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Modeling and inference of multisubject fMRI data

Modeling and inference of multisubject fMRI data

The analysis of single-subject fMRI data has drawn heav- ily on signal processing techniques. As discussed in the fol- lowing, linear time invariant systems are the standard way to specify the model for the experimentally related signal in fMRI. When more than one subject is considered, the model must account for differing response magnitudes in each sub- ject. While it is easy to specify a multisubject model that fits different responses for each subject, standard inference procedures do not account for the random subject-to-subject variation in response magnitude. When this random varia- tion is neglected, the inferences are specific to the cohort of subjects studied. As most experimenters want to make infer- ence on the population average magnitude, inference meth- ods must account for heterogeneity in the population, and specifically, a significant result must be based on statistical confidence that the population from which these subjects were drawn shows a given effect on average. Population inference is the goal of group modeling, and it is a statistical challenge not met by direct application of methods found in a first-year statistics course. Basic statistics and regression usually only cover ordinary least squares (OLS), linear regression, and other fixed-effects models that do not yield population inferences.
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Classification of Spatio-Temporal fMRI Data in the Spiking Neural Network

Classification of Spatio-Temporal fMRI Data in the Spiking Neural Network

In this paper, we addressed the classification accuracy for fMRI StarPlus dataset for the subject of 04847 data and divided into two experiments involving twenty samples and fifty samples for each class; PicS vs. SentP. The experiments have been run total 50 times with the 5 tests (10 times per test) by using the same data obtained from SNR feature selection technique. For the experiment with 20 samples; classification accuracy of the class PicS was inconsistent while the class SentP achieved 100% accuracy for all 5 tests (see Figure 5). Whereas; for the group of 50 samples, the accuracy of class PicS was 60% while the class SentP achieved accuracy as same as the group of 20 samples which is 100% (see Figure 5). Therefore, according to the experimental results, the SNR feature selection technique produced high accuracy in SentP than PicS in all 5 tests. Figure 7 and Figure 8 show a simple illustration of the result obtained by the above experiments. The results achieved from this experiment demonstrate that using SNR as a feature selection technique for fMRI data gives high accuracy for reading the text but not well in identifying images. Based on the simulation results, it can be concluded that the performance of SNR is noteworthy in maximum data samples which is 50 samples because the SNR have more choice on selecting the most relevant features than it has with 20 data samples.
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Potential pitfalls when denoising resting state fMRI data using nuisance regression

Potential pitfalls when denoising resting state fMRI data using nuisance regression

In resting state fMRI, it is necessary to remove signal variance associated with noise sources, leaving cleaned fMRI time-series that more accurately re fl ect the underlying intrinsic brain fl uctuations of interest. This is commonly achieved through nuisance regression, in which the fi t is calculated of a noise model of head motion and physiological processes to the fMRI data in a General Linear Model, and the “ cleaned ” residuals of this fi t are used in further analysis. We examine the statistical assumptions and requirements of the General Linear Model, and whether these are met during nuisance regression of resting state fMRI data. Using toy examples and real data we show how pre-whitening, temporal fi ltering and temporal shifting of regressors impact model fi t. Based on our own observations, existing literature, and statistical theory, we make the following recommendations when employing nuisance regression: pre-whitening should be applied to achieve valid statistical inference of the noise model fi t parameters; temporal fi ltering should be incorporated into the noise model to best account for changes in degrees of freedom; temporal shifting of regressors, although merited, should be achieved via optimisation and validation of a single temporal shift. We encourage all readers to make simple, practical changes to their fMRI denoising pipeline, and to regularly assess the appropriateness of the noise model used. By negotiating the potential pitfalls described in this paper, and by clearly reporting the details of nuisance regression in future manuscripts, we hope that the fi eld will achieve more accurate and precise noise models for cleaning the resting state fMRI time-series.
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Bayesian spatiotemporal model of fMRI data using transfer functions

Bayesian spatiotemporal model of fMRI data using transfer functions

problem. It also constitutes a natural but rigorous theory for combining prior and experimental information. Most Bayesian approaches to the modelling of fMRI data use GMRF as prior distributions, in order to account for the spatial structure present in the data, e.g. Gossl et al. (2001) use GMRF to spatially regularise regression coefficients and Woolrich et al. (2004b) to spa- tially regularise AR coefficients. Moreover, several choices of the precision matrix of the GMRF prior on regression coefficients of a GLM-AR model have been considered in the Bayesian literature, these include uninformative priors (Penny et al., 2003), global-shrinkage priors Friston and Penny (2003) and Laplacian priors (Penny et al., 2005) among others. An interesting com- parison of these priors can also be found in Penny et al. (2005).
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Motion related artefacts in EEG predict neuronally plausible patterns of activation in fMRI data

