A Polynomial Method for Fitting Continuous Distributions of Exponentials with Positivity Constraint

The need to fit sums of decaying exponentials to data is ubiquitous in the life sciences, where biological systems are often modeled as collections of interconnected compartments. When the number of compartments is extremely large, it becomes more appropriate to consider the data concerned as the integral of a continuous distribution of exponentials. A method is presented for determining distributions of exponentials from data which can be implemented on a personal computer. The technique, termed the "polynomial method," assumes that the distributions are smooth and slowly varying and can be represented by a low-order polynomial. An iterative addition to the technique is also described that allows positive distributions to be recovered, should this be appropriate. The technique is applied to simulated data and to relaxed expiration volume data obtained from dogs.