Analysis of biexponential nuclear magnetic resonance relaxation curves: studies on simulated data

Application of a Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence to a nuclear spin system consisting of two components, whose spins do not exchange or exchange slowly on the scale of the shorter time constant, results in the nuclear magnetization Mz of the spin system decaying according to the relation Mz = Ma exp(-t/Ta)+Mb exp(-t/Tb)+K+E where Ma,Ta are the intensity and transverse relaxation time of one component, Mb and Tb are the corresponding values for the second component, K is a constant and E is the contribution due to noise. Data simulation according to the above function was carried out with different values for the parameters Ma, Ta, Mb, Tb and K, the noise component being normally distributed with mean zero. For each set of parameters, the data generation was repeated a number of times with a different noise content and in each case, the parameters were estimated using a non-linear least square curve fitting procedure. The mean and percent coefficient of variation (CV) of each parameter was calculated. The value of CV is taken as a measure of the uncertainty in the estimated value of the parameter. It is found that the uncertainty in the estimated values of the parameters is due to the random noise. The range of data points is more critical than the number of data points used in curve fitting. Moreover, the uncertainty associated with each parameter increases with decreasing Ma/Mb ratio and increases with increasing Ta/Tb ratio. Higher signal to noise ratios will be required to analyse data with low Ma/Mb and high Ta/Tb ratios.(ABSTRACT TRUNCATED AT 250 WORDS)