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The NMR signal can be calculated from the equation $$S = KH ({1 -e^{-TR/T1}}) {e^{-TE/T2}} $$ Reference
If we alter the TR of a sequence and keep the T2, let the resultant signals be $$S1 = KH ({1 -e^{-TR1/T1}}) {e^{-TE/T2}} $$ and $$S2 = KH ({1 -e^{-TR2/T1}}) {e^{-TE/T2}} $$

So, $$ S1/S2 = \frac{1 -e^{-TR1/T1}} {1-e^{-TR2/T1}} $$

S1, S2, TR1 and TR2 are known.
Is there any way find T1 from this ?

Rad S
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1 Answers1

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writing your equation in the form $$\frac{S_1}{S_2}=\frac{1-\left(e^{-TR_1}\right)^{1/T_1}}{1-\left(e^{-TR_2}\right)^{1/T_1}}$$ you will get an equation of the form $$\frac{S_1}{S_2}=\frac{1-a^{1/T_1}}{1-b^{1/T_1}}$$ you can only use a numerical method, if $$a=b$$ you will get a symbolic solution

Dr. Sonnhard Graubner
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