Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


Authors: Somesh Chattopadhyay, Daniel M. Keenan and Johannes D. Veldhuis
Journal: Quart. Appl. Math. 66 (2008), 401-421
MSC (2000): Primary 62F15; Secondary 62P10
DOI: https://doi.org/10.1090/S0033-569X-08-01024-4
Published electronically: March 18, 2008
MathSciNet review: 2445520
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


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Additional Information

Somesh Chattopadhyay
Affiliation: Department of Statistics, Florida State University, Tallahassee, FL 32306-4330
Email: somesh@stat.fsu.edu

Daniel M. Keenan
Affiliation: Department of Statistics, University of Virginia, Charlottesville VA 22904
Email: dmk7b@virginia.edu

Johannes D. Veldhuis
Affiliation: Division of Endocrinology and Metabolism, Department of Internal Medicine, Mayo Clinic and Mayo Graduate School of Medicine, Rochester, MN 55905
Email: veldhuis.johannes@mayo.edu

DOI: https://doi.org/10.1090/S0033-569X-08-01024-4
Keywords: Pulse detection, simulation by diffusion, hormonal secretion, estimation
Received by editor(s): January 27, 2006
Published electronically: March 18, 2008
Additional Notes: Support provided by NSF DMS-0107680 and NIH AG19164, AG19695, AG23133, AG29215, AG14759, DK60717, and M01 RR00585
Article copyright: © Copyright 2008 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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