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When a magnetic moment is directed at some finite angle with respect to the magnetic field direction such as H nuclei in tissue, the field will exert a torque on the magnetic moment. This causes it to precess about the magnetic field direction. This is analogous to the precession of a spinning top around the gravity field. It can also be visualized quantum mechanically in terms of the quantum energy of transition between the two possible spin states for spin 1/2. The angular frequency associated with a "spin flip", a resonant absorption or emission involving the spin quantum states is often written in the general form;
If the frequency, Ï‰ of the Radio Frequency (RF) pulse matches the frequency of the precession of the protons (H nuclei), then resonance occurs, e.g. 1H has a Larmor frequency of 42.58 MHz at 1T so applying a RF pulse with that frequency will result in resonance and spin flipping in 1H protons. Before the application of this RF pulse, the net magnetization vector, M0 precesses about the external magnetic field (B0 (usually along Z axis), termed the longitudinal axis/plane) but is out of phase with it. When the RF pulse is applied, M0 precesses about the magnetic field of the RF pulse with a frequency equal to the Larmor frequency, in phase with the magnetic field of the RF pulse and in the transverse plane (XY plane). Simultaneously, the magnetic field of the RF pulse causes a spiral downward motion of the protons. The angle to which M0 moves out of alignment with the external magnetic field is the flip angle, Î±. For Î± = 90o, M0 is anti-parallel to the external magnetic field, i.e., flipped onto transverse plane. These processes would not occur if the resonance condition was not fulfilled.
Classically the spin population states are divided into "parallel" and "antiparallel": what is the approximate population difference between these two states at 1.5T?
In MRI, the precessing magnetization induces an oscillating signal in a pick-up coil. The strength of this magnetization (M0) is determined not only by the (extremely small) size of the magnetic moments of the nuclei in question, but also by the net difference between the number of nuclear spins aligned parallel and anti-parallel to B0. This fractional population difference is known as the polarization, P. The population difference is dictated by the Boltzmann distribution to give:
N = number of spins in a given state
Î³ = gyromagnetic ratio for the given nuclei (Ï‰/B0)
kB = Boltzmann constant
T = sample temperature (K).Â
Because of the weakness of nuclear magnetic moments, the difference in energy between "spin up" and "spin down" states is very small.Â This forces the populations of the spin states to be very nearly equal (often differing by only ~0.001% or less)-thus yielding very little net magnetization.Â
I calculated P â‰ˆ 0 using the following values; Î³ = 42.58 MHz, T = 310K, B0 = 1.5T.
Describe what is meant by the Free Induction Decay (FID) of the MR signal
When the RF pulse is switched off, M0 is again influence only by B0 and it tries to realign with it. Amount of magnetization in the transverse plane gradually decreases. This reduction in induced signal in Transverse coil is called the Free Induction Decay (FID) Signal.
Describe what is meant by spin-lattice relaxation. How is it described mathematically?
Spin-lattice relaxation is also known as T1 Recovery. It is caused by the nuclei giving up their energy to the surrounding environment or lattice. T1 is the time constant that characterizes the rate at which the MZ component (longitudinal component) recovers its initial magnetization M0. This rate of recovery is an exponential process and it is the time it takes 63% of the longitudinal magnetization to recover in the tissue.
MZ(t) = M0 (1 - e -t/T1)
Describe what is meant by spin-spin relaxation. How is it described mathematically?
Spin-spin relaxation or T2 Decay is caused by nuclei exchanging energy with neighbouring nuclei through interaction of the B fields of each nucleus. This results in loss of magnetization in the XY plane (transverse magnetization). The time constant T2 is the time it takes 63% of transverse magnetization to be lost.
MXY(t) = M0 e -t/T2
Using the spin echo sequence, describe how the timing parameters can be adjusted to reflect T1, T2 and proton density in the image
a = Echo Time (TE), the time between the 90Â° RF pulse and MR signal sampling, corresponding to maximum of echo (shown at the peak of signal, g). b = TR, Repetition Time is the time between 2 excitations pulses (time between two 90Â° RF pulses).
d is the phase of the signal. The input radiofrequency signal causes dephasing in the sample. This signal is applied for a relatively short period of time at the start of the scan. The dephasing is reversed by applying the 180o pulse.
The signal at e is related to the 'slice'.
The plot at g is the echo signal.
Question 3: (a) Describe briefly the physical basis of the following MRI artefacts:
Truncation or Gibbs
A data truncation artefact may occur when the interface between high and low signal intensities is encountered in one imaging plane. This artefact is found in both frequency and phase axes. Complex shapes are specified by series of sine and cosine waves of various frequencies, phase and amplitude. Some shapes are more difficult to encode than others. The most difficult shapes to represent with Fourier series of terms are waveforms with tissue discontinuities or edges. If not enough samples are taken, these areas cannot be accurately represented. The truncation of the infinite data series results in a ringing artefact because of the inability to accurately approximate this tissue discontinuity with a shorter truncated data set. Therefore, the ringing that occurs at all tissue boundaries on MR is called truncation artefact.
