TY - JOUR
T1 - Impulsive model of endocrine regulation with a local continuous feedback
AU - Taghvafard, Hadi
AU - Medvedev, Alexander
AU - Proskurnikov, Anton V.
AU - Cao, Ming
PY - 2019
Y1 - 2019
N2 - Whereas development of mathematical models describing the endocrine system as a whole remains a challenging problem, visible progress has been demonstrated in modeling its subsystems, or axes. Models of hormonal axes portray only the most essential interactions between the hormones and can be described by low-order systems of differential equations. This paper analyzes the properties of a novel model of a hypothalamic-pituitary axis, portraying the interactions in a chain of a release hormone (secreted by the hypothalamus), a tropic hormone (produced by the pituitary gland) and an effector hormone (secreted by a target gland). This model, unlike previously published ones, captures two prominent features of neurohormonal regulation systems, namely, the pulsatile (episodic) production of the release hormone and a complex non-cyclic feedback mechanism that maintains the involved hormone concentrations within certain biological limits. At the same time, the discussed model is analytically tractable; in particular, the existence of a so-called 1-cycle featured by a single pulse over one period is proven mathematically.
AB - Whereas development of mathematical models describing the endocrine system as a whole remains a challenging problem, visible progress has been demonstrated in modeling its subsystems, or axes. Models of hormonal axes portray only the most essential interactions between the hormones and can be described by low-order systems of differential equations. This paper analyzes the properties of a novel model of a hypothalamic-pituitary axis, portraying the interactions in a chain of a release hormone (secreted by the hypothalamus), a tropic hormone (produced by the pituitary gland) and an effector hormone (secreted by a target gland). This model, unlike previously published ones, captures two prominent features of neurohormonal regulation systems, namely, the pulsatile (episodic) production of the release hormone and a complex non-cyclic feedback mechanism that maintains the involved hormone concentrations within certain biological limits. At the same time, the discussed model is analytically tractable; in particular, the existence of a so-called 1-cycle featured by a single pulse over one period is proven mathematically.
UR - http://www.scopus.com/inward/record.url?scp=85062297380&partnerID=8YFLogxK
U2 - 10.1016/j.mbs.2019.02.006
DO - 10.1016/j.mbs.2019.02.006
M3 - Article
AN - SCOPUS:85062297380
SN - 0025-5564
VL - 310
SP - 128
EP - 135
JO - Mathematical Biosciences
JF - Mathematical Biosciences
ER -