 100,000 triangles. 2. A coarser mesh was obtained by resampling the fine mesh to about 5,000 triangles. The downsampling was performed with an adaptive algorithm designed to represent with a sufficient number of triangles the parts of the cortex where the radius of curvature was high (for instance, during the bending of a sulcus) while attempting to represent with few triangles the flatter parts of the cortical surface (for instance, on the upper part of the gyri). 3. An orthogonal unitary equivalentcurrent dipole was placed in each node of the triangulated surface, with its direction parallel to the vector sum of the normals to the surrounding triangles. 11.2.5.3 EEG Recordings Eventrelated potential (ERP) data were recorded with 96 electrodes; data were recorded with a leftear reference and submitted to an artifactremoval process. Six hundred ERP trials of 600 msec of duration were acquired. The analog–digital sampling rate was 250 Hz. The surface electromyographic (EMG) activity of the muscle was also collected. The onset of the EMG response served as zero time. All data were visually inspected, and trials containing artifacts were rejected. We used Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 409 semiautomatic supervised threshold criteria for the rejection of trials contaminated by ocular and EMG artifacts, as described in detail elsewhere 54. After the EEG recording, the electrode positions were digitized using a threedimensional localization device with respect to the anatomic landmarks of the head (nasion and two preauricular points). The analysis period for the potentials timelocked to the movement execution was set from 300 msec before to 300 msec after the EMG trigger (zero time). The ERP time course was divided into two phases relative to the EMG onset: the first, labeled as “PRE” period, marked the 300 msec before the EMG onset and was intended as a generic preparation period; the second, labeled as “POST,” lasted up to 300 msec after the EMG onset and was intended to signal the arrival of the movement somatosensory feedback. We kept the same PRE and POST nomenclature for the signals estimated at the cortical level. 11.2.5.4 Statistical Evaluation of Connectivity Measurements by SEM and DTF As described previously, the statistical significance of the connectivity pattern estimated with the SEM technique was ensured by the fact that — in the context of the multivariate, normally distributed variables — the minimum of the maximum likelihood function FML, multiplied by (N − 1), follows a χ 2 distribution with p(p+ 1)2 − t degrees of freedom, where t is the number of parameters to be estimated, and p is the total number of observed variables (endogenous + exogenous). Then, the χ 2 statistic test can be used to infer the statistical significance of the structural equation model obtained. The situation for the statistical significance of the DTF measurements is different because the DTF functions have a highly nonlinear relation to the timeseries data from which they are derived, and the distribution of their estimators is not well established. This makes tests of significance difficult to perform. A possible solution to this problem was proposed by Kaminski et al. 37. Their solution involves the use of a surrogate data technique 55 in which an empirical distribution for random fluctuations of a given estimated quantity is generated by estimating the same quantity from several realizations of surrogate data sets where the deterministic interdependency between variables has been removed. To ensure that all features of each data set are as similar as possible to the original data set, with the exception of channel coupling, the very same data are used, and any timelocked coupling between channels is disrupted by shuffling phases of the original multivariate signal. Because the EEG signal had been divided into single trials, each surrogate data set was built up by scrambling the order of epochs, using different sequences for each channel. In this procedure, every singlechannel EEG epoch was used once and only once, and only occasionally (and with a very low probability), two channels in the same surrogate trial came from the same actual trial. The set properties of univariate surrogate signals are not influenced by this shuffling procedure, because only the epoch order is varied. Moreover, because no shuffling was performed between single samples, the temporal correlation, and thus the spectral features, of univariate signals is the same for the original and surrogate data sets, thus making it possible to estimate different distributions of DTF fluctuations for each frequency band. A total of 1000 Copyright 2005 by Taylor Francis Group, LLC 410 Medical Image Analysis surrogate data sets was generated, as described previously, and DTF spectra were estimated from each data set. For each channel pair and for each frequency bin, the 99th percentile was computed and subsequently considered as a significance threshold. 11.2.5.5 Estimation of Cortical Source Current Density The solution of the following linear system Lz = d + e (11.23) provides an estimate of the dipole source configuration z that generates the measured EEG potential distribution d. The system also includes the measurement noise n, assumed to be normally distributed 39. In Equation 11.23, L is the lead field, or the forward transmission matrix, in which each jth column describes the potential distribution generated on the scalp electrodes by thejth unitary dipole. The currentdensity solution vector ξ was obtained as follows 39: (11.24) where M, N are the matrices associated with the metrics of the data and of the source space, respectively, λ is the regularization parameter, and ||z||M represents the Mnorm of the vector z. The solution of Equation 11.24 is given by the inverse operator G as follows: , (11.25) An optimal regularization of this linear system was obtained by the Lcurve approach 56, 57. As a metric in the data space, we used the identity matrix, but in the source space, we use the following metric as a norm (11.26) where (N−1 ) ii is the ith element of the inverse of the diagonal matrix N, and all the other matrix elements Nij , for each i j, are set to 0. The L2 norm of the ith column of the lead field matrix L is denoted by ||L.i ||. Here, we present two characterizations of the source metric N that can provide the basis for the inclusion of the information about the statistical hemodynamic activation of ith cortical voxel into the linearinverse estimation of the cortical source activity. In the fMRI analysis, several methods have been developed to quantify the brain hemodynamic response to a particular task. However, in the following, we ξ= − + () arg min z Lz d z MN 2 2 2 λ ξ=Gb GNLLNL M = ′′+ () −− −− 11 11 λ N − ⋅ − ()= 1 2 ii i L Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 411 analyze the case in which a particular fMRI quantification technique — the percent change (PC) technique — has been used. This measure quantifies the percent increase of the fMRI signal during the task performance with respect to the rest state 58. The visualization of the voxels’ distribution in the brain space that is statistically increased during the task condition with respect to the rest is called the PC map. The difference between the mean rest and movementrelated signal intensity is generally calculated voxel by voxel. The restrelated fMRI signal intensity is obtained by averaging the premovement and recovery fMRI. A Bonferronicorrected student’s ttest is also used to minimize alphainflation effects due to multiple statistical voxelbyvoxel comparisons (Type I error; p < 0.05). The introduction of fMRI priors into the linearinverse estimation produces a bias in the estimation of the currentdensity strength of the modeled cortical dipoles. Statistically significantly activated fMRI voxels, which are returned by the percentage change approach 58, are weighted to account for the EEGmeasured potentials. In fact, a reasonable hypothesis is that there is a positive correlation between local electric or magnetic activity and local hemodynamic response over time. This correlation can be expressed as a decrease of the cost in the functional PHI of Equation 11.24 for the sources zj in which fMRI activation can be observed. This increases the probability for those particular sources z j to be present in the solution of the electromagnetic problem. Such thoughts can be formalized by particularizing the source metric N to take into account the information coming from the fMRI. The inverse of the resulting metric is then proposed as follows 59: (11.27) in which (N−1 ) ii and ||A⋅i|| have the same meaning as described previously. The term g(αi ) is a function of the statistically significant percentage increase of the fMRI signal assigned to the ith dipole of the modeled source space. This function is expressed as (11.28) where αi is the percentage increase of the fMRI signal during the task state for the ith voxel, and the factor K tunes fMRI constraints in the source space. Fixing K= 1 lets us disregard fMRI priors, thus returning to a purely electrical solution; a value for K» 1 allows only the sources associated with fMRI active voxels to participate in the solution. It was shown that a value for K on the order of 10 (90% of constraints for the fMRI information) is useful to avoid mislocalization due to overconstrained solutions 60–62. In the discussion that follows, the estimation