Additional MRI Vocabulary

1. On 2D and 3D MR image
The earlier posts on MRI/fMRI are not exhaustive and now I would like to add some more points. Let's begin by refreshing our memory on how an image is reconstructed (a 2D image, I mean). We have RF excitation pulses and we assign a gradient to localize the position in 2D space. Once we get acquire the data on the whole k-space trajectory, we have to inverse them through Inverse Fourier Transform to obtain the actual image.

Fig-1: An illustration showing a T1-weighted image transformed from its k-space equivalent data. Adapted from [1].

Okay, more basic vocabulary in MRI image formation: a slice, field of view, image matrix, slice thickness, and in-plane image resolution. Refer to the following diagram showing an anatomical or structural T₁ image. If we take just the 2D image of a particular slice, it is basically a matrix of 32 ´ 32 data points, each point is acquired consecutively for every row. With the in-plane resolution of 3 ´ 3 mm, the slice field of view 32 x 3 = 96 mm. In reality, the slice is captured with a certain thickness as well. The smallest entity of an MR image is called a voxel and its size represents the image resolution. To construct a three-dimensional image, we repeatedly acquire and combine 2D slices. Now, an acquired 3D image is also called a volume or simply an MR image. A voxel that has the same size on all three sides is called isotropic, e.g. 3 ´ 3 ´ 3 mm. One volume is acquired within one TR (repetition time).

Take note that although one volume is acquired within 1 TR, all slices are not captured at once. The way we acquire or record slices follows what we called slice order that is defined by the scanner operator. Essentially, the slice order can be ascending, descending, or interleaved. The ascending slice order means that the first slice will be captured first and the difference in time point between the first and the last would be almost 1 TR. The effect of this difference on subsequent statistical stages can be detrimental! I have mentioned the slice time correction as one of the preprocessing steps.

Fig-2: A slice is made up of rows of voxels. A volume is a collection of different slices acquired in one TR.

2. More On Functional Image
The structural image consists of only one 3D image or volume and it is a T₁-based image. On the other hand, a functional MRI image is a T₂*-weighted image in 4D, the fourth being the time information. What it means is that what we get in fMRI is a collection of volumes, each acquired one after the other at different time points. Note that a time point corresponds to one repetition time (TR), and thus, one volume per TR. To summarize: functional MRI gives us 3D space × time dataset. In practice, the first few points ~ 2 sec are removed because the hardware (magnet) isn't yet stable.

Refer to the following diagram. Suppose we select just a slice of every volume acquired in every 2 seconds (TR = 2 sec) for 5 minutes. There are 2 experimental conditions involved. And we select a region of interest or ROI as our apriori assumption to look for brain activation.

Fig-3: In functional MRI, volumes are recorded to obtain 4-dimensional data to represent the brain's dynamic. From [3].

3. What is Spatial Normalization?
As mentioned earlier, EPI is the most common fMRI method. Although the acquisition is quick, the resulting image quality with EPI is poor. Coregistration attempts to register these poor images to the T₁-weighted structural image of the same subject or patient. Why? Because the structural image carries a much higher spatial resolution. To do this, we simply perform a rigid body transformation with 6 or 7 DOF, consisting of 3 translation and 3 rotation. The goal of this transformation is to maximize the intensity-based correlation between two images, that is, the target and the reference image. This is achieved through an iterative process by minimizing some cost function.

A detailed example of 2D coregistration is as follows. We have two images, together with the information on the intensity values of every voxel. We then plot that in the histogram and assign a bin number. After that, we create another plot based on the bin number of images 1 and 2. Suppose a voxel at location [x, y] has a bin number 23 for the first image and a bin number 8 for the second image. We plot this particular voxel at [23, 8]. Once finished, we can see how this plot resembles a correlation map. If two images are aligned, the plot will be more or less a straight line.

If we then want to know the common activation happening across different subjects, we have to use a template or atlas. This is because individual brain differences can be huge. The most popular standard templates: the Talairach space and the MNI-152. I personally only use the MNI-152 template with a 2 mm resolution. Registering a structural scan of a person to the structural scan of a standard template is called normalization. Normalization is indeed crucial for group or higher-level analysis where different we want to combine different subjects. All these can be done with the currently available software. Klein et al. (NeuroImage, 2009) wrote a neat article on different methods of image registration available, e.g. SyN, ART, SPM, FNIRT, etc.

In general, spatial normalization essentially requires two steps.

1. The first step is to align the subject image to the standard template using affine transformation with 12 DOF. This is a linear process of translation, rotation, scaling and skewing, each for the three axes. Because the resolution of the image isn't always the same with the reference image, we need to perform interpolation somehow. 
2. The next step is to perform  non-linear transformation or geometric warping. This is a lengthy process that may require loads of iteration by minimizing some cost function (or maximizing certain 'similarity' measure). Ideally, this non-linear transformation makes use of a 'function' that is diffeomorphic. What it means is that the function maps a point in space U to exactly one and only one point in space V and the relationship is invertible. After normalization is done for all subjects, our position in space follows the standard coordinate.
3. Note that the MNI template (by Collins et al at the MNI) has different revisions. FSL uses the MNI nonlinear template obtained from 152 healthy adults. You can choose to use the 1mm or 2mm resolution.  
   

Fig-4: An illustration on how we divide an anatomical slice into 6 bins of different intensity. We need to 'match' bin-1 of the source image to bin-1 of the target image, etc.

4. Orientation Convention in MRI
I find this website is useful. Note that neurological convention (RAS) is the opposite of the traditional radiological convention (LAS). The summary is shown below. In other words, the axial or transverse plane is R-L x A-P plane, coronal is R-L x S-I plane and sagittal is A-P x S-I plane.

