Statistical Modeling through Analytical and Monte Carlo Methods of the Fat Fraction in Magnetic Resonance Imaging (MRI)

Our project studies the quantification of the uncertainty in fat-fraction estimates using Magnetic Resonance Imaging (MRI). The measured fat fraction is |F | |F |+ |W | , where F is the fat signal and W is the water signal obtained using MRI. The fat and water signal magnitudes have a Rician distribution. However, the fat fraction has an unknown probability distribution. Knowing the fat-fraction probability distribution will provide us with a better understanding of the uncertainty of fat-fraction estimates used for the diagnosis of liver disease. Our current research focuses on finding the analytic distribution of the fat fraction and numerical simulation using Monte Carlo methods. In the analytic approach, we derived the probability density function of the fat fraction where the fat and water magnitudes follow a normal distribution (restricted to non-negative values) because the normal distribution approximates a Rician distribution for large signal-tonoise ratio (SNR). In the numerical approach, we applied Monte Carlo methods to optimize the fat-fraction estimation, compared analytic with numerical results, and found cases where current estimates of the fat fraction are inaccurate for low SNR.