The Answers of MRI Tutorial Videos
By Frank Luo
This is my answers of the MRI Tutorial Videos How MRI Works - Part 2: The Spin Echo and How MRI Works - Part 3:Fourier Transform and K-Space .
Part 2: The Spin Echo
Questions
Answers
Question 1:
- The Boltzmann Magetization , then after elimination the units is .
- The Polarization is , then after elimination we can get that is a special number depends on the material, no SI units.
Question 2:
- The polarization is .
- The magnet field strength should be .
- The temperature should be .
Question 3:
- Since the Boltzmann Magetization Equation is , so we can calculate the signal.
The signal of Tissue : .
The signal of Tissue : .
Surely Tissue will deliver more signal.
- We have calculated that Tissue will deliver more signal if both Tissue and has the same Boltzmann Magetization.
If Tissue is of Tissue , then the Tissue signal will become lesser, so Tissue deliver more signal.
- Let function reprent the signal of time .
Consider the function: reaches its PEAK at about , so the should be .
Question 4:
If both tissues deliver the SAME signal, which means .
Put the data in, then we can get , solve it and get .
So the echo time is: .
Question 5:
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, so the signal is .
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If the magetic field of inhomogeneity of ppm, the signal can be calculated by such equation:
Put the data in, we can , so the signal amplitude is .
- We should delivered the 180° pulses at times 20ms and times 40ms if we wish to detect echoes at times 40ms and 80ms.
The signal will be at times 40ms and at times 80ms.
Question 6:
From the equation , then we can solve , the answer is .
Therefore, we can get the echoes at times 10ms, 30ms, 50ms, 70ms, 90ms, 110ms, 130ms, so we can get echoes.
Part 3: Fourier Transform and K-Space
Questions
Answers
The amplitude of the result is . We need to times to get the correct answer.
The reason are as follows:
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Both the positive and negative frequency contribute the answer, but we only use the positive, so have to multiply .
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Each operation we have to sum once, so we need the result to multiply to get the final answer.