Model-Free Analysis of Single fMRI Time Series Based on Spatial Synchronization

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Model-Free Analysis of Single fMRI Time Series Based

on Spatial Synchronization

Ngoc Dung Bui

Management and Science

University, Malaysia

David Asirvatharm

University of Malaya,

Malaysia

MdGaparMd Johar

Management and Science

University, Malaysia

Siew Ann Cheong

Nanyang Technological

University

Abstract – We propose a new model-free approach to analyze fMRI time series data. Instead of testing a parametric model for statistical significance and thereby obtaining an activation map of the brain, we use synchronization of fMRI voxels as the basis of our analysis. Synchronization between large voxel cross sections are expected when the brain responds to a stimulus. Therefore, the dependency of analysis to the baseline assumptions can be avoided by using a definition of synchronization in which the phenomenon is insensitive to the choice of thresholds over a wide range. We also provide an example on how a functional

picture of the brain’s response to a visual-motor task can be obtained by examining differential fractional synchronizations in the primary motor cortex, the supplementary motor cortex, the primary visual cortex, and the occipital cortex.

Keywords – fMRI Time Series, Model-Free Approach, Negative Synchronization, Positive Synchronization, Synchronization Patterns.

I. I

NTRODUCTION

Functional Magnetic Resonance imaging (fMRI) is a powerful tool to study brain activity by measuring the Blood Oxygen Level Dependent (BOLD) signal [1]. During a fMRI experiment, a series of brain images are acquired with each image consisting of thousands of voxels while the subject performs a series of tasks. Changes in themeasured signal betweenindividual images are then usedto make inferences concerning task-related activationsin the brain. By comparing the brain responses to different tasks in a single subject, and also to the same task in different subjects, fMRI experiments have allowed us to better understand how the human brain works [2]. In particular,there is great potential for using fMRI to characterize brain disorders such as Alzheimer’s disease [3],[ 4],Parkinson’s disease[5], and schizophrenia[6].

Neuroscientists have long known that the brain is physiologically similar from one individual to another. We thus expect brain activation patterns to be largely similar for lower-level brain functions such as vision or motor responses. Indeed, a common theme in fMRI studies is to find a common activity model. In this method, all subjects are spatially normalized to a common template to create the voxel correspondence [7]. Thereafter, the activation profiles of different Region of Interest ROIs are averaged across subjects. However, empirical evidences reveal that activation varies strongly from subject to subject [8],[9] and from group to group [3]. Therefore, simply normalizing data across subjects and pooling the normalized data into ROI super-voxels [10] is not necessarily the best. In our view, averaging multiple fMRI

time series should only be done after getting deeper understand the sources of variations in the data.

In a typical fMRI data set, it is common to find a nonzero BOLD signal in a large cross section of voxels. Thecommon practice is first to perform statistical parametric model (SPM) analysis of each voxel independently. The estimated parameters from this analysis can be used to create images of brain activation, but more importantly, they can go into statistics tests to be assessed for significance [7]. However, this approach does not take into account the spatial nature of the image data and does not take advantage of the spatially contiguous patterns of activation. Moreover, the time series of individual voxels frequently appear very noisy, making ithard to reliably identify the responses to tasks.These problemsare partially solved by averaging the fMRI time series over large brain areas [11]. However, the selection of brain area is subjective, and there are many existing anatomical maps of the brain [12], [13]. This selection problem can be solved by statistically clustering voxels whose activation patterns are similar before averaging them [14, 15].Nevertheless with simple averaging, the information contained in all voxels is not fully exploited.

In this paper, we present in Section 2 a model-free approach to analyze fMRI data. Instead of using SPM analysis, which is based on the general linear model (GLM), to identify voxels that are significantly activated [16], we observe that for a brain area to be strongly activated, the voxel in this area must be synchronized. If we look at synchronization instead of activation, there is no need to assume any model for the time series data.In Section 3, we will also show that there is no need to havean accurate baseline. The synchronization patterns of different parts of the brain then give us a functional picture of how it responds to stimuli. Finally, we make a conclusion in Section 4.

