Modeling the glucose–insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays
Abstract
In the glucose-insulin regulatory system, ultradian insulin secretory oscillations are observed to have a period of 50-150 min. After pioneering work traced back to the 1960s, several mathematical models have been proposed during the last decade to model these ultradian oscillations as well as the metabolic system producing them. These currently existing models still lack some of the key physiological aspects of the glucose-insulin system. Applying the mass conservation law, we introduce two explicit time delays and propose a more robust alternative model for better understanding the glucose-insulin endocrine metabolic regulatory system and the ultradian insulin secretory oscillations for the cases of continuous enteral nutrition and constant glucose infusion. We compare the simulation profiles obtained from this two time delay model with those from the other existing models. As a result, we notice many unique features of this two delay model. Based on our intensive simulations, we suspect that one of the possibly many causes of ultradian insulin secretion oscillations is the time delay of the insulin secretion stimulated by the elevated glucose concentration.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Time delays are common in modeling the metabolic system.
“Time delays, which are common in modeling the metabolic system (82–85), may induce uncertainty and make machine learning challenging to capture chaotic phenomena (86, 87).”
From The progression of secondary diabetes: A review of modeling studies (2022) · cites this paper as [85]
Both Sturis' and Li's models simulated earlier glucose oscillation than insulin oscillation.
“Both Sturis' and Li's models simulated earlier glucose oscillation than insulin oscillation.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
Li's model predicted the time difference between glucose and insulin peak levels to be about 20 min, which depended on the glucose infusion rate.
“For example, Li's model predicted the time difference between glucose and insulin peak levels to be about 20 min, which also depended on the glucose infusion rate.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
The simulated oscillation amplitudes of blood glucose and insulin in the current model were within the amplitude ranges predicted by Li's model.
“It was confirmed that the simulated oscillation amplitudes of blood glucose and insulin in the current model were within the amplitude ranges predicted by Li's model.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
Li's model demonstrated that both the oscillation amplitude of blood glucose and that of blood insulin depended on the glucose infusion rate.
“Li's model demonstrated that both the oscillation amplitude of blood glucose and that of blood insulin depended on the glucose infusion rate.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
In a mathematical approach, the shapes of the functions, instead of their mathematical forms, are more important.
“Such assumption is acceptable in a mathematical approach because the shapes of the functions, instead of their mathematical forms, are more important [8].”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
The model simulation results are consistent with those of currently existing theoretical models, such as the models of Sturis et al. and Li et al., both of which were developed to mimic experimental findings of ultradian oscillations during constant glucose infusion.
“The model simulation results are consistent with those of currently existing theoretical models, such as the models of Sturis et al. and Li et al. [7,8], both of which were developed to mimic experimental findings of ultradian oscillations during constant glucose infusion.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
The hypothesis that ultradian insulin secretion represents an instability in peripheral GIG interactions has been the subject of a number of studies, including the mathematical model originally proposed by Sturis et al. and lately modified by Li et al., where time-delay is included implicitly or explicitly to produce ultradian oscillation.
“The hypothesis that ultradian insulin secretion represents an instability in peripheral GIG interactions has been the subject of a number of studies, including the mathematical model originally proposed by Sturis et al. and lately modified by Li et al. [7,8], where time-delay is included implicitly or explicitly to produce ultradian oscillation.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
The present model has similar characteristics of the models of Sturis et al. and Li et al., in simulating ultradian oscillation, without including any time-delay.
“The present model has similar characteristics of the models of Sturis et al. and Li et al. [7,8], in simulating ultradian oscillation, without including any time-delay.”
