Patient-specific modeling of the neuroendocrine HPA-axis and its relation to depression: Ultradian and circadian oscillations

Gudmand-Hoeyer, Johanne; Timmermann, Stine; Ottesen, Johnny T.

doi:10.1016/j.mbs.2014.07.013

Cited by 20 publications

(18 citation statements)

References 51 publications

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“…Without GnRH stimulation, i.e. for R(t) ≡ 0, system (15) has equilibrium at (L, T ) = (L b , T b ), whose coordinates…”

Section: Discussionmentioning

confidence: 99%

“…Cortisol (C) is a hormone involved in the response to stress and inflammation as well as in metabolism. Similar to the case of Te regulation, the C regulation loop essentially comprises two more hormones [14][15][16][17]. Corticotropin-releasing hormone (CRH) is secreted in the hypothalamus in pulses and stimulates the release of adrenocorticotropic hormone (ACTH) from the pituitary gland to the bloodstream.…”

Section: Endocrine Axesmentioning

confidence: 99%

“…equations (15) reduce to their counterparts (1), where (R, L, T ) is replaced by (z 1 , z 2 , z 3 ) and b 2 , b 3 are replaced bỹ…”

Section: The State Transformation Of the Systemmentioning

confidence: 99%

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Impulsive model of endocrine regulation with a local continuous feedback

Taghvafard

Medvedev

Proskurnikov

et al. 2019

Mathematical Biosciences

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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 a low-order system 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. (Alexander Medvedev), anton.p.1982@ieee.org (Anton V. Proskurnikov), m.cao@rug.nl (Ming Cao)

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“…Without GnRH stimulation, i.e. for R(t) ≡ 0, system (15) has equilibrium at (L, T ) = (L b , T b ), whose coordinates…”

Section: Discussionmentioning

confidence: 99%

Section: Endocrine Axesmentioning

confidence: 99%

See 1 more Smart Citation

Impulsive model of endocrine regulation with a local continuous feedback

Taghvafard

Medvedev

Proskurnikov

et al. 2019

Mathematical Biosciences

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“…During the past decade, the mathematical modelling of the HPA axis has been intensively studied [1,2,3,4,5,6,7,8,9,10,11,12]. In 2005, Savic and Jelic [10] presented one of the mathematical models of HPA axis described by a system with three nonlinear differential equations with one delay.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a hypothalamic-pituitary-adrenal axis model with inclusion of glucocorticoid receptor and memory

Kaslik¹,

Navolan²,

Neamţu³

2017

AIP Conference Proceedings

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Abstract. This paper analyzes a four-dimensional model of the hypothalamic-pituitary-adrenal (HPA) axis that includes the influence of the glucocorticoid receptor in the pituitary. Due to the spatial separation between the hypothalamus, pituitary and adrenal glands, distributed time delays are introduced in the mathematical model. The existence of the positive equilibrium point is proved and a local stability and bifurcation analysis is provided, considering several types of delay kernels. The fractional-order model with discrete time delays is also taken into account. Numerical simulations are provided to illustrate the effectiveness of the theoretical findings.

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“…Several mathematical models of the HPA axis have been developed and analyzed by Andersen et al (2013); Bairagi et al (2008); Conrad et al (2009);Gudmand-Hoeyer et al (2014); Jelić et al (2005); Kyrylov et al (2005); Lenbury & Pornsawad (2005); Markovic et al (2011); Pornsawad (2013); Savić & Jelić (2005); Savić et al (2006); Vinther et al (2011). Experimental data show the circadian as well as ultradian rhythm of hormone levels Carroll et al (2007); Veldhuis et al (2008) , which should be reflected by the mathematical models of the HPA axis, through the existence of oscillatory solutions.…”

Section: Introductionmentioning

confidence: 99%

Stability and Hopf bifurcation analysis for the hypothalamic-pituitary-adrenal axis model with memory

Kaslik

Neamţu

2016

Math Med Biol

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This paper generalizes the existing minimal model of the hypothalamic-pituitary-adrenal (HPA) axis in a realistic way, by including memory terms: distributed time delays, on one hand and fractional-order derivatives, on the other hand. The existence of a unique equilibrium point of the mathematical models is proved and a local stability analysis is undertaken for the system with general distributed delays. A thorough bifurcation analysis for the distributed delay model with several types of delay kernels is provided. Numerical simulations are carried out for the distributed delays models and for the fractionalorder model with discrete delays, which substantiate the theoretical findings. It is shown that these models are able to capture the vital mechanisms of the HPA system.

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Patient-specific modeling of the neuroendocrine HPA-axis and its relation to depression: Ultradian and circadian oscillations

Cited by 20 publications

References 51 publications

Impulsive model of endocrine regulation with a local continuous feedback

Impulsive model of endocrine regulation with a local continuous feedback

Stability analysis of a hypothalamic-pituitary-adrenal axis model with inclusion of glucocorticoid receptor and memory

Stability and Hopf bifurcation analysis for the hypothalamic-pituitary-adrenal axis model with memory

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