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.

Introduction to MRI Physics

The Magnetic Resonance Effect

Around 70% of our bodily tissues, including the brain, contain water molecules composed of hydrogen atoms. A single hydrogen atom has a nucleus with a single proton that freely rotates around its axis. In general, their axes point randomly but when placed inside a magnetic field B, they become aligned with it. What happens next? There are protons pointing with and against the direction of B the antiparallel spins. The net polarity under such equilibrium is measured as M, the net magnetization. The direction of M is always along B. 

While in equilibrium, the protons are also behaving like a spinning top with a particular angular frequency. This phenomenon is called precession. The frequency is called Larmor frequency, the value of which is proportional to B. Ideally, B is always constant and homogeneous, so it is called the static magnetic field. By convention, the direction of B is in the longitudinal axis. Its strength, measured in Tesla (T), defines the MRI scanner specification, for example 1.5 T and 3.0 T.

Suppose there is this second magnetic field B₁ applied to these realigned protons, two things will happen. First, they get more energy and begin to wobble. As a result, the precession axes start to point further away from the longitudinal axis B. Look at the diagram below. Second, the protons then become in-phase and this yields to a growing net magnetization in the transverse plane, 

M_xy perpendicular to the original M. The longer we apply this field, the higher the precession angle so much so that the new M' is now fully flipped 90º to the transverse plane.

Fig-1: An excitation pulse changes the net magnetization that yields to detectable RF signals used in MRI. (a) In the body, each hydrogen atom or proton has a random orientation. (b) If the body is under the influence of static magnetic field B, the protons will try to align themselves with B, producing a net M. (c) The application of external excitation field will destabilize the alignment, the resulting new M will be perpendicular to the original M. (d) Once this external field is switched off, we can measure the relaxation process through an RF detector. 

The field B₁ is also called the excitation pulse and is switched on only for a certain period. What happens when we switch it off suddenly? The protons try to align back with the static magnetic field, the process of which is called relaxation. At the same time, they emit RF signals with Larmor frequency matched with B₁. If we put an RF detector or receiver coil nearby, we are able to capture this signal. Hence, the word ‘resonance’ makes sense because what we measure is the resonance effect.  Following Faraday’s Law, the change in RF pulses induces an electric current that we can measure externally.  This is the basic principle of Magnetic Resonance Imaging (MRI) as discovered independently by Bloch and Purcell in 1946. This technology was originally called NMR or Nuclear Magnetic Resonance.

Gradient Field for Spatial Localization
Before being able to image an object, we need to have a coordinate system for spatial localization. Why? We want to know the “composition” of protons at a different location in the brain in order to produce the 3D brain structure. Without this feature, our RF detector is not able to know where in the brain produces what signal. The very first idea of spatial localization came from the 1D imaging experiment by P. Lauterbur in 1973. 

Spatial localization is achieved by using a gradient field. This means that instead of giving a constant external magnetic field, we vary the intensity slightly according to the distance in a certain direction. Because Larmor frequency depends on the magnetic field strength, there will be varying frequency components at different positions captured by the RF detector. The number of protons is reflected as the signal intensity. Because this gradient field yields to different frequencies at a different location, this particular external pulse is also called frequency encoding. It is usually denoted as G_x. 

To create a full volumetric or 3D brain image, we require the second and third gradient fields. By convention, the Z-axis is parallel to the direction of the static magnetic field and is called the longitudinal axis. The scanner bore is along the longitudinal axis. The X and Y axes form a perpendicular plane called the transverse plane w.r.t the longitudinal axis. Obviously, the remaining gradient fields are set along the X and Y-axis. Because a gradient field in one axis will modulate the spin precision frequency on that particular axis, the three cannot be switched on at the same time.

Fig-2: Creating a full 3D brain image requires 3 different gradient pulses on top of the external RF pulse B₁ (from [4]).

