A model for the hepatic glucose metabolism based on Hill and step functions

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• 作者：Marcello D&rsquo ; Abbicco^a ; ^{m.dabbicco@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Nicoletta Del Buono^a ; ^{nicoletta.delbuono@uniba.it" class="auth_mail" title="E-mail the corresponding author} ; Patrizia Gena^b ; ^{annapatrizia.gena@uniba.it" class="auth_mail" title="E-mail the corresponding author} ; Marco Berardi^c ; ^d ; ^{marco.berardi@ba.irsa.cnr.it" class="auth_mail" title="E-mail the corresponding author} ; Giuseppe Calamita^b ; ^{giuseppe.calamita@uniba.it" class="auth_mail" title="E-mail the corresponding author} ; Luciano Lopez^a ; ^{luciano.lopez@uniba.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Glucose&ndash ; insulin model ; Hill function ; Step function ; Metabolic dysfunction
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：292
• 期：Complete
• 页码：746-759
• 全文大小：552 K

文摘

We propose a system of first-order ordinary differential equations to describe and understand the physiological mechanisms of the interplay between plasma glucose and insulin and their behaviors in diabetes. The proposed model is based on Hill and step functions which are used to simulate the switch-like behavior that occurs in metabolic regulatory variables when some of the threshold parameters are approached. A simplified piecewise-linear system is also proposed to study the possible equilibria and solutions and used to introduce simple theoretical control mechanisms representing the action of an artificial pancreas and regulating exogenous insulin.