MR Signal Equations

• Spin Echo (assuming 90 deg flip):

   S = k * PD * (1 - exp(-TR / T1)) * exp(-TE / T2)

• Inversion Recovery (assuming 90 deg flip):

   S = k * PD * (1 – 2 * exp(-TI / T1) + exp(-TR / T1))

• Gradient Echo:

   S = k * PD * Sin(θ) * (1-exp(-TR/T1)) * exp(-TE/T2*)  / (1-Cos(θ) * exp(-TR/T1))

Parameters:

   k: instrumental scaling constant
   PD: proton density
   T1: longitudinal recovery rate
   T2: transverse decay rate (spin-spin)
   T2*: transverse decay rate (spin-spin + field inhomgeneities)
   TE: Echo Time
   TR: Time between repetitions
   TI: Inversion Time
   θ: Flip Angle