Result: Foliation-Based Parameter Tuning in a Model of the GnRH Pulse and Surge Generator

Title:
Foliation-Based Parameter Tuning in a Model of the GnRH Pulse and Surge Generator
Authors:
Clément, Frédérique, Vidal, Alexandre
Contributors:
SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Source:
SIAM Journal on Applied Dynamical Systems. 8(4):1591-1631
Publisher Information:
CCSD; Society for Industrial and Applied Mathematics, 2009.
Publication Year:
2009
Collection:
collection:INRIA
collection:INRIA-ROCQ
collection:INRIA_TEST
collection:TESTALAIN1
collection:INRIA2
collection:TDS-MACS
collection:INRIA-300009
Subject Terms:
Coupled Oscillators, Hysteresis, Fast-Slow Dynamics, Amplitude and Frequency Control, Ovulation, Neuroendocrinology, GnRH Pulsatility, GnRH Surge, ACM: I.: Computing Methodologies, I.6: SIMULATION AND MODELING, I.6.4: Model Validation and Analysis, ACM: G.: Mathematics of Computing, G.1: NUMERICAL ANALYSIS, G.1.7: Ordinary Differential Equations, G.1.7.7: Multistep and multivalue methods, [MATH.MATH-DS]Mathematics [math], Dynamical Systems [math.DS], [SDV.BDLR]Life Sciences [q-bio], Reproductive Biology
Original Identifier:
ARXIV: 0809.1722
HAL:
Document Type:
Journal article<br />Journal articles
Language:
English
ISSN:
1536-0040
Relation:
info:eu-repo/semantics/altIdentifier/arxiv/0809.1722; info:eu-repo/semantics/altIdentifier/doi/10.1137/080732237
DOI:
10.1137/080732237
Access URL:
https://inria.hal.science/inria-00319866
https://inria.hal.science/inria-00319866v1/document
https://inria.hal.science/inria-00319866v1/file/Clement_Vidal.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.inria.00319866v1
Database:
HAL

Further Information

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We investigate a model of the GnRH pulse and surge generator, with the definite aim of constraining the model GnRH output with respect to a physiologically relevant list of specifications. The alternating pulse and surge pattern of secretion results from the interaction between a GnRH secreting system and a regulating system exhibiting fast-slow dynamics. The mechanisms underlying the behavior of
We investigate a model of the GnRH pulse and surge generator, with the definite aim of constraining the model GnRH output with respect to a physiologically relevant list of specifications. The alternating pulse and surge pattern of secretion results from the interaction between a GnRH secreting system and a regulating system exhibiting fast-slow dynamics. The mechanisms underlying the behavior of the model are reminded from the study of the Boundary-Layer System according to the "dissection method" principle. Using singular perturbation theory, we describe the sequence of bifurcations undergone by the regulating (FitzHugh-Nagumo) system, encompassing the rarely investigated case of homoclinic connexion. Basing on pure dynamical considerations, we restrict the space of parameter search for the regulating system and describe a foliation of this restricted space, whose leaves define constant duration ratios between the surge and the pulsatility phase in the whole system. We propose an algorithm to fix the parameter values to also meet the other prescribed ratios dealing with amplitude and frequency features of the secretion signal. We finally apply these results to illustrate the dynamics of GnRH secretion in the ovine species and the rhesus monkey.