The slice selection field G_z  along the Z-axis is switched on simultaneously with the excitation pulses. ‘Slice’ here literally refers to brain slice. We now acquire MRI signals for that particular slice and then resolve them based on the X and Y position on the transverse plane using 2 additional gradient fields. The X- gradient field can resolve position based on frequency components as mentioned earlier on, i.e. frequency encoding. The Y-gradient G_y allows us to resolve position based on the phase difference, that is, the phase encoding. By convention, the frequency encoding is also known as the readout gradient.

Refer to the diagram above. The excitation pulses and the three gradient pulses during MRI acquisition are collectively called the pulse sequence.

Relaxation Time and Image Contrast
As mentioned earlier, a brief excitation pulse B₁ will cause the protons to spin along the transverse plane; sometimes called the 90º excitation. Spinning protons return back to the longitudinal baseline position in the direction of the static magnetic field B once the pulse B₁ is switched off. This process is called relaxation. Bear in mind that different tissues have a different composition, and thus, different relaxation times. In the early 1970s, R. Damadian attempted the first full-body NMR image using different relaxation times.

Fig-3: Different relaxation time constants observed once the external pulse is switched off. Taken from [4].

There are two types of relaxation. The first relaxation is caused by spin-spin interaction that results in the gradual dephasing effect in the transverse plane. T₂ represents the rate of relaxation in the transverse plane M_xy and T₂-value decay over time. A variant of T₂, called T₂*, accounts for local field inhomogeneity due to tissue properties. In addition, the magnetization M_z along the longitudinal axis is restored over time and the recovery time is represented by T₁. The process is also called spin-lattice relaxation because there is a transfer of energy to the surrounding tissue, causing less antiparallel and more parallel spins.

In MRI, tissues with different relaxation times yield different image contrast. So a contrast can be created by exploiting T₁, T₂ , or T₂*. As such, there are two important time parameters in MRI: 

1. Repetition time (TR), i.e. the time interval between two consecutive excitation pulses. 
2. Echo time (TE), i.e. the interval between the start of an excitation pulse and data acquisition during the peak of the signal. This is akin to a reply of an echo that is captured by the receiver.

The T₁-weighted image makes use of the T₁ relaxation effect on different tissues. This effect is clearly seen by providing a short repetition time TR. T₂-weighted images, on the other hand, can be clearly seen with long TE, allowing more time for the spins to dephase completely. Another important parameter is the "How" which determines the sequence to produce this echo, e.g. gradient echo and spin echo. What does it mean by echo here?

k-space and Fourier Transform

The introduction of k-space is useful to elucidate the process of image reconstruction from mere nuclear magnetic equations. The k-value is an integral operation of the gradient curve across time, i.e. the area under the gradient curve. If the gradient point is below the axis, its value is negative and its integration over time t yields to a negative value too. Changes in k-values over time are represented by the k-space trajectory. In our example below, the frequency and phase-encoding gradient are shown as orange and brown color respectively. The k-space trajectory is shown in green on the right-hand side panel.
  

Fig-4: A simplified version of how to generate 2D k-space trajectory using two gradient pulses, Gx and Gy.

Suppose we are acquiring one brain slice. The k-space contains k_x and k_y coordinates. Before we are able to reconstruct the slice image, we have to fill up the entire coordinate with relevant data. Which data? The data acquired or sampled by the RF detector, each for each plane. How do we create the trajectory to plot the data at different k_x and k_y coordinates? By varying the frequency and phase encoding gradient fields across time. When there is no gradient field, the coordinate remains the same over time as no trajectory is formed.

Data points are measured in a discrete manner. The number of k-space measurements we make per slice determines how good the spatial resolution of the slice is. After the whole k-space contains relevant data, Inverse Fourier Transform operation can subsequently be done to produce an image.