From A mathematical model of brain glucose homeostasis (2009) · cites this paper as [8]
Cites
Keener, J. P., & Sneyd, J. (2009) · Interdisciplinary applied mathematics · doi:10.1007/978-0-387-75847-3 · Cited by 2,213 · see citing works
Keener, J. P., & Sneyd, J. (1998) · Interdisciplinary applied mathematics · doi:10.1007/b98841 · Cited by 1,543 · see citing works
Assessment of Insulin Sensitivityin Vivo*
Bergman, R. N., Finegood, D. T., & Ader, M. (1985) · Endocrine Reviews · doi:10.1210/edrv-6-1-45 · Cited by 1,062 · see citing works
Insulin Degradation: Progress and Potential
Duckworth, W. C., Bennett, R. G., & Hamel, F. G. (1998) · Endocrine Reviews · doi:10.1210/edrv.19.5.0349 · Cited by 875 · see citing works
Shampine, L. F., & Thompson, S. E. R. (2001) · Applied Numerical Mathematics · doi:10.1016/s0168-9274(00)00055-6 · Cited by 553 · see citing works
Makroglou, A., Li, J., & Kuang, Y. (2006) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2005.04.023 · Cited by 367 · see citing works
Mathematical modelling of the intravenous glucose tolerance test
Gaetano, A. D., & Arino, O. (2000) · Journal of Mathematical Biology · doi:10.1007/s002850050007 · Cited by 353 · see citing works
Coefficients of normal blood glucose regulation
Bolie, V. W. (1961) · Journal of Applied Physiology · doi:10.1152/jappl.1961.16.5.783 · Cited by 349 · cited 1× · see citing works
“Pioneering work on modeling the glucose–insulin regulatory system and the ultradian insulin secretory oscillations can be traced back to Bolie (1961), in which the linearized system of the glucose–insulin regulation in terms of the differential equations of feedback was analysed with the so-called…”
BackgroundA model of β-cell mass, insulin, and glucose kinetics: pathways to diabetes
TOPP, B., PROMISLOW, K., DEVRIES, G., MIURA, R. M., & FINEGOOD, D. T. (2000) · Journal of Theoretical Biology · doi:10.1006/jtbi.2000.2150 · Cited by 330 · see citing works
The evolution of β‐cell dysfunction and insulin resistance in type 2 diabetes
Bergman, R. N., Finegood, D. T., & Kahn, S. E. (2002) · European Journal of Clinical Investigation · doi:10.1046/j.1365-2362.32.s3.5.x · Cited by 302 · see citing works
Computer model for mechanisms underlying ultradian oscillations of insulin and glucose
Sturis, J., Polonsky, K. S., Mosekilde, E., & Van Cauter, E. (1991) · American Journal of Physiology-Endocrinology and Metabolism · doi:10.1152/ajpendo.1991.260.5.e801 · Cited by 262 · cited 38× · see citing works
“These functions take the following forms with experimentally determined parameters given in Table 1 (Sturis et al., 1991; Tolic et al., 2000).”
BackgroundMethodResultInfluentialPulsatile Insulin Secretion: Detection, Regulation, and Role in Diabetes
Pørksen, N., Hollingdal, M., Juhl, C., Butler, P., Veldhuis, J. D., & Schmitz, O. (2002) · Diabetes · doi:10.2337/diabetes.51.2007.s245 · Cited by 223 · see citing works
Modeling the Insulin–Glucose Feedback System: The Significance of Pulsatile Insulin Secretion
Tolić, I. M., Erik Mosekilde, B., & Sturis, J. (2000) · Journal of Theoretical Biology · doi:10.1006/jtbi.2000.2180 · Cited by 213 · see citing works
Prager, R., Wallace, P., & Olefsky, J. M. (1986) · Journal of Clinical Investigation · doi:10.1172/jci112599 · Cited by 204 · see citing works
Luzi, L., & DeFronzo, R. A. (1989) · American Journal of Physiology-Endocrinology and Metabolism · doi:10.1152/ajpendo.1989.257.2.e241 · Cited by 186 · see citing works
The effect of physical exercise on the dynamics of glucose and insulin.
Derouich, M., & Boutayeb, A. (2002) · Journal of Biomechanics · doi:10.1016/s0021-9290(02)00055-6 · Cited by 184 · see citing works
Control mechanisms of the oscillations of insulin secretion in vitro and in vivo.