of the cortical activity obtained with this metric will be denoted as diagfMRI, because the previous definition of the source metric N results in a matrix in which the offdiagonal elements are zero. NA− ⋅ − ()= 122 ii ii g() α gK K i i i i () max( ) ,, α α α α 2 11 1 0 =+ − () ≥≥ Copyright 2005 by Taylor Francis Group, LLC 412 Medical Image Analysis 11.2.5.6 Regions of Interest (ROIs) Several cortical regions of interest (ROIs) were drawn by two independent and expert neuroradiologists on the computerbased cortical reconstruction of the individual head models. In cases where the SEM methodology was adopted, we selected ROIs based on previously available knowledge about the flow of connections between different cortical macroareas, as derived from neuroanatomy and fMRI studies. In particular, information flows were hypothesized to exist from the parietal (P) areas toward the sensorimotor (SM), the premotor (PM), and the prefrontal (PF) areas 63–65. The prefrontal areas (PF) were defined by including the Brodmann areas 8, 9, and 46; the premotor areas (PM) by including the Brodmann area 6; the sensorimotor areas (SM) by including the Brodmann areas 4, 3, 2, and 1; and the parietal areas (P), generated by the union of the Brodmann areas 5 and 7 (see colored areas in Figure 11.3). In cases where the DTF method was used, we selected the ROIs representing the left and right primary somatosensory (S1) areas, which included the Brodmann areas (BA) 3, 2, 1, while the ROIs representing the left and right primary motor (MI) included the BA 4. The ROIs representing the supplementary motor area (SMA) were obtained from the cortical voxels belonging to the BA 6. We further separated the proper and anterior SMA indicated into regions labeled BA 6P and 6A, respectively. Furthermore, ROIs from the right and the left parietal areas (BA 5, 7) and the occipital areas (BA 19) were also considered. In the frontal regions, the BA 46, 8, 9 were also selected (see Color Figure 11.4following page 274.). 11.2.5.7 Cortical Current Waveforms By using the relations described above, at each time point of the gathered ERP data, an estimate of the signed magnitude of the dipolar moment for each of the 5000 cortical dipoles was obtained. In fact, since the orientation of the dipole was already defined to be perpendicular to the local cortical surface of the model, the estimation process returned a scalar rather than a vector field. To obtain the cortical current waveforms for all the time points of the recorded EEG time series, we used a unique quasioptimal regularization λ value for all the analyzed EEG potential distributions. This quasioptimal regularization value was computed as an average of the several λ values obtained by solving the linearinverse problem for a series of EEG potential distributions. These distributions are characterized by an average global field power (GFP) with respect to the higher and lower GFP values obtained during all the recorded waveforms. The instantaneous average of the dipole’s signed magnitude belonging to a particular ROI generates the representative time value of the cortical activity in that given ROI. By iterating this procedure on all the time instants of the gathered ERP, the cortical ROI currentdensity waveforms were obtained, and they could be taken as representative of the average activity of the ROI during the task performed by the experimental subjects. These waveforms could then be subjected to the SEM and DTF processing to estimate the connectivity pattern between ROIs, by taking into account the timevarying increase or decrease of the power spectra in the Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 413 FIGURE 11.3 Cortical connectivity patterns obtained with the SEM method for the period preceding and following the movement onset in the alpha (8 to 12 Hz) frequency band. The patterns are shown on the realistic head model and cortical envelope (obtained from sequential MRIs) of the subject analyzed. Functional connections are represented with arrows moving from one cortical area to another. The colors and sizes of the arrows code the strengths of the functional connectivity observed between ROIs. The labels are relative to the name of the ROIs employed. (a) Connectivity pattern obtained from ERP data before the onset of the rightfinger movement (electromyographic onset, EMG). (b) Connectivity patterns obtained after the EMG onset. 0.44 0.42 0.4 0.38 0.36 0.34 0.32 0.3 0.28 0.26 0.44 0.42 0.4 0.38 0.36 0.34 0.32 0.3 0.28 0.26 (a) (b) SMr SMr PMr PMr PFr PFr Pr PI PFI PFI PMI PMI SMI SMI PI Copyright 2005 by Taylor Francis Group, LLC 414 Medical Image Analysis FIGURE 11.4 Cortical connectivity patterns obtained with the DTF method for the period preceding and following the movement onset in the alpha (8 to 12 Hz) frequency band. The patterns are shown on the realistic head model and cortical envelope (obtained from sequential MRIs) of the subject analyzed. Functional connections are represented with arrows moving from one cortical area to another. The colors and sizes of the arrows code the strengths of the connections. (a) Connectivity pattern obtained from ERP data before the onset of the rightfinger movement (electromyographic onset, EMG). (b) Connectivity patterns obtained after the EMG onset. (a) (b) 0.4 0.38 0.36 0.34 0.32 0.3 0.28 0.26 0.24 0.22 0.2 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 415 frequency bands of interest. Here, we present the results obtained for the connectivity pattern in the alpha band (8 to 12 Hz), because the ERP data related to the movement preparation and execution are particularly responsive within this frequency interval (for a review, see Pfurtscheller and Lopes da Silva 32). 11.3 RESULTS 11.3.1 COMPUTERSIMULATIONS FOR SEM Each set of signals was generated as described in the Methods section (Section 11.2) to fit a predefined connection model as well as to respect different levels of the two factors SNR and LENGTH of the recordings. The resulting signals were analyzed by means of the freeware software LISREL, which gave as a result an estimation of the connection strengths. Figure 11.2shows the connection model used in the signal generation and in the parameter estimation. The arrows represent the existence of a connection directed from the signal z i toward the signal z j, and the values on the arcs aij represent the connection parameters described in Equation 11.20. The results obtained for the statistical analysis performed on the 50 repetitions of the procedure are reported in Figure 11.5,representing the plot of means of the relative error with respect to signal LENGTH and SNR. ANOVA has identified a strong statistical significance of both factors considered. The factors SNR and LENGTH were both highly significant (factor LENGTH F = 288.60, p < 0.0001; factor SNR F = 22.70, p < 0.0001). Figure 11.5(a) shows the plot of means of the relative error with respect to the signal length levels, which reveals a decrease of the connectivity estimation error with an increase in the length of the available data. Figure 11.5(b) shows the plot of means with respect to the different SNR levels employed in the simulation. Because the main factors were found highly statistically significant, post hoc tests (Duncan at 5%) were then applied. Such tests showed statistically significant differences between all levels of the factor LENGTH, although there is no statistically significant difference between levels 3, 5, and 10 of the factor SNR. 11.3.2 COMPUTERSIMULATIONS FOR DTF The connectivity model used in the signal generation was the same as was used for the SEM simulation, which is shown in Figure 11.2.A multivariate autoregressive model of order 8 was fitted to each set of simulated data. Then, the normalized DTF functions were computed from each autoregressive model. The procedure of signal generation and DTF estimation was carried out 50 times for each level of factors SNR and LENGTH. The index of performances used, i.e., the relative error, was computed for each generationestimation procedure performed and then subjected to ANOVA. In this statistical analysis, relative error was the dependent variable, and the different SNR and LENGTH imposed in the signal generation were the main factors. ANOVA revealed a strong statistical influence of all the main factors (SNR and LENGTH; for relative error we obtained: SNR: F = 3295.5, p < 0.0001; LENGTH: F = 1012.4, p < 0.0001). Copyright 2005 by Taylor Francis Group, LLC 416 Medical Image Analysis FIGURE 11.5 (Color figure follows p. 274.)Results of ANOVA performed on the relative error resulting from SEM simulations. (a) Plot of means with respect to signal LENGTH as a function of time (seconds). ANOVA shows a high statistical significance for factor LENGTH (F = 288.60, p < 0.0001). Duncan post hoctest (performed at 5% level of significance) shows statistically significant differences between all levels. (b) Plot of means with respect to signaltonoise ratio. Here, too, a high statistical influence of factor SNR on the error in the estimation is shown (F = 22.70, p < 0.0001). Duncan post hoc test (performed at 5% level of significance) shows that there is no statistically significant difference between levels 3, 5, and 10 of factor SNR. Relative Error 0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 60 190 Length (sec) (a) 310 610 Relative Error 0.036 0.034 0.032 0.030 0.028 0.026 0.024 0.022 0.020 13SNR (b) 510100 Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 417 Figure 11.6shows the influence of factors SNR and LENGTH on relative error. In detail, Figure 11.6(a) shows the plot of means of the relative error with respect to the signal LENGTH levels, which reveals a decrease of the connectivity estimation error with an increase in the length of the available data; Figure 11.6(b) shows the plot of means with respect to different SNR levels employed in the simulation. In particular, for a SNR between 3 and 10, the expected error in the estimation of the connectivity pattern was generally under 7%, and the same values were obtained for ERP recording longer than 150 sec. Because the main factors were found to be statistically significant, post hoc tests (Duncan test at 5%) were then applied. The results showed statistically significant differences between the levels 15 and 45 sec (960 and 2880 samples, respectively) of the factor LENGTH and the other levels, but there is no statistically significant difference between levels 3, 5, and 10 of the factor SNR. 11.3.3 APPLICATION TOHIGHRESOLUTIONEVENTRELATED POTENTIALRECORDINGS The results of the application of the SEM method for estimating the connectivity on the eventrelated potential recordings is depicted in Figure 11.3,which shows the statistically significant cortical connectivity patterns obtained for the period preceding the movement onset in subject no. 1, in the alpha frequency band. Each pattern is represented with arrows that connect one cortical area (the source) to another one (the target). The colors and sizes of arrows code the level of strength of the functional connectivity observed between ROIs. The labels indicate the names of the ROIs employed. Note that the connectivity pattern during the period preceding the movement in the alpha band involves mainly the parietal left ROI (Pl) coincident with Brodmann areas 5 and 7 functionally connected to the left and right premotor cortical ROIs (PMl and PMr), the left sensorimotor area (SMl), and both the prefrontal ROIs (PFl and PFr). The stronger functional connections are relative to the link between the left parietal and the premotor areas of both cerebral hemispheres. After the preparation and the beginning of the finger movement in the POST period, changes in the connectivity pattern can be noted. In particular, the origin of the functional connectivity links is positioned in the sensorimotor left cortical areas (SMl). From there, functional links are established with prefrontal left (PFl) and both the premotor areas (PMl and PMr). A functional link emerged in this condition connecting the right parietal area (Pr) with the right sensorimotor area (SMr). The left parietal area (Pl) that was so active in the previous condition was instead linked with the left sensorimotor (SMl) and right premotor (PMr) cortical areas. Connectivity estimations performed by DTF on the movementrelated potentials were first analyzed from a statistical point of view via the previously described shuffling procedure. The order of the MVAR model used for each DTF estimation had to be determined for each subject and in each temporal interval of the cortical waveform segmentations (PRE and POST interval). The Akaike information criterion (AIC) procedure was used and returned an optimal order between 6 and 7 for all the subjects in both PRE and POST intervals. On such cortical waveforms, the DTF computational procedure described in the Methods section (Section 11.1) was Copyright 2005 by Taylor Francis Group, LLC 418 Medical Image Analysis FIGURE 11.6(Color figure follows p. 274.)Results of ANOVA performed on the relative error resulting from DTF simulations. (a) Plot of means with respect to signal LENGTH as a function of time (seconds). ANOVA shows a high statistical significance for factor LENGTH (F = 1012.36, p < 0.0001). Duncan post hoc test (performed at 5% level of significance) shows statistically significant differences between levels 15 and 45 sec at 64Hz sampling rate (equivalent of 960 and 2880 samples, respectively) of the factor LENGTH and all the other levels. (b) Plot of means with respect to signaltonoise ratio. Here, too, a high statistical influence of factor SNR on the error in the estimation is shown (F = 3295.45, p < 0.0001). Duncan post hoc test (performed at 5% level of significance) shows that there is no statistically significant difference between levels 3, 5, and 10 of factor SNR. 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 15 45 75 150 300 600 Relative Error Length (sec) (a) 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.1 1 3 5 10 Relative Error SNR (b) Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 419 applied. Figure 11.4shows the cortical connectivity patterns obtained for the period preceding and following the movement onset in subject no. 1. Here, we present the results obtained for the connectivity pattern in the alpha band (8 to 12 Hz), as the ERP data related to the movement preparation and execution are particularly responsive within this frequency interval (for a review, see Pfurtscheller and Lopes da Silva 32). The taskrelated pattern of cortical connectivity was obtained by calculating the DTF between the cortical currentdensity waveforms estimated in each ROI depicted on the realistic cortex model. The connectivity patterns between the ROIs are represented by arrows pointing from one cortical area to another. The arrows’ color and size code the strength of the functional connectivity estimated between the source and the target ROI. Labels indicate the ROIs involved in the estimated connectivity pattern. Only the cortical connections statistically significant at p < 0.01 are represented, according to the thresholds obtained by the shuffling procedure. It can be noted that the connectivity patterns during the period preceding and following the movement in the alpha band involve bilaterally the parietal and sensorimotor ROIs, which are also functionally connected with the premotor cortical ROIs. A minor involvement of the prefrontal ROIs is also observed. The stronger functional connections are relative to the link between the premotor and prefrontal areas of both cerebral hemispheres. After the preparation and the beginning of the finger movement in the POST period, slight changes in the connectivity patterns can be noted. 11.3.4 APPLICATION OF THEMULTIMODAL EEGFMRI INTEGRATIONTECHNIQUES TO THEESTIMATION OFSOURCES OFSELFPACEDMOVEMENTS In this section, we provide a practical example of the application of the multimodal integration techniques of EEG and fMRI (as theoretically described in the previous sections) to the problem of detection of neural sources subserving unilateral selfpaced movements in humans. The highresolution EEG recordings (128 scalp electrodes) were performed on normal healthy subjects by using the facilities available at the laboratory of the Department of Human Physiology, University of Rome. Realistic head models were used, each one provided with a cortical surface reconstruction tessellated with 3000 current dipoles. Separate block design and eventrelated fMRI recordings of the same subjects were performed by using the facilities of the Instituto Tecnologie Avanzate Biomediche (ITAB) of Chiety, Italy. Distributed linearinverse solutions by using hemodynamic constraints were obtained according to the previously described methodology. Figure 11.7presents the typical situation that occurred when different imaging methods were used to characterize the brain activity generated during a specific task. In particular, the task performed by the subject was the selfpaced movement of the middle finger of the right hand. This task was performed three times under three different scanners, namely the fMRI, the HREEG, and the MEG. On the left of Figure 11.7,there is a view of some cerebral areas active during the movement, as reported by fMRI. The maximum values of the fMRI responses are located in the Copyright 2005 by Taylor Francis Group, LLC 420 Medical Image Analysis voxels roughly corresponding to the primary somatosensory and motor areas (hand representation) contralateral to the movement. In fact, during the selfpaced unilateral finger extension, somatosensory reafference inputs from finger joints as well as cutaneous nerves are directed to the primary somatosensory area, while centrifugal commands from the primary motor area are directed toward the spinal cord via the pyramidal system. At the center of the figure is represented the dura mater potential distribution estimated with the use of the SL operator over a cortical surface reconstruction. The deblurred distribution is obtained at 100 msec after the EMG onset of the right middle finger. Note the characteristic reverse negative and positive SL fields on the left hemisphere. It is easy to appreciate the different time resolutions of the different techniques, with the fMRI data being relative to the whole time course of the experiment, and the highresolution EEG data being relative to a particular span of milliseconds of the cortical electromagnetic field evolution related to the same experiment. Simulations performed to test the efficacy of the multimodal integration of HREEG and fMRI return the information that the inclusion of fMRI priors improves the reconstruction of cortical activity 22, 60. Figure 11.8(a) presents three cortical currentdensity distributions. The left one shows the cortical regions roughly corresponding to the supplementary motor area and the left