Echo Planar Imaging

If we turn the excitation pulse longer, it is possible to flip M all the way to 180º in the opposite direction. This result is interesting as at this position, there is no resonance effect captured by the detector. We can also do something different. First, we apply 90º excitation pulse so that the precision is on the transverse plane, then we switch it off. Transverse magnetization M_xy experiences gradual dephasing on the transverse plane. Now half-way through we apply a strong pulse called the 180º refocusing pulse. It turns out that we are able to flip the direction of rotation (or phase) around the X-axis. The effect is interesting. The M_xy will increase again once more like an 'echo' before gradually dying off. This sequence is called the spin echo. As shown in Fig-5, the period from the 90º excitation pulse up to the appearance of the maximum detectable signal is called the echo time (TE), i.e. the whole panel (a) to (d). 

Almost similar to the spin echo is a sequence called the gradient echo that makes use of gradient fields to introduce 180º flip instead of using refocusing pulses. There are several techniques to produce MRI echos and to allow a very rapid acquisition, but the topic is out of scope at the moment. A type of pulses called gradient recalled echo (GRE) forms the basis of most angiographic MRI.

Fig-5: In the first instance (a), the magnetization has been flipped onto the XY plane. Afterward, a spin-echo can be produced by introducing a refocusing RF pulse in (b) that flips the net magnetization vector along the X-axis. See panel (c) that depicts the moment just after the 180-deg flip. After the flip in (d) the vector position shown becomes similar to that in (a) when the 90-deg excitation pulse was just briefly introduced. At this point, the resonance signal is at its maximum, and it is the best time to acquire or "Read". Adapted from [1].

Further development of gradient echo is the Echo Planar Imaging (EPI). An EPI sequence forms the basis for functional MRI and diffusion-weighted imaging. In the EPI sequence, multiple refocusing pulses are applied in the phase encoding G_y continuously. Rather than returning to (0,0) EPI sequence allows a transition to the next level simply by continuing the trajectory controlled by positive and negative frequency encoding gradient G_x. This allows for the continuous streaming of readout. What happens in k-space? We are able to cover k-space as quickly as possible by filling up one axis within a single shot of spin-echo, resulting in much faster image acquisition. Refer to Fig-6 below and see the arrow upward at either side denoting the image reconstruction process (compared it with Fig-4). The drawback of the EPI sequence is its poor resolution and contrast, e.g. 3 mm is very common. The EPI method was proposed by Peter Mansfield. More on EPI can be found here.

Fig-6: The pulse diagram for EPI sequence mainly used in functional MRI (fMRI). Taken from [1]. Although EPI sequence is attractive, it invites some issues with respect to local distortion, image ghosting, and high requirement in data sampling rate. For these and other tradeoffs, EPI yields to a poorer resolution.

Epilogue
There are three main imaging modalities popular for brain imaging I would say. The first two, CT scan and PET scan, have been popular since the early '90s. CT scanning stands for computerized tomography and it makes use of X-ray principles to produce high-resolution brain images. CT images are static. PET or positron emission tomography makes use of radioactive tracer injected into the body to produce functional brain images. PET is able to detect biochemical processes in the brain and thus dynamic. The third imaging tool, MRI, makes use of the nuclear magnetic resonance effect of the spinning protons. MRI is attractive because it provides better spatial resolution and hydrogen atoms are already abundant in the body.

The basic physics of NMR has previously been explained. In brief, MRI technology makes use of the magnetic properties of hydrogen atoms or protons. When placed under the influence of changing magnetic fields, different tissues in the brain have different properties of spinning protons. These differences can be observed in terms of relaxation time (T₁ or T₂). To produce a full 3D image we utilize three different gradient fields. Lastly, different imaging quality and quantity are influenced by different pulse sequence parameters. In practice, MRI physicists often use a dummy model called phantom to test the performance of a new pulse sequence.

In the subsequent post, functional MRI or fMRI will be discussed. This type of functional imaging is derived from MRI technology that is able to capture changes related to neuronal function in successive images. Unlike MRI, fMRI is not static. And unlike PET, there is no need to administer any radioactive tracer to produce image contrast. Rather, we can make use of our blood as the natural contrast agent. The method is called blood-oxygen level-dependent fMRI or BOLD-fMRI and this invention was discovered by Seiji Ogawa in 1990 using a gradient-echo imaging sequence. 

