There are two adjacent tissues in an image with a T2 of 30 and 50 ms.
You wish to produce a spin-echo image of the tissues such that the contrast between the tissues is maximized.
What TE should be used?
C = S1 - S2
where:
C = contrast
S1 = signal from tissue 1
S1 = signal from tissue 2
We need to find the maximum C, or dC/dTE = 0.
dC/dTE = d(S1 - S2)= 0
d(e-TE/T2(2))/dTE - d(e-TE/T2(1))/dTE = 0
(e-TE/T2(2))/T2(2) = (e-TE/T2(1))/T2(1)
T2(2)/T2(1) = (e-TE/T2(2))/(e-TE/T2(1))
T2(2)/T2(1) = exp(-TE/T2(2)+ TE/T2(1))
ln(T2(2)/T2(1)) = TE/T2(1) + TE/T2(2)
ln(T2(2)/T2(1)) = TE (T2(2) - T2(1))/ (T2(2) T2(1))
TE = T2(2) T2(1) ln[T2(2)/T2(1)]/(T2(2) - T2(1))
TE = 38.3 ms