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» Time Constants

An understanding of time constants allows easier understanding of MRI signal equations. This tool allows you to build up the equations describing the change of magnetisation in basic pulse sequences.

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Time Constant Tool: y = 1-2·exp(-x/400)

A simple exponential recovery may be turned into inversion recovery.


The construction of this recovery curve is simply 1 (representing full recovery,) minus two times exponential decay. This represents recovery after a 180° pulse. The 180° pulse inverts the spin system (sets all longitudinal magnetisation to -M0, or -1 in a graph already normalised to M0=1). The equation of this curve is, therefore, the equation of inversion recovery:

S = 1 - 2·exp(-TR/T1)

where S is signal intensity, TR is the repetition time and T1 is the longitudinal relaxation time.

The tool now considers the recovery and decay equations discussed thus far with different values of T1 and T2 (the time constants of the curves). Navigate below to the transverse decay section.

Navigate through the tool...
  1. Introduction.
  2. exp (x/400)
  3. exp (-x/400)
  4. 1 - exp (-x/400)
  5. 1 - 2·exp (-x/400)

Other sections of this tool:

Remember, T1, T2 and T2* are time constants.

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