Most recently, the introduction of the multiband (MB) or simultaneous multi-slice (SMS) EPI technique effectively shortens acquisition time without decreasing TE and maintaining the same SNR by simultaneous acquisition of multiple slices at one go. For a review, refer to Feinberg and Setsompop (2013).

References
[1]  Jezzard, P., Mathhews, P. M., and Smith, S. M. (2001). Functional MRI: An Introduction to Methods. Oxford University Press.    
[2]  Missimo, Filippi. (2009). fMRI Techniques and Protocols, 1st ed.. Humana Press - Springer. 
[3]  Basic MRI principles (Youtube)
[4]  Box 19-3 of Chapter 19 (pp.370-374). In Kandel E.R. et. al. (2000). Principles of Neural Science 4e, McGraw-Hill.     

Gross Anatomy of The Brain

This is a huge topic. It should have been published the first in my blog, but it's still not too late to do it now I guess. The gross anatomy of the brain is fundamental knowledge every neuroscientist has to know.

Fig-1: The main divisions of the central nervous system (top-left), together with major anatomical axes; adapted from [1].

The Forebrain: Telencephalon
We usually refer to this part of the brain as the cerebral hemisphere. It consists of the cerebral cortex and the subcortical region beneath it. The cerebral cortex serves as the main computational unit and contains mainly cell bodies and glass. That's why its appearance is grayish tan, also known as the gray matter. On the other hand, the subcortical region consists mainly of myelinated axons and therefore it is called white matter. The forebrain is encapsulated inside a layer of cerebrospinal fluid or CSF a colorless fluid important for mechanical and immunological protection. The ventricles also contain CSF.

1. The cerebral cortex.
This is the outermost layer of the cerebral hemisphere. In humans, it is greatly convoluted and consists of: sulci (sulcus - singular) or small grooves, fissures (large grooves), and gyri (gyrus - singular) which are bulges between adjacent sulci or fissures. What's the reason behind it? Well, by "hiding" most of the cortical areas in the grooves, we have a much bigger brain region, suggesting a more computational advantage. The thickness is ~ 3 mm with a total surface area of 0.24 m². K. Brodmann was the first person who did an excellent job identifying various cortical areas based on cytoarchitectonic features, that is, differences in cortical layer architectures.

Traditionally, the cerebral cortex is divided into 4 regions, i.e. frontal, parietal, temporal, and occipital. The frontal lobe is known for motor and executive functions. Three regions of the cerebral cortex are sensory, meaning, they receive afferent inputs from the peripherals, sensory organs:

• The primary visual cortex (V1, BA-17), on the occipital lobe.
• The primary somatosensory cortex (S1, BA-3, BA-1, BA-2), on the parietal lobe.
• The primary auditory cortex (A1, BA-41), on the temporal lobe.
• The other two are hidden, i.e. the primary olfactory cortex, near the piriform cortex, and primary gustatory cortex, near the insular cortex. 

With the exception of olfaction and gustation, sensory information is sent from the contralateral side of the body. Regions adjacent to the primary sensory area are called the association areas which are involved in more higher-order cognition and perhaps memory. Their lesions are insightful to understand their functions. Patients with damage to S1 are unable to perceive tactile sensation and recognize the object in general. Clearly, S1 sends projections to the adjacent association area. Damage to the somatosensory association cortex allows the person to sense the presence of the stimuli, but he or she is unable to recognize, call or name, or perceive the shape or contour or the objects.

The regions further away from these primary areas, e.g. around the border of temporal, occipital, and parietal lobes, are called multimodal sensory areas where multisensory integration occurs. The region of the prefrontal cortex is involved not with movement or sensory perception, but with formulating plans and strategies. To plan and make a decision, we have to depend on the current sensory inputs, past experience or memory, and action selection (sometimes called executive functions).

