Identification of a pulsatile endocrine model from hormone concentration data

This paper presents two approaches to estimate parameters of a mathematical model of a bipartite endocrine axis. Secretion of one of the involved hormones is stimulated by the concentration of another one, with the latter secreted in a pulsatile manner. The system output can be modeled as the response of a linear time-invariant system to a train of Dirac delta functions with unknown weights and fired at unknown instants. The hormone mechanism in question appears often in animal and human endocrine systems, e.g. in the regulation of testosterone in the human male. The model has been introduced elsewhere and makes use of pulse-modulated feedback for describing pulsatile endocrine regulation. The first identification approach is based on the mathematical machinery of constrained nonlinear least-squares minimization, while the second one is based on Laguerre domain identification of continuous time-delay systems. Both algorithm perform reasonably well on actual biological data yielding accurate fitting of luteinizing hormone concentration profiles.