Magnetic Resonance Imaging - Essay Example

MAGNETIC RESONANCE IMAGING Insert name Insert supervisor name Insert date QUESTION 1 Magnetic moment when defined from the perspective of a magnet is a measure of the quantity that determines the force that can be exerted on electric currents by the magnet and the torque produced when the magnet is under the influence of a magnetic field. (Slichter 9) An electron can be taken as an example to show the notion of magnetic moment. The movement of an electron around the nucleus produces a magnetic field. The electron spinning around the nucleus has an angular momentum, L defined thus; L = Mass x Radius of orbit x Velocity The electron forms a current loop that creates a magnetic moment  which is defined as;  = IA, where in this case A is the loop area and I is current. When the magnetic moment is quantised in units of the Bohr magnetron we get; = m B, where: B = eh/4me (~9.27x10-24 Am2), where e=electron charge, h=Planck’s constant and me = electron mass. Another example that can be used to portray magnetic moment is the solenoid. A solenoid can be considered to be a combination of several current loops. A current loop has a magnetic moment defined; M=IS, where I = current and S = vector area. For the solenoid composed of several identical single layer turns or windings, the magnetic moment is the sum of individual turns so that we have; m = NIS, where N is the number of turns, I is current and S the vector area. (Westbrook and Kaunt 18)  Figure 1; An illustration of the magnetic moment Source Hoult, D I (2000) The principle of reciprocity in signal strength calculation - A mathematical guide, Concepts in Magnetic Resonance 12(4): 173-187 QUESTION 2 Energy of photon E = hf where h is Planck’s constant and f = frequency E = 6.626 X 10 -34 X 2 x 10-19 Hz = 1.33 X 10-52 J Doubling of magnetic field strength Doubling of the magnetic field strength will lead to a corresponding doubling of the energy difference of hydrogen nucleus spin states. Magnetic strength is directly proportional to energy differences of spin state according to the formula below. This is the case if μ is held constant so that E is directly proportional to BO. (Hoult 87) E = -μ • B0, where E is the energy of the initial spinning particle                 μ is the individual magnetic moments                 • is the dot product of the vectors μ and B0 Significance of relative energies used The energies used for MRI are higher than for CT. The principle behind MRI is to use a strong magnetic field to bring about magnetisation and alignment of selected atoms (mainly hydrogen) in the body. Radio frequencies are then used realign the magnetisation of the atoms in a systematic manner. The result is that a magnetic field is produced by the rotating nucleus which is detected by a scanner. CT on the other hand makes use of traditional x-rays to eventually produce images. (Squire 42) MRI uses relatively higher energy compared to X-ray. MRI requires strong magnetic fields to produce good images which are possible only with superconducting magnets. These require more energy to sustain in addition to the energy required to generate the radio frequencies. CT requires x-rays which need a lot of energy to create but is only required for short moments. (Squire 42)  Figure 2; The protons in the diagram above are aligned to an external magnetic field Bo in either an anti-p parallel or parallel form. The parallel state surpasses the anti-parallel in energy frequency. Source : C. P. Slichter, Principles of Magnetic Resonance, 3rd ed., Springer Verlag, New York, 1989, pp. 35-36. Question 3.Calculate the resonance frequencies of the following nuclides at 1.5T and 4T: 1H, 13C and 31P. Atoms such as hydrogen-1 (1H) and phosporous-31 (31P) resonate at different Larmor radio frequencies because of differences in the magnetic properties of their nuclei Hydrogen-1 (1H) Since 1H oscillates at 42.573 MHz (Tesla, unit for measuring magnetic flux), and T is inversely proportional to frequency, T=1/f and f = 1/T. Hydrogen = 42.573 MHz / T Resonance frequency (Rf) of IH at 1.5T can be calculated using the first formula as: 1.5 T= Rf (MHz) / 42.573MHz Rf (MHz) =1.5 T x 42.573 MHz Resonance frequency of 1H at 1.5 T =63.86 MHz Or using the second formula as 42.573 MHz = Rf (MHz) / 1.5T Rf (MHz) = 1.5 T x 42.573 MHz Resonance frequency = 63.86 b. 1H at 4T will be: f = 1/ T 42.573 MHz = Rf (MHz) /4T Rf = 42.573 x 4 Resonance frequency of IH at 4T = 170.292MHz. 2. Phosporous-31 (31P) Phosporous-31 = 42.573 MHz / T Phosporous-31 oscillates at a frequency of 17.25 MHz at 1T. As such, its resonance frequency: At 1.5T is: T= 1/f and f = 1/ T 1.5 T = Rf (MHz) /17.25 MHz Rf= 1.5 T x 17.25 MHz Resonance frequency of 31P at 1.5 T = 25. 875 MHz. At 4 T is: f = 1/ T 17.25 MHz = Rf (MHz)/ 4T Rf = 17.25 KHz x 4T Resonance frequency of 31P at 4 T = 69 MHz. Carbon-13 (13C) resonance frequency Carbon-13 = 42.573 MHz / T 13C oscillates at a frequency of 10.71 MHz at 1T. At 1.5 T: T=1/ f 1.5 T= Rf (MHz)/10.71 MHz Rf = 10.71 MHz x 1.5T The resonance frequency of 13C at 1.5T = 16.07 MHz At 4T: T=1/ f 4 T= Rf (MHz)/10.71 MHz Rf = 10.71 MHz x 4T The resonance frequency of 13C at 4T = 42.84 MHz Question 4 Rotating frames When a RF pulse is applied at 900 at the resonance frequency, the protons absorb energy and a single proton jumps to a higher energy state at the quantum level. At the macro level, if we assume an observer in the laboratory frame [where the laboratory is stationary and the protons are spinning], the magnetisation vector, Mø, is observed to spiral downwards towards the XY plane. If the observer would somehow get on-board Mø, then the laboratory would appear to be rotating around the observer. This constitutes the rotating frame of reference and the magnetisation vector would tip down smoothly. This tip angle is a function of the duration and strength of the RF pulse. (Madhu 12)  Figure 3; The figure shows both rotating and non rotating coordinate systems Source : C. P. Slichter, Principles of Magnetic Resonance, 3rd ed., Springer Verlag, New York, 1989, pp. 35-36. Works cited Madhu, P K and Kumar, A (1997) Bloch equations revisited: New analytical solutions for the generalized Bloch equations. Concepts in Magnetic Resonance 9(1): 1-12 Hoult, D I (2000) The principle of reciprocity in signal strength calculation - A mathematical guide, Concepts in Magnetic Resonance 12(4): 173-187 Squire LF, Novelline RA (1997). Squire's fundamentals of radiology (5th ed.). Harvard University Press Westbrook, Catherine and Kaut, Carolyn (1998) 1. Basic principles 2. Image weighting and contrast. in MRI in Practice, 2nd end.. Oxford: Blackwell Science, pp. 4-15; 17-32. C. P. Slichter, Principles of Magnetic Resonance, 3rd ed., Springer Verlag, New York, 1989, pp. 35-36. Henkelman, R M, Hardy, P A, Bishop J E, Poon, C S and Plewes, D B (1992) Why Fat Is Bright in RARE and Fast Spin-Echo Imaging. JMRI 2(5): 533-540. Denker, J. “Multi-Dimensional Rotations, Including Boosts” ./rotations.htm Read More