fMRI, BOLD and the Beautiful

When we want to examine the brain of a person noninvasively by Computed Tomography (CT) or MRI, we get a ‘snapshot’ of the anatomy (or pathology, if any) of the subject’s brain. We are however clueless as to its functional aspect. fMRI or Functional Magnetic Resonant Imaging allows us to do just that. The difference is not unlike a ‘still picture’ versus a ‘video of a moving train’. PET scans, previously described, also can asses the functional state of the brain.

Whenever we do a task, think, dream, memorize, speak or see things, the brain is not activated as a whole; but only certain portions of it are activated. Activation, here, means increased metabolic activity of neurons in certain areas of the brain. Naturally, these ‘metabolically active’ neurons would demand more energy which would power them. The blood supply to these areas increases as a result of this metabolically driven vasodilation. The arteries then bring in glucose and oxygen with them, with Oxygen being transported in the form of Oxyhemoglobin (oxygenated hemoglobin or HbO2). Neurons on the other hand use up the oxygen contained in the blood, thereby reducing it to de-oxyhemoglobin or simply Hb. However, the alteration in tissue perfusion exceeds the extraction of oxygen by the neurons, so the concentration of deoxyhemoglobin within ‘the areas’ decreases. This causes molecular inhomogeneities in the magnetic field.

Oxyhemoglobin is diamagnetic, meaning that they align perpendicularly to magnetic field lines. On the other hand, deoxyhemoglobin is paramagnetic, i.e. it aligns parallely and proportinately with the intensity of the magnetic field. This causes the inhomogeneity within the magnetic field (magnetic susceptibility) in the tissue sampled. This inhomogeneity is exploited in fMRI in terms of decay of transverse magnetization, T2*, with longer T2* values in HbO2 blood and shorter values in Hb (paramagnetic) blood.Since this stems from the oxygen content in blood, fMRI is also known as the BOLD ((blood oxygenation level dependent) effect.

The machine is essentially the same as the MRI machine with echo planar imaging technology that permits faster imaging due to faster gradient switching, improved algorithm and faster CPU processing power. The patient/subject is placed inside the magnetic chamber and MRI signals are acquired, Fourier transformed and corrected for artifacts. Finally the computer reconstructs a 3D fMRI image out of this.

As is obvious, we can learn about the motor areas of a patient by asking him to grasp an object or giving him any motor task and noticing which area(s) of the brain lights up. A neurosurgeon can then be cautious about not hurting these areas. Similarly, the mapping will help spare motor and other vital areas like auditory, visual and language areas from damage in radiotherapy procedures, in addition to neurosurgery. It can also detect occult Alzheimer’s disease and cognitive deficits including those of the autism spectrum and dyslexia (reading disorder).

fMRI can also be employed to ‘read peoples’ minds’, thoughts, intentions including lie detection. Watch the video below which explains how an fMRI scan is done and interpreted.


Thus the legal and forensic implications are obvious. However, in fMRI, correlation doesn't always mean causation. Whatever it may be, it seems that fMRI is very much here to stay, both in the clinics as well as in cognitive neuroscience research. It may also be combined with tractography, MRI or other diagnostic radiologic modalities.

Hardenbergh et al combined Tractography techniques with fMRI, using a technique capable of rendering multiple color-coded functional activation volumes and fiber tract bundles. Many pharmacologically active drugs have effect on memory impairment, which can be seen in ‘telltale’ fMRI scans. Sperling et al studied the effects of lorazepam (a benzodiazepine) and scopolamine (an anticholinergic drug once used as ‘truth serum’ by the CIA) on healthy volunteers and found that they did impair memory and their functional coordinates could be reproducively mapped on fMRI scans (see figure on the left). I still shudder at the thought of what happened during my PG exam when I took a benzodiazepine.

Last modified: Mar 09, 2014
Reference: Integrated 3D Visualization of fMRI and DTI tractography
Gore, J. (2003). Principles and practice of functional MRI of the human brain Journal of Clinical Investigation, 112 (1), 4-9 DOI: 10.1172/JCI200319010

Relaxation in the Nuclear Microcosm

All of us want to give themselves a hard earned ‘rest’ after a “hard day’s night”, don’t we? So do the protons, perturbed by the destabilizing magnetic component of the radio-frequency pulse [which previously ‘happily’ aligned themselves to the externally applied magnetic field; one way (parallel) or the other (antiparallel)] applied at the Larmor frequency. It is like slapping an individual in a “merry go round” each time he came near a person who is paid just for slapping that person. But, when we call ‘spin’, we do not mean ‘spin’ the way we see them in a classical world. [We’ve given various names to the ‘quarks’: up, down, strange, bottom etc. depending on ‘something’ called ‘flavor’; and red, green and blue depending on ‘something’ called ‘color’.However, spin, flavor, color etc.‘in the quantum world’ have ‘no relevance’ to what we usually attribute to them in our everyday life. Things are a bit crazy in the quantum world, but I will take recourse to some ‘classical world’ analogies to make the description lucid.]