Motion related artefacts in EEG predict neuronally plausible patterns of activation in fMRI data

The simultaneous acquisition and subsequent analysis of EEG and fMRI data is challenging owing to increased noise levels in the EEG data. A common method to integrate data from these two modalities is to use aspects of the EEG data, such as the amplitudes of event-related potentials (ERP) or oscillatory EEG activity, to predict fluctuations in the fMRI data. However, this relies on the acquisition of high quality datasets to ensure that only the correlates of neuronal activity are being studied. In this study, we investigate the effects of head- motion-related artefacts in the EEG signal on the predicted T2*-weighted signal variation. We apply our analyses to two independent datasets: 1) four participants were asked to move their feet in the scanner to generate small head movements, and 2) four participants performed an episodic memory task. We created T2*-weighted signal predictors from indicators of abrupt head motion using derivatives of the realignment parameters, from visually detected artefacts in the EEG as well as from three EEG frequency bands (theta, alpha and beta). In both datasets, we found little correlation between the T2*-weighted signal and EEG predictors that were not convolved with the canonical haemodynamic response function (cHRF). However, all convolved EEG predictors strongly correlated with the T2*-weighted signal variation in various regions including the bilateral superior temporal cortex, supplementary motor area, medial parietal cortex and cerebellum. The fi nding that movement onset spikes in the EEG predict T2*-weighted signal intensity only when the time course of movements is convolved with the cHRF, suggests that the correlated signal might reflect a BOLD response to neural activity associated with head movement. Furthermore, the observation that broad-spectral EEG spikes tend to occur at the same time as abrupt head movements, together with the finding that abrupt movements and EEG spikes show similar correlations with the T2*-weighted signal, indicates that the EEG spikes are produced by abrupt movement and that continuous regressors of EEG oscillations contain motion-related noise even after stringent correction of the EEG data. If not properly removed, these artefacts complicate the use of EEG data as a predictor of T2*-weighted signal variation.
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Studies on 
		classification of FMRI data using deep learning approach

Studies on classification of FMRI data using deep learning approach

Brain as main server for entire human body is a complex composition. It is a challenging task to read and interpret the brain. Functional magnetic resonance imaging (fMRI) has become one of the means to do the task. fMRI is a non- invasive technique to measure brain activity of a human subject according to various stimuli. However, the fMRI datasets for each subject is huge and high-dimensional. For instance, the dataset has four dimensions for 3D images time series. Pre-processing and analysing using pattern recognition are insignificance for datasets with varied anatomical structures and dimensions. On the other hand, supervised learning or biomarker is employed to reduce the curse-of-dimensionality of fMRI datasets. Yet, the process is difficult and subjective to the labeled datasets. Therefore, a well-versed approach in signal processing, natural language processing (NLP) and object recognition, known as deep learning is seen to have higher standard than usual classification approach. Deep learning is the improved version of neural network with higher capability and accuracy. This paper aims to review the deep learning approach in fMRI classifications based on three studies on fMRI data classifications.
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The Pipeline of Processing fMRI data with Python Based on the Ecosystem NeuroDebian

The Pipeline of Processing fMRI data with Python Based on the Ecosystem NeuroDebian

As mentioned before, with the development of supercomputer and machine learning, more and more data is produced from society. In the neuroscience research field, the traditional data analysis approaches face a big challenge and bottleneck when the big data fade into it, so that’s why deep learning make very popular in the neuroscience research area that specific for fMRI data analysis, through deep learning model that we can train enough data to dig more medical information or cognitive mechanism. When we back to see the published paper in the recent year, the research topic related to deep learning already become a hot topic. So what kind of tools that we can use to neuroscience data analysis, in the next section, I will introduce some famous, classical and friendly model or library that we can use in our research.
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Prediction of Brain Connectivity Map in Resting-State fMRI Data Using Shrinkage Estimator