Fig-5: Orientation conventions in brain imaging. MRI uses the LAS convention i.e. the left brain is on the right-hand side.

Wait! There is another rule. Suppose you have conducted your experiments and gotten the raw DICOM images from the machine. These images are acquired following a certain convention as well. The following is useful, especially when you work with both AFNI and FSL. This convention dictates us how a row is constructed to a slice, then a volume.

Let's say we have an AFNI image with "orientation" RAI.  This means that:
a) Voxels ordered from: Right to Left to store a row.
b) Rows ordered from: Anterior to Posterior to store a slice.
c) Slices stored from: Inferior to Superior to store a volume.
Importing a DICOM volume using to3d will create an AFNI file with RAI orientation by default. Importing a DICOM volume using dcm2nii will create an NIFTI file with RPI orientation by default.   [from: source]

5. What is AC-PC alignment?
We have just mentioned the orientation convention in the MRI. Having known the jargon, how then, should I place a patient's head in the scanner? By default, the axial or transverse plane has to cut through two important anatomical landmarks of the brain, the anterior commissure, and posterior commissure. They are usually called as AC-PC. Once the head positioning and orientation are determined prior to the acquisition, the slice orientation follows will follow the AC-PC alignment, acting as a reference or anchor. Take a look at Fig-2 above. If the head is tilted in such a way that the AC-PC is not horizontal, it is said that the head is oblique.

Why is this orientation important in the experiment? Imagine that an MRI scanner can only acquire anywhere within a certain "box". Ideally, we would want to cover the full brain as much as possible but the head size may vary. In order to fully cover important brain regions that we want, we may want to tilt the head slightly, e.g. -30 degree w.r.t. AC-PC.

Fig-6: The sagittal view of the head with the location of AC-PC.

6. What is Localizer? What is Auto-align?
Initially, when we put a subject into the bore, the scanner uses its geometric center of the bore (magnet) as its reference. This location may not be the same as the head center, which is calibrated as with the laser before we bring the subject in, Once the subject is inside, we acquire a low-resolution T1 image so that we roughly know the head position with respect to the magnet. This image, called a localizerallows the scanner software to ‘know’ where your head is. Throughout the whole session, the scanner will reference all subsequent images relative to that first reference image. This allows you to prescribe slices on each subsequent image however you like, and the scanner will track where you are in space.

Auto-align is an algorithm (Siemens scanner?) that allows you to prescribe slices on each image throughout the scan, even with different sessions. It basically does some kind of geometric transformations, taking the localizer as the reference. In the Siemens machine, this feature is called AAHScout. AAHScout plays a major role when we are scanning with multiple sessions of the same subject or patient, or when we bring the subject in/out of the bore.

7. Some more jargons to remember
Lastly, it is good to talk about the same vocabulary when discussing the design of fMRI experiments. Some useful jargons may include:
(a)   A session: all MRI/fMRI scans collected for a subject or patient in one day.
(b)   A run or scan: a continuous fMRI scanning, may last up to 7-10 minutes.
(c)   A condition: a task, a type of stimulus presented to the subject or patient.
(d)   An experiment: a set of conditions designed to answer a scientific question.
(e)   A paradigm: a set of manipulation comprising different experimental conditions.
(f)   A pulse sequence: a set of parameters, e.g. TR/TE, flip angle, slice thickness, in-plane resolution. A more recent technology called the multiband sequence becomes widely used.

A session usually consists of one or more experiments. Each experiment consists of several runs. In one run, the subject may be presented with an orderly set of two or more conditions, that is, types of behavioral manipulation or stimulus presentation. More volumes and/or runs are commonly needed when signal-to-noise (SNR) is low or the effect size is small. Thus each session consists of numerous runs, e.g. 5-10 runs, that may last to hours.

8. What is parallel imaging?
More recently, parallel imaging becomes popular to shorten acquisition time and improve SNR, while at the same time obtaining more data points. Broadly speaking, parallel imaging is a generic name denoting multiple acquisitions of images at the same time, thus parallel. In different MRI machines, the algorithm naming can be different but essentially this feature falls into 2 categories:
     (a)  Image space (encoding) following reconstruction, e.g. SENSE.
     (b)  k-Space or frequency domain, e.g. GRAPPA.

I mentioned k-space earlier. This k-space often refers to a temporary image space in matrix format, in which data from digitized MR signals are stored during acquisition. The final image is produced by some mathematical operations when the storage is full, a process sometimes known as image reconstruction. 

Parallel imaging induces more noise and the SNR is reduced by g.√R where g is the noise amplification or g-factor, and R is the acceleration factor. For example, if R = 2 then it reduces imaging time by half, but decreases the original SNR by 1/√2 ≈ 0.71.

Now, which method of parallel imaging should we choose? Well, it really depends on various factors: total time taken, SNR, coverage, etc. Parallel imaging promotes the birth of multiband acquisition in the Human Connectome Project by NIH.

References
[1]  Jezzard, P., Mathhews, P. M., and Smith, S. M. (2001). Functional MRI: An Introduction to Methods. Oxford University Press.
[2]  Lindquist M. (2008). The statistical analysis of fMRI data. Statistical Science 23: 439–464.
[3]  Lecture01 in - culhamlab.ssc.uwo.ca/fmri4newbies/Tutorials.html
[4]  FAQs from http://bic.berkeley.edu/scanning.
[5]  http://mriquestions.com/two-types-of-pi.html

Nice neuroimaging data processing, that covers some basics of the 3 most popular software packages: SPM, FSL, and AFNI.