Faraday's laws of induction. e. This signal is in the form of a sinusoidal wave with ampli- tude decreasing with time. f. Without any modulations on the spins, they ...
GENERAL ¨ ARTICLE Keywords Magnetic resonance imaging, medical diagnostics, image processing.
Figure 1. Schematic overview of generation of an FID signal. a. Protons in a small region of space (voxel) with spins oriented in random directions b. Application of B 0 field causes splitting of energy states (+1/2 & –1/2) and spins with a lower energy level (+1/2) align parallel and those with higher energy (–1/2) level align anti-parallel to the B0 field. c. Application of 90o RF pulse causes rotation of the spin moments onto a transverse axis which revert back to their equilibrium positions at different rates depending on their environments. This phenomenon is called relaxation. d. During relaxation, the rotating spins induce an emf in the receiver coil according to Faraday’s laws of induction. e. This signal is in the form of a sinusoidal wave with amplitude decreasing with time. f. Without any modulations on the spins, they are expected to return to their equilibrium positions approximately at a time equal to five times their longitudinal relaxation constants.
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It allows the generation of images by subjecting them to a static magnetic field and understanding their environment through the phenomenon of resonance. The human body is composed of approximately 70% of water molecules. Protons in these water molecules have their spin angular moments oriented in random directions as shown in Figure 1a. An MRI system applies a static magnetic field B0 (in the order of 0.1T to 3T in clinical environments) which aligns all the protons in a direction parallel/anti-parallel to the field as shown in Figure 1b. The frequency of precession, called the Larmor frequency (ω) is directly proportional to B0 and is given by: ω = γB0 . (1) Here, γ is gyromagnetic ratio (rads−1 T−1 ), γ = 42.57 MHz/T for hydrogen atom at 1T. A radio-frequency field (B1 ) applied from an axis perpendicular to B0 , flips them away on a transverse plane as shown in Figure 1c. When the B1 field is turned off, the protons tend to realign in their equilibrium position through a process called relaxation as shown in Figure 1d. This is predominantly experienced as a re-growth of the longitudinal
RESONANCE ¨November 2015
GENERAL ¨ ARTICLE
magnetization through the spin–lattice relaxation rate (R1 ) and decay in the transverse magnetization through the spin–spin interaction (R2 ). This phenomenon produces an electromotive force (emf) in the RF receiver coil and the signal obtained is called free induction decay (FID) as shown in Figure 1e. The time domain signal created by the transverse magnetization S(t) is given as: S(t) = M⊥ (r)B⊥ (r)e−iφ(r,t)d3 r . (2) where, r is a vector representing 3-dimensional space, M⊥ (r) is the transverse magnetization, B⊥ (r) is the transverse component of the receiver coil B1 field as shown in Figure 2a, and the accumulated phase (in radians) is: t
φ(r, t) = γ
′)dt′ r · G(t
(3)
0
This process is modulated with the help of magnetic field gradients (G(t)) as shown in Figure 2a, produce spatially-varying magnetic fields in addition to B0 to spatially encode phase and frequency of the precessing protons.
RESONANCE ¨ November 2015
Figure 2. a. Schematic diagram showing components of an MRI system, magnet coil shown in red, gradient coils for three axes (Gx, Gy, Gz) shown in blue, and a radio-frequency transmit coil shown in green. The position-dependent frequency and phase information of the spins as an output of each scan is discretized and stored in k-space b. 2D Fourier transform of the k-space gives the image. c. T1-weighted image of a human brain with clear differentiation of white matter and gray matter.
