Probabilistic recovery of neuroendocrine pulsatile, secretory and kinetic structure: An alternating discrete and continuous scheme

The brain (hypothalamus) directs hormone secretion by the pituitary gland via burst-like (pulsatile) release of specific peptides at inferentially random times. These pulsatile signals supervise growth, reproduction, lactation, stress adaptations, water balance and immune responses. However, hypothalamic molecules are diluted $>$ 3000-fold in systemic blood, leaving pituitary-hormone pulses as measurable surrogates. The latter (roughly) mirror hypothalamic peptide bursts on a 1:1 basis, albeit being observed in a noisy environment. As a window to the brain, one must accurately recover the pulse (onset) times, and thereby estimate hormone secretion and kinetic parameters ($\theta \in \overline {\Theta }$) without distortion. Based upon limited observed data, one would like to obtain probability statements about underlying pulsatility, secretion and kinetics. Moreover, to be applicable in today’s clinical setting, it is important that any such procedure require minimal or no human input. We propose and justify the following method. First, the data (a pituitary hormone concentration time-profile) is “selectively smoothed” by a nonlinear diffusion equation, whose diffusion coefficient is inversely related to the degree of rapid increase. This procedure generates a collection of potential pulse time sets $(\mathbb {T})$. Then, via an algorithm which alternates between a Metropolis algorithm on $\mathbb {T}$ and a time-homogeneous diffusion process on $\overline {\Theta }$, a compact manifold with boundary, simulation from an appropriately formulated (posterior) probability measure is achieved. The method is applied to recover the underlying structure of brain-pituitary regulation in disease and aging.