Longitudinal relaxation rate equal to reciprocal of T1 relaxation time (R1= 1/T1).

Longitudinal relaxation rate equal to reciprocal of T2 relaxation time (R2 = 1/T2).

The basis of T1 weighted imaging is the longitudinal relaxation. A T1 weighted magnetic resonance image is created typically by using short TE and TR times.
The final image is a reflection of more than one of these pulse sequence parameters, weighted according to the type of sequence and its timing. T1 signals determine predominantly the contrast and brightness in this type of images but proton density will always contribute to the image intensity. The T1 dependence is mainly determined by the repetition time or any pre-pulses (such as in an inversion recovery pulse sequence).
Due to the larger longitudinal and transverse magnetization, fat has a higher signal and will appear bright on a T1 contrast MR image. Conversely, water has less longitudinal magnetization prior to a RF pulse, therefore less transverse magnetization after a RF pulse yielding low signal appearing dark on a T1 contrast image. Often, a paramagnetic contrast agent, a gadolinium compound, is administered, and both pre-contrast T1 weighted images and post-contrast T1 weighted images are obtained.

The relaxation effect is the transition of an atom or molecule from a higher energy level to a lower one. The return of the excited proton from the high energy to the low energy level is associated with the loss of energy to the surrounding tissue. The T1 and T2 relaxation times define the way that the protons return to their resting levels after the initial radio frequency (RF) pulse. The T1 and T2 relaxation rates have an effect of the signal to noise ratio (SNR) of MR images.
The relaxation process is a result of both T1 and T2, and can be controlled by the dependency of one of the two biological parameters T1 and T2 in the recorded signal. A T1 weighted spin echo sequence is based on a short repetition time (TR) and a change of it will affect the acquisition time and the T1 weighting of the image. Increased TR results in improved SNR caused by longer recovering time for the longitudinal magnetization. Increased TE improves the T2 weighting, combined with a long TR (of several T1 times) to minimize the T1 effect.