A sample has a T2 of 100 ms. How long will it take for any transverse magnetization to decay to 37% of its starting value?

Given: T2 = 100ms.

The relationship between the initial transverse magnetization (Mxyo) and the transverse magnetization at any time t, Mxy(t), is:


Mxy(t) = Mxyoe-t/T2

When the transverse magnetization (Mxy) has decayed to 37% of its starting value:

0.37 = Mxy(t) / Mxy0 = e-t/T2

0.37 = e-t/T2

ln( 0.37 ) = -t/T2

-T2 * ln( 0.37 ) = t

-100ms * ln( 0.37 ) = 99.4ms = t