motor cortex, with the imposed activations represented in black. The imposed activations generated a potential distribution over the scalp electrodes (not shown in the figure). From this potential distribution, different inverse operators with and without the use of fMRI priors (located in the supplementary and left motor areas) attempted to estimate the currentdensity distribution. The currentdensity reconstruction at the center of Figure 11.8(a) shows the results of the estimation of sources presented on the left map (obtained using the minimumnorm estimate procedure) without the use of fMRI FIGURE 11.7 (Color figure follows p. 274.) (Left) A view of some cerebral areas active during the selfpaced movement of the right finger, as reported by fMRI. (Right) Dura mater potential distribution estimated with the use of the SL operator over a cortical surface reconstruction. The deblurred distribution is obtained at 100 msec after the EMG onset of the right middle finger. Copyright 2005 by Taylor Francis Group, LLC Estimation of Human Cortical Connectivity 421 priors. The currentdensity reconstruction on the right of the figure presents the cortical activations recovered by the use of fMRI priors in agreement with the Equation 11.27. Figure 11.8(b) illustrates the cortical distributions of the current density (estimated with the linearinverse approaches from the potential distribution relative to the movement preparation) about 200 msec before the extension of a right middle finger. Such an approach used no fMRI constraint as well the fMRI constraints based FIGURE 11.8 (Color figure follows p. 274.) (a) Three cortical currentdensity distributions. The left one shows the simulated cortical regions roughly corresponding to the supplementary motor area and the left motor cortex, with the imposed activations represented in black. The currentdensity reconstruction at the center of the figure presents the results of the estimation of sources (obtained using the minimumnorm estimate procedure) presented on the left map without the use of fMRI priors. The currentdensity reconstruction on the right of the figure presents the cortical activations recovered by the use of fMRI priors in agreement with Equation 11.27. (b) Distributions of the current density estimated with the linearinverse approaches from the potential distribution relative to the movement preparation, about 200 msec before a right middle finger extension. The distributions are represented on the realistic subject’s head volume conductor model. (Left) Scalp potential distribution recorded 200 msec before movement execution. (Center) Cortical estimate obtained without the use of fMRI constraints, based on the minimumnorm solutions. (Right) Cortical estimate obtained with the use of fMRI constraints based on Equation 11.27. Original Minimum Norm fMRI–constrained Scalp potential Minimum Norm fMRI–constrained (a) (b) 1 0.8 0.6 0.4 0.2 −0.2 −0.4 −0.6 −0.8 −1 0 1 0.8 0.6 0.4 0.2 −0.2 −0.4 −0.6 −0.8 −1 0 0.4 0.3 0.2 0.1 −0.1 −0.2 −0.3 −0.4 0 Copyright 2005 by Taylor Francis Group, LLC 422 Medical Image Analysis on Equations 11.27 and 11.28. The left of Figure 11.8(b) shows the topographic map of readiness potential distribution recorded at the
Trang 111 Estimation of Human
Cortical Connectivity with Multimodal
Integration of fMRI and High-Resolution EEG
Laura Astolfi, Febo Cincotti, Donatella Mattia, Serenella Salinari, and Fabio Babiloni
CONTENTS
11.1 Introduction11.2 Methods11.2.1 Monitoring the Cerebral Hemodynamic Response by fMRI11.2.2 Structural Equation Modeling
11.2.3 Directed Transfer Function11.2.4 Computer Simulation11.2.4.1 The Simulation Study11.2.4.2 Signal Generation for the SEM Methodology11.2.4.3 Signal Generation for the DTF Methodology11.2.4.4 Performance Evaluation
11.2.4.5 Statistical Analysis11.2.5 Application to Movement-Related Potentials11.2.5.1 Subject and Experimental Design11.2.5.2 Head and Cortical Models11.2.5.3 EEG Recordings
11.2.5.4 Statistical Evaluation of Connectivity Measurements
by SEM and DTF 11.2.5.5 Estimation of Cortical Source Current Density11.2.5.6 Regions of Interest (ROIs)
11.2.5.7 Cortical Current Waveforms11.3 Results
11.3.1 Computer Simulations for SEM11.3.2 Computer Simulations for DTF2089_book.fm copy Page 395 Wednesday, May 18, 2005 3:32 PM
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11.3.3 Application to High-Resolution Event-Related PotentialRecordings
11.3.4 Application of the Multimodal EEG-fMRI Integration Techniques to the Estimation of Sources of Self-PacedMovements
11.4 Discussion11.4.1 Simulation Results for SEM11.4.2 Simulation Results for DTF11.4.3 Application of Connectivity Estimation Methods to RealEEG Data
11.4.4 Application of Connectivity Estimation Methods to RealEEG Data
11.5 ConclusionsAcknowledgmentReferences
11.1 INTRODUCTION
Human neocortical processes involve temporal and spatial scales spanning severalorders of magnitude, from the rapidly shifting somatosensory processes character-ized by a temporal scale of milliseconds and a spatial scale of a few square milli-meters to the memory processes, involving time periods of seconds and a spatialscale of square centimeters Information about the brain activity can be obtained bymeasuring different physical variables arising from the brain processes, such as theincrease in consumption of oxygen by the neural tissues or a variation of the electricpotential over the scalp surface All these variables are connected in direct or indirectway to the ongoing neural processes, and each variable has its own spatial andtemporal resolution The different neuroimaging techniques are then confined to thespatio-temporal resolution offered by the monitored variables For instance, it isknown from physiology that the temporal resolution of the hemodynamic deoxyhe-moglobin increase/decrease lies in the range of 1 to 2 sec, while its spatial resolution
is generally observable with the current imaging techniques at the scale of a fewmillimeters Today, no neuroimaging method allows a spatial resolution on a milli-meter scale and a temporal resolution on a millisecond scale Hence, it is of interest
to study the possibility of integrating the information offered by the different iological variables in a unique mathematical context This operation is called the
phys-“multimodal integration” of variable X and Y, where the X variable typically has aparticularly appealing spatial resolution property (millimeter scale), and the Y vari-able has particularly attractive temporal properties (on a millisecond scale) Never-theless, the issue of several temporal and spatial domains is critical in the study ofthe brain functions, because different properties could become observable, depending
on the spatio-temporal scales at which the brain processes are measured
Electroencephalography (EEG) and magnetoencephalography (MEG) are twointeresting techniques that present a high temporal resolution, on the millisecondscale, adequate to follow brain activity However, both techniques have a relatively
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modest spatial resolution, beyond the centimeter Spatial resolution for these niques is fundamentally limited by the intersensor distances and by the fundamentallaws of electromagnetism [1] On the other hand, the use of a priori informationfrom other neuroimaging techniques like functional magnetic resonance imaging(fMRI) with high spatial resolution could improve the localization of sources fromEEG/MEG data
tech-The initial part of this chapter then deals with the multimodal integration ofelectrical, magnetic, and hemodynamic data to locate neural sources responsible forthe recorded EEG/MEG activity The rationale of the multimodal approach based
on fMRI, MEG, and EEG data to locate brain activity is that neural activity ating EEG potentials or MEG fields increases glucose and oxygen demands [2].This results in an increase in the local hemodynamic response that can be measured
gener-by fMRI [3, 4] On the whole, such a correlation between electrical and namic concomitants provides the basis for a spatial correspondence between fMRIresponses and EEG/MEG source activity
hemody-However, static images of brain regions activated during particular tasks do notconvey the information of how these regions communicate with each other Theconcept of brain connectivity is viewed as central for the understanding of theorganized behavior of cortical regions beyond the simple mapping of their activity[5, 6] This organization is thought to be based on the interaction between differentand differently specialized cortical sites Cortical-connectivity estimation aims atdescribing these interactions as connectivity patterns that hold the direction andstrength of the information flow between cortical areas To achieve this, severalmethods have already been applied on data gathered from both hemodynamic andelectromagnetic techniques [7–11] Two main definitions of brain connectivity havebeen proposed over the years: functional and effective connectivity [12] Whilefunctional connectivity is defined as temporal correlation between spatially remoteneurophysiologic events, the effective connectivity is defined as the simplest braincircuit that would produce the same temporal relationship as observed experimentallybetween cortical sites As for the functional connectivity, the several computationalmethods proposed to estimate how different brain areas are working together typi-cally involve the estimation of some covariance properties between the differenttime series measured from the different spatial sites during motor and cognitive tasksstudied by EEG and fMRI techniques [13–16] In contrast, structural equationmodeling (SEM) is a different technique that has been used for a decade to assesseffective connectivity between cortical areas in humans by using hemodynamic andmetabolic measurements [7, 17–19] The basic idea of SEM differs from the usualstatistical approach of modeling individual observations, because SEM considersthe covariance structure of the data [17] However, the estimation of cortical effectiveconnectivity obtained with the application of the SEM technique on fMRI data has
