The Bolztmann equation tells us that N_{}/N_{+} = e^{ΔE/kT}
Where N_{}/N_{+} is the ratio of spins in the upper to those in the lower spin states. The MRI signal is proportional to ( N_{+}  N_{} ), and
( N_{+}  N_{} ) = [1  N_{}/N_{+} ] / [1 + N_{}/N_{+}].
Taking only Boltzmann statistics into account and assuming that T=310K (body temperature):
















In calculating the relative signals, we must take into account the natural abundances of the isotopes (N_{ISO}). In calculating the relative signals from the body we must also include the biological abundances (N_{BIO}).
Signal = k N_{ISO} N_{BIO} (N_{+}  N_{})
In this euation, k is a proportionality constant.
N_{ISO}  N_{BIO}  
 99.98  0.63 



100  0.00041 



100  0.0024 


Therefore, of the three nuclei, hydrogen will have the best signal. Of the two field strengths, 4.7 T will have the better signal. The signal will be proportional to the gyromagnetic ratio and the field strength.