Fuentes Aranda, José Andrés

Gamboa, Diana, Mrs.

Valle Trujillo, Paul Antonio, Mr.

English

ISU ReD: Research and eData

Presentation for the Symposium on BEER November 2020Nonlinear analysis for a diabetes model focus on liverhandling of glucose and glucose uptake byinsulin-dependent tissuesJosé A. Fuentes-Aranda1,*, Diana Gamboa1, Paul A. Valle11Postgraduate Program in Engineering Sciences, BioMath Research Group, Tecnológico Nacional de México / ITTijuana, Mexicojose.fuentes19@tectijuana.edu.mxDiabetes Mellitus is in the top ten causes of death worldwide. Over the past few years, the interest inanalyzing this type of disease, either in a biological or mathematical sense, has been based on the search for atreatment that guarantees full control of glucose levels. Mathematical models inspired by natural phenomenaare proposed under the prey-predator scheme and in this case as a complex relation between insulin andglucose. The analyzed model in this research is described as a fifth-order nonlinear system of ordinarydifferential equations that involves the variables of plasma insulin, glucose in the digestive system, regularglucose level, glucose in urine and insulin into the subcutaneous compartment. The mathematical analysispresented in this work was made by applying nonlinear control theory to define the maximum carryingcapacity for each variable, establishing a bounded positively invariant domain (BPID). A particularity ofthe model consists in its dependency on H that is a function of glycaemia, which represents renal excretionof glucose. When plasma glucose level is lower than Gu H is zero, and there is not renal glucose excretion.When the plasma glucose level is higher than Gu, H is 1, and the renal glucose excretion depends on thedifference between G and Gu. The invariant plane existence associated to insulin into the subcutaneouscompartment defines a baseline to study diabetes mellitus where the model can describe a type-1 Diabetesmellitus (T1-DM) and type-2 Diabetes mellitus model (T2-DM).Keywords:Diabetes mellitus; Nonlinear control theory; Bounded positive invariant domain; Glucose esti-mation.

Nonlinear Analysis for a Diabetes Model Focus on Liver Handling of Glucose and Glucose Uptake by Insulin-dependent Tissues

https://ir.library.illinoisstate.edu/cgi/viewcontent.cgi?filename=0&article=1536&context=beer&type=additional

Nonlinear Analysis for a Diabetes Model Focus on Liver Handling of Glucose and Glucose Uptake by Insulin-dependent Tissues

Abstract

Similar works

Full text

Available Versions

ISU ReD: Research and eData