a low temporal resolution (on the order of 10 sec), which is far from the time scale
at which the brain operates normally Hence, it becomes of interest to understandwhether the SEM technique could be applied to cortical activity estimated by apply-ing the linear-inverse techniques to the high-resolution EEG (HREEG) data [20–23]
In this way, it would be possible to study time-varying patterns of brain connectivitylinked to the different parts of the experimental task studied
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So far, the estimation of functional connectivity on EEG signals has beenaddressed by applying either linear or nonlinear methods, both of which can trackthe direct flow of information between scalp electrodes in the time domain, althoughwith different computational demands [21, 24–31] In addition, given the evidencethat important information in the EEG signals is often coded in the frequency ratherthan time domain (reviewed in [32]), research attention has been focused on detectingfrequency-specific interactions in EEG or MEG signals by analyzing the coherencebetween the activity of pairs of structures [33–35] However, coherence analysisdoes not have a directional nature (i.e., it just examines whether a link exists betweentwo neural structures by describing instances when they are in synchronous activity),and it does not directly provide the direction of the information flow In this respect,
a multivariate spectral technique called directed transfer function (DTF) was posed [36] to determine the directional influences between any given pair of channels
pro-in a multivariate data set This estimator can simultaneously characterize both thedirectional and spectral properties of the brain signals, requiring only one multivariateautoregressive (MVAR) model that is estimated from all of the EEG channel recordings.The DTF technique has recently been demonstrated [37] to rely on the key concept ofGranger causality between time series [38], according to which an observed time series
x(n) generates another series y(n) if knowledge of x(n)’s past significantly improves theprediction of y(n) This relation between time series is not reciprocal, i.e., x(n) maycause y(n) without y(n) necessarily causing x(n) This lack of reciprocity is what allowsthe evaluation of the direction of information flow between structures
In this study, we propose to estimate the patterns of cortical connectivity byexploiting the SEM and DTF techniques applied on high-resolution EEG signals,which exhibit a higher spatial resolution than conventional cerebral electromagneticmeasures Indeed, this EEG technique includes the use of a large number of scalpelectrodes, realistic models of the head derived from structural magnetic resonanceimages (MRIs), and advanced processing methodologies related to the solution ofthe linear-inverse problem These methodologies facilitate the estimation of corticalcurrent density from sensor measurements [39–41] To pursue the aim of this study,
we first explored the behavior of the SEM and DTF methods in a simulation contextunder various conditions that affect the EEG recordings, mainly the signal-to-noiseratio (factor SNR) and the length of the recordings (factor LENGTH) In particular,the following questions were addressed:
What is the influence of a variable SNR level (imposed on the high-resolutionEEG data) on the accuracy of the estimation of pattern connectivity obtained
Trang 5Estimation of Human Cortical Connectivity 399
were performed by ANOVA (analysis of variance) and Duncan post hoc tests, withthese error indexes as dependent variables Subsequently, both SEM and DTF methodswere applied to the cortical estimates obtained from high-resolution EEG data related
to a simple finger-tapping experiment in humans to underline the capability of theproposed methodology to draw patterns of cortical connectivity between brain areasduring a simple motor task Finally, we also present both the mathematical principleand the practical applications of the multimodal integration of high-resolution EEG andfMRI for the localization of sources responsible for intentional movements
11.2 METHODS
11.2.1 M ONITORING THE C EREBRAL H EMODYNAMIC R ESPONSE BY F MRI
A brain-imaging method, known as functional magnetic resonance imaging (fMRI),has gained favor among neuroscientists over the last few years Functional MRIreflects oxygen consumption, and because oxygen consumption is tied to processing
or neural activation, it can give a map of functional activity When neurons fire, theyconsume oxygen, and this causes the local oxygen levels to decrease briefly andthen actually increase above the resting level as nearby capillaries dilate to let moreoxygenated blood flow into the active area The most commonly used acquisitionparadigm is the so-called blood-oxygen level dependence (BOLD), in which thefMRI scanner works by imaging blood oxygenation The BOLD paradigm relies onthe brain mechanisms, which overcompensate for oxygen usage (activation causes
an influx of oxygenated blood in excess of that used, and therefore the local hemoglobin concentration increases) Oxygen is carried to the brain in the hemo-globin molecules of blood red cells
oxy-Figure 11.1 shows the physiologic principle at the base of the generation offMRI signals This figure shows how the hemodynamic responses elicited byincreased neuronal activity (Figure 11.1(a)) reduce the deoxyhemoglobin content ofthe blood flow in the same neuronal district after a few seconds (Figure 11.1(b)).Themagnetic properties of hemoglobin when saturated with oxygen are different thanwhen it has given up oxygen Technically, deoxygenated hemoglobin is "paramag-netic" and therefore has a short relaxation time As the ratio of oxygenated todeoxygenated hemoglobin increases, so does the signal recorded by the MRI Deox-yhemoglobin increases the rate of depolarization of the hydrogen nuclei creating the
MR signal, thus decreasing the intensity of the T2 image The bottom line is thatimage intensity increases with increasing brain activation The problem is that at thestandard intensity used for the static magnetic field (1.5 Tesla), this increase is small(usually less than 2%) and easily obscured by noise and various artifacts By increas-ing the static field of the fMRI scanner, the signal-to-noise ratio increases to moreconvenient values Static-field values of 3 Tesla are now commonly used for research
on humans, while an fMRI scanner at 7 Tesla was recently employed to maphemodynamic responses in the human brain [42] At such a high field value, there
is a possibility of detecting the initial increase of deoxyhemoglobin (after the initial
“dip”) The interest in the detection of the dip is based on the fact that this hemodynamicresponse happens on a time scale of 500 msec (as revealed by hemodynamic optical
Trang 6400 Medical Image Analysis
measures [43]) compared with 1 to 2 sec needed for the response of the vascularsystem to the oxygen demand Furthermore, in the latter case, the response has atemporal extension well beyond the activation that has occurred (10 sec)
As a last point, the spatial distribution of the initial dip (as described by usingthe optical dyes [43]) is sharper than those related to the vascular response of theoxygenated hemoglobin Recently, with high-field-strength MR scanners at 7 or even9.4 Tesla (on animals), a resolution down to the cortical-column level has beenachieved [44] However, at the standard field intensity commonly used in fMRIstudies (1.5 or 3 Tesla), the identification of such initial transient increase of deox-yhemoglobin is controversial Compared with positron-emitted tomography (PET)
or single-photon-emitted tomography (SPECT), fMRI does not require the injection
of radio-labeled substances, and its images have a higher resolution (as reviewed inthe literature [45]) PET, however, is still the most informative technique for directlyimaging metabolic processes and neurotransmitter turnover
11.2.2 S TRUCTURAL E QUATION M ODELING
In structural equation modeling (SEM), the parameters are estimated by minimizingthe difference between the observed covariances and those implied by a structural
or path model In terms of neural systems, a measure of covariance represents thedegree to which the activities of two or more regions are related
FIGURE 11.1 (Color figure follows p 274.) Physiologic principle at the base of the eration of fMRI signals (a) Neurons increase their firing rates, which increases oxygen consumption (b) Hemodynamic response in a second scale increases the diameter of the vessel close to the activated neurons The induced increase in blood flow overcomes the need for oxygen supply As a consequence, the percentage of deoxyhemoglobin in the blood flow decreases in the vessel with respect to (a).