Thus, the already aligned nuclei (parallel or anti-parallel to the applied steady external magnetic field B0), has now been perturbed owing to the ‘knocking’ by the ‘magnetic component’ (B1) of the electromagnetic RF pulse. The nuclei gain energy and sway away from the perpendicular to the horizontal (90 degree) depending on how long the RF pulse is applied. So, now the nuclei behave like ‘punch-drunk’( like a person who’s been reeling due to a strong blow to the head!). Remember, that this new angular momentum is also a vector quantity having magnitude and direction. It can be resolved in terms of a horizontal component (Mxy) and a vertical component Mz. Anyway, the proton does recover from this situation, after some time, once the external RF field has stopped. Typically, Mxy component decays faster than the recovery of Mz.

The excited proton recovers in two ways and both forms occur simultaneously: (1) The excited nuclei which now have been ‘forced’ to lie horizontally (90 degree), ‘re-align’ themselves back to their ‘original position’ as they were before the RF pulse (perpendicularly towards the field of externally applied field B0); and (2) the energized protons dissipate their energies to the surrounding nuclei (horizontally) at their level. The first example, obviously, is called the (spin-lattice, or longitudinal) relaxation; while the second one, transverse relaxation (T2). There is little energy loss due to RF emission.

T1 relaxation, also known as, longitudinal relaxation or spin-lattice relaxation can be best understood if you see the following Youtube video. [The spiral trajectory, in this case, reminds me of the laser experiment I did to satisfy my lesser friends. Analogically, the trajectory would be such, if the power supply were switched off.] In T1 relaxation, the proton loses energy to the surrounding lattice, by interacting with nuclei in the lattice which are in vibrational, translational and rotational motion. Clearly, the surrounding nuclei (lattice) having the same (or nearly same) Larmor frequency will efficiently absorb energy of the excited proton, resulting in a tiny rise of temperature.

T2 relaxation (transverse or spin-spin relaxation) on the other hand, does not involve exchange of energy with the lattice.
The magnetic moments of the protons merely changes phase. Here, the nuclei exchange “quantum states” (kind of, what Einstein called ‘spooky action at a distance’): an excited nucleus (proton) will transfer its energy and relax, while the neighboring nucleus in the lower energy state that absorbs it becomes excited. This loss of phase coherence of spins can be clearly seen in this beautiful video.

It can be understood easily that T1 and T2 values would depend on the surrounding molecular environment (tissues, for example). Hence, the values differ in different tissues. Again, since Mxy decays faster, as described, it may be understood why T1 is greater than T2 (usually, T1=5T2). Both T1 and T2 contribute toward contrast in tissues. T1 relaxation time is the time needed for 63% of protons to return to their previous equilibrium state. Likewise, T2 relaxation time is the time needed for 63% of protons to become dephased owing to their interaction with nearby protons. The contrast, naturally depends on the water content of the tissues. Grey matter has about 10% more water than white matter and this creates a contrast. We can also create contrast by varying TR and TE times.

TR (Repetition Time) refers to the time gap at which consecutive RF pulses are applied; while TE (Echo Time) refers to the time delay between the applied RF pulse and its reception (echo). T1 weighted images (T1W) are produced by keeping TR and TE relatively short, while T2 weighted images (T2W) are produced by keeping TR and TE relatively long. Water molecules being relatively light spins much faster than the Larmor frequency, making energy transfer rather tough (exchanging of packets of energy becomes more efficient as the relative angular velocity narrows). Consequently, water has a long T1 time. Proteins and nucleic acids being rather heavy, spin slowly. They also have problem with energy exchanging, and thus have a long T1. Cholesterol, a medium sized molecule, precesses near the Larmor frequency, efficiently absorbing the energy and giving a small T1 value.Thus (fat) liquid cholesterol in craniopharyngiomas, a benign tumor, appears bright on T1W images (T1 being small, the rate at which RF energy is released is fast. Hence, the signal intensity in NMR is high).

