Stability of Parameter Estimates from Multiexponential Decay in MR Relaxometry and Related Experiments in One, Two, and Three Dimensions

Analysis of one-dimensional (1D) multiexponential decay has remained a topic of active research for over 200 years. This attests to the ubiquity of such signals as well as the difficulty in deriving parameters of the underlying monoexponential decays. However, we have shown in the context of nuclear magnetic resonance (NMR) relaxometry that parameter estimates derived from two-dimensional (2D) exponential decays, with two distinct time variables, exhibit substantially greater accuracy than those obtained from analysis of 1D data with a single time variable [1]. Here, we present statistical underpinnings of this remarkable fact and indicate applications in 2D NMR relaxometry and related experiments. These may be constructed, for example, as T₁-T₂ experiments correlating longitudinal (T₁) and transverse (T₂) relaxation times or as T₂-diffusion (T₂-D) correlation experiments. These results are readily generalizable to higher dimensions and may provide a means of circumventing conventional limits on multiexponential parameter estimation.

1. Stabilization of the inverse Laplace transform of multiexponential decay through introduction of a second dimension. Celik, …, Spencer et al., J Magn Res 235:134, 2013