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.