gen-Hemoglobin
Oxygen
fMRI
Trang 7Estimation of Human Cortical Connectivity 401
The SEM consists of a set of linear structural equations containing observed
variables and parameters defining causal relationships among the variables Variables
in the equation system can be endogenous (i.e., dependent on the other variables in
the model) or exogenous (independent of the model itself) The structural equation
model specifies the causal relationship among the variables, describes the causal
effects, and assigns the explained and the unexplained variance
Let us consider a set of variables (expressed as deviations from their means)
with N observations In this study, these variables represent the activity estimated
in each cortical region, obtained with the procedures described in the following
section
The SEM for these variables is the following:
y = By + ΓΓΓΓx + ζζζζ (11.1)where:
y is a (m× 1) vector of dependent (endogenous) variables
x is a (n× 1) vector of independent (exogenous) variables
ζζζζ is a (m× 1) vector of equation errors (random disturbances)
B is a (m×m) matrix of coefficients of the endogenous variables
ΓΓΓΓ is a (m×n) matrix of coefficients of the exogenous variables
It is assumed that ζζζζ is uncorrelated with the exogenous variables, and B is
supposed to have zeros in its diagonal (i.e., an endogenous variable does not influence
itself) and to satisfy the assumption that (I−B) is nonsingular, where I is the identity
matrix
The covariance matrices of this model are the following:
Φ = E[xxT] is the (n×n) covariance matrix of the exogenous variables
Ψ = E[ζζζζζζζζT] is the (m×m) covariance matrix of the errors
If z is a vector containing all the p = m + n variables, exogenous and endogenous,
in the following order:
zT = [x1 … x n, y1 … y m] (11.2)then the observed covariances can be expressed as
ΣΣΣΣobs = (1/(N− 1))⋅Z⋅ZT (11.3)where Z is the p×N matrix of the p observed variables for N observations
The covariance matrix implied by the model can be obtained as follows:
Trang 8402 Medical Image Analysis
where
E[yyT] = E[(I−B)−1 (ΓΓΓΓx + ζζζζ)(ΓΓΓΓx + ζζζζ)T ((I −−−− B)−1)T]
= (I −−−− B)−1 (ΓΓΓΓΦΦΓΓΓΓ + ΨΦ ΨΨ) ((I − B)−1)T (11.5)because the errors ζζζζ are not correlated with the x, and where
E[yxT] = ((I − B)−1 ΦΦ)T (11.8)because ΣΣΣΣmod is symmetric The resulting covariance matrix, in terms of the model
parameters, is the following:
(11.9)
Without other constraints, the problem of the minimizing the differences between
the observed covariances and those implied by the model is undetermined, because
the number of variables (elements of matrices B, ΓΓΓΓ, ΨΨ, and ΦΨ ΦΦ) is greater than the
number of equations (m + n)(m + n + 1)/2 For this reason, the SEM technique is
based on the a priori formulation of a model on the basis of anatomical and
physiological constraints This model implies the existence of just some causal
relationships among variables, represented by arcs in a “path” diagram; all the
parameters related to arcs not present in the hypothesized model are forced to zero
For this reason, all the parameters to be estimated are called free parameters If t is
the number of free parameters, it must be that t ≤ (m + n)(m + n + 1)/2.
These parameters are estimated by minimizing a function of the observed and
implied covariance matrices The most widely used objective function for SEM is
the maximum likelihood (ML) function:
FML = log|ΣΣΣΣmod| + tr(ΣΣΣΣobs⋅ΣΣΣΣmod −1) − log|ΣΣΣΣobs| − p (11.10)where tr(·) is the trace of matrix In the context of multivariate, normally distributed
variables, the minimum of the ML function multiplied by (N − 1) follows a χ2
distribution with [p(p + 1)/2] – t degrees of freedom, where t is the number of
parameters to be estimated, and p is the total number of observed variables
(endog-enous + exog(endog-enous) The χ2 statistic test can then be used to infer statistical
signif-icance of the structural equation model obtained In the present study, the software
package LISREL [46] was used to implement the SEM technique
Trang 911.2.3 DIRECTED TRANSFER FUNCTION
In this study, the DTF technique was applied to the set of cortical estimated forms S
wave-z(t)= [z1(t), z2(t), …, zN(t)]T (11.11)
obtained for the N ROIs considered, as will be described in detail in the following
sections The following MVAR process is an adequate description of the data set Z
, with (0) = I (11.12)
where e(t) is a vector of a multivariate zero-mean uncorrelated white noise process;
(1), (2), …, (q) are the N × N matrices of model coefficients, and q is the model
order chosen, in our case, with the Akaike information criterion for MVAR processes[37] To investigate the spectral properties of the examined process, Equation 11.12
is transformed to the frequency domain
Here, H( f ) is the transfer matrix of the system whose element Hij represents the
connection between the jth input and the ith output of the system With these definitions, the causal influence of the cortical waveform estimated in the jth ROI
on that estimated in the ith ROI (the directed transfer function θ2ij( f )) is defined as
(11.16)
To enable comparison of the results obtained for cortical waveforms with ferent power spectra, a normalization was performed by dividing each estimatedDTF by the squared sums of all elements of the relevant row, thus obtaining the so-called normalized DTF [36]
Trang 1011.2.4.1 The Simulation Study
The experimental design we adopted was meant to analyze the recovery of theconnectivity patterns obtained under the different levels of SNR and signal temporallength that were imposed during the generation of sets of test signals simulatingcortical average activations As described in the following subsections, the simulatedsignals were obtained from actual cortical data estimated with the high-resolutionEEG procedures available at the high-resolution EEG Laboratory of the University
of Rome
11.2.4.2 Signal Generation for the SEM Methodology
Different sets of test signals were generated to fit an imposed connectivity pattern(shown in Figure 11.2) and to respect imposed levels of temporal duration(LENGTH) and signal-to-noise ratio (SNR) In the following discussion, using a
more compact notation, signals have been represented with the z vector defined in
Equation 11.2, containing both the endogenous and the exogenous variables Channel
z1 is a reference-source waveform, estimated from a high-resolution EEG (128electrodes) recording in a healthy subject during the execution of unaimed self-paced
movements of the right finger Signals z2, z3, and z4 were obtained by the contribution
of signals from all other channels, with an amplitude variation plus zero-mean related white noise processes with appropriate variances, as shown in Equation 11.19
uncor-z[k] = A*uncor-z[k] + W[k] (11.19)
where z[k] is the [4 ×1] vector of signals, W[k] is the [4×1] noise vector, and A is the
[4×4] parameters matrix obtained from the ΓΓΓΓ and B matrices in the following way:
γij
ij
im m
N f
2 1
1
( )=
=
∑
Trang 11It is worth noting that the levels chosen for both SNR and LENGTH factors coverthe typical range for the cortical activity estimated with high-resolution EEG tech-niques.
FIGURE 11.2 Connectivity pattern imposed in the generation of simulated signals z1, …,
z4 represent the average activities in four cortical areas Values on the arcs represent the
Trang 1211.2.4.3 Signal Generation for the DTF Methodology
Different sets of test signals were generated to fit an imposed coupling schemeinvolving four different cortical areas (shown in Figure 11.2) while also respectingimposed levels of signal-to-noise ratio (factor SNR) and duration (factor LENGTH)
Signal z1(t) was a reference cortical waveform estimated from a high-resolution
EEG (96 electrodes) recording in a healthy subject during the execution of
self-paced movements of the left finger Subsequent signals z2(t) to z4(t) were iteratively
obtained according to the imposed scheme (Figure 11.2) by adding to signal zj
contributions from the other signals, delayed by intervals τij and amplified by factors
a ij plus an uncorrelated Gaussian white noise Coefficients of the connection
strengths were chosen in a range of realistic values as met in previous studies duringthe application of other connectivity-estimation techniques, such as structural equa-tion modeling, in several memory, motor, and sensory tasks [7] Here, the values
used for the connection strength were a21 = 1.4, a31 = 1.1, a32 = 0.5, a42 = 0.7, and
a43 = 1.2 The values used for the delay from the ith ROI to the jth one (τij) ranged from one sample up to the q − 2, where q was the order of the MVAR model used.