2. The basal ganglia and subcortical structures.
Regions immediately below the cerebral cortex form the white matter and the subcortical structures. Some of the most important structures are the amygdala, fornix, parts of the hypothalamus. Amygdala, together with parts of the cingulate gyrus and parahippocampal gyrus of the cerebral cortex, are parts of the limbic system. These structures play a role in learning and emotional expression. Immediately below the cingulate gyrus is the corpus callosum. Immediately above it is the folding or sulcus, originated from the medial wall and goes down to the rostral end beneath the prefrontal cortex. This folding, called the cingulate sulcus, separates the frontal lobe and the cingulate gyrus. Amygdala is important for emotion and recognizing the emotional reactions of others.

More discussion on basal ganglia is in a separate blog post. Large and intricate bundles of fibers called the fasciculi form what is known as the white matter. Some of these fibers pass through the nuclei of the basal ganglia forming the internal, external, and extreme capsules. This part will not be presented here.

The brain has two hemispheres separated by the longitudinal fissure. Are the two hemispheres talking to each other? Yes, and the left parietal region knows what the right one is doing; and this is the job of the corpus callosum, containing bundles of commissural fibers, i.e. neurons that connect the two cerebral hemispheres. Another type of fibers which allows different cortical regions of the same hemisphere talk to each other is called association fibers.

The Interbrain: Diencephalon
The structure of diencephalon is quite small. It is located between the telencephalon and mesencephalon around the third ventricle. There are two main components, i.e. the thalamus and hypothalamus, both contain two lobes spanning the right and left hemisphere. In the medical field, the hypothalamus has been known as a thermostat to control body temperature. The thalamus and hypothalamus are further subdivided into several regions or nuclei, each of which contains a collection of neuronal cell bodies with a distinct functional role.

Thalamus is composed mainly of projection fibers, i.e. axons of the neurons from one part of the brain that form a synapse with the neurons of another region. The hypothalamus is important in controlling the autonomous nervous system, endocrine or hormonal system, and survival-related behaviors. Pituitary gland serves as the master gland because it controls the secretion of other endocrine glands (the details are not presented here). Anterior to the pituitary gland is the optic chiasm where optic nerves from both eyes cross.

The Midbrain: Mesencephalon
Midbrain is the middle portion of the brain surrounding the cerebral aquaduct. There are two major components: the tectum and tegmentum. Tectum is the dorsal part of the midbrain containing 2 principal structures: a pair of superior colliculi (part of the visual system) and a pair of inferior colliculi (part of the auditory system). Tegmentum is situated beneath the tectum and includes several important midbrain nuclei such as the rostral end of the reticular formation, periaqueductal gray matter, red nucleus, substantia nigra, and the ventral tegmental area. The last two structures are well-known as the source of dopamine.

The Hindbrain: Metencephalon and Myelencephalon
The hindbrain consists of the cerebellum, pons, and medulla. The part on the cerebellum, in itself the 'small brain', is being presented elsewhere in this blog. The two remaining regions, pons, and medulla (or medulla oblongata), are part of the brainstem and located anterior to the cerebellum.

Pons contains part of the reticular formation and pontine nuclei. It is involved in the facial somatosenses and automatic repetitive movements such as breathing and swallowing. The medulla is the most caudal region of the brainstem, adjacent to the rostral end of the spinal cord. As a very important structure in the autonomic nervous system (ANS), the medulla controls respiration, cardiac rate, and some other reflex centers such as swallowing, coughing, and sneezing.

Fig-2: Anatomy of the brainstem with the right hemisphere of the cerebellum. Adapted from [2].

What is beyond the cortex? Well, the central nervous system (CNS) consists of both the cerebral cortex and the spinal cord. The brainstem connects the cortex with the spinal cord. A more detailed part will be for another blog entry but the gist is this:

1. The white/gray matter location is swapped as you enter the spinal column. As we know, white matter contains myelinated axons, while gray matter contains cell bodies. The center gray matter core of the spinal cord is made up of cell bodies of spinal interneurons that connect motor-motor, motor-sensory (as in reflex arc), and propriospinal neurons. Indeed, the anatomical connections are rather intricate!
2. The central core has an inverted H-shaped. It is divided into ventral (motoric) and dorsal (somatic). Mechanoreceptors send information to the sensory neurons whose cell bodies are in the dorsal root ganglion. They enter the spinal cord through the dorsal side up. On the other hand, pyramidal cells from the motor cortex enter the spinal cord through the ventral horn where they synapse with the alpha motor neurons that target a specific muscle.
3. The spinal cord is important for low-level, stereotyped reflex behavior, as well as locomotion.

