### Abstract

Blood-borne neurohormonal signals reflect the intermittent burst-like release of peptides and steroids from neurons, glands and target tissues. Hormones control basic physiological processes, such as growth, metabolism, reproduction and stress-related adaptations. Secreted molecules undergo combined diffusion, advection and irreversible elimination from the circulation. Quantification of these interdependent processes by a structurally relevant model embodying discrete event times, continuous rates of secretion and elimination, and stochastic variations poses a formidable challenge. In an experimental setting, one observes only the hormone concentrations, which comprise a time-varying composite of secretion and elimination. The number, shape and location of underlying bursts (pulses) and attendant secretion and kinetic parameters are unobserved. The ability to estimate the properties of these processes from the observed data is fundamental to an understanding of regulated hormonal dynamics. The present formulation allows objective simultaneous appraisal of discrete (pulse times) and continuous (secretion/elimination) properties of neuroglandular activity in the presence of random variability. A probability distribution is constructed for the structural parameters (secretion/elimination, pulsing), and an algorithm is developed by which one can, based upon observed hormone concentration data, make probabilistic statements about the underlying structure: pulse frequency per day, total basal (constitutive) and pulsatile secretion per day, and half-lives of elimination. The algorithm consists of the following steps: first, explicit construction of a family of sequentially decreasing putative pulse-time sets for a given neurohormone concentration time series; and then, recursive iteration between the following two: (a) for a given pulse-time set, generate a sample from the probability distribution of unknown underlying hormone secretion and elimination rates; and (b) determine whether or not a probability-based transition from one pulse-time set to another is merited (i.e., add/remove a pulse-time or stay the same). We apply this procedure illustratively to joint estimation of pulse times, secretion rates and elimination kinetics of selected pituitary hormones (ACTH, LH and GH).

Original language | English (US) |
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Pages (from-to) | 242-255 |

Number of pages | 14 |

Journal | Journal of Theoretical Biology |

Volume | 236 |

Issue number | 3 |

DOIs | |

State | Published - Oct 7 2005 |

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### Keywords

- Analysis
- Elimination
- Kinetics
- Pituitary
- Pulsatile
- Secretion

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Journal of Theoretical Biology*,

*236*(3), 242-255. https://doi.org/10.1016/j.jtbi.2005.03.008