The least-squares algorithm is known to bias apparent diffusion coefficient (ADC) values estimated from magnitude MR data, although this effect is commonly assumed to be negligible. In this study the effect of this bias on tumor ADC estimates was evaluated in vivo and was shown to introduce a consistent and significant underestimation of ADC, relative to those given by a robust maximum likelihood approach (on average, a 23.4 ؎ 12% underestimation). Monte Carlo simulations revealed that the magnitude of the bias increased with ADC and decreasing signal-to-noise ratio (SNR). In vivo, this resulted in a much-reduced ability to resolve necrotic regions from surrounding viable tumor tissue compared with a maximum likelihood approach. This has significant implications for the evaluation of diffusion MR data in vivo, in particular in heterogeneous tumor tissue, when evaluating bi-and multiexponential tumor diffu- Diffusion MR is currently a key area of clinical research due to its proposed ability to characterize properties such as cellularity in tumor (1-6) and normal tissues (7), architecture of the interstitium (8,9), tumor histological type (10), and to elucidate tissue structure (for example, mapping the paths of white matter fibers in the brain (11)). In cancer, the apparent diffusion coefficient (ADC) is of particular interest due to observations of its reduced value in tumors relative to surrounding, radiologically normal tissues (12-21), its ability to detect and characterize regional necrosis (22)(23)(24)(25)(26), and increases in ADC resulting from successful response to treatment of cancer (27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37).Diffusion-weighting is introduced into a spin-echo sequence by applying diffusion gradients either side of a 180°refocusing pulse. The duration, magnitude, and spacing of these gradients define a "b-value." In cancer, due to the disorganized structure of the tissue, water diffusion is assumed to be isotropic and measurements are usually acquired with the diffusion gradients applied in just one direction. This contrasts with structured tissues such as the brain, in which multiple directions must be measured in order to characterize diffusion anisotropy. The ADC is then estimated from the rate of the exponential decay of MR signal magnitude with respect to its b-value.Generally, the least-squares (LS) algorithm is used to estimate ADC due to its speed, ease of implementation, and wide availability, yet it assumes the noise corrupting the measured signal magnitude to be normally distributed. By taking the magnitude of complex MR data in order to form an image, the otherwise normally distributed noise in the complex domain becomes Rice-distributed (38). The Rice distribution tends toward a normal distribution at higher signal-to-noise ratios (SNRs) (38). However, due to the inherently decaying nature of the signal magnitude in a diffusion measurement, the distribution of the noise in higher b-value measurements can become nonnormal and its variance will have a complex relationship ...