# An analytical Model which Determines the Apparent T1 for Modified Look-Locker Inversion Recovery (MOLLI) -- Analysis of the Longitudinal Relaxation under the Influence of Discontinuous Balanced and Spoiled Gradient Echo Readouts

## TL;DR

This paper develops an analytical model to accurately determine the true T1 relaxation time in MRI from apparent measurements obtained using MOLLI sequences, accounting for readout parameters and heart rate effects.

## Contribution

It provides a rigorous analysis of how discontinuous readout sequences influence apparent T1, enabling more precise tissue characterization in cardiac MRI.

## Key findings

- Apparent relaxation rate is the time average of rates during readout and relaxation periods.
- Model allows calculation of real T1 from apparent T1 using heart rate and sequence parameters.
- Analysis applies to both balanced steady state free precession and spoiled gradient echo readouts.

## Abstract

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.