Appendix: The cerebral cortex
I want to add some more information regarding the cerebral cortex. In particular, with regards to the Brodmann Areas.

Fig-3: Parts of parietal, temporal, and occipital lobes: a The area V1, V2 and V3 of the occipital lobe (BA 17, 18, and 19). b The area postcentral gyrus, superior parietal lobule (BA 5, 7), and inferior parietal lobule (consisting angular gyrus or BA 39; and supramarginal gyrus or BA 40). c The temporal lobe bounded by the lateral fissure. Adapted from [3].

Fig-4: Parts of frontal lobe: The area corresponding to prefrontal cortex with dorsolateral prefrontal cortex (dlPFC) and a more caudal part consisting: superior, middle, and inferior frontal gyrus (F1, F2, and F3 respectively). The region associated with motor functions (M1). The medial view of the frontal lobe is also shown on the right with regions more intimately related to reflective and stimulus-driven inputs. Adapted from [3].

References
[1]  Figure 17-2 (p.320), 17-3 (p.321), and 17-5 (p.325). In Kandel E.R. et. al. (2000). Principles of Neural Science 4e, McGraw-Hill.
[2]  Chapter 3 - Structure of The Nervous System. In Carlson, Neil R. (2013). Physiology of Behavior 11e, Pearson Education.
[3]  David, C. L., et. al. (2010). The Brain and Behavior: An Introduction to Behavioral Neuroanatomy, 3e. Cambridge Press.

Organization of Movements

Human beings always on the move. We were once clumsy toddlers who eventually learn and readapt our movements to become more skillful. This adaptation occurs not only to make us more skillful, but also to adjust our motor system to the change in our growing body structure. There are 3 specifics domains of knowledge of 'motor behavior': motor control & planning, motor learning, and motor development across age. Motor control and motor learning have become popular, forming an intersection between neurophysiology and kinesiology.

To begin, there are three basic types of movements: 

1. Reflexive. Reflexes are born as a result of external stimuli and they are involuntary. The most popular example is the knee-jerk or patellar reflex and it employs the simplest form of lower-level connection called the monosynaptic circuit. Another example of reflex, the stretch reflex, occurs as a response to overextension to prevent muscle injury, e.g. it limits your movement when you flex your hand. A more complex movement will be the withdrawal reflex when our hand accidentally touches a sharp or hot object. 
2. Rhythmic. The second type, rhythmic movement, includes chewing, swallowing, breathing, scratching, and walking. The spinal cord and the brainstem participate in the production of these repetitive rhythmic motions and they are mostly stereotyped.  
3. Voluntary. The last type of movement includes any type of movement done to achieve certain objectives or a response to external stimuli. Voluntary movements are goal-directed and under the control of the cerebral cortex. We perform goal-directed movements with the blessing of the ability to learn, improve, or make corrections.

Simplified Sequence of Events

It is long postulated that movement production involves a series of events. At rest, motor unit activity is at a subthreshold level. The muscle state at rest is called muscle tone. What happens when one decides to move? Being the highest in the movement hierarchy, the cerebral cortex defines the objectives or goals and the intention to move. The prefrontal cortex is thought to be the place that this happens. This area receives projections from the parietal lobe that provides the body spatial information and body image. Not only do you need tactile and kinesthetic information of the body (the somatosenses), you also have to depend on the visual and auditory inputs from the environment. This information converges in the parietal region where multisensory integration occurs.

