TR, TE and TI
Repetition time influences longitudinal recovery and scan timing. Echo time controls how much transverse decay occurs before signal is sampled. In inversion-recovery acquisitions, inversion time helps determine which tissue is nulled. Their exact effect depends on sequence family and implementation.
FOV, matrix and voxel size
Field of view and acquisition matrix determine in-plane pixel dimensions. Combined with slice thickness, they define voxel volume. Smaller voxels improve spatial detail but generally reduce signal per voxel. Changing matrix can also influence acquisition burden depending on which dimension is altered.
Slice thickness and NEX
Thicker slices collect signal from more tissue and generally increase SNR at the cost of through-plane resolution and partial-volume effects. Increasing the number of excitations or averages can improve SNR approximately with the square root of averages, but usually increases acquisition time.
Receiver bandwidth
Higher receiver bandwidth reduces chemical-shift displacement in the frequency direction and can reduce some distortion effects, but it admits more noise and therefore tends to reduce SNR. Lower bandwidth can improve SNR but increases sensitivity to frequency-related displacement and susceptibility.
A systems approach
The best parameter choice is not the maximum of any one metric. MRI optimization balances contrast, SNR, spatial resolution, temporal efficiency, artifact sensitivity, SAR or other safety constraints, and the diagnostic or educational goal of the acquisition.