Because the statistical analysis performed with different values of such delay samplesreturned the same information with respect to the variation of this parameter, in thefollowing we particularized the results to the case τ21 = τ31 = τ32 = τ42 = τ43 = 1sample, which for a sampling rate of 64 Hz became a delay of 15 msec
All procedures of signal generation were repeated under the following conditions:SNR factor levels = (0.1, 1, 3, 5, 10)
LENGTH factor levels = (960, 2,880, 4,800, 9,600, 19,200, 38,400) datasamples, corresponding to signals length of (15, 45, 75, 150, 300, 600) sec
at a sampling rate of 64 Hz, or to (7, 22, 37, 75, 150, 300) EEG trials of
2 sec each
The levels chosen for both SNR and LENGTH factors cover the typical range forthe cortical activity estimated with high-resolution EEG techniques
The MVAR model was estimated by means of the Nuttall-Strand method or the
multivariate Burg algorithm, which is one of the most common estimators for MVAR
models and has been demonstrated to provide the most accurate results [48–50]
11.2.4.4 Performance Evaluation
The quality of the performed estimation was evaluated using the Frobenius norm ofthe matrix, which reports the differences between the values of the estimated (viaSEM) and the imposed connections (relative error) The norm was computed for theconnectivity patterns obtained with the SEM methodology
m
ij i
m
ij j m
1 2
==
∑
1
m
Trang 13In the case in which the DTF method was used, the statistical evaluation of DTFperformances required a precise definition of an error function describing the good-ness of the pattern recognition performed This was achieved by focusing on theMVAR model structure described in Equation 11.12 and comparing it with the
signals-generation scheme The elements of matrices (k) of MVAR model
coeffi-cients can be put in relation with the coefficoeffi-cients used in the signal generation, and
they are different from zero only for k = τij, where τij is the delay chosen for each
pair ij of ROIs and for each direction among them In particular, for the independent reference source waveform z1(t), an autoregressive model of the same order of the MVAR has been estimated, whose coefficients a11(1), …, a11(q) correspond to the
elements Λ11(1), …, Λ11(q) of the MVAR coefficients matrix Thus, with the
esti-mation of the MVAR model parameters, we aim to recover the original coefficients
a ij(k) used in signal generation In this way, reference DTF functions have been
computed on the basis of the signal-generation parameters The error function wasthen computed as the difference between these reference functions and the estimatedones (both averaged in the frequency band of interest) To evaluate the performances
in retrieving the connections between areas, the same index used in the case of theSEM was adopted, but with light differences of notation, i.e., the Frobenius norm
of the matrix reporting the differences between the values of the estimated and theimposed connections (total relative error)
(11.22)
In Equation 11.22, represents the average value of the DTF function
from j to i within the frequency band of interest For both SEM and DTF, the
simulations were performed by repeating each generation-estimation procedure 50times to increase the robustness of the successive statistical analysis
11.2.4.5 Statistical Analysis
The results obtained were subjected to separate ANOVA The main factors of theANOVAs for the DTF method were the SNR (with five levels: 0.1, 1, 3, 5, 10) andthe signal LENGTH (with six levels: 960, 2,880, 4,800, 9,600, 19,200, 38,400 datasamples, equivalent to 15, 45, 75, 150, 300, 600 sec at 64 Hz of sampling rate) Inthe case of the SEM method, the main factors were identical, but the LENGTH hasonly four levels (equal to 60, 190, 310, and 610 sec at 64 Hz) For all of themethodologies used, ANOVA was performed on the error index that was adopted(relative error) The correction of Greenhouse-Gasser for the violation of the spher-
ical hypothesis was used The post hoc analysis with the Duncan test at the p = 0.05
statistical significance level was then performed
E
ij j
m
ij i
m
ij j m
2 1
γij( )f
band
Trang 1411.2.5 APPLICATION TO MOVEMENT-RELATED POTENTIALS
The estimation of connectivity patterns by using the DTF and SEM on lution EEG recordings was applied to the analysis of a simple movement task Inparticular, we considered a right-hand finger-tapping movement that was externallypaced by a visual stimulus This task was chosen because it has been very widelystudied in literature with various brain-imaging techniques such as EEG or fMRI[51–53]
high-reso-11.2.5.1 Subject and Experimental Design
Three right-handed healthy subjects (age 23.3 ± 0.58, one male and two females)participated in the study after providing informed consent Subjects were seatedcomfortably in an armchair with both arms relaxed and resting on pillows, and theywere asked to perform fast, repetitive right-finger movements During this motortask, the subjects were instructed to avoid eye blinks, swallowing, or any movementother than the required finger movements
11.2.5.2 Head and Cortical Models
A realistic head model of the subjects, reconstructed from T1-weighted MRIs, wasemployed in this study Scalp, skull, and dura mater compartments were segmentedfrom MRIs with software originally developed at the Department of Human Phys-iology of Rome, and such structures were triangulated with about 1,000 trianglesfor each surface The source model was built with the following procedure:
1 The cortex compartment was segmented from MRIs and triangulated toobtain a fine mesh with about 100,000 triangles
2 A coarser mesh was obtained by resampling the fine mesh to about 5,000triangles The downsampling was performed with an adaptive algorithmdesigned to represent with a sufficient number of triangles the parts ofthe cortex where the radius of curvature was high (for instance, duringthe bending of a sulcus) while attempting to represent with few trianglesthe flatter parts of the cortical surface (for instance, on the upper part ofthe gyri)
3 An orthogonal unitary equivalent-current dipole was placed in each node
of the triangulated surface, with its direction parallel to the vector sum ofthe normals to the surrounding triangles
11.2.5.3 EEG Recordings
Event-related potential (ERP) data were recorded with 96 electrodes; data wererecorded with a left-ear reference and submitted to an artifact-removal process Sixhundred ERP trials of 600 msec of duration were acquired The analog–digitalsampling rate was 250 Hz The surface electromyographic (EMG) activity of themuscle was also collected The onset of the EMG response served as zero time Alldata were visually inspected, and trials containing artifacts were rejected We used
Trang 15semiautomatic supervised threshold criteria for the rejection of trials contaminated
by ocular and EMG artifacts, as described in detail elsewhere [54] After the EEGrecording, the electrode positions were digitized using a three-dimensional localiza-tion device with respect to the anatomic landmarks of the head (nasion and twopreauricular points) The analysis period for the potentials time-locked to the move-ment execution was set from 300 msec before to 300 msec after the EMG trigger(zero time) The ERP time course was divided into two phases relative to the EMGonset: the first, labeled as “PRE” period, marked the 300 msec before the EMGonset and was intended as a generic preparation period; the second, labeled as
“POST,” lasted up to 300 msec after the EMG onset and was intended to signal thearrival of the movement somatosensory feedback We kept the same PRE and POSTnomenclature for the signals estimated at the cortical level
11.2.5.4 Statistical Evaluation of Connectivity Measurements
by SEM and DTF
As described previously, the statistical significance of the connectivity pattern mated with the SEM technique was ensured by the fact that — in the context of themultivariate, normally distributed variables — the minimum of the maximum like-
esti-lihood function FML, multiplied by (N − 1), follows a χ2 distribution with [p(p +
1)/2] − t degrees of freedom, where t is the number of parameters to be estimated,
and p is the total number of observed variables (endogenous + exogenous) Then,
the χ2 statistic test can be used to infer the statistical significance of the structuralequation model obtained
The situation for the statistical significance of the DTF measurements is differentbecause the DTF functions have a highly nonlinear relation to the time-series datafrom which they are derived, and the distribution of their estimators is not wellestablished This makes tests of significance difficult to perform A possible solution
to this problem was proposed by Kaminski et al [37] Their solution involves theuse of a surrogate data technique [55] in which an empirical distribution for randomfluctuations of a given estimated quantity is generated by estimating the samequantity from several realizations of surrogate data sets where the deterministicinterdependency between variables has been removed To ensure that all features ofeach data set are as similar as possible to the original data set, with the exception
of channel coupling, the very same data are used, and any time-locked couplingbetween channels is disrupted by shuffling phases of the original multivariate signal.Because the EEG signal had been divided into single trials, each surrogate data setwas built up by scrambling the order of epochs, using different sequences for eachchannel In this procedure, every single-channel EEG epoch was used once and onlyonce, and only occasionally (and with a very low probability), two channels in thesame surrogate trial came from the same actual trial The set properties of univariatesurrogate signals are not influenced by this shuffling procedure, because only theepoch order is varied Moreover, because no shuffling was performed between singlesamples, the temporal correlation, and thus the spectral features, of univariate signals
is the same for the original and surrogate data sets, thus making it possible to estimatedifferent distributions of DTF fluctuations for each frequency band A total of 1000
Trang 16surrogate data sets was generated, as described previously, and DTF spectra wereestimated from each data set For each channel pair and for each frequency bin, the99th percentile was computed and subsequently considered as a significance thresh-old.