Prediction of Brain Connectivity Map in Resting-State fMRI Data Using Shrinkage Estimator

unctional Magnetic Resonance Imaging (fMRI) is one of the valuable instruments to discover the function of the human brain. The fMRI is a non-invasive method that uses Blood Oxygen Level Dependent (BOLD) contrast mechanism (Daliri & Behroozi, 2012). In re- cent years, lots of researchers studied the patterns of brain functional connectivity (Behroozi, Daliri, & Boy- aci, 2011; Ghaderi et al., 2017; Sadeghi et al., 2017). Functional connectivity focuses on how brain voxels and regions interact and function with each other.Some studiesare conducted on Resting-State (rs)-fMRI data to understand patterns ofbrainconnectivity and their role in brain diseases and disturbances (Zhang, Guindani, & Vannucci, 2015).In the resting-state imaging, without the stimulus, the subject is requested to lie down in the scan- ner device and not to move until the end of the imaging time (Daliri & Behroozi, 2013). Low-frequency fluctua- tions (<0.1 Hz) are observed in resting-state networks (Biswal et al., 1995).
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Group analysis based on multilevel Bayesian for FMRI data

Group analysis based on multilevel Bayesian for FMRI data

Bayesian methods summarize evidences for statistical inference with conditional or posterior inference based on the posterior distribution of the activations. The first paper based on Bayesian inference was on PET in 1993 and the first Bayesian approaches in fMRI with point estimation Maximum a Posterior Bayesian approaches to incorporate prior information. A fully Bayesian statistics approach as the first paper considered the full posterior probability distribution was appeared in 1998 [ Mar12 ]. Most methods [ Fri02a, Fri02b ] describe Bayesian on hierarchical linear model to form first level recursively. Some combine hierarchical model with classical by Empirical Bayesian, called all in one [ Woo04 ] that two methods are based on the same principle by covariance components and EM. And also the two methods can complement more activated voxels each other. All in one method includes fixed effects and random effects. On the model, its higher level estimator for parameters could be prior in lower level, and parameters estimation uses EM algorithm. Some methods [ Woo04, Bec03 ] analyzed fMRI data
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A Review on Dependence Measures in Exploring Brain Networks from fMRI Data

A Review on Dependence Measures in Exploring Brain Networks from fMRI Data

The information of BOLD signal as a function of time is measured from different points in the brain. These spatial coordinates can be used in different two scales, voxel or region of interest (ROI). Voxel is a cubic representing a spatial resolution unit in 3D fMRI image, e.g., 3 × 3 × 3 mm 3 . Brain regions of interest (ROIs) can be determined as a group of voxels defined by using some prior anatomical knowledge or from some post-processed analysis such as activity map. Either using fMRI signals collected from voxel level or ROIs is considered to be features that must be defined before exploring brain connectivity. There are two approaches to define these features. The first approach is the use of model dependent method or seed method which defines the brain region as “seed". A seed can be a brain region of interest (ROI) or it can be chosen from traditional task-dependent activation map from fMRI paradigm [2]. A limitation of this approach is a difficulty in applying to the whole brain scale. In other words, this approach is only suitable for analysis of brain connectivity in a small number of brain regions of interest (ROIs). The second approach that solves such limitation is the use of model-free method. This approach does not need to define a seed region or reference region from prior knowledge, and it may use some mathematical techniques, such as principal component analysis (PCA) in [17, 18, 19, 20] or independent component analysis (ICA) in [21, 22, 19], for defining voxels. PCA maps fMRI data to a new space via an orthogonal transformation and defines a set of components having the greatest variances as voxels. ICA uses fMRI data to seek for a mixture of underlying sources and defines these sources that are maximally independent from each other as voxels. Techniques for defining voxels like PCA and ICA are called Exploratory Matrix Factorization (EMF) that aims to extract blind source from observation and defines a set with some predefined properties as components. Other EMF techniques e.g., SVD, nonnegative matrix and tensor factorization (NMF/NTF), are explained in [7]. As the voxels from these techniques are mapped in the new space, the result may be difficult to justify by anatomical knowledge since the interpretation is based on the information on the new space [7, §3.2].
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Statistical approaches for resting state fMRI data analysis