Gilon, P., Ravier, M., Jonas, J., & Henquin, J. (2002) · Diabetes · doi:10.2337/diabetes.51.2007.s144 · Cited by 166 · see citing works
Numerical bifurcation analysis of delay differential equations arising from physiological modeling
Engelborghs, K., Lemaire, V., Bélair, J., & Roose, D. (2001) · Journal of Mathematical Biology · doi:10.1007/s002850000072 · Cited by 122 · see citing works
Ultradian Oscillations of Insulin Secretion in Humans
Simon, C., & BRANDENBERGER, G. (2002) · Diabetes · doi:10.2337/diabetes.51.2007.s258 · Cited by 108 · see citing works
Analysis of IVGTT glucose-insulin interaction models with time delay
Li, J., Kuang, Y., & Li, B. (2001) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2001.1.103 · Cited by 94 · see citing works
Mukhopadhyay, A., Gaetano, A. D., & Arino, O. (2004) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2004.4.407 · Cited by 77 · see citing works
Bennett, D. L., & Gourley, S. A. (2003) · Applied Mathematics and Computation · doi:10.1016/s0096-3003(03)00332-1 · Cited by 68 · see citing works
Mathematical modeling in glucose metabolism and insulin secretion
Mari, A. (2002) · Current Opinion in Clinical Nutrition & Metabolic Care · doi:10.1097/00075197-200209000-00007 · Cited by 67 · see citing works
Pathogenesis and prediction of diabetes mellitus: lessons from integrative physiology.
Bergman, R. N. (2002) · PubMed · Cited by 65 · see citing works
Physiological consequences of phasic insulin release in the normal animal
Cherrington, A. D., Sindelar, D., Edgerton, D., Steiner, K., & McGuinness, O. P. (2002) · Diabetes · doi:10.2337/diabetes.51.2007.s103 · Cited by 63 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Makroglou, A., Li, J., & Kuang, Y. (2006) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2005.04.023 · Cited by 367 · see citing works
Mathematical modeling of the glucose–insulin system: A review
Palumbo, P. J., Ditlevsen, S., BERTUZZI, A., & Gaetano, A. D. (2013) · Mathematical Biosciences · doi:10.1016/j.mbs.2013.05.006 · Cited by 183 · see citing works
Pawelek, K. A., Liu, S., Pahlevani, F., & Rong, L. (2011) · Mathematical Biosciences · doi:10.1016/j.mbs.2011.11.002 · Cited by 166 · see citing works
On the Dynamics of the Adenylate Energy System: Homeorhesis vs Homeostasis
la Fuente, I. M. D., Cortés, J. M., Valero, E., Desroches, M., Rodrigues, S., Malaina, I., & Martínez, L. (2014) · PLoS ONE · doi:10.1371/journal.pone.0108676 · Cited by 135 · see citing works
Modeling impulsive injections of insulin: towards artificial pancreas
Huang, M., Li, J., Song, X., & Guo, H. (2012) · SIAM Journal on Applied Mathematics · doi:10.1137/110860306 · Cited by 119 · see citing works
Mathematical models of diabetes progression
Gaetano, A. D., Hardy, T. A., Beck, B., Abu-Raddad, E., Palumbo, P. J., Bue‐Valleskey, J. M., & Pørksen, N. K. (2008) · American Journal of Physiology-Endocrinology and Metabolism · doi:10.1152/ajpendo.90444.2008 · Cited by 119 · see citing works
Regmi, P. R., Kempen, T. A. T. G. V., Matte, J. J., & Zijlstra, R. T. (2011) · Journal of Nutrition · doi:10.3945/jn.110.132449 · Cited by 100 · see citing works
Analysis of a model of the glucose-insulin regulatory system with two delays
Li, J., & Kuang, Y. (2007) · SIAM Journal on Applied Mathematics · doi:10.1137/050634001 · Cited by 96 · see citing works
Pharmacokinetic/Pharmacodynamic Modelling in??Diabetes Mellitus
Landersdorfer, C. B., & Jusko, W. J. (2008) · Clinical Pharmacokinetics · doi:10.2165/00003088-200847070-00001 · Cited by 95 · see citing works
An, Q., Beretta, E., Kuang, Y., Wang, C., & Hao Wang, A. (2018) · Journal of Differential Equations · doi:10.1016/j.jde.2018.11.025 · Cited by 94 · see citing works
