Analysis of decay-type data

Abstract

A comparative study has been made of a variety of numerical techniques for fitting experimental data of the decay type by forms involving the sums of exponentials. Statistical errors of the fitted parameters are also calculated. These methods have been applied to artificially-generated sets of data as well as to the results of experiments with radioactive tracers on both human and animal subjects. Results show that the values of the fitted parameters are very sensitive to variations in the fitting procedure. Therefore great care must be exercised in identifying such values with physical constants. Although the values of functions derived from these fitted parameters which can definitely be associated with physical entities are generally more stable under variations in the fitting techniques, error bounds can be so large that no great confidence can be placed even in them. It would therefore appear best to select a uniform technique both for running the experiments and for analyzing the data, and then to consider as significant only relative results between one subject and the next.

Towards an acoustic model-based poroelastic imaging method: I. Theoretical Foundation

“…Eqn 17 contains a sum of exponential terms. The difficulties associated with fitting such an equation to data, particularly in relation to the uniqueness with which the constituent exponents may be separated, are well documented (Atkins 1969;Lanczos 1957;Worseley 1964). In this case, however, the multi-exponential fit is greatly simplified by the fact that the exponents in eqn 17 are related through the roots of the characteristic equation (eqn 13).…”

Analysis of exponential curves by a method of moments, with special attention to sedimentation equilibrium and fluorescence decay

“…The pitfalls of relying on these procedures in various biological applications have been discussed previously. In particular, Worsley and Lax (1962) and Worsley (1964) have examined the iterative least-squares techniques in general terms, while Glass and de Carreta (1967) have attempted to define their limits when applied specifically to transfer rates in clinical studies where data are sparse. In addition, the problems and prospects of least-squares fitting to hydrogenexchange data were pointed out by Laiken and Printz (1970).…”