The next step is the preparation of a movement. The secondary motor areas (premotor cortices) are involved in this, and the basal ganglia play a role in providing supporting signals, i.e. the go or no-go behavior. The supplementary motor area (SMA), in particular, defines sequential information of muscle activation. Lastly, the primary motor cortex comes into play to activate specific muscles required for producing the movements. It determines how much force each muscle group must exert, and then sends these commands as many sets of action potentials to alpha motor neurons. 

At the level of the spinal cord, the upper motor neurons (the pyramidal cells) make contact with the lower motor neurons that innervate the muscles, either directly or indirectly via the spinal cord interneurons. Alpha motor neurons are neurons that generate actual movements.  At the neuromuscular junction, acetylcholine is released from the presynaptic terminal. Subsequently, cross-bridges are formed and the muscles will contract or stretch out, producing the intended movement. 

Lastly, it should be noted that movement production is not a one-time off thing, but spans for a certain duration. While performing the movement, there are two other parts of the CNS that are quite essential. Postural maintenance and balance while making certain movements are ensured by the brainstem. The temporal and spatial accuracy of the movement is monitored continuously by the cerebellum, the area responsible for error-detecting mechanisms. 

Movements as Sensorimotor Transformations

Movements are created by motor outputs, basically, neural commands that act on the muscles, causing them to contract and then produce movements. How do we get these outputs? They are derived from sensory inputs. The sensory information has gone through sensorimotor transformations. Sensory inputs provide both extrinsic states of the world as well as intrinsic (bodily) information. Two important components of intrinsic information: kinematics (position, velocity, acceleration, joint angles, muscle stretch) and dynamic or kinetic (forces) generated and experienced by the body.

Unlike reflexes, complex motor actions such as reaching to a cup of coffee in front of you involve a series of processes:

1. Spatial localization of items in the workspace in front of you. Our visual system is typically crucial for this. We also depend on the somatosensory system to tell where our arm is. You know you want to reach the cup with your hand (the end-effector) connected with your upper limb segments.
2. Movement planning based on the direction and distance to reach the cup based on the visual and proprioceptive information.
3. Inverse kinematics and inverse dynamics to achieve this movement goal. The first operation is to get the end-point trajectory of your hand. The second one deals with joint torque and muscle activities (forces) necessary to move your arm along the trajectory.

The end-point location can be computed from a set of joint angles of the arm through a forward kinematic transformation. The opposite, to know the joint angles to achieve the end-point, is called the inverse kinematic transformation. The same holds true for generating motor commands that are translated into joint torques and muscle forces to move your arm to the target, i.e. forward and inverse dynamic transformation. It is thought that our nervous system is able to perform both inverse and forward operations.

Fig-1: Two types of internal models that have been prescribed by theorists lately, taken from [1], 5th ed.

           
Recently, scientists have adopted engineering theories to model motor control and learning. It is thought that sensorimotor transformations involve internal models that serve as a controller to do forward and inverse transformations.

Feedback and Feedforward Mechanism

There are essentially two mechanisms involved in performing goal-directed movements, i.e. feedback and feed-forward. These mechanisms are performed by the central nervous system using the internal models. Updates of internal models take place during motor learning.

In a feedback mechanism, we have our desired state that acts as a reference signal. A comparator compares this against any incoming information fed back from the sensory afferents. The difference, called the error signal, will go through a controller with a specific gain. The gain represents the proportion of future output w.r.t current error. The output signal produced by the controller subsequently controls the actuator, i.e. our skeletal muscles. A movement is produced and our sensory system re-evaluates the performance. The online feedback mechanism then continues.

For example, a ball is landing on the hand. The desired state is to grab the ball with the correct amount of force and to position our arm at a certain angle in space. Our muscle and cutaneous receptors provide feedback information on the weight and current position of the ball in space. The comparator in the brain first compares the current or actual situation with the desired state. The motor system in the brain then sends appropriate commands to the skeletal muscles accordingly. In control engineering, high gain causes the controller to be easily unstable if there are large delays across the loop. It is known that our nervous system has certain delays, so the gain has to be kept small. Fortunately, IMHO we are amazingly flexible. It is unthinkable how we become unstable (‘to miss’, will be a better word maybe).