II. M

ATERIALS AND

M

ETHODS

A. Subjects and tasks

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structure images were obtained in a series of three to four separate T1-weighted MP-RAGE anatomic images with following parameters: resolution = 1 × 1 × 1.25 mm; TR = 9.7 ms; TE = 4 ms; flip angle = 10°; TI = 20 ms; TD = 500 ms. Functional images were obtained using asymmetric spin-echo sequence sensitive to BOLD contrast with following parameters: TR=2.68s; 3.75 × 3.75 mm in-plane resolution; T2* evolution time = 50ms; alpha = 90°. Whole brain volumes were obtained using 16 contiguous 8-mm think slices with parallel to the plane of the anterior-posterior commissure. The raw data were received from the fMRI Data Center at Dartmouth College and preprocessed using SPM8 [18]. Images were motion corrected and normalized to coordinates of Talairach and Tournoux [12]. They were also smoothed with a 4-mm Gaussian kernel to decrease spatial noise.

We apply group independent component analysis (ICA) [19] on the group of subjects to extract the activation areas. Recent studies showed that ICA can be used to separate fMRI data into meaningful components, classified as task-related, transiently task-related and motion-related [20]. Thesensory-motor experiment suggests that the regions of interest (ROIs) are those associated with visual processing and motor response. We created a brain mask consisting of these regions using the Brodmann template. After applying ICA, an activation map consisting of voxels whose spatial map shows the highest correlation with the mask was selected. The ROIs identified were the primary motor cortex (PMC, BA4, 1267 voxels), the supplementary motor area (SMA, BA6, 3601 voxels),the primary visual cortex (PVC, BA17, 1137 voxels), and the

extrastriate visual cortical areas (EVC, BA18 and BA19,

5949 voxels).

B. Approach

In a typical fMRI experiment, a subject is scanned while he or she is presented with a stimulus while in a rest or fixation state. The task-induced activation profile frequently shows an activity peak shortly after the stimulation, and an activity dip at the end of the stimulation episode. There is frequently also a dip in activity before the activation. For repeated presentations of tasks, it is not easy to determine the baseline level of activity [21], because the activity triggered by a stimulus may not have relaxed back to the baseline level before the next stimulus is presented. In [3], Buckner et al. assumed that the brain responses to different stimuli are linearly additive. They then presented the stimuli with different delays to their subjects, and thereafter perform linear deconvolution to extract the underlying activation profile. This procedure will also determine the baseline at the same time. However, there is no evidence that the brain responses to multiple stimuli are additive [22]. In fact, given how strongly nonlinear individual neurons behave, it is doubtful that the GLM can represent anything more than a first approximation. When we assume that brain responses are linearly additive when they are in fact not, two possible problems can arise. First, if two overlapping responses enhance each other, then subtracting one response from the sum leads to an overestimation of the other response. Second, if the two overlapping responses

suppress each other, then subtracting one response from the sum leads to an underestimation of, or even negative amplitude for the other response. Both scenarios can be puzzling. One of the goals in this study is therefore to analyze fMRI data without assuming linear additivity between responses.

In general, we start analyzing fMRI data by grouping voxels into those whose signals we are interestedin and those whose signals we are not interested in [19]. Signals that we deemed uninteresting may be physiology-related or motion-related. Normally, the task presented to the subject triggers a signal that rises distinctively above the noise level. Such signals can therefore be used to distinguish between actual brain activation and noise. More importantly, isolated voxels are hardly responding to a task. Activated voxels are almost always grouped into active regions in the brain. For a particular active region, many voxels must be activated at the same or similar times in order for the response to be strong. This implies that a large cross section of voxels must be synchronized in response to a stimulus.These cross sections of voxels can be discovered through statistical clustering based on the magnitude of their responses to the experiment [14].

C. Synchronization

In the literature, we find different ways to measure synchronization, such as coherence [23]and the duration of coupling between a pair of (neurophysiological) processes [24]. Coherence measures synchronization in the frequency domain, by comparing the average cross and power spectra of the two time series across the low-frequency band. As such, it is given by.