There are various causes for zipper artefacts in images. Most of them are related to radiofrequency interference. The zipper artefacts that can be controlled easily are those due to RF entering the scanning room when the door is open during acquisition of images. RF from some radio transmitters will cause zipper artefacts that are oriented perpendicular to the frequency axis of your image. Frequently there is more than one artefact line on an image from this cause. Other equipment and software problems can cause zippers in either axis.
The chemical shift artefact is commonly noticed in the spine, in the abdomen, and in the orbits where fat and other tissues form borders. In the frequency direction, the MRI scanner uses the frequency of the signal to indicate spatial position. Since water in organs and muscle resonate at a different frequency than fat, the MRI scanner mistakes the frequency difference as a spatial (positional) difference. As a result, fat containing structures are shifted in the frequency direction from their true positions. In the abdomen and orbits, this causes a black border at one fat-water interface, and a bright border at the opposite border. This artefact is greater at higher field strengths and lesser at higher gradient strengths.
(b) In a magnetic field, fat precesses at a lower frequency that water giving rise to a "Chemical shift". At 1.5T, the frequency difference is 210Hz. For an image matrix of 256 x 256 and a receive coil bandwidth of 16 kHz, calculate the size of the "shift" between water and fat in pixels.
Chemical Shift = bandwidth / pixels.
Chemical Shift = 32 kHz / 256 pixels = 125 Hz / pixels.
Frequency difference/ Chemical Shift = 210 Hz / 125 Hz/pixel = 1.68 pixels.
Question 4: Using diagrams where appropriate, briefly describe k-space under the following headings
what does k-space represent
K-space represents a temporary image space. Data from the MRI signal is stored in k-space while more data is being acquired (during an MRI scan). At the end of a scan, when k-space is full, a Fourier Transform is applied to produce the image. K-space is in the spatial frequency domain.
how is k-space normally filled
If k-space is thought of as a grid, lines of k-space are often numbered with the lowest numbers nearest to the central axis and the higher numbers towards the outer edges. Lines in the top half of the k-space 'grid' are positive lines and in the bottom half they are called negative lines. The line to be filled during a pulse sequence is determined by the polarity and the slope of the phase gradient. In order to fill different lines of k-space with data the phase gradient is altered every TR (TR = repetition time, between pulses). Steep slopes (of either positive or negative polarity) fill the outer lines, while shallow slopes correspond to the central lines. Therefore, for image resolution both the polarity and slope of the phase gradient must be altered. K-space is filled in a linear fashion, either from top to bottom or from bottom to top.
what determines k-space co-ordinates
The discussion outlined in (b) above indicates how each section of k-space is filled with data. The coordinates in k-space are spatial frequencies. These describe how image features change as a function of position in the image. The object has low spatial frequency, whereas edges have high spatial frequencies.
how does an absence of data in k-space affect the image
If the image is constructed using only low spatial frequencies (from the centre of k-space) it will have low resolution. In the opposite case, using only high spatial frequencies the resulting images has poor contrast with only the borders between objects visible. Increasing the amount of peripheral information used in constructing the image increases the spatial resolution. Information from the centre of k-space corresponds to contrast and information from the edges corresponds to resolution.
Question 5: (a) Describe four important safety hazards in MRI.
Heating: Bodily fluids contain carrying concentrations of ionized chemical species; these conduct the flow of electrical current to produce nerve signals. The electrical and magnetic forces for the radiofrequency signal cause the ions to oscillate many times per second. Heat is produced by ions colliding with each other and the surroundings. This is usually a very small temperature increase and should not exceed 1oC (according to the FDA in the US).
Electrical Interference: this is too low to alter heart rate or brain function and cause heart attacks or seizures. In machines with magnetic field strength of 4T short term effects such as aural and visual hallucinations have been reported, however, no lasting consequences have been recorded.
Magnet Safety: there is a so-called 'missile effect' associated with the magnet in the MRI machine. This is where magnetic objects in the area are attracted very forcefully towards the strong magnet. Such objects include surgical tools, keys and respiratory gas tanks. These objects should not be allowed into the MRI room if injury is to be prevented. Biological implants such as pins or plates and pacemakers and cochlear implants are also contraindications for an MRI exam. The field outside the scanner drops rapidly but should still be considered when locating and building an MRI room.
Weight: MRI scanners are extremely heavy (approximately 100 tons) and as a result many MRI rooms are in basements or, at very least, on strong, stable structures to prevent a ceiling collapse.
(b) What is meant by SAR? Define the units used to measure this parameter. What is the whole body limit and note which sequences are a particular concern and may give rise to radio-frequency effects?
SAR is the specific absorption rate of heat into tissue. It is measured in Watts per kilogram (W/kg). In the USA, the Food and Drug Administration (FDA) states that the legal SAR limit is 4 W/kg averaged over the whole body for any 15 minute period.
Since SAR increases with the Power of the incident Radiofrequency, sequences with higher power are most likely to cause Radiofrequency effects. A TR with longer than the minimum time needed provides time for the sample tissue to cool down.