Head Motion Correction

The head motion during MEG experiments will affect the accuracy of source localiza-tion. The simplest solution is that fixing the subject’s head. However, this may cause many other problems such as fatigue. And to many people, like Parkinson’s patients or to chil-dren, it is difficult for them to keep heads fixed. For the above reasons, many algorithm proposed to solve this problem.

The easiest way is to discard the recordings with head motion. But this leads to longer time for experiments and may cause many other artifacts. Another approach is to correct head motion by incorporating the effect of the head motion into the magnetic field forward calculations [24, 25]. This may cause another problem of information loss.

Usually, the resolution of the solution to the MEG inverse problem can be improved by increasing the number of MEG sensors. The sensor number can only increase to some limited number. But this phenomenon is different to beamformer. To the problem about the sensor number needed [26, 27], we can understand that the sensor number of beamformer can be significantly large. The detail description is stated in Chapter 4.

A newly-proposed novel method can improve the localization accuracy by conceptually increasing sensor numbers, instead of using motion correction [34]. By combining record-ings of different head poses, this algorithm can not only reduce the error induced from head motion but simultaneously improve the accuracy of source localization by conceptually in-creasing sensor numbers; i.e., super resolution. We describe this algorithm in the below sections.

2.3.1 Stabilized Linear Model

Starting from the same simplified form of MEG recordings, we assume that there are E epochs measured in an MEG study and there are N data samples collected for each epoch.

Let m_jbe the SxN matrix that denotes the epoch j of recordings and S is the MEG sensor number, then

m_j = L_jqs + n_j, j = 1, . . . , E (2.5)

where L_j is the lead field matrix and s represents the dipole moment at each dipole loca-tion. If there exists head motion during the period of recordings acquisition, Lj and s will not remain the same for each epoch. Consequently, that directly averaging all epochs of recordings is incorrect and that may blurs the data and leads to a location bias.

In [34], a proposed method, Stabilized Linear Model (SLIM), can solve the problem of head motion. By continuously tracking the head pose, we can get the relationship of magnetic MEG sensors to the head with different poses and this relationship can be mod-eled as the forward problem which is necessary for the inverse problem [21]. Using SLIM, we can ransform the head motion during recordings acquisition into the increase of MEG sensor number. And by this concept, we can consider the dipole moment remains the same and ignore the subindex j. We can see this concept in Figure 2.2. Then, we can virtually have multiple sets of sensors measuring the MEG signals, m_j, j = 1, ..., E, generated from dipoles with moment s. The stabilized linear model is then obtained by combining the forward model for each epoch



Using SLIM, we can improve the accuracy of source localization by conceptually in-creasing the sensor number. Even the recordings with head motion, by combining multiple set of recordings with different head poses, we can transform the localization bias induced by head motion into the improvement of the accuracy of source localization.

2.3.2 Solutions to Inverse Problem with Maximum Contrast Beam-former

Because the resolution of the solution to the MEG inverse problem can be improved by increasing the number of MEG sensors, we apply the stabilized linear model into MCB to get higher accuracy of source localization.

Then we modified Eq (2.6) by l = Lrq where L is lead field matrix and l is lead field,

Figure 2.2: This graph shows the concept of the algorithm of Stabilized Linear Model.

If two epochs of MEG recordings with head motion are measured, we can represent the recordings as (a). If we transform the head motion into the increase of the MEG sensor number, by aligning the head in gray and in black in (a), we get (b). [34]

we can get

where ˜m, ˜l and ˜n are all the combination from multiple sets of epochs with different head poses.

With Eq (2.7), the Beamformer spatial filter becomes w˜_θ = ( ˜C + αI)⁻¹˜lθ

˜l^t_θ( ˜C + αI)⁻¹˜lθ

(2.11)

where ˜C = cov{ ˜m(t)}.

With this linear model, we can virtually increase the sensor number of MCB model and get higher source localization accuracy, which can be called as ”super resolution”.

Simultaneously, it can solve the problem induced from head motion.

Experiment Results

3.1 Material

We used three kinds of data to verify the proposed methods depicted in Chapter 2, including simulation, phantom and the real measurement from the experiment of gender discrimination. For each proposed method, we select the appropriate data for validation.

We will describe some information of these data in the below statements.

I. MEG Device

A whole head MEG system at the Taipei Veterans General Hospital (Neuromag Vectorview 306 , Neuromag Ltd., Helsinki, Finland) is used for recording of the minute magnetic field generated by electrical activity within the living human brain.

The MEG system is placed in a magnetically shielded room and has capability of 306 channels simultaneous recording at 102 distinct sites, 24 bits analog to digital con-version, and up-to-8 kHz sampling rate which is sufficient to probe the fast dynamic changes inside human brains.

II. Anatomical Data

The Magnetic Resonance Imaging (MRI) images were from the 1.5T GE scanner at the Taipei Veterans General Hospital with TR = 8.672 ms, TE=1.86 ms, FOV = 26x26x10cm³, matrix size = 256x256, slices = 124, voxel size = 1.02x1.02x1.5mm³. III. Simulations

We simulate the MEG recordings by the forward model adding some noises with a dipole or dipoles given in advance. There are two kind of noises, background sources and sensor noises. We simulate background sources as random dipoles with zero-mean Gaussian strength and uniformly distributed in the putative sphere of head model. The variances of sensor noises are estimated from the empty room recordings of the MEG system. We also use 1 kHz sampling rate as sampling frequency of the simulated recordings. Before data analysis, we do preprocessing depicted in Section 3.2.

IV. Phantom Data

We use MEG phantom (Neuromag Ltd., Finland) to validate the localization ac-curacy of the proposed methods. Eight fixed current dipoles located on two orthogo-nal planes were activated sequentially to generate magnetic recordings. The strength of each dipole was set to be 100 nAm. For each dipoles, there are four combination of 20 trials from total 80 trials.We processed the phantom signals with bandpass filter and baseline correction. The device and configuration of MEG phantom are shown in Figure 3.1.

Figure 3.1: The device of MEG phantom. We can activate the dipole at the location of interest and retrieve the recordings of phantom data.

V. Experiment Paradigm of Gender Discrimination

Twenty normal subjects and twelve bipolar disorder patients participate this ex-periment. Face images are grayscale photographs of faces, depicting neutral, angry, happy and sad (Table 3.1). 306 channels were recorded during passive observation of face images in a electrically shielded MEG room. The task is to specify the gender of the presented faces that prevents the subject’s explicit recognition or categorization of the emotion expressed. Subjects are instructed to lift the right or left index finger while recognizing the presented face image as female or male. For each condition,

Figure 3.2: The dipole of phantom is generated by a triangular conductor with two radial lines connected by a tangential line. The location of each dipole is shown in this figure.

about 288 trials, 20 minutes are retrieved. The whole experiment paradigm is shown in Figure 3.3. We take the recordings of one normal subject for analysis. We also measure the finger lifting recordings while the subject is discriminating the gender of the presented faces. Both two kinds of data are included for the validation of our algorithms.

Figure 3.3: The experiment paradigm of gender discrimination. The task was to specify the gender of the presented faces. Subjects were instructed to lift the right or left index finger while recognizing the presented face image as female or male

Table 3.1: The stimuli were grayscale photographs of faces, depicting neutral, angry, happy and sad. Every kind of stimuli can also separate into male and female. The number of female stimuli is larger than the number of male stimuli.

state stimuli

neutral male

female

angry male

female

happy male

female

sad male

female