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For both coherence and duration of coupling measures of synchronization, we need to choose a time window over which the frequency spectrum is measured. If we use too large a time window, then brief synchronizations will be missed. If we use too small a time window, the frequency spectrum obtained becomes too sparse and again brief synchronizations will be missed. In these two synchronization measures, no assumption is made about the synchronized cross section, i.e. so long as the synchronization is persistent in time, then it can be detected even if only two out of K voxels are synchronized. However, as we have explained above, physiologically meaningful synchronizations must present large spatial cross sections. In this paper, we show how we can take advantage of this large spatial cross section of synchronized voxels to detect even brief synchronizations. To do so, we adopt a simpler definition of synchronization. Let xi(t) and xj(t) be the BOLD signals from two voxels i

and j.Their standardized fMRI activities are defined as following:

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It is observedthat the activities of two voxels tend to rise and dip together (synchronized) when the activities are strong, and move independently of each other (desynchronized) when the activities are weak. Therefore, it is likely that strong activities represent signals induced by stimuli, whereas the weak noise-like activities represent intrinsic levels of brain activation. To ensure that we pick up only stimulation signals, we count two voxels as being instantaneously synchronized only if they emerge together from a rejection band. Except in Section 3.1, where we vary the size of the rejection band, we set the rejection band to be(− , + )for the rest of the paper, where

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Fig.1. The mean time course (black) of the primary motor cortex (BA4) in Alzheimer subject 2. Also shown on the plot are the dynamic standard deviation ( )and its negative value,− ( ). The standardized fMRI signals of most voxels lie within the interval(− ( ), + ( )). Finally, we show the standardized fMRI signals of voxel 50 (green) and voxel 600 (blue). Standardized fMRI activity that goes above the average standard deviation can be considered stronger-than-average activation, whereas fMRI activity that goes below – can be considered weaker-than-average activitation.

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( ) and ( )represent the spatial cross sections of positive and negative synchronizations.

In Figure 2 we plot the positive and negative synchronization fractions on top of the mean time course. The positive synchronization peaks coincide withpeaks of the mean time course and the negative synchronization peaks coincide with troughs of the mean time course. The relative strengths of the synchronization peaks are also similar to the relative strengths of the mean time course peaks. This gives us assurance that the synchronization patterns observed are functionally meaningful, or at least as meaningful as the mean time course in measuring cognitive functions. Ultimately, no fMRI experiment can say for sure that hemodynamically active regions of the brain are involved in cognition, whereas hemodynamically inactive regions are not, unless high spatial resolution electroencephalogram (EEG) or magnetoencephalogram (MEG) data are also simultaneously recorded for comparison.

Fig.2. The synchronization patterns of BA4 in Alzheimer subject 2. In this figure, the black curve is the mean time course, the red curve is the positive synchronization fraction (voxels with standardized fMRI activity exceeding+ ), and the blue curve is the negative synchronization fraction (voxels with standardized fMRI activity below– ).

Fig.3. Positive (top) and negative (middle) synchronization patterns of four Brodmann areas (primary motor cortex (PMC) (red), supplementary motor area (SMA) (green), primary visual cortex (PVC) (blue), and extrastriate visual cortical areas (EVC) (cyan) in Alzheimer subject 2. These synchronization patterns in the four ROIs can be better visualized in a single color map (bottom), where blue indicates strong negative synchronization and red indicates strong positive synchronization. In this color map, green indicates the absence of strong positive or negative synchronizations.

D. Differentiated functional response

But what do all these synchronization patterns mean? Let us start by giving an analogy from microelectronics. In a microprocessor we find many transistors. If these transistors can only turn on or turn off altogether, then the microprocessor has no information processing capability. For the microprocessor to process information we must have some transistors in the on state and other transistors in the off state at one given time and a different pattern of transistors that are on and off at a later time. We believe this differentiated response to information must also happen in the brain. Therefore we look out for such differentiated responses in different ROIs in the brain. There are two ways for the responses of different ROIs to be different. First we can have one ROI synchronize before and another ROI does so. Second we can have one ROI synchronize more strongly than another ROI. In fMRI experiments, it may be difficult to see the first type of differentiation because of the low time resolution, so we concentrate on looking for the second type of differentiated response, as shown in Figure 3.