Modeling oscillatory control in NF-κB, p53 and Wnt signaling
Pers, B. M., Hunziker, A., Pedersen, L., Trusina, A., Jensen, M. H., & Krishna, S. (2010) · Current Opinion in Genetics & Development · doi:10.1016/j.gde.2010.08.008 · Cited by 81 · see citing works
Modeling a simplified regulatory system of blood glucose at molecular levels
Liu, W., & Tang, F. (2008) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2008.02.021 · Cited by 76 · see citing works
Review and Analysis of Blood Glucose (BG) Models for Type 1 Diabetic Patients
Balakrishnan, N. P., Rangaiah, G. P., & Lakshminarayanan, S. (2011) · Industrial & Engineering Chemistry Research · doi:10.1021/ie2004779 · Cited by 73 · see citing works
Mathematical modeling and qualitative analysis of insulin therapies
Wang, H., Li, J., & Kuang, Y. (2007) · Mathematical Biosciences · doi:10.1016/j.mbs.2007.05.008 · Cited by 65 · see citing works
Numerical simulation for fractional delay differential equations
Singh, H. (2020) · International Journal of Dynamics and Control · doi:10.1007/s40435-020-00671-6 · Cited by 63 · see citing works
Mathematical models of energy homeostasis
Pattaranit, R., & van den Berg, H. A. (2008) · Journal of The Royal Society Interface · doi:10.1098/rsif.2008.0216 · Cited by 61 · see citing works
Modeling the physiological glucose–insulin system on normal and diabetic subjects
Chen, C., & Tsai, H.-W. (2009) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2009.06.005 · Cited by 53 · see citing works
Time delay in physiological systems: Analyzing and modeling its impact
Batzel, J. J., & Kappel, F. (2011) · Mathematical Biosciences · doi:10.1016/j.mbs.2011.08.006 · Cited by 50 · see citing works
Enhanced modelling of the glucose–insulin system and its applications in insulin therapies
Wang, H., Li, J., & Kuang, Y. (2008) · Journal of Biological Dynamics · doi:10.1080/17513750802101927 · Cited by 46 · see citing works
Analysis of HIV models with two time delays
Alshorman, A., Wang, X., Meyer, M. J., & Rong, L. (2016) · Journal of Biological Dynamics · doi:10.1080/17513758.2016.1148202 · Cited by 45 · see citing works
Mathematical models of subcutaneous injection of insulin analogues: A mini-review
Li, J., & Johnson, J. D. (2009) · Discrete and Continuous Dynamical Systems - B · doi:10.3934/dcdsb.2009.12.401 · Cited by 45 · see citing works
A molecular mathematical model of glucose mobilization and uptake
Liu, W., Hsin, C., & Tang, F. (2009) · Mathematical Biosciences · doi:10.1016/j.mbs.2009.07.005 · Cited by 42 · see citing works
The range of time delay and the global stability of the equilibrium for an IVGTT model
Li, J., Wang, M., Gaetano, A. D., Palumbo, P. J., & Panunzi, S. (2011) · Mathematical Biosciences · doi:10.1016/j.mbs.2011.11.005 · Cited by 41 · see citing works
Wang, M., Li, J., Lim, G. E., & Johnson, J. D. (2013) · PLoS ONE · doi:10.1371/journal.pone.0064860 · Cited by 36 · see citing works
Modeling the physiological glucose–insulin dynamic system on diabetics
Chen, C., Tsai, H.-W., & Wong, S.-S. (2010) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2010.05.002 · Cited by 35 · see citing works
Modeling impulsive insulin delivery in insulin pump with time delays
Song, X., Huang, M., & Li, J. (2014) · SIAM Journal on Applied Mathematics · doi:10.1137/130933137 · Cited by 35 · see citing works
Li, J., & Kuang, Y. (2008) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2009.6.41 · Cited by 35 · see citing works
Hopf bifurcation and chaos in time-delay model of glucose-insulin regulatory system
Al-Hussein, A.-B. A., Rahma, F., & Jafari, S. (2020) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2020.109845 · Cited by 34 · see citing works
