A short-term food intake model involving glucose, insulin and ghrelin

Massimo Barnabei; Alessandro Borri; Andrea De Gaetano; Costanzo Manes; Pasquale Palumbo; Jorge Guerra Pires

doi:10.3934/dcdsb.2021114

Article Contents

2022, Volume 27, Issue 4: 1913-1926. Doi: 10.3934/dcdsb.2021114

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A short-term food intake model involving glucose, insulin and ghrelin

1.
High School Melchiorre Delfico, Teramo, Italy
2.
CNR-IASI Biomathematics Laboratory, National Research Council of Italy, Rome, Italy
3.
CNR-IRIB Institute for Biomedical Research and Innovation, National Research Council of Italy, Palermo, Italy
4.
Department of Information Engineering, Computer Science, and Mathematics, University of L'Aquila, L'Aquila, Italy
5.
Department of Biotechnologies and Biosciences, University of Milano-Bicocca, Milan, Italy
6.
Centro de Desenvolvimento Tecnológico em Saúde/Oswaldo Cruz Foundation, Rio de Janeiro, Brazil

^* Corresponding author: Alessandro Borri (e-mail: alessandro.borri@biomatematica.it)
^* Corresponding author: Alessandro Borri (e-mail: alessandro.borri@biomatematica.it)

Received: November 30, 2020

Early access: April 2021

Published: April 2022

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Abstract

Body weight control is gaining interest since its dysregulation eventually leads to obesity and metabolic disorders. An accurate mathematical description of the behavior of physiological variables in humans after food intake may help in understanding regulation mechanisms and in finding treatments. This work proposes a multi-compartment mathematical model of food intake that accounts for glucose-insulin homeostasis and ghrelin dynamics. The model involves both food volumes and glucose amounts in the two-compartment system describing the gastro-intestinal tract. Food volumes control ghrelin dynamics, whilst glucose amounts clearly impact on the glucose-insulin system. The qualitative behavior analysis shows that the model solutions are mathematically coherent, since they stay positive and provide a unique asymptotically stable equilibrium point. Ghrelin and insulin experimental data have been exploited to fit the model on a daily horizon. The goodness of fit and the physiologically meaningful time courses of all state variables validate the efficacy of the model to capture the main features of the glucose-insulin-ghrelin interplay.

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Mathematics Subject Classification: Primary: 92-10, 92B05; Secondary: 93C95.

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Figure 1. Graphical scheme of the model. Continuous lines represent transfer of mass, dashed lines represent signals

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Figure 2. Plasma insulin and ghrelin evolutions

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Figure 3. Food volume in the gastrointestinal tract dynamics

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Figure 4. Plasma glucose dynamics

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Figure 5. Ghrelin dynamics in a day with 3 and with 2 meals

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Table 1. Model parameters and initial conditions

Parameter	Units	Value	Reference
$ r $	$ ml/min $	$ 35 $	[23]
$ k^{max}_{JS} $	$ min^{-1} $	$ 0.0201 $	Identification
$ \lambda_{JS} $	$ min^{-1} $	$ 9.1871 \cdot 10^{-4} $	Identification
$ k_S,k_J $	$ mml/min $	$ 6.2568 $	Identification
$ k_{XJ} $	$ min^{-1} $	$ 0.0737 $	Identification
$ Ca $	$ - $	$ 0.5558 $	[3]
$ k_{GJ} $	$ ml/min $	$ 50.1503 $	Identification
$ k_G $	$ mmol/min $	$ 0.2066 $	Steady State
$ V_G $	$ l $	$ 10.483 $	[22]
$ BW $	$ kg $	$ 68.97 $	[3,7]
$ k_{xGI} $	$ min^{-1} $	$ 5.3\cdot 10^{-5} $	[22]
$ k_{IRG} $	$ min^{-1} $	$ 0.0049 $	Steady state
$ \gamma_{IRG} $	$ - $	$ 3.0763 $	Identification
$ V_I=V_H $	$ l $	$ 17.2425 $	[22]
$ k_{xI} $	$ min^{-1} $	$ 0.059 $	[21]
$ k_{RG} $	$ min^{-1} $	$ 17.6948 $	Steady state
$ k^{min}_H $	$ pmol/ml $	$ 650407.4627 $	Identification
$ k^{max}_H $	$ pmol/ml $	$ 899990.4238 $	Identification
$ t_{H} $	$ pmol/ml $	$ 1195.2917 $	Identification
$ \lambda_{HJ} $	$ min^{-1} $	$ 0.007 $	Identification
$ k_{XH} $	$ l $	$ 0.239 $	[1]
$ S_0 $	$ ml $	$ 363.3046 $	Steady state
$ J_0 $	$ ml $	$ 169.8402 $	Steady state
$ G_{S0} $	$ mmol $	$ 0 $	Steady state
$ G_{J0} $	$ mmol $	$ 0 $	Steady state
$ G_0=G_b $	$ mM $	$ 4.6239 $	Identification
$ I_0 $	$ pM $	$ 80.4264 $	[3]
$ R_0 $	$ pmol $	$ 16581.6656 $	Identification
$ H_0 $	$ pg/ml $	$ 524.5618 $	Identification

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