Analysis of multi-exponential relaxation data with very short components using linear regularization.

Linear regularization is a common and robust technique for fitting multi-exponential relaxation decay data to obtain a distribution of relaxation times. The regularization algorithms employed by the Uniform-Penalty inversion (UPEN) and CONTIN computer programs have been compared using simulated transverse (T2) relaxation data derived from a typical bimodal distribution observed in cartilage tissue which contain a component shorter than t(0), the time of the first decay sample. We examined the reliability of detecting sub-t(0) relaxation components and the accuracy of statistical estimates of T2 distribution parameters. When the integrated area of the sub-t(0) component relative to that of the total distribution was greater than 0.25, our results indicated a signal-to-noise threshold of about 300 for detecting the presence of the sub-t(0) component with a probability of 0.9 or greater. This threshold was obtained using both the UPEN and CONTIN algorithms. In addition, when using the second-derivative-squared regularizer, UPEN solutions provided statistical estimates of T2 distribution parameters which were substantially free of the biasing effect of the regularizer observed in analagous CONTIN solutions.