Identification of signal bias in the variable flip angle method by linear display of the algebraic Ernst equation

A novel linear parameterization for the variable flip angle
method for longitudinal relaxation time T1 quantification from
spoiled steady state MRI is derived from the half angle tangent
transform, t, of the flip angle. Plotting the signal S at coordinates
x=St and y=S/t, respectively, establishes a line that
renders signal amplitude and relaxation term separately as y-intercept
and slope. This representation allows for estimation of
the respective parameter from the experimental data. A comprehensive
analysis of noise propagation is performed. Numerical
results for efficient optimization of longitudinal relaxation
time and proton density mapping experiments are derived.
Appropriate scaling allows for a linear presentation of data that
are acquired at different short pulse repetition times, TR << T1
thus increasing flexibility in the data acquisition by removing the
limitation of a single pulse repetition time. Signal bias, like due
to slice-selective excitation or imperfect spoiling, can be readily
identified by systematic deviations from the linear plot. The
method is illustrated and validated by 3T experiments on phantoms
and human brain.