The Imaging

Abstract

In the presence of an external static magnetic field H₀ say applied in the Z-direction the isolated non-interacting (no quantum correlation) spins will try to align themselves along the field. The spins do not stay stationary along the Z-direction. Instead they precess (rotate) randomly at a resonance frequency of ω₀ around the field H₀. Here ω₀ = γ H₀, γ being the gyromagnetic ratio (GMR) = (μ_b/ђ), ђ is the angular Planck’s constant and μ_b is the fundamental dipole magnetic moment moment of an atom called as the Bohr magneton. The frequency ω₀ is referred to as the Larmor frequency. Now if an additional RF electromagnetic field say H₁ in the form of a pulse is applied along a perpendicular direction to H₀, say in the X-direction the angle of precession around the Z-direction of the spins acquires new angle α = (γH₁ τ). This angle α is called as the flip angle and the time τ is called as the pulse time. This simplified picture is true if the applied RF signal has a single frequency and is in exact resonance with the natural frequency of vibration of a single spin i.e. the Larmor frequency. But the pulse has a bandwidth of frequencies Ω_i. Further a single spin is not in vacuum and is surrounded by many others of varied nuclear structure. The angle α should thus be α = (Ω_i − ω₀) τ, different angle for each frequency. In fact it should be α = (Ω_i − ω₀) T, where T is the time when signal is measured and the time T ≫ τ. The response of the pulse is measured as a decay of the maximum amplitude with time. The rate of decay will be different in different directions. In the X–Z and Y–Z planes it is taken as T₁ and in X–Y plane it is T₂. The mapping of the anisotropic structure of T₁ and T₂ in different directions (X, Y, Z) leads to T₁ and T₂ weighted images.