Subacute hemorrhage also has shorter T1, due to the presence of paramagnetic iron in methemoglobin present in the tissue, hence high signal intensity. Cerebrospinal fluid (CSF), edema (collection of fluid in tissue space or ECF) having more water content have both long T1 & T2 relaxation time. They give low signal intensity in T1 (dark) but higher signal intensity (bright) in T2W images. T2W images are superior to their T1 counterparts in case of infarction, edema, demyelination etc. Contrast agents like the heavy metal Gadolinium, a paramagnetic substance, has been used to reduce both T1 and T2 times by introducing inhomogeneity in the magnetic field. Gadolinium is complexed (chelated) with a substance called DTPA to prevent toxic build-up inside body tissues. This gives high signal in T1W but a low signal in T2W. It (the complex) does not cross the blood brain barrier (BBB); but disruption in the BBB or parts of the brain where it is deficient (circumventricular organs), take-up the substance and affects relaxation properties.

Below is an MRI showing changes in Subacute Sclerosing Panencephalitis, a complication of measles. Note: Panels A and C are T1-weighted images; B and D are T2-weighted images. The hypointense (darker) signal on the T1-weighted image (arrow in A) and a hyperintense (bright) signal on the T2-weighted image (arrow in B) can be clearly seen.

Given all these, it can be said that relaxation parameters of nuclei have enabled us in visualizing biological tissues nonivasively, identifying chemicals spectroscopically and a lot more as we shall see later.

• References: Magnetic Resonance Imaging: David D. Stark, William. G. Bradley, Jr.

• NMR spectroscopy
• Magnetic Resonance Imaging
• Principles of NMR
• William P. Dillon. Neuroimaging in Neurologic Disorders. In: Harrison's Principles of Internal Medicine, 17th Ed., Volume 2, McGraw Hill; 2008. p. 2491-2497.
• Ian L. Pykett, Ph.D., Jeffrey H. Newhouse, M.D., Ferdinando S. Buonanno, M.D., Thomas J. Brady, M.D., Mark R. Goldman, M.D., J. Philip Kistler, M.D., & Gerald M. Pohost, M.D. (1982). Principles of Nuclear Magnetic Resonance Imaging Radiology
• Time constants

Last Modified: Aug 19, 2010

Fourier Analysis: The Art and Science of Finding The Needle in a Haystack

Every time I listen to the heavy metal band Pantera my wife would invariably wonder aloud why I listen to all this ‘noise’. True, many music lovers would rather refer bands like Pantera as quintessential noise than music; there are persons like me who can dissect the melody from the apparent chaos of runaway frequencies of guitars, drums and so on. I can even analyze and follow individual instruments over time. This is what Fourier is about, or stated otherwise, my ear & brain can be said to be doing a Fourier transform on the said musical piece.

Joseph Fourier, a French mathematician, realized that all periodic waves could be ‘synthesized’ by mixing sine waves of right frequency, amplitude and phase. For example, a square wave could be prepared by ‘adding’ the fundamental frequency (the lowest frequency; say 70Hz) with an infinite number of its odd harmonics (e.g. 210Hz, 350Hz, 490Hz and so on. Harmonics are multiples of the fundamental frequency.) This is Fourier synthesis. Similarly, you could break down a periodic signal in which the amplitude varies over time into one of a frequency versus time graph. This is Fourier analysis, and it can be seen that here we are actually ‘decomposing’ the ‘signal’ into its frequency spectrum, over time. The process of decomposing a function into its constituent frequencies is known as Fourier transform. You can have a ‘hands on experience’ at what a square wave ‘looks’ or ‘sounds’ like and how a periodic wave is decomposed into its constituent parts here. Do experiment on the sine, cosine, triangle wave and square wave functions as well and turn on the sound of your PC while you are at this site!

While Fourier originally devised this to solve the problem of heat propagation, the impact of Fourier analysis can now be felt in almost every field of science, instrumentation, entertainment and telecommunications, and even arts. Whenever you use your audio graphic equalizer to suit a piece of musical performance to your taste, you are doing a Fourier. Here you are boosting some particular audio frequencies while suppressing others, obtained by a Fourier analysis of the audio signal. You are assigning relative weights to the frequencies by sliding those sliders. Likewise, when you compress a picture (graphic) file using software such as JPEG, an inbuilt program does a Fourier transform,--> eliminates the weaker components from the analysis and--> then saves the information in a compact way.

In Nuclear Magnetic Resonance Imaging (NMRI), the emitted radio frequency is Fourier transformed to give frequency versus time, throwing valuable information about nuclear spins. Fourier analysis may also be employed to remove mains AC hum frequencies, in mobile telephony and many other situations.

One day, we may expect, that Fourier analysis may be used to pick up the ‘right frequency’ in the brain EEG waves and may put the study of ‘mirror neuron’ and ‘thought controlled devices’ into a whole new domain.

Last modified: May15, 2013
Reference: Fourier analysis (Wikipedia),
Explained: The Discrete Fourier Transform