Spin-lattice relaxation time

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Spin-lattice relaxation time, known as T₁, is a time constant in Nuclear Magnetic Resonance and Magnetic Resonance Imaging. It is named in contrast to T₂, the spin-spin relaxation time.

T₁ characterizes the rate at which the longitudinal M_z component of the magnetization vector recovers. It is thus the time it takes for the signal to recover 63% [1-(1/e)] of its initial value before being flipped into the magnetic transverse plain. Hence the relation:

M_z(t)= M₀(1-e^-t/T₁)

The name spin-lattice relaxation refers to the time it takes for the spins to give the energy they obtained from the RF pulse back to the surrounding lattice in order to restore their equilibrium state.

The sample in which the nuclei are held is called the lattice. Nuclei in the lattice are in vibrational and rotational motion, which creates a complex magnetic field. The magnetic field caused by motion of nuclei within the lattice is called the lattice field. This lattice field has many components. These components of the lattice field can interact with nuclei in the higher energy state, and cause them to lose energy (returning to the lower state). The energy that a nucleus loses increases the amount of vibration and rotation within the lattice (resulting in a tiny rise in the temperature of the sample).

The relaxation time, T₁ (the average lifetime of nuclei in the higher energy state) is dependant on the gyromagnetic ratio of the nucleus and the mobility of the lattice. As mobility increases, the vibrational and rotational frequencies increase, making it more likely for a component of the lattice field to be able to interact with excited nuclei. However, at extremely high mobilities, the probability of a component of the lattice field being able to interact with excited nuclei decreases. Different tissues have different T₁ values. For example, fluids have long T₁s (1500-2000 mSec), and water based tissues are in the 400-1200 mSec range, while fat based tissues are in the shorter 100-150 mSec range.

[edit] T₁ weighted images

In MRI, T₁ weighted images can be obtained by setting short TR ( < 750mSec ) and TE ( < 40mSec ) values in conventional Spin Echo sequences, while in Gradient Echo Sequences they can be obtained by using flip angles of larger than 50^o while setting TE values to less than 15 mSec.