Fig-2: Two types of hypothetical mechanisms on how humans perform a movement, taken from [1].

Unlike the feedback system which is adaptive in nature, the feed-forward mechanism is an anticipatory control that relies on the information before the feedback loop is put to work. This feature is important for rapid and sudden movements and usually depends on prior knowledge. In other words, feed-forward control allows us to predict the sensory consequences. E.g. we want to catch a ball. Relying heavily on visions, we position our arms in a certain way. Only when the ball hits our hand can the feedback system begin working.

Characteristics of Goal-directed Movements 
The motor system can be seen as the opposite of the sensory system. Our central nervous system resembles a black box where sensory afferents as the inputs and motor efferents as the outputs. What is sensory perception? It is the representation of external stimuli coming in contact with our five senses. We utilize this representation to produce a goal-directed action. In other words, there is a transformation involved from sensory maps into motor commands, a process that makes use of the internal model in the brain.

It is thought that the brain has extensive representations to plan voluntary movement called motor program. Goal-directed movements improve with practice and this implies that we always readjust our sets of motor programs. Not only does the motor program code movement specification, but it also contains the simplest forms of action spatially and temporally called motor primitives. These primitives can be in the form of kinematic (strokes, submovements with varying speed), dynamic (force, muscles-joint torque synergies, and control policies), or both. The program defines the intricate relationships among the spatial extent and speed, acceleration, skeletal joint angles, and force.

The time delay between the stimulus onset and the required movement is called the reaction time (RT). It varies with the amount of information processed. At the lower level, it reflects the number of synapses, and thus, neural circuits, involved. Voluntary movements due to proprioceptive stimuli are typically ~120 msec, and 150 – 200 msec due to visual stimuli. The shortest latency of a monosynaptic reflex is about 40 msec. Reaction time can be shortened by providing a person with the knowledge of the event and reducing the number of choices to make (minimizing choice effect).

What are the salient physical features of a voluntary movement? Typically,
1. The spatial trajectory is smooth. If it's not smooth, it can be an indication of movement disorder.
2. The velocity profile resembles a bell-shaped curve with acceleration and deceleration steps.
3. The endpoint variability increases as movement distance increases.
4. It displays a speed-accuracy trade-off (Woodworth, 1890).
We make less accurate movements when we are asked to move faster. Using the appropriate term, there is an increase in motor variability. This may be due to more recruitment of neurons and muscle, and the noise of the nervous system is well-known.

Lastly, in the context of voluntary movements of the upper limb, reaching and grasping are widely studied for many decades. Grasping usually follows reaching for an object. Are the two terms independent? Recent anatomical studies and neuroimaging have shed new light on this debate. We now know that reaching and grasping have two different neural substrates,  These two channels are:
(1) Reaching primarily involves the visual cortex → superior parietal lobule → dorsal premotor (PMd).
(2) Grasping primarily involves the visual cortex → supramarginal gyrus → ventral premotor (PMv).

Prelude: Motor Learning

Our motor system must adapt to our own biological development such as growth in limb size, muscle power, etc., and the environment through experience. More recent concepts say that motor learning involves adapting internal models for novel kinematics and dynamic conditions. As mentioned, sensorimotor transformations have kinematic and dynamic components. In learning dynamic tasks, tasks that require manipulation of force and joint torque, we depend heavily on our proprioception. Such tasks can be learned well with and without vision. Deafferented patients have difficulty controlling the dynamic properties of the limb without vision. Kinematic tasks involve vision more to define movement trajectories and speed. 

References
[1]  Chapter 33 - The Organization of Movement. In Kandel E.R. et. al. (2000). Principles of Neural Science 4e, McGraw-Hill.
[2]  Tamar, F. and Hochner, B. (2005). "Motor Primitives in Vertebrates and Invertebrates". Current Opinion in Neurobiology, 15:1-7.
[3]  The Brain: From Top to Bottom.