Hu, R., & Li, C. (2015) · Computational and Mathematical Methods in Medicine · doi:10.1155/2015/281589 · Cited by 33 · see citing works
ODE models for the management of diabetes: A review
Rathee, S., & Nilam (2016) · International Journal of Diabetes in Developing Countries · doi:10.1007/s13410-016-0475-8 · Cited by 33 · see citing works
Chuedoung, M., Sarika, W., & Lenbury, Y. (2009) · Nonlinear Analysis · doi:10.1016/j.na.2009.01.129 · Cited by 31 · see citing works
Giang, D. V., Lenbury, Y., Gaetano, A. D., & Palumbo, P. J. (2008) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2008.02.016 · Cited by 30 · see citing works
A mathematical model of brain glucose homeostasis
Gaohua, L., & Kimura, H. (2009) · Theoretical Biology and Medical Modelling · doi:10.1186/1742-4682-6-26 · Cited by 29 · see citing works
Stable Numerical Approach for Fractional Delay Differential Equations
Singh, H., Pandey, R. K., & Bǎleanu, D. (2017) · Few-Body Systems · doi:10.1007/s00601-017-1319-x · Cited by 29 · see citing works
Virtual metabolic human dynamic model for pathological analysis and therapy design for diabetes
Kurata, H. (2021) · iScience · doi:10.1016/j.isci.2021.102101 · Cited by 28 · see citing works
Physiological analysis on oscillatory behavior of glucose–insulin regulation by model with delays
Wu, Z., Chui, C., Hong, G. S., & Chang, S. K.-Y. (2011) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2011.03.032 · Cited by 28 · see citing works
Mathematical model of glucose–insulin homeostasis in healthy rats
Lombarte, M., Lupo, M., Campetelli, G., BASUALDO, M. S., & Rigalli, A. (2013) · Mathematical Biosciences · doi:10.1016/j.mbs.2013.07.017 · Cited by 27 · see citing works
Determination of personalized diabetes treatment plans using a two-delay model
Kissler, S. M., Cichowitz, C., Sankaranarayanan, S., & Bortz, D. M. (2014) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2014.06.005 · Cited by 27 · see citing works
Srivastava, A., Yadav, V. K., Nilam, Kumar, M., & Srivastava, A. P. (2024) · International Conference on Sustainable Computing and Integrated Communication in Changing Landscape of AI (ICSCAI) · doi:10.1109/icscai61790.2024.10866055 · Cited by 26 · see citing works
Active insulin infusion using fuzzy-based closed-loop control
Yasini, S., Sistani, M. B. N., & Karimpour, A. (2008) · International Conference on Intelligent Systems and Knowledge Engineering (ISKE) · doi:10.1109/iske.2008.4730968 · Cited by 26 · see citing works
Gallenberger, M., zu Castell, W., Hense, B. A., & Kuttler, C. (2012) · Theoretical Biology and Medical Modelling · doi:10.1186/1742-4682-9-46 · Cited by 28 · see citing works
Saber, S., & Alalyani, A. (2022) · Mathematical Modelling and Analysis · doi:10.3846/mma.2022.14007 · Cited by 24 · see citing works
Mathematical model for glucose regulation in the whole-body system
Kang, H., Han, K., & Choi, M. Y. (2012) · Islets · doi:10.4161/isl.19505 · Cited by 25 · see citing works
Belkić, D. (2018) · Journal of Mathematical Chemistry · doi:10.1007/s10910-018-0985-3 · Cited by 24 · see citing works
Oscillatory dynamics of an intravenous glucose tolerance test model with delay interval
Shi, X., Kuang, Y., Makroglou, A., Mokshagundam, S. L., & Li, J. (2017) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5008384 · Cited by 23 · see citing works
Mathematical Modeling of Glucose Homeostasis and Its Relationship With Energy Balance and Body Fat
Smith, J. M. D., Maas, J. A., Garnsworthy, P. C., Owen, M. R., Coombes, S., Pillay, T. S., Barrett, D. A., & Symonds, M. E. (2009) · Obesity · doi:10.1038/oby.2008.604 · Cited by 23 · see citing works
