Hi,
Excuse me, can you help me to solve?
The normal human brain at 3 T has tissue T1 and T2 times. Which of the following shows the correct tissue-longitudinal magnetization pair after 30∘ flip angle and 400 ms time delay if the initial magnetization M0=1? (At 3 T, T1 and T2 values of gray matter are 1331ms and 80ms respectively. T1 and T2 values of white matter are 832ms and 110ms)
Gray Matter, Mz=0.55
White Matter, Mz=0.36
White Matter, Mz=0.74
Gray Matter, Mz=0.90
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The normal human brain at 3 T has tissue T1 and T2 times. Which of the following shows the correct tissue-transverse magnetization pair after 60∘ flip angle and 50 ms time delay if the initial magnetization M0=1? (At 3 T, T1 and T2 values of gray matter are 1331ms and 80ms respectively. T1 and T2 values of white matter are 832ms and 110ms)
Gray Matter, Mz=0.36
White Matter, Mz=0.55
Gray Matter, Mz=0.67
White Matter, Mz=0.74
Gray matter
To solve these questions regarding tissue-longitudinal and tissue-transverse magnetization, we need to understand the concept of T1 and T2 relaxation times and their effect on the magnetization of different tissues in the human brain.
T1 relaxation time is the time it takes for the longitudinal magnetization (Mz) to return to 63% of its equilibrium value after a radiofrequency (RF) pulse is applied. It represents the time it takes for the spins to recover their original alignment along the magnetic field.
T2 relaxation time is the time it takes for the transverse magnetization (Mxy) to decay to 37% of its original value after an RF pulse is applied. It represents the time it takes for the magnetization to lose its phase coherence.
Now, let's solve the first question:
The flip angle is 30°, and the time delay is 400 ms. We need to find the tissue-longitudinal magnetization pair after these conditions. We are given the T1 and T2 values for gray matter (T1 = 1331 ms, T2 = 80 ms) and white matter (T1 = 832 ms, T2 = 110 ms).
To find the tissue-longitudinal magnetization (Mz), we can use the equation:
Mz = M0 * (1 - exp(-t / T1))
For gray matter:
Mz = 1 * (1 - exp(-400 / 1331))
Mz ≈ 0.55
For white matter:
Mz = 1 * (1 - exp(-400 / 832))
Mz ≈ 0.74
Therefore, the correct tissue-longitudinal magnetization pair after a 30° flip angle and 400 ms time delay is:
Gray Matter, Mz = 0.55
White Matter, Mz = 0.74
Now, let's solve the second question:
The flip angle is 60°, and the time delay is 50 ms. We need to find the tissue-transverse magnetization pair after these conditions. Again, we are given the T1 and T2 values for gray matter (T1 = 1331 ms, T2 = 80 ms) and white matter (T1 = 832 ms, T2 = 110 ms).
To find the tissue-transverse magnetization (Mxy), we can use the equation:
Mxy = M0 * exp(-t / T2) * sin(α)
For gray matter:
Mxy = 1 * exp(-50 / 80) * sin(60)
Mxy ≈ 0.36
For white matter:
Mxy = 1 * exp(-50 / 110) * sin(60)
Mxy ≈ 0.67
Therefore, the correct tissue-transverse magnetization pair after a 60° flip angle and 50 ms time delay is:
Gray Matter, Mxy = 0.36
White Matter, Mxy = 0.67