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.

Functional MRI - a brief overview

How does BOLD-fMRI work?
To begin, two material properties are important in BOLD, i.e. diamagnetism and paramagnetism. In essence, a diamagnetic material does not introduce a significant change in the magnetic field, whereas a paramagnetic material tends to increase the magnetic field. If these two types of material are close to each other, they cause a local distortion of the magnetic field near the interface. The field becomes less homogeneous. Brain tissue is mainly diamagnetic. In contrast, the magnetic property of the blood may change depending on the oxygen molecules attached to haemoglobin. This is crucial. When the blood contains more haemoglobin without oxygen attached (deoxyhaemoglobin or deoxyHB), it is paramagnetic.

The more deoxyHB the blood has, the more local field distortion it creates. The local field inhomogeneity causes faster spin dephasing in the transverse plane, causing a lower T₂* value. In this case, the image intensity drops. Now, what happens when there is neuronal activity? More oxygen molecules are needed by the neurons or brain tissues, so the oxyHB concentration increase and deoxyHB concentration drops. With more oxyHB the blood becomes less paramagnetic, causing the image intensity to increase. These properties are being exploited in fMRI to capture neuronal activities in the brain. The EPI sequence has been known to be highly sensitive to such changes in magnetic properties, making it the most popular fMRI method to use.

The way the BOLD behaves in the event of neuronal activity is called the haemodynamic response, or BOLD response. The physiology of this response is not straightforward and depends on, e.g. the cerebral blood flow (CBF), the cerebral blood volume (CBV), and the metabolic rate of oxygen consumption (CMRO2). In response to a stimulus, the CBF goes up to deliver more oxygen to the site of neuronal activation. On the other hand, the CMRO2 is increased or more oxygen is consumed, which reduces the BOLD effect.

Fig-1: The relationship between a stimulus, neuronal activity, neurovascular coupling, and BOLD in fMRI scanning [2].

 

Does fMRI measures brain activity? No. It does not directly measure neuronal activity, but rather, it uses blood deoxyHB level as a proxy or indirect measure of neuronal or functional activation. In other words, fMRI measures the degree of neurovascular coupling. Scientists have noted that while the neuronal activation is very fast, the BOLD response is slower.

Experimental Paradigm using fMRI
The experimental paradigm is directly related to research questions in mind and influenced by the fact that the BOLD response is slow. Although the response is more or less reproducible, the shape and the onset may vary depending on the brain region and stimulus duration. Refer to the diagram above. A good paradigm is able to take into account the slow response but carries high statistical power for making any conclusion. At the same time, it should also ensure that the task is not biased, and prevents subjects from anticipating or getting bored, that is.

1. Blocked design: by far the most common paradigm in functional MRI. In this case, one block represents one task or experimental condition, and one scan session involves more than 1 block. The duration may range from 20 - 35 seconds, allowing a fully restored or complete profile of the haemodynamic response (HRF). The HRF can be viewed as a filter (Josephs & Henson, 1999). The most efficient design is a sinusoidal modulation of neural activity with T = 25 sec (e.g., boxcar with 12 sec on/ 12sec off), capturing fully the BOLD signal and its peak. We should design the block in that way. The signal of one particular block is then compared with the haemodynamic signal produced during a rest or baseline period. Thus, the blocked design is actually a subtraction or a contrast between Task vs. Rest brain activity. We can always expand this by using more tasks within a scan (e.g. other stimuli or conditions) which we would compare against the REST block. If any, the interaction effect between task conditions must be taken into account. With regards to this kind of design,
• Advantage: simpler in execution, high statistical power, does not require an accurate HRF model.
• Disadvantage: doesn't allow separation of individual trials, induce boredom and anticipation, and is not suitable for all behavioural tasks.
2. Event-related design: this is the second paradigm where individual events related to the different tasks or experimental conditions are measured. Here, an event is presented at a certain short duration with inter-trial stimulus (ISI) time, and is assumed to evoke a set of neural responses in the brain. The task presentation does not follow a block-by-block arrangement but is presented in a random fashion, each may last only for 2-3 seconds. Event-related design requires the MRI pulse sequence to be fast enough to catch up with the changing task event (e.g. with a relatively shorter TR), giving a higher temporal resolution. The advantage of this paradigm is its flexibility in the experimental design, and the tendency to prevent boredom or fatigue. In practice, there are a few variants such as rapid ER design, jittered ER, and randomized ER. 
• Advantage: flexible, remove anticipation, can separate response to different stages.
• Disadvantage: tedious implementation, low statistical power and sensitivity, require good HRF model (sensitive to error), thus requiring more #trials per stimulus.

Fig-2: The difference between blocked and event-related design with three different behavior conditions.

An important finding that makes the event-related paradigm simpler is the fact that the BOLD response of the event tends to be evoked similarly even when the response of the event before that has not decayed fully. In other words, the responses sum up linearly.

fMRI Signal and Noise
In fMRI, the evoked BOLD response is our signal of interest whose behaviour is not straightforward. Scientists have spent efforts to model this response because this is the first step before making any inferences. It allows us to know in the time domain which one is activation, which one is not. The most common model is the one that assumes the BOLD response to be a linear time-invariant system. Under this assumption, there is a linear relationship between neuronal response to a stimulus and the BOLD response. It is time-invariant and does not depend on any previous stimuli. With this assumption, its characterization is known in a noisy system.

Using this framework, a burst of neural activity or spike can be presented as discrete impulse responses. Then, the observed BOLD response of a voxel can be modelled as the convolution between the incoming stimulus waveform and the impulse response. The resulting response is now called the canonical haemodynamic response function or simply, HRF. The general agreement is to use the double gamma function as the HRF. What are the drawbacks of this model? The linearity assumption may be too simplistic. Also, the shape and onset of BOLD responses may vary across subjects. Notably, the same region doing different functions for the same task may show different evoked responses. Scientists have proposed more robust models for HRF (see [1] and Glover et al., 1999).

The fMRI signals are prone to corruption due to noise and artifacts, collectively known as nuisance signals. Just imagine! The signal change is usually about 2% of the total signal magnitude. Unwanted signals can typically be in the form of:

• Hardware noise: thermal noise (higher magnetic field strength gives more noise) and the scanner drift (usually f < 0.01 Hz, we can filter this out or model it).
• Participant's head movements. Sometimes it appears as a sudden spike.
• Physiological noise: heart rate and respiration, the most challenging one to model/remove. The spectral components of heart-related noise are between 0.9 - 1.0 Hz, while respiration, 0.3 - 0.4 Hz.
• Others: structural-related noise. In 2007, Fox et al reported that spontaneous BOLD follow a 1/f distribution (pink noise), meaning that there is increasing power in the low frequencies.

The presence of nuisance signals distort the wanted BOLD response. This eventually obscures the actual neural activations seen in the image. In other words, noise reduces detection sensitivity.

Brain Connectivity and fMRI
fMRI is extremely useful to identify brain areas associated with a particular task. But what happens if we scan the brain at rest? The brain is never at rest. In 1995, Bishwal found that there is spontaneous low-frequency fluctuation of BOLD in the human brain at rest, that is when the brain is not engaged in doing any specific tasks. The term "resting-state" became popular. Separate research by Raichle and colleagues found specific brain regions called the default mode network or DMN. The unique feature of this network is that the activity decreases when the subjects are engaged in tasks. A group of scientists from FMRIB-Oxford, has identified several consistent RSNs such as those of the visual cortex, sensorimotor, and executive function.

There are a few reasons why this resting-state fMRI (rs-fMRI) is attractive. It does not require the subjects to perform any task inside the scanner. This is important if the devices are not MRI compatible. Until recently, there is an increasing number of publications showing the application of rs-fMRI in the clinical setting such as Alzheimer's Disease, ageing brain, epilepsy, and some pharmacological studies.

In short, fMRI is useful to localize brain activities and study the brain at rest. Recently, scientists become more interested in studying how more than one location interact in the brain. Terms such as network and connectivity are then introduced. We now have three different types of connectivity:

• Anatomical connectivity: as the name implies, it is a hardwired structure of one brain region with the other. It can be studied elegantly with Diffusion Tensor Imaging. Such a technique complements earlier histological methods such as retrograde tracing.
• Functional connectivity: connectivity of two or more brain regions whose time series are correlated. This is studied using resting-state fMRI performed while the person is at rest. Applying ICA on resting state data produces different sets of spatial maps called the functional connectivity network.
• Effective connectivity: connectivity of two or more brain regions where one region influences the other regions. Rather than depicting temporal correlation, effective connectivity emphasizes causal relationship among brain areas.

Data Analysis Pipeline
I would like to end this post by presenting the most common data analysis pipeline. Whatever innovative pipeline one takes, it bears the same objective: to allow valid statistical inferences. There are two categories of data analysis pipeline: task-based and resting-state data. The most common statistical framework used in the analysis is called GLM, the general linear modelling. Here, we input a certain design matrix or schema associated with the experimental or task paradigm and find the brain regions that fit the schema the most. A certain post-hoc (correction) step is required to keep the statistical principles valid. The model-free method called the Independent Component Analysis (ICA) is more attractive to work with resting-state images.

Fig-3: The most common data analysis pipeline in functional MRI. The preprocessing steps are more or less fixed, but the researcher has to choose between the model-based (GLM) or model-free (data-driven) method. Task-based analysis mostly employs GLM, while resting-state fMRI employs a data-driven ICA method. Although there are many versions to this, the basic idea remains the same.

 

Once the experiments have been conducted, we obtain a series of imaging data in DICOM format. The data have to go through preprocessing steps before we perform any statistical analysis. The pipeline produces a final product as a statistical parametric map (after Friston), a form of graphical representation where we can visually see parts of the brain associated with our experimental paradigm. NOTE: There is no one correct pipeline that fits-for-all scenarios. Most researchers tailor it to their research needs.

References
[1]  Jezzard, P., Mathhews, P. M., and Smith, S. M. (2001). Functional MRI: An Introduction to Methods. Oxford University Press.
[2]  Arthurs, O.J. and Boniface S. (2002). How well do we understand the neural origins of the fMRI BOLD signal?. TRENDS 
      Neurosci, vol. 25: 27-31
[3]  Lindquist M. (2008). The statistical analysis of fMRI data. Statistical Science 23: 439–464.
[4]  Cole, D.M., Smith, S.M., Beckmann, C.F. (2010). Advances and Pitfalls in the Analysis and Interpretation of Resting-State FMRI
      Data. Front Syst. Neurosci., vol. 4.