Statistical approaches for resting state fMRI data analysis

continuously recorded through a 10/20 systems with 32 Ag/AgCl electrodes attached to the scalp with conductive cream. EEG electrodes were connected to a BrainAmp amplifier, with a sampling rate of 5 kHz. The EEG data was processed offline to filter out MR artifacts and remove ballistocardiogram artifacts (Brain Vision Analyzer 2.0, Germany). Onset and end time of epileptic discharges were marked and classified according to both spatial distribution and morphology. For more detail about the EEG dataset, see our previous studies (Liao et al., 2013a; Zhang et al., 2014b). The resting-state fMRI data was preprocessed in line with the healthy subject, except to re-sliced at a resolution of 6×6times6mm3 to minimize storage and computational requirements. Voxel- to-voxel analysis computed the bivariate FC between every pair of voxels without using a priori seed/ROI. We used the FLS analysis strategy here. In this case, we obtained the functional connectivity strength (FCS) maps for each time points as shown in Fig. 6.7 (see Supplementary Movie 5 ). According to information from simultaneously collected EEG data, the FCS maps were separated into preictal (time before seizure onset), ictal, and postictal (time after seizure end) time periods (see (Liao et al., 2013a)). As previously suggested, the thalamus and PCC were involved in seizure initiation, maintenance, and termination during absence seizures. We selected these two core brain regions as the ROIs to tracking the FCS dynamics. As seen from d-FCS network dynamics, there is a higher FCS of the thalamus (THA) during the ictal period relative to the periods before and after seizures (blue line). Conversely, the PCC d-FCS time series are lower during the ictal period (red line). These findings suggest that the total connections of thalamus and the PCC relate to mechanisms of seizure generation and suspension of default mode of brain function is consistent with an inhibitory effect of seizures on the default mode of brain function, respectively.
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Artificial Neural Networks for fMRI Data Analysis: A Survey

Artificial Neural Networks for fMRI Data Analysis: A Survey

The steps involved in performing MVPA (Fig 1) includes the following: defining features and classes, feature selection, choosing a classifier, training and testing the classifier and examining results. For defining what information to be used as features there are many possible choices like the raw fMRI data over space and time, averaged fMRI data over a block, Beta values from a GLM analysis or average of several voxels in an ROI. The choice of the class labels depends upon the research question. In fMRI the number of features is usually larger than the number of observations. Hence it is beneficial to reduce the number of features through feature selection. This could involve using only voxels from a particular ROI or by dimensionality reduction technique such as SVD (Singular Value Decomposition) or PCA (Principle Component Analysis) or meta-analysis data. In literature, there are methods like Principal Feature Analysis [8], Gray Level Co-occurrence Matrix (GLCM) [1] which have been used for feature selection. The next step is selection of a suitable classifier. Classifiers can be either linear or non-linear. Most MVPA studies have used linear classifiers, including Correlation-based classifiers, Neural Networks without a hidden layer, Linear Discriminant Analysis, Linear Support Vector Machines (SVMs),
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A spatiotemporal nonparametric Bayesian model of multi-subject fMRI data

A spatiotemporal nonparametric Bayesian model of multi-subject fMRI data

algorithm for posterior inference, we develop a suitable variational Bayes algo- rithm that does not rely on numerical integration but rather find a suitable ap- proximation of the true posterior density. Variational Bayes methods have been employed successfully in Bayesian models for single-subject fMRI data [Flandin and Penny (2007), Harrison and Green (2010), Penny, Kiebel and Friston (2003), Penny, Trujillo-Barreto and Friston (2005), Woolrich, Behrens and Smith (2004)]. Typically, these approaches provide good estimates of means, although they tend to underestimate posterior variances and also to poorly estimate the correlation structure of the data [Bishop (2006), Rue, Martino and Chopin (2009)]. In a com- parative study on simulated data, we show that the variational Bayes algorithm achieves robust estimation results at much reduced computational costs, therefore allowing scalability of our methods. Additionally, we demonstrate on synthetic data how our unified, single-stage, multiple-subject modeling approach, with vari- ational Bayes inference, achieves improved estimation performance with respect to two-stage approaches.
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A Better Looking Brain: Image Pre-Processing Approaches for fMRI Data

