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Subsections


4.3 fMRI Data

4.3.1 Design of an fMRI Experiment

There are at least three aspects to the design of an fMRI experiment: (1) the underlying psychological question, (2) the MR physics that will drive the data collection, and (3) traditional statistical design issues. These factors are not exclusive of each other and must be carefully considered prior to the initiation of the study.

The psychological component of design depends on the type of experimental subjects in question as well as the nature and location of the expected response. For example, regions of brain activity could be explored for a single group of subjects, or the location and extent of brain activation could be compared in two different subject groups. The experimental task must also be designed in order to elicit a functional response specific to the area of interest in the brain. A control state (such as a fixation in a visually guided saccade task) is typically alternated with a functional state (the saccade) in order to compare the two states and find the differentially active brain areas.

The MR physics component depends on the nature of the psychological stimuli, the particular MR scanner being used, and the location of the expected response. Several scanning parameters, such as the number and orientation of slices to be collected, the echo time, $ T_E$, the time of repetition, $ T_R$, the flip angle, and others, must be first chosen. The physics of the scan will depend on these chosen parameters. The physical method for collecting each slice of data, termed the pulse sequence, must also be selected. The pulse sequence is a small program run in the scanner to manipulate the magnetic and rf fields, and is thus dependent on the type of MR scanner and the pulse sequences available for use.

The statistical aspects of design will help to determine how the data will be analyzed after collection. For example, as mentioned above, the experimental design is often set so that the task state is alternated with a control state. The two conditions can then be statistically compared using methods which rely on hypothesis testing (such as $ t$-tests). This type of experimental design is called a block design. The block design is robust in that many repetitions of the two conditions can be carried out, and the experimenter can then average all trials for each voxel. Although this technique can find spatial areas of activation, it has the disadvantage of losing most temporal aspects of the data.

Figure 4.4: BOLD hemodynamic response curve showing the expected contrast changes elicited from a single event. Because the contrast changes are actually due to blood flow changes rather than a direct measure of neural activity, the time scale over which they occur is relatively slow
\includegraphics[width=63mm,clip]{text/4-4/fig4.eps}

In order to capture the time-dependent features of the data as well as the spatial aspects, single trial fMRI experiments have recently become popular. These experiments examine fMRI signal changes over time as the task is being performed (on a voxel-by-voxel basis) rather than relying on the averaging of large time blocks. The results from these single trial experiments are generally not as robust as those for block designs. Furthermore, since fMRI data is typically very noisy, the data must be pre-processed prior to analysis. The techniques for analyzing single trial fMRI data often model those used for processing evoked potentials EEG data (such as filtering or time-averaging of trials). Because of this, single trial fMRI experiments have often been mislabeled as ''event-related'' fMRI experiment. Figure 4.4 shows the temporal BOLD response that is generally expected from these types of experiments.

4.3.2 Data Collection

The raw data from an MR scanner is spatial frequency data. That is, the data are the coefficients of the Fourier representation of the object being imaged. Alternatively we can say that the data are the inverse Fourier transform of the object. The spatial frequency domain has been called ''Fourier Space'', ''frequency space'', or most popularly ''k-space''. The process of taking the inverse Fourier transform to obtain the image has been termed ''data reconstruction''. Letting $ \mathcal{F}$ be the Fourier transform, we have for an $ n\times m$ pixel image I,

$\displaystyle \notag {\mathcal F} (I) = \widehat{I}\left(k_x,k_y\right) = n^{-1}m^{-1} \sum_x^n\sum_y^m I(x,y)\exp(-i2\pi(xk_x + yk_y))$    

In k-space, the low frequencies are located in the center of the image with the frequencies increasing outward with distance from the origin. In a typical k-space plot (see Fig. 4.5), the bulky features of the image lie in the lower frequencies of k-space while the higher frequencies contain the details of the image. In fMRI both the low and high frequency information are important, and the pulse sequence should be designed accordingly.

Figure 4.5: Collected fMRI data. The plot on the left shows the modulus of the k-space data, and the plot on the right shows the modulus of the image. Darker pixels indicate larger values (the opposite of the ''radiological convention'' derived from X-ray images on photographic film)
\includegraphics[width=\textwidth,clip]{text/4-4/fig5.eps}

A typical fMRI data set might consist of a $ 128$ by $ 128$ array of $ 16\,$bit complex values recorded for each of $ 32$ two-dimensional slices at each of $ 450\,$time points spaced about $ 1.5\,$seconds apart. This yields a data set of $ \,2\times 2\times 128\times 128\times 32\times
450=943{,}718{,}400\,$bytes, that is approximately $ 1\,$gigabyte of data collected in less than $ 12\,$minutes. If many experiments are performed on a single subject within the period of an hour or so, and several subjects are examined over time, the necessary storage requirements can become quite extensive. In one of our current studies, we anticipate collecting a total of about $ 700\,$GB of data. To help deal with this quantity, offline data storage systems are useful. For example, optical disks, CDs, or DVDs can be used to store large amounts of data with minimal effort.

4.3.3 Sources of Bias and Variance in the Data

Areas of brain activity that are found due to specific tasks are dependent on the image to image changes in the measurements within a voxel. Therefore, to produce valid results these changes must be specifically attributable to functional differences in the brain elicited by the performed tasks. Unfortunately, fMRI data is beset with many sources of bias and variability, which can lead to erroneous regions of brain activity and false conclusions about the study. Problems in the data can arise from many sources including the MR scanner itself, the experimental subject, and external interference. Each of these will be discussed with a brief description of the errors that they introduce into the data. The sources of noise in fMRI data can be quite extensive. Although many are covered here, this summary is not exhaustive.