Yasini, S., Karimpour, A., & Sistani, M. B. N. (2012) · IETE Journal of Research · doi:10.4103/0377-2063.102314 · Cited by 22 · see citing works
Pei, L., Wang, Q., & Shi, H. (2010) · Nonlinear Dynamics · doi:10.1007/s11071-010-9812-5 · Cited by 22 · see citing works
Agent-Based Simulation For Blood Glucose Control In Diabetic Patients
Yasini, S., Sistani, M. B. N., & Karimpour, A. (2009) · doi:10.5281/zenodo.1060214 · Cited by 22 · see citing works
Benhammouda, B., & Vázquez-Leal, H. (2016) · SpringerPlus · doi:10.1186/s40064-016-3386-8 · Cited by 22 · see citing works
Mbé, J. H. T., Woafo, P., & Chembo, Y. K. (2019) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5064679 · Cited by 21 · see citing works
An adaptive technique based blood glucose control in type‐1 diabetes mellitus patients
Belmon, A. P., & Auxillia, J. (2020) · International Journal for Numerical Methods in Biomedical Engineering · doi:10.1002/cnm.3371 · Cited by 21 · see citing works
Mathematical modelling of glucose dynamics
Huard, B., & Kirkham, G. (2022) · Current Opinion in Endocrine and Metabolic Research · doi:10.1016/j.coemr.2022.100379 · Cited by 20 · see citing works
Robust closed-loop control of plasma glycemia: A discrete-delay model approach
Palumbo, P. J., Pepe, P., Panunzi, S., & Gaetano, A. D. (2008) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2008.4738940 · Cited by 20 · see citing works
An adaptive back-stepping control for blood glucose regulation in type 1 diabetes
Sepasi, S., Kalat, A. A., & Seyedabadi, M. (2021) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2021.102498 · Cited by 19 · see citing works
Huard, B., Easton, J. F., & Angelova, M. N. (2015) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2015.02.017 · Cited by 19 · see citing works
A Unifying Organ Model of Pancreatic Insulin Secretion
Gaetano, A. D., Gaz, C., Palumbo, P. J., & Panunzi, S. (2015) · PLoS ONE · doi:10.1371/journal.pone.0142344 · Cited by 19 · see citing works
Shabestari, P. S., Rajagopal, K., Safarbali, B., Jafari, S., & Duraisamy, P. (2018) · Complexity · doi:10.1155/2018/6815190 · Cited by 19 · see citing works
Mathematical Modeling of the Blood Glucose Regulation System in Diabetes Mellitus Patients
Александрович, К. В., Philippov, Y. I., Tarasov, Y. V., Boyarsky, M. D., Mayorov, A. Y., Shestakova, M. V., & Dedov, I. I. (2015) · Annals of the Russian academy of medical sciences · doi:10.15690/vramn.v70.i5.1441 · Cited by 18 · see citing works
Dubey, V. P., Kumar, R., & Kumar, D. (2019) · International Journal of Biomathematics · doi:10.1142/s1793524519500591 · Cited by 17 · see citing works
Modelling the regulatory system for diabetes mellitus with a threshold window
Yang, J., Tang, S., & Cheke, R. (2014) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2014.08.012 · Cited by 17 · see citing works
Identifiability of Control-Oriented Glucose-Insulin Linear Models: Review and Analysis
Hoyos, J. D., Villa-Tamayo, M. F., Builes-Montaño, C. E., Rincón, A. R., Godoy, J. L., Garcia‐Tirado, J., & Rivadeneira, P. S. (2021) · IEEE Access · doi:10.1109/access.2021.3076405 · Cited by 17 · see citing works
Modeling and qualitative analysis of diabetes therapies with state feedback control
Huang, M., & Song, X. (2014) · International Journal of Biomathematics · doi:10.1142/s1793524514500351 · Cited by 17 · see citing works
Optimal homeostasis necessitates bistable control
Wang, G. (2012) · Journal of The Royal Society Interface · doi:10.1098/rsif.2012.0244 · Cited by 17 · see citing works
Murillo, A. L., Li, J. X., & Castillo‐Chávez, C. (2019) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2019288 · Cited by 17 · see citing works