A Better Looking Brain: Image Pre-Processing Approaches for fMRI Data

In order to derive the functional templates, fMRI data is decomposed into multiple spatial inde- pendent components (intrinsic networks) using group spatial ICA implemented within the GIFT toolbox (Calhoun et al., 2001b) available online (http://icatb.sourceforge.net/). ICA is data- driven method that only requires one parameter to be set prior to application - number of desired independent components. In our approach, we utilize a high model order of 50 components for extracting large number of intrinsic networks. A recent study by Abou Elseoud et al. (2010) ex- plains the effects of increasing model order on independent component analysis of resting state fMRI data. A low model order used for resting state is expected to yield a rather less informative set of large-scale brain networks. Whereas, there is loss of repeatability if a very high model order (¿100) is used. They also presented evidence depicting spatially overlapping components separated as different signal sources as a result of using model order of 30 - 40. The motivation to use a high model order also comes from recent studies (Allen et al., 2011, Biswal et al., 2010) that show separation of artefactual networks from meaningful components. A previous study (Calhoun et al., 2008) that utilized the same resting and task data sets, also summarized in Section 2.4.2, set a much lower model order - 19 components. However, we use a higher order keeping in sight a goal to develop a multi-network functional template, that is, to combine multiple known resting state networks into a single functional template that may further be used to co-register data from any cognitive paradigm.
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Hemodynamic-Informed Parcellation of fMRI Data in a Joint Detection Estimation Framework

Hemodynamic-Informed Parcellation of fMRI Data in a Joint Detection Estimation Framework

Identifying brain hemodynamics in event-related functional MRI (fMRI) data is a crucial issue to disentangle the vascular response from the neuronal activity in the BOLD signal. This question is usually addressed by estimating the so-called Hemodynamic Response Function (HRF). Voxelwise or region-/parcelwise inference schemes have been proposed to achieve this goal but so far all known contributions commit to pre-specified spatial supports for the hemodynamic territories by defining these supports either as individual voxels or a priori fixed brain parcels. In this paper, we introduce a Joint Parcellation-Detection-Estimation (JPDE) procedure that incorporates an adaptive parcel identification step based upon local hemodynamic properties. Efficient inference of both evoked activity, HRF shapes and supports is then achieved using variational approximations. Validation on synthetic and real fMRI data demonstrates the JPDE performance over standard detection estimation schemes and suggests it as a new brain exploration tool.
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Detection of Cognitive States from fMRI data using Machine Learning Techniques

Detection of Cognitive States from fMRI data using Machine Learning Techniques

Over the past decade functional Magnetic Reso- nance Imaging (fMRI) has emerged as a powerful technique to locate activity of human brain while engaged in a particular task or cognitive state. We consider the inverse problem of detecting the cog- nitive state of a human subject based on the fMRI data. We have explored classification techniques such as Gaussian Naive Bayes, k-Nearest Neighbour and Support Vector Machines. In order to reduce the very high dimensional fMRI data, we have used three feature selection strategies. Dis- criminating features and activity based features were used to select features for the problem of identifying the instantaneous cognitive state given a single fMRI scan and correlation based features were used when fMRI data from a single time in- terval was given. A case study of visuo-motor se- quence learning is presented. The set of cognitive states we are interested in detecting are whether the subject has learnt a sequence, and if the subject is paying attention only towards the position or to- wards both the color and position of the visual stimuli. We have successfully used correlation based features to detect position-color related cog- nitive states with 80% accuracy and the cognitive states related to learning with 62.5% accuracy.
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Knowledge Discovery through Computational Methods on EEG and fMRI Data

Knowledge Discovery through Computational Methods on EEG and fMRI Data

is a generalization of multiple linear regression models when there is a case of more than one dependent variable being involved. The GLM is used to determine whether the means of two or more groups differ. While using GLM to analyse the EEG or fMRI data, it is required to parametrize the data. On the other hand, ICA allows one to explore the factors that contribute the data alone. The authors in [1] study fMRI which is a noninvasive method to understand the state of ones brain. Moreover, it has excellent spatial resolution and the experiment can be repeated any number of times. But fMRI lacks temporal resolution. However, this is compensated by EEG. fMRI might not be able to capture the immediate changes in brain state as it is a slower experiment compared to EEG. The latter records brain wave patterns on a continuous basis and the level of activity or an abnormality at a point in time can be easily monitored. In this paper, ICA is considered to be a superior method of analysis over Principal Component Analysis, which de-correlates the data. ICA involves higher-order statistics to achieve independence. The ICA algorithms used on EEG and fMRI data are InfoMax and FastICA. The interesting feature of ICA is that it is able to disentangle the mixed brain signal and bring out the important signals. It is considered a powerful way to remove artefacts from EEG data. While GLM tends to generalize to a method suitable for drawing inferences from multiple subjects, ICA requires significant clustering effort even if components share similarities across different subjects. Temporal ICA is useful for disentangling mixed EEG signals and also finds use in the preprocessing stage of simultaneously acquired EEGfMRI data. Joint ICA is another approach, which enables the joint decomposition of multi-modal data that have been collected from the same sample of subjects. Since fMRI images are accumulative and cannot capture brain activity at a particular point in time, it is assumed that many fMRI networks affect a particular EEG feature. And so, one way of addressing this problem is by employing multiple regression where modulations are performed on a trial by trial basis on all fMRI for the prediction of EEG activity.
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Temporally constrained ICA with threshold and its application to fMRI data

