2009, 6(1): 41-58. doi: 10.3934/mbe.2009.6.41

Systemically modeling the dynamics of plasma insulin in subcutaneous injection of insulin analogues for type 1 diabetes

1. 

Department of Mathematics, University of Louisville, Louisville KY 40292, United States

2. 

Department of Math & Statistics, College of Liberal Arts and Sciences, Arizona State University, Tempe, AZ 85287 - 1804

Received  May 2008 Revised  July 2008 Published  December 2008

Type 1 diabetics must inject exogenous insulin or insulin analogues one or more times daily. The timing and dosage of insulin administration have been a critical research area since the invention of insulin analogues. Several pharmacokinetical models have been proposed, and some are applied clinically in modeling various insulin therapies. However, their plasma insulin concentration must be computed separately from the models' output. Furthermore, minimal analytical study was performed in these existing models. We propose two systemic and simplified ordinary differential equation models to model the subcutaneous injection of rapid-acting insulin analogues and long-acting insulin analogues, respectively. Our models explicitly model the plasma insulin and hence have the advantage of computing the plasma insulin directly. The profiles of plasma insulin concentrations obtained from these two models are in good agreement with the experimental data. We also study the dynamics of insulin analogues, plasma insulin concentrations, and, in particular, the shape of the dynamics of plasma insulin concentrations.
Citation: Jiaxu Li, Yang Kuang. Systemically modeling the dynamics of plasma insulin in subcutaneous injection of insulin analogues for type 1 diabetes. Mathematical Biosciences & Engineering, 2009, 6 (1) : 41-58. doi: 10.3934/mbe.2009.6.41
[1]

Jiaxu Li, James D. Johnson. Mathematical models of subcutaneous injection of insulin analogues: A mini-review. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 401-414. doi: 10.3934/dcdsb.2009.12.401

[2]

Igor G. Vladimirov. The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 575-600. doi: 10.3934/dcdsb.2013.18.575

[3]

Saloni Rathee, Nilam. Quantitative analysis of time delays of glucose - insulin dynamics using artificial pancreas. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3115-3129. doi: 10.3934/dcdsb.2015.20.3115

[4]

Jiaxu Li, Yang Kuang, Bingtuan Li. Analysis of IVGTT glucose-insulin interaction models with time delay. Discrete & Continuous Dynamical Systems - B, 2001, 1 (1) : 103-124. doi: 10.3934/dcdsb.2001.1.103

[5]

Pasquale Palumbo, Simona Panunzi, Andrea De Gaetano. Qualitative behavior of a family of delay-differential models of the Glucose-Insulin system. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 399-424. doi: 10.3934/dcdsb.2007.7.399

[6]

Peter W. Bates, Yu Liang, Alexander W. Shingleton. Growth regulation and the insulin signaling pathway. Networks & Heterogeneous Media, 2013, 8 (1) : 65-78. doi: 10.3934/nhm.2013.8.65

[7]

Kimberly Fessel, Jeffrey B. Gaither, Julie K. Bower, Trudy Gaillard, Kwame Osei, Grzegorz A. Rempała. Mathematical analysis of a model for glucose regulation. Mathematical Biosciences & Engineering, 2016, 13 (1) : 83-99. doi: 10.3934/mbe.2016.13.83

[8]

Gennadi M. Henkin, Victor M. Polterovich. A difference-differential analogue of the Burgers equations and some models of economic development. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 697-728. doi: 10.3934/dcds.1999.5.697

[9]

Houda Hani, Moez Khenissi. Asymptotic behaviors of solutions for finite difference analogue of the Chipot-Weissler equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (5) : 1421-1445. doi: 10.3934/dcdss.2016057

[10]

Gokhan Yener, Ibrahim Emiroglu. A q-analogue of the multiplicative calculus: Q-multiplicative calculus. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1435-1450. doi: 10.3934/dcdss.2015.8.1435

[11]

Ionel Sorin Ciuperca, Erwan Hingant, Liviu Iulian Palade, Laurent Pujo-Menjouet. Fragmentation and monomer lengthening of rod-like polymers, a relevant model for prion proliferation. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 775-799. doi: 10.3934/dcdsb.2012.17.775

[12]

Lela Dorel. Glucose level regulation via integral high-order sliding modes. Mathematical Biosciences & Engineering, 2011, 8 (2) : 549-560. doi: 10.3934/mbe.2011.8.549

[13]

Zahra Al Helal, Volker Rehbock, Ryan Loxton. Modelling and optimal control of blood glucose levels in the human body. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1149-1164. doi: 10.3934/jimo.2015.11.1149

[14]

Danilo T. Pérez-Rivera, Verónica L. Torres-Torres, Abraham E. Torres-Colón, Mayteé Cruz-Aponte. Development of a computational model of glucose toxicity in the progression of diabetes mellitus. Mathematical Biosciences & Engineering, 2016, 13 (5) : 1043-1058. doi: 10.3934/mbe.2016029

[15]

Xilin Fu, Zhang Chen. New discrete analogue of neural networks with nonlinear amplification function and its periodic dynamic analysis. Conference Publications, 2007, 2007 (Special) : 391-398. doi: 10.3934/proc.2007.2007.391

[16]

Dingjun Yao, Rongming Wang, Lin Xu. Optimal dividend and capital injection strategy with fixed costs and restricted dividend rate for a dual model. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1235-1259. doi: 10.3934/jimo.2014.10.1235

[17]

Gongpin Cheng, Rongming Wang, Dingjun Yao. Optimal dividend and capital injection strategy with excess-of-loss reinsurance and transaction costs. Journal of Industrial & Management Optimization, 2018, 14 (1) : 371-395. doi: 10.3934/jimo.2017051

[18]

Jorge Duarte, Cristina Januário, Nuno Martins. A chaotic bursting-spiking transition in a pancreatic beta-cells system: observation of an interior glucose-induced crisis. Mathematical Biosciences & Engineering, 2017, 14 (4) : 821-842. doi: 10.3934/mbe.2017045

[19]

Amitava Mukhopadhyay, Andrea De Gaetano, Ovide Arino. Modeling the intra-venous glucose tolerance test: A global study for a single-distributed-delay model. Discrete & Continuous Dynamical Systems - B, 2004, 4 (2) : 407-417. doi: 10.3934/dcdsb.2004.4.407

[20]

Noreen Sher Akbar, Dharmendra Tripathi, Zafar Hayat Khan. Numerical investigation of Cattanneo-Christov heat flux in CNT suspended nanofluid flow over a stretching porous surface with suction and injection. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 583-594. doi: 10.3934/dcdss.2018033

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (6)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]