Final answer:
In MRI, the maximum difference in transverse magnetization between two materials with the same equilibrium magnetization but different relaxation times occurs at a specific time which can only be calculated.
Step-by-step explanation:
In Magnetic Resonance Imaging (MRI), the difference in transverse and longitudinal magnetization for materials A and B with equal equilibrium magnetization (M0) but different relaxation time constants (T1 and T2) is of interest. Immediately following a 90° excitation, the longitudinal magnetization (Mz) in both materials will be zero since all the magnetization is in the transverse plane. As time progresses, materials A and B will relax back to their equilibrium states at different rates due to their different T1 (recovery of Mz) and T2 (decay of transverse magnetization, Mxy) values.
To maximize the absolute value of the difference in transverse magnetization ∆Sxy, one would need to calculate the rates of change of magnetizations for both materials and find the time at which the difference between these values is greatest. However, without the specific T1 and T2 values for materials A and B, an explicit expression cannot be provided. The transverse magnetization decays exponentially with time constant T2, and it is during this decay that the maximum difference will occur. For ∆Sz, the longitudinal magnetization, the recovery follows an exponential approach to M0 with a time constant T1.
The application of MRI in medical imaging is highly effective in providing detailed images of internal tissues and organs, using the property of nuclear magnetic resonance. Different tissues have characteristic T1 and T2 relaxation times, which assists in distinguishing between them for diagnostic purposes.
SUMUP: