Signal modeling and the Cramér-Rao Bound for absolute Magnetic Resonance thermometry in fat tissue

Magnetic Resonance Imaging of tissues with both fat and water resonances allows for absolute temperature mapping through parametric modeling. The fat resonance is used as a reference to determine the absolute water resonance frequency which is linearly related to the temperature. The goal of this paper is to assess whether or not resonance frequency based absolute temperature mapping is feasible in fat tissue. This is done by examining identifiability conditions and analyzing the obtainable performance in terms of the Cramér-Rao Bound of the temperature estimates. We develop the model by including multiple fat peaks, since even small fat resonances can be significant compared to the small water component in fat tissue. It is showed that a high signal to noise ratio is needed for practical use on a 1.5 T scanner, and that higher field strengths can improve the bound significantly. It is also shown that the choice of sampling interval is important to avoid aliasing. In sum, this type of magnetic resonance thermometry is feasible for fat tissue in applications where high field strength is used or when high signal to noise ratio can be obtained.