  Quantitative nuclear magnetic resonance imaging (MRI) shifts more and more
into the focus of clinical research. Especially determination of relaxation
times without/and with contrast agents becomes the foundation of tissue
characterization, e.g. in cardiac MRI for myocardial fibrosis. Techniques which
assess longitudinal relaxation times rely on repetitive application of readout
modules, which are interrupted by free relaxation periods, e.g. the Modified
Look-Locker Inversion Recovery = MOLLI sequence. These discontinuous sequences
reveal an apparent relaxation time, and, by techniques extrapolated from
continuous readout sequences, the real T1 is determined. What is missing is a
rigorous analysis of the dependence of the apparent relaxation time on its real
partner, readout sequence parameters and biological parameters as heart rate.
This is provided in this paper for the discontinuous balanced steady state free
precession (bSSFP) and spoiled gradient echo readouts. It turns out that the
apparente longitudinal relaxation rate is the time average of the relaxation
rates during the readout module, and free relaxation period. Knowing the heart
rate our results vice versa allow to determine the real T1 from its measured
apparent partner.
