An efficient non-iterative algorithm to estimate the apparent diffusion coefficient of water molecules in the magnetic resonance diffusion imaging experiments

Many studies have shown that the magnetic resonance signal decay with an extend range of diffusion weighting (b-factor) is a bi-exponential attenuation in the diffusion-weighted magnetic resonance imaging experiments in vivo. Based on this feature and the two-compartmental model, we propose a twice-linear-fitting (TLF) algorithm to estimate the apparent diffusion coefficient (ADC) of the water molecules instead of the commonly used iterative Levenberg–Marquardt (LM) method. The TLF algorithm consists of two liner fitting steps to estimate the fast and the slow apparent diffusion coefficients and their sizes, respectively. It is unnecessary to guess the initial values in the whole fitting process. The time consumption of the TLF algorithm is much less than that of the iterative LM method. Moreover, the TLF algorithm may avoid the extraneous solutions, which often deteriorates the results of the LM method. Compared with the iterative fitting method, the TLF algorithm is a reliable and time-efficient approach to estimate the ADC of water molecules in vivo in magnetic resonance diffusion-weighted imaging experiments.