Models, Devices, Properties, and Verification of Artificial Pancreas Systems
Kushner, T., Bequette, B. W., Cameron, F. M., Forlenza, G. P., Maahs, D. M., & Sankaranarayanan, S. (2019) · Computational biology · doi:10.1007/978-3-030-17297-8_4 · Cited by 16 · see citing works
A Novel Model and its Analysis on the Metabolic Regulations of Glucose, Insulin, and Glucagon
Cohen, R. B., & Li, J. (2021) · SIAM Journal on Applied Mathematics · doi:10.1137/21m1390876 · Cited by 16 · see citing works
Yang, J., Tang, S., & Cheke, R. (2016) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2016.02.001 · Cited by 16 · see citing works
Huard, B., Bridgewater, A., & Angelova, M. N. (2017) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2017.01.039 · Cited by 17 · see citing works
Frøslie, K. F., Røislien, J., Qvigstad, E., Godang, K., Bollerslev, J., Henriksen, T., & Veierød, M. B. (2014) · PLoS ONE · doi:10.1371/journal.pone.0090798 · Cited by 15 · see citing works
An islet population model of the endocrine pancreas
Palumbo, P. J., & Gaetano, A. D. (2009) · Journal of Mathematical Biology · doi:10.1007/s00285-009-0297-0 · Cited by 16 · see citing works
Modeling Spruce Budworm Population Revisited: Impact of Physiological Structure on Outbreak Control
Vaidya, N. K., & Wu, J. (2008) · Bulletin of Mathematical Biology · doi:10.1007/s11538-007-9278-x · Cited by 16 · see citing works
Tao, Y., Sun, Y., Zhu, H., Lyu, J., & Ren, J. (2023) · Journal of Nonlinear Science · doi:10.1007/s00332-023-09907-z · Cited by 15 · see citing works
A Mathematical Model of the Human Metabolic System and Metabolic Flexibility
Pearson, T., Wattis, J. A. D., King, J. R., Macdonald, I. A., & Mazzatti, D. J. (2014) · Bulletin of Mathematical Biology · doi:10.1007/s11538-014-0001-4 · Cited by 14 · see citing works
Mostafa Adimy, A., & Fabien Crauste, A. (2012) · Mathematical Modelling of Natural Phenomena · doi:10.1051/mmnp/20127601 · Cited by 14 · see citing works
Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays
Nguimdo, R. M. (2018) · Physical review. E · doi:10.1103/physreve.97.032211 · Cited by 13 · see citing works
A Novel Three‐Compartmental Model for Artificial Pancreas: Development and Validation
Piemonte, V., Capocelli, M., Santis, L. D., Maurizi, A. R., & Pozzilli, P. (2017) · Artificial Organs · doi:10.1111/aor.12980 · Cited by 12 · see citing works
A mathematical model for the robust blood glucose tracking
Liu, W. (2019) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2019036 · Cited by 12 · see citing works
Glucose-Insulin System Based on Minimal Model: A Realistic Approach
Gonzalez, A. A., Voos, H., & Darouach, M. (2015) · UKSim International Conference on Computer Modelling and Simulation (UKSim) · doi:10.1109/uksim.2015.65 · Cited by 12 · see citing works
Delay-induced uncertainty for a paradigmatic glucose–insulin model
Karamched, B., Hripcsak, G., Albers, D., & Ott, W. (2021) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0027682 · Cited by 12 · see citing works
Comparison of MLP and Elman Neural Network for Blood Glucose Level Prediction in Type 1 Diabetics
Quchani, S. A., & Tahami, E. (2007) · World Congress on Medical Physics and Biomedical Engineering, September 7 - 12, 2009, Munich, Germany · doi:10.1007/978-3-540-68017-8_15 · Cited by 12 · see citing works
Robust adaptive observer-based control of blood glucose level for type 1 diabetic patient
Seyedabadi, M., & Kalat, A. A. (2024) · Journal of Applied Biomedicine · doi:10.1016/j.bbe.2024.03.003 · Cited by 11 · see citing works
Grant, A. D., Lewis, D. M., & Kriegsfeld, L. J. (2021) · Journal of Diabetes Science and Technology · doi:10.1177/1932296821994825 · Cited by 11 · see citing works
