If the flip angle is doubled, how much does RF deposition increase by?

When the flip angle in MRI is doubled, the amount of radiofrequency (RF) energy deposited in the tissue increases by the square of the change in the flip angle. This is a result of the relationship between RF pulse power and the induced magnetic fields when the flip angle is modified.

In MRI, the RF pulse is responsible for tipping the spins of hydrogen nuclei (or other nuclei of interest) in the magnetic field. The flip angle is the angle through which the net magnetization vector is rotated away from its initial orientation along the z-axis. When the flip angle is increased, more energy is deposited into the tissue.

Mathematically, if the original flip angle is represented as θ, and it is doubled to 2θ, the RF energy deposition can be expressed as proportional to the sine of the flip angle. The increase in energy deposition would be calculated as the sine of 2θ divided by the sine of θ. Using the sine double angle identity, you find that:

sin(2θ) = 2 * sin(θ) * cos(θ).

Thus, when comparing the power deposition of the double flip angle to that of the initial angle, you find that RF energy deposition indeed increases by a factor of four,