11.2.5.5 Estimation of Cortical Source Current Density
The solution of the following linear system
Lz = d + e (11.23)
provides an estimate of the dipole source configuration z that generates the measured
EEG potential distribution d The system also includes the measurement noise n,
assumed to be normally distributed [39]
In Equation 11.23, L is the lead field, or the forward transmission matrix, in
which each jth column describes the potential distribution generated on the scalp electrodes by the jth unitary dipole The current-density solution vector ξξξξ was
obtained as follows [39]:
(11.24)
where M, N are the matrices associated with the metrics of the data and of the
source space, respectively, λ is the regularization parameter, and ||z|| M represents the
M-norm of the vector z The solution of Equation 11.24 is given by the inverse
operator G as follows:
, (11.25)
An optimal regularization of this linear system was obtained by the L-curve
approach [56, 57] As a metric in the data space, we used the identity matrix, but
in the source space, we use the following metric as a norm
(11.26)
where (N−1)ii is the ith element of the inverse of the diagonal matrix N, and all the
other matrix elements N ij , for each i j, are set to 0 The L2 norm of the ith column
of the lead field matrix L is denoted by ||L .i||.
Here, we present two characterizations of the source metric N that can provide
the basis for the inclusion of the information about the statistical hemodynamic
activation of ith cortical voxel into the linear-inverse estimation of the cortical source
activity In the fMRI analysis, several methods have been developed to quantify thebrain hemodynamic response to a particular task However, in the following, we
Trang 17analyze the case in which a particular fMRI quantification technique — the percentchange (PC) technique — has been used This measure quantifies the percent increase
of the fMRI signal during the task performance with respect to the rest state [58].The visualization of the voxels’ distribution in the brain space that is statisticallyincreased during the task condition with respect to the rest is called the PC map.The difference between the mean rest- and movement-related signal intensity isgenerally calculated voxel by voxel The rest-related fMRI signal intensity isobtained by averaging the premovement and recovery fMRI A Bonferroni-correctedstudent’s t-test is also used to minimize alpha-inflation effects due to multiplestatistical voxel-by-voxel comparisons (Type I error; p < 0.05) The introduction offMRI priors into the linear-inverse estimation produces a bias in the estimation ofthe current-density strength of the modeled cortical dipoles Statistically significantlyactivated fMRI voxels, which are returned by the percentage change approach [58],are weighted to account for the EEG-measured potentials
In fact, a reasonable hypothesis is that there is a positive correlation betweenlocal electric or magnetic activity and local hemodynamic response over time Thiscorrelation can be expressed as a decrease of the cost in the functional PHI of
Equation 11.24 for the sources zj in which fMRI activation can be observed This increases the probability for those particular sources zj to be present in the solution
of the electromagnetic problem Such thoughts can be formalized by particularizing
the source metric N to take into account the information coming from the fMRI.
The inverse of the resulting metric is then proposed as follows [59]:
(11.27)
in which (N−1)ii and ||A⋅i|| have the same meaning as described previously The term
g(αi) is a function of the statistically significant percentage increase of the fMRI
signal assigned to the ith dipole of the modeled source space This function is
expressed as
(11.28)
where αi is the percentage increase of the fMRI signal during the task state for the
ith voxel, and the factor K tunes fMRI constraints in the source space.
Fixing K = 1 lets us disregard fMRI priors, thus returning to a purely electrical solution; a value for K » 1 allows only the sources associated with fMRI active voxels to participate in the solution It was shown that a value for K on the order
of 10 (90% of constraints for the fMRI information) is useful to avoid mislocalizationdue to overconstrained solutions [60–62] In the discussion that follows, the estima-tion of the cortical activity obtained with this metric will be denoted as diag-fMRI,
because the previous definition of the source metric N results in a matrix in which
the off-diagonal elements are zero
Trang 1811.2.5.6 Regions of Interest (ROIs)
Several cortical regions of interest (ROIs) were drawn by two independent and expertneuroradiologists on the computer-based cortical reconstruction of the individualhead models In cases where the SEM methodology was adopted, we selected ROIsbased on previously available knowledge about the flow of connections betweendifferent cortical macroareas, as derived from neuroanatomy and fMRI studies Inparticular, information flows were hypothesized to exist from the parietal (P) areastoward the sensorimotor (SM), the premotor (PM), and the prefrontal (PF) areas[63–65] The prefrontal areas (PF) were defined by including the Brodmann areas
8, 9, and 46; the premotor areas (PM) by including the Brodmann area 6; thesensorimotor areas (SM) by including the Brodmann areas 4, 3, 2, and 1; and theparietal areas (P), generated by the union of the Brodmann areas 5 and 7 (see coloredareas in Figure 11.3)
In cases where the DTF method was used, we selected the ROIs representingthe left and right primary somatosensory (S1) areas, which included the Brodmannareas (BA) 3, 2, 1, while the ROIs representing the left and right primary motor(MI) included the BA 4 The ROIs representing the supplementary motor area (SMA)were obtained from the cortical voxels belonging to the BA 6 We further separatedthe proper and anterior SMA indicated into regions labeled BA 6P and 6A, respec-tively Furthermore, ROIs from the right and the left parietal areas (BA 5, 7) andthe occipital areas (BA 19) were also considered In the frontal regions, the BA 46,
8, 9 were also selected (see Color Figure 11.4 following page 274.)
11.2.5.7 Cortical Current Waveforms
By using the relations described above, at each time point of the gathered ERP data,
an estimate of the signed magnitude of the dipolar moment for each of the 5000cortical dipoles was obtained In fact, since the orientation of the dipole was alreadydefined to be perpendicular to the local cortical surface of the model, the estimationprocess returned a scalar rather than a vector field To obtain the cortical currentwaveforms for all the time points of the recorded EEG time series, we used a uniquequasi-optimal regularization λ value for all the analyzed EEG potential distributions.This quasi-optimal regularization value was computed as an average of the several
λ values obtained by solving the linear-inverse problem for a series of EEG potentialdistributions These distributions are characterized by an average global field power(GFP) with respect to the higher and lower GFP values obtained during all therecorded waveforms
The instantaneous average of the dipole’s signed magnitude belonging to aparticular ROI generates the representative time value of the cortical activity in thatgiven ROI By iterating this procedure on all the time instants of the gathered ERP,the cortical ROI current-density waveforms were obtained, and they could be taken
as representative of the average activity of the ROI during the task performed bythe experimental subjects These waveforms could then be subjected to the SEMand DTF processing to estimate the connectivity pattern between ROIs, by takinginto account the time-varying increase or decrease of the power spectra in the
Trang 19FIGURE 11.3 Cortical connectivity patterns obtained with the SEM method for the period
preceding and following the movement onset in the alpha (8 to 12 Hz) frequency band The patterns are shown on the realistic head model and cortical envelope (obtained from sequential MRIs) of the subject analyzed Functional connections are represented with arrows moving from one cortical area to another The colors and sizes of the arrows code the strengths of the functional connectivity observed between ROIs The labels are relative to the name of the ROIs employed (a) Connectivity pattern obtained from ERP data before the onset of the right-finger movement (electromyographic onset, EMG) (b) Connectivity patterns obtained after the EMG onset.
0.44 0.42 0.4 0.38 0.36 0.34 0.32 0.3 0.28 0.26
0.44 0.42 0.4 0.38 0.36 0.34 0.32 0.3 0.28 0.26 (a)
(b)
SMr
SMr PMr
PMr PFr