III. R

ESULTS

As mentioned earlier, when a brain area becomes activated, not only will there be a statistically significant increase in blood flow that follows, but there will also increasesynchronization between different points in the brain area. This can be seen in Figure 2 (top and middle), where activations peaks are follow by inhibition peaks in all ROIs. To be sure that the synchronization we see is functionally meaningful, we need to check how sensitive it is to the choice of threshold. In Figure 4, we show the (12)

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fractional synchronizations for three different thresholds. The positions of the peaks do not change, and the relative strengths of peaks also do not change much. More importantly, the absolute strengths of most peaks remain the same for thresholds up to approximately . For higher thresholds, the absolute strengths of most peaks drop dramatically. This tells us that there is a natural cutoff to the threshold we can use to measure synchronization. Below the cutoff the fractional synchronizations measured are highly robust.

Referringagain to Figure 3, we see that all 4 ROIs are positively synchronized for certain stimulation episodes. In other episodes we can have the motor ROIs becoming synchronized when the visual ROIs are not, and vice versa. In the bottom of Figure 3, blue indicates negative synchronization while red indicates positive synchronization. If an ROI is green in the color map at a given time point, then there is no significant positive or negative synchronizations. As we can see, at about t = 25, 130, 180 and 230s, there are strong positive synchronization in all ROIs, whereas at about t = 150s, there is strong negative synchronization in all ROIs.At about t = 10, 70, 100, 220s, there arenegative synchronizations of motor areas followed by visual areas, whereas at t = 180 and 280s, there are positive synchronizations of the motor areas followed by visual areas. Finally, at about t = 80 and 240s, there arepositive synchronizations of visual areas followed by motor areas. Therefore, we see both differentiated and undifferentiated responses in the subject. For the differentiated responses, we sometimes find motor areas leading visual areas, and sometimes the other way round.

Fig.4. The positive (top) and negative (bottom) synchronization fractions obtained for BA4 in Alzheimer

subject 2 with three different thresholds.

IV. C

ONCLUSION

We have presented a model-free approach to analyzing fMRI datato find the meaningful functional differences between areas in the brain. Instead of looking for tell-tale average activation profiles, we examinesynchronization patterns in different parts of the brain. In this method, we have shown that the synchronization has advantages over

the mean time course because there is no need to determine the baseline accurately or beforehand. Because of positions and relative strengths of synchronization peaks are extremely robust, we can construct reliable and meaningful functional pictures of the brain’s responses even if we do not get the magnitudes of the fractional synchronizations completely right. While the approach has been illustrated using fMRI data in this paper, synchronization analyses can also be applied to electroencephalogram (EEG) or magnetoencephalogram (MEG) data.

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A

UTHOR

’

S

P

ROFILE

Ngoc Dung Bui

received the BS and MS degrees in information

technology from Military Technical Academy,

Vietnam in 2002 and 2004, respectively. He is currently a Ph.D. candidate in Management and Science University, Malaysia. His current research interests include machine learning, computer vision and brain informatics.

David Asirvatharm

received the BS and MS degrees in computer science from University of Malaya and Brunel University, respectively, and the Ph.D degree in information

technology from the University Multimedia

Malaysia. He is a Director Information Technology of Center for Information Technology, University of Malaya, Malaysia.

MdGaparMdJohar

is Vice President Academic and Director of

Information Technology and Innovation Center of Management and Science University, Malaysia. He holds PhD in Computer Science, MSc in Data Engineering and BSc (Hons) in Computer Science. His research interests include learning content management system, knowledge management system, e-commerce, image processing, character recognition and healthcare management system.

Dr. Cheong Siew Ann

was born in Singapore in 1969. After getting

through his primary, secondary, and junior college education in AmaKeng Primary School, the Chinese High School, and Hwa Chong Junior College respectively, and thereafter a contract service with the Singapore Armed Forces, he studied physics at the National University of Singapore. He graduated in 1997 with a BSc (Hons) degree in physics, and went on to obtain his PhD in theoretical