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Modeling the dynamics of glucose, insulin, and free fatty acids with time delay: The impact of bariatric surgery on type 2 diabetes mellitus

1 Simon A Levin Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ, USA
2 Department of Biostatistics, School of Public Health, University of Alabama at Birmingham, 1720 2nd Ave S, Birmingham, Alabama, USA
3 Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island, USA
4 Department of Mathematics, University of Louisville, 328 Natural Sciences Building, Louisville, Kentucky, USA

The role of free fatty acids (FFA) on Type 2 diabetes mellitus (T2DM) progression has been studied extensively with prior studies suggesting that individuals with shared familial genetic predisposition to metabolic-related diseases may be vulnerable to dysfunctional plasma FFA regulation. A harmful cycle arises when FFA are not properly regulated by insulin contributing to the development of insulin resistance, a key indicator for T2DM, since prolonged insulin resistance may lead to hyperglycemia. We introduce a hypothesis-driven dynamical model and use it to evaluate the role of FFA on insulin resistance progression that is mathematically constructed within the context of individuals that have genetic predisposition to dysfunctional plasma FFA. The dynamics of the nonlinear interactions that involve glucose, insulin, and FFA are modeled by incorporating a fixed-time delay with the corresponding delay-differential equations being studied numerically. The results of computational studies, that is, extensive simulations, are compared to the known minimal ordinary differential equations model. Parameter estimation and model validation are carried out using clinical data of patients who underwent bariatric surgery. These estimates provide a quantitative measure that is used to evaluate the regulation of lipolysis by insulin action measured by insulin sensitivity, within a metabolically heterogeneous population (non-diabetic to diabetic). Results show that key metabolic factors improve after surgery, such as the effect of insulin inhibition of FFA on insulin and glucose regulation, results that do match prior clinical studies. These findings indicate that the reduction in weight or body mass due to surgery improve insulin action for the regulation of glucose, FFA, and insulin levels. This reinforces what we know, namely, that insulin action is essential for regulating FFA and glucose levels and is a robust effect that can be observed not only in the long-term, but also in the short-term; thereby preventing the manifestation of T2DM.
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Keywords type 2 diabetes; mathematical model; free fatty acids

Citation: Anarina L. Murillo, Jiaxu Li, Carlos Castillo-Chavez. Modeling the dynamics of glucose, insulin, and free fatty acids with time delay: The impact of bariatric surgery on type 2 diabetes mellitus. Mathematical Biosciences and Engineering, 2019, 16(5): 5765-5787. doi: 10.3934/mbe.2019288

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