gigablochs.bloch.inverted_magnetization

gigablochs.bloch.inverted_magnetization(magnetization, time, T1, position, magindex=-1, time_axis=0, space_axis=-1, M0=1)

Calculate labelling efficiency from final longitudinal magnetization at the end of the simulation by correcting for the T1 decay experienced by the spin isochromat since crossing the labelling plane Dai et al. [DGdBA08].

This provides a natural way to estimate the central tendency of the ringing/oscillatory magnetization signal at the time of inversion.

Notes

The longitudinal magnetization is corrected by:

\[M_{inversion} = (M_{final} - M_0) \exp\left(\frac{t_{final} - t_{inversion}}{T_1}\right) + M_0\]

where: - \(M_{inversion}\) is the longitudinal magnetization resulting from inversion. - \(M_{final}\) is the longitudinal magnetization at the final time point. - \(M_0\) is the initial longitudinal magnetization. - \(t_{final}\) and \(t_{inversion}\) are final and inversion times, respectively. - \(T_1\) is the longitudinal relaxation.