On the least-square estimation of parameters for statistical diffusion weighted imaging model

Statistical model for diffusion-weighted imaging (DWI) has been proposed for better tissue characterization by introducing a distribution function for apparent diffusion coefficients (ADC) to account for the restrictions and hindrances to water diffusion in biological tissues. This paper studies the precision and uncertainty in the estimation of parameters for statistical DWI model with Gaussian distribution, i.e. the position of distribution maxima (D_m) and the distribution width (σ), by using non-linear least-square (NLLS) fitting. Numerical simulation shows that precise parameter estimation, particularly for σ, imposes critical requirements on the extremely high signal-to-noise ratio (SNR) of DWI signal when NLLS fitting is used. Unfortunately, such extremely high SNR may be difficult to achieve for the normal setting of clinical DWI scan. For D_m and σ parameter mapping of in vivo human brain, multiple local minima are found and result in large uncertainties in the estimation of distribution width σ. The estimation error by using NLLS fitting originates primarily from the insensitivity of DWI signal intensity to distribution width σ, as given in the function form of the Gaussian-type statistical DWI model.