A measure of curve fitting error for noise filtering diffusion tensor MRI data.

A parameter, chi2p, based on the fitting error was introduced as a measure of reliability of DT-MRI data, and its properties were investigated in simulations and human brain data. Its comparison with the classic chi2 revealed its sensitivity to both the goodness of fit and the pixel signal-to-noise-ratio (SNR), unlike the classic chi2, which is sensitive only to the goodness of fit. The new parameter was thus able to separate effectively pixels with coherent signals (having small fitting error and/or high SNR) from those with random signals (having inconsistent fitting and/or low SNR). A practical advantage of chi2p over the classic chi2 was that chi2p is quantified directly from the data of each pixel, without requiring accurate estimation of data-dependent parameters (such as noise variance), which often makes application of the classic chi2 problematic. Analytical approximations of chi2p enabled an objective (data-independent) and automated calculation of a threshold value, used for internal scaling of the chi2p map. Apart from assessing data reliability on a pixel-by-pixel basis, chi2p was used to develop an objective and generic methodology for the exclusion of pixels with unreliable DT information by discarding pixels with chi2p values exceeding the threshold. Pixels corresponding to very low SNR, and poorly fitted cerebrospinal fluid and surrounding brain tissue, had increased chi2p values and were successfully excluded, providing DT anisotropy maps free from artifactual anisotropic appearance.