Nonparametric deconvolution of hormone time-series: a state-space approach

The instantaneous secretion rate (ISR) of endocrine glands is not directly measurable and it can be reconstructed only indirectly by applying deconvolution algorithms to time-series of plasma hormone concentrations. In particular, nonparametric regularization-based deconvolution hinges on a variational problem whose solution is usually approximated by discretizing the continuous-time axis. The paper shows how to perform regularized deconvolution avoiding any form of discretization. In view of the equivalence between regularization and Bayesian estimation, it is seen that the estimated ISR is a weighted sum of N basis-functions, where N is the number of data. State-space methods are used to derive analytically the basis functions as well as the entries of the matrix of the linear system used to compute the weights. Alternatively, the weights can be computed in O(N) operations by a suitable algorithm based on Kalman filtering. As an illustration of the method, we estimate the spontaneous pulsatile ISR of luteinizing hormone (LH) from time series of plasma LH concentrations sampled every 5 min