Short and long time MR signal behavior of randomly distributed water and fat-numerical simulations

The MR time-signal behavior of water has been reported to be different on short and long time scales for systems of randomly distributed perturbers in water in the static dephasing regime. Up to now, the signal of the perturbers in such systems has not been taken into consideration. Water-fat emulsions are macroscopically homogeneous systems and can be considered as microscopically randomly distributed perturbing fat spheres embedded in water. In such water-fat systems, the signal of the perturber, fat, cannot be ignored. Since water and fat are within the same system, the fat signal behavior may show similarities with water, with differences in short and long time scales. This could complicate fat-referenced MR thermometry (MRT) methods such as multi-gradient echo-based (MGE) MRT. Simulations were performed using a numerical phantom comprising spherical fat objects embedded in a spherical water medium. To characterize the fat signal, the theoretical signal description of water was fitted to the simulated fat signal. The simulated signals were sampled as an MGE signal and MGE MRT was used to calculate temperatures. The sampling was done with and without delay, to investigate the effect on the temperature error of the time ranges in which the signal was sampled. It was confirmed that the fat signal behavior was similar to that of water and consisted of two regimes. The separation between the short and long time scales was approximately at 55 ms for fat, as compared with 8.9 ms for water. Without delayed signal sampling, the MGE MRT temperature error was about 2.5°C. With delayed sampling such that both the water and the fat signals were either in the short or in the long time scale the error was reduced to 0.2°C.