# T1 relaxation time

The T1 relaxation time, also known as the spin-lattice relaxation time, is a measure of how quickly the net magnetisation vector (NMV) recovers to its ground state in the direction of B0. The return of excited nuclei from the high energy state to the low energy or ground state is associated with loss of energy to the surrounding nuclei. Nuclear magnetic resonance was originally used to examine solids in the form of lattices, hence the name "spin-lattice" relaxation. Two other forms of relaxation are the T2 relaxation time (spin-spin relaxation) and T2* relaxation.

T1 relaxation is an exponential process as shown in the figure to the right. The length of the net magnetisation vector for a spin echo sequence is given by the following equation:

###### Mt = Mmax(1-e-t/T1)

Where Mt is the magnetisation at time = t, the time after the 90o pulse, Mmax is the maximum magnetisation at full recovery.

At a time = one T1, the signal will recover to 63% of its initial value after the RF pulse has been applied. After two T1 times, the magnetisation is at 86% of its original length. Three T1 times gives 95%. Spins are considered completely relaxed after 3-5 T1 times.

Another term that you may hear is the T1 relaxation rate. This is merely the reciprocal of the T1 time (1/T1). T1 relaxation is fastest when the motion of the nucleus (rotations and translations or "tumbling rate") matches that of the Larmor frequency. As a result, T1 relaxation is dependent on the main magnetic field strength that specifies the Larmor frequency. Higher magnetic fields are associated with longer T1 times.

T1 weighted images can be obtained using an inversion recovery sequence or by setting short TR (<750ms) and TE (<40ms) values in conventional spin echo sequences. In gradient echo sequences, T1WI can be obtained by using flip angles over 50o and setting the TE to less than 15 ms.

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rID: 6315
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