Temporally constrained ICA with threshold and its application to fMRI data

unmixing space, is smaller than the threshold. For the TCICA-Thres method, the threshold of ρ is an important parameter that is similar to the weight between the TCICA part and the FastICA part. A bigger ρ indicates a higher weight of TCICA and a smaller weight of Fas- tICA. However, it is impossible in most applications to obtain accurate prior temporal information in fMRI data before ICA processing. Therefore, a bigger threshold does not mean better results. On the other hand, if the threshold is too small, more irrelevant components may be included during FastICA iteration for TCICA-Thres. Taking these aspects into consideration, the threshold of ρ was set to an empirical value of 0.5, which meant that TCICA and FastICA had the same weight in the TCICA-Thres algorithm. Moreover, because the number of components that are related to a task in fMRI data is unknown, the threshold is also used to determine whether the extracted IC is related to the task. The esti- mated component was considered a task-related compo- nent when the correlation coefficient between the temporal reference and the time course of IC was greater than 0.5. Otherwise, the TCICA-Thres algorithm will terminate. The TCICA algorithm is terminated when the correlation between the time course of IC and the temporal reference is lower than 0.5. The results from both simulated and real fMRI experiments demon- strate that the value of threshold works well.
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Thought experiment: Decoding cognitive processes from the fMRI data of one individual

Thought experiment: Decoding cognitive processes from the fMRI data of one individual

Cognitive processes, such as the generation of language, can be mapped onto the brain using fMRI. These maps can in turn be used for decoding the respective processes from the brain activation patterns. Given individual variations in brain anatomy and organization, ana- lyzes on the level of the single person are important to improve our understanding of how cognitive processes correspond to patterns of brain activity. They also allow to advance clin- ical applications of fMRI, because in the clinical setting making diagnoses for single cases is imperative. In the present study, we used mental imagery tasks to investigate language pro- duction, motor functions, visuo-spatial memory, face processing, and resting-state activity in a single person. Analysis methods were based on similarity metrics, including correlations between training and test data, as well as correlations with maps from the NeuroSynth meta-analysis. The goal was to make accurate predictions regarding the cognitive domain (e.g. language) and the specific content (e.g. animal names) of single 30-second blocks. Four teams used the dataset, each blinded regarding the true labels of the test data. Results showed that the similarity metrics allowed to reach the highest degrees of accuracy when predicting the cognitive domain of a block. Overall, 23 of the 25 test blocks could be correctly predicted by three of the four teams. Excluding the unspecific rest condition, up to 10 out of 20 blocks could be successfully decoded regarding their specific content. The study shows how the information contained in a single fMRI session and in each of its single blocks can allow to draw inferences about the cognitive processes an individual engaged in. Simple methods like correlations between blocks of fMRI data can serve as highly reliable
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Temporal-spatial modeling for fMRI data

Temporal-spatial modeling for fMRI data

stimulus sequence and an estimated HRF. The coefficient β j shows the magnitude of the linear dependence of the observed fMRI signal at the jth voxel on the corrected stimuli. Here the HRF is modeled as a two-parameter Gamma distribution whose Fourier transform can be evaluated analytically. The two parameters of the HRF, which vary at different voxels, are estimated simultaneously when estimating β j . The analysis in this work is carried out in frequency domain too and the “non-linearity” resides in its iterative way for estimating the parameters. Residual images are also obtained in this work. But different from traditional SPM, where random field theory is used for global thresholding to detect the activation regions, this work uses focused tests of activation. Namely, the detection is focused on the potential activation areas given by neuroscientists. In each of such region of interest (ROI), residual spatial autocorrelation functions (ACF) are modeled by exponential and Gaussian forms. This modeling incorporates both the spatial and temporal features of the fMRI data and gives the estimation of the variance- covariance matrix W of the estimated β. In each ROI, under the null hypothesis (no ˆ any effect in that region) the statistic β ˆ 0 W −1 β ˆ follows a χ 2 -distribution with degrees of
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