4.3.3.1 Noise from the Equipment

One main source of bias and systematic variation in fMRI data arises from the MR scanner. The performance of an MR scanner can vary, which can introduce fluctuations in the data, even when the stability measures are well within the instrumental norms ([49]). Noise from the equipment can occur as systematic or random errors.

Sources of systematic error in the data from the equipment include DC shifts and Nyquist ghosts. DC shifts are also known as baseline errors. This source of data bias is caused by the miscalibration of the analog-to-digital (A/D) converter; the baseline value is not reported as zero. Nyquist ghosts, which are present only in echo-planar imaging, also produce systematic bias in the data. Echo-planar pulse sequences traverse k-space on a boustrophedonic path (back-and-forth as the ox plows the field). Nyquist ghosts are introduced through the mistiming of the oscillating magnetic gradients. The exact time at which the gradient crosses zero is incorrect. This timing error causes an aliasing effect in the reconstructed image and is most prominent in the phase-encode or $ y$ direction of the fMRI scan (leading to a ghost of the image repeated at the top and bottom of the true image). Both DC shift errors and Nyquist ghosts that are present in the fMRI data can be corrected to a reasonable extent.

Random errors from the equipment can also cause introduce problems in the fMRI data. One source of unpredictable instability results from inhomogeneities in the static magnetic field of the equipment. Magnetic field inhomogeneities have been reported as one of the most prominent sources of distortion in fMRI studies ([25]). Local variations in the static magnetic field during fMRI will lead to blurring and pixel shifts, which can introduce gross geometric distortions in the images. This problem is especially prominent at regional boundaries in the sample containing different magnetic susceptibility properties, for example, air-tissue interfaces around the frontal lobes and bone-tissue interfaces ([25,11]).

Additionally, random instability in the MR machine can result from imperfections in the B1 field. The B1 field is ideally a linear magnetic gradient that selects certain regions of tissue to be excited, thereby leading to the collection of single slices. Again, problems with this linear magnetic field can lead to blurring and geometric distortions in the data.

4.3.3.2 Noise from the Experimental Subject

As with other types of human studies, the experimental subjects can lead to large amounts of bias and variability in the data. While the subjects themselves have a great deal of intrinsic variability due to differences in brain sizes, shapes, and functionality in general, the subjects can also introduce additional variability that will ''drown out'' the desired results from brain activity if the investigator is not careful.

One important source of noise from the experimental subject is due to head motion. As previously described, BOLD fMRI studies compare very small regions of brain tissue across a sequence of images that are taken over the course of several minutes. While BOLD has the advantage that it requires no exogenous contrast agents, its measurable effects are very small. Typical changes in the MR signal due to BOLD are on the order of 1-5 %, making this technique highly susceptible to noise. If the subject makes a small movement during the scan, adjacent voxels, which can vary in signal value by more than $ 10\,{\%}$, cause distortions in the recorded signal information and can lead to false negative and false positive regions of activation ([10,8]).

Thus, to obtain valid fMRI data, the subject must remain motionless throughout the scanning period. Motion has been shown to be correlated with stimulus related events during visual and motion stimulation, thereby contributing to the likelihood that the computed regions of activation are due to motion artifact rather than neural activity ([22]). The amount of subject motion has also been shown to increase over time during the course of a scanning session ([20]). Additionally, children, elderly subjects, and subjects with mental disorders tend to move more than healthy young adults, thereby increasing the difficulty of studying these subjects using fMRI.

A second source of error from the experimental subject is due to ''physiological noise'', which is noise that results from the subject's heart beat and respiration. This type of complex noise is thought to interfere with the MR data through various mechanisms. For example, the pulsatile motions of the brain and cerebral spinal fluid (CSF) induced from pressure changes during both the cardiac and respiratory cycle lead to volume changes within the head which cause displacement of tissue; see [6]. Large organ movements due to respiration are also thought to cause fluctuations in the magnetic field, and effects of the oscillating cardiac cycle on the BOLD signal response are unknown; see, e.g., [24], [44], [6].

There are many sources of noise associated with the experimental subject. Thermal noise is caused by atomic vibration that occurs at any temperature above absolute zero. Susceptibility artifacts arise from local sharp changes in magnetic susceptibility; these occur at the boundaries of tissue types and are typically greatest at air/tissue boundaries. Chemical shift artifacts arise from small changes in the Larmor frequency caused by the local chemical environment. For example, hydrogen as a component of water has a resonant frequency at $ 3\,$Tesla that is about $ 200\,$Hz higher than hydrogen as a component of fat. Typical pulse sequences include a ''fat saturation pulse'' to eliminate this effect.

4.3.3.3 External Noise

Interference from outside sources can also lead to distortions and artifacts in the data. Examples of interference sources include mechanical vibrations from other equipment in the building or passing vehicles, and $ 60$ (or $ 50$) Hertz RF noise from other nearby electrical equipment. These sources are usually considered before installing the MR machines, and precautions are normally taken. For example, an isolated foundation will reduce the effect of external sources of vibration; copper shielding will reduce the effect of nearby sources of microwave radiation, and iron shielding will reduce the effect of nearby electrical equipment (and help contain the magnetic field itself).


next up previous contents index
Next: 4.4 Modeling and Analysis Up: 4. Functional Magnetic Resonance Previous: 4.2 Background