Читать книгу Essentials of MRI Safety - Donald W. McRobbie - Страница 13

Hydrogen is the simplest element in the universe with the atomic number of one, meaning its nucleus possesses a single proton. The proton is said to exhibit a property known as spin. The consequences of spin only become observable in an externally applied magnetic field (denoted B₀) in which the proton spins precess, like spinning tops or gyroscopes, around the direction of B₀. In the external field the proton spins must adhere to specific energy levels or quantum basis states (Figure 1.3a). A slight imbalance between the populations of these results in a net magnetization, M₀ (Figure 1.3b). M₀ can be manipulated by applying the appropriate frequency (or energy) of electromagnetic radiation. This is the Larmor or resonance frequency:

(1.1)

where the subscript “0” means “at resonance”. γ (“gamma bar”) is the gyromagnetic ratio of the hydrogen nucleus. When frequency f is expressed in MHz and B₀ in tesla, γ has a value of approximately 42.58 MHz T^‐1. This simple relationship underpins all of MRI.

Figure 1.3 Nuclear magnetism: (a) basis state energy differences; (b) formation of macroscopic magnetization M₀ from the sum of basis state spin vectors.

The radiofrequency energy is applied as a magnetic field B₁ orthogonal to the direction of B₀ (Figure 1.4). Whilst B₁ is present the magnetization precesses around both B₀ and B₁ directions, tipping away from the z‐axis (usually head–foot) of the scanner. B₁ is applied in a short burst as a RF pulse. The angle of deflection away from the z‐axis is known as the flip angle α. For a simple rectangular shaped RF pulse this is

(1.2)

where t_p is the duration of the pulse (in seconds), B₁ is the amplitude of the “excitation” pulse (in tesla), and γ = 2π × γ (2.68 × 10⁸ radians s^‐1).