Analysis of a Fractional-order Glucose-Insulin Biological System with Time Delay
FERNÁNDEZ-CARREÓN, B., Munoz-Pacheco, J. M., Zambrano-Serrano, E., & Félix-Beltrán, O. (2021) · Chaos Theory and Applications · doi:10.51537/chaos.988758 · Cited by 11 · see citing works
Sharma, A., Nilam, & Singh, H. P. (2022) · Applied Intelligence · doi:10.1007/s10489-022-03416-4 · Cited by 11 · see citing works
Dynamics of a glucose–insulin model
Ma, M., & Li, J. (2022) · Journal of Biological Dynamics · doi:10.1080/17513758.2022.2146769 · Cited by 10 · see citing works
Yan, S., Ding, L., & Cai, Y. (2025) · Nonlinear Dynamics · doi:10.1007/s11071-025-11192-2 · Cited by 10 · see citing works
Review Study of Detection of Diabetes Models through Delay Differential Equations
Chalishajar, D. N., Geary, D. H., & Cox, G. (2016) · Applied Mathematics · doi:10.4236/am.2016.710097 · Cited by 10 · see citing works
Model-Based Insulin Therapy Scheduling: A Mixed-Integer Nonlinear Dynamic Optimization Approach
Chen, C., & Tsai, H.-W. (2009) · Industrial & Engineering Chemistry Research · doi:10.1021/ie9005673 · Cited by 10 · see citing works
Liu, S.-W., Huang, H., Lin, C.-H., & Chien, I. (2012) · Industrial & Engineering Chemistry Research · doi:10.1021/ie202308w · Cited by 10 · see citing works
Fuzzy Control System for Regulating the Blood Glucose Level of Diabetes Patients Implemented on FPGA
Gharghory, S. M., & El-Dib, D. A. (2016) · Journal of Circuits Systems and Computers · doi:10.1142/s0218126616501619 · Cited by 10 · see citing works
Sumner, T. (2010) · UCL Discovery (University College London) · Cited by 10 · see citing works
Model Predictive Control for the Artificial Pancreas
Capocelli, M., Santis, L. D., Maurizi, A. R., Pozzilli, P., & Piemonte, V. (2018) · doi:10.1002/9781119296034.ch5 · Cited by 10 · see citing works
Delay in ATP-dependent calcium inflow may affect insulin secretion from pancreatic beta-cell
Das, P. N., Halder, S., Bairagi, N., & Chatterjee, S. (2020) · Applied Mathematical Modelling · doi:10.1016/j.apm.2020.03.030 · Cited by 9 · see citing works
LMI Based Robust Blood Glucose Regulation in Type-1 Diabetes Patient with Daily Multi-meal Ingestion
Mandal, S., Bhattacharjee, A., & Sutradhar, A. (2014) · Journal of The Institution of Engineers (India) Series B · doi:10.1007/s40031-014-0083-2 · Cited by 9 · see citing works
A model for the hepatic glucose metabolism based on Hill and step functions
D’Abbicco, M., Buono, N. D., Gena, P., Berardi, M., Calamita, G., & Lopez, L. (2015) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2015.01.036 · Cited by 9 · see citing works
Strilka, R. J., Stull, M. C., Clemens, M. S., McCaver, S. C., & Armen, S. B. (2016) · Theoretical Biology and Medical Modelling · doi:10.1186/s12976-016-0029-2 · Cited by 9 · see citing works
Analysis of a stochastic IVGTT glucose-insulin model with time delay
Shi, X., Zheng, Q., Yao, J., Li, J., & Zhou, X. (2020) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2020123 · Cited by 9 · see citing works
Rao, F., Zhang, Z., & Li, J. (2023) · Journal of Mathematical Biology · doi:10.1007/s00285-023-02003-6 · Cited by 8 · see citing works
Asymptotic tracking and disturbance rejection of the blood glucose regulation system
Ashley, B. K., & Liu, W. (2017) · Mathematical Biosciences · doi:10.1016/j.mbs.2017.05.001 · Cited by 8 · see citing works
- Authors
- Li, J., Kuang, Y., & Mason, C. C.
- Affiliations
- Arizona State University (US)
- Corresponding author
- Li, Jiaxu
- Venue
- Journal of Theoretical Biology
- Publisher
- Elsevier BV
- Published
- 2006-10
- Volume
- 242
- Issue
- 3
- Pