TR calculation in MRI image.

Question

Conventionally, a 90-degree RF pulse is used during MRI to flip the magnetization to the transverse plane (x-y plane). However, sometimes instead of using a 90-degree pulse, a 180-degree RF pulse is used to flip the magnetization to the negative Z-axis (i.e. flip the magnetization by 180 degrees). Assuming T1 of the gray matter at 3T is 1.6 sec, calculate the TR so that the gray matter signal is zero in the MRI image.

Answer 1

To calculate the TR required for the gray matter signal to be zero in the MRI image, we can use the formula for longitudinal magnetization (Mz) as a function of time (t):

Mz(t) = M0 * (1 - exp(-t / T1))

where M0 is the initial magnetization, T1 is the longitudinal relaxation time, and exp is the exponential function.

When a 180-degree RF pulse is used, the magnetization is flipped by 180 degrees and the longitudinal magnetization becomes negative. Therefore, to reach zero signal, the longitudinal magnetization needs to recover to the original value of M0. The time required for this to occur is given by the formula:

TR = 3 * T1

where TR is the repetition time.

Substituting the given value of T1 for gray matter at 3T (1.6 sec), we get:

TR = 3 * 1.6 sec = 4.8 sec

Therefore, the TR required for the gray matter signal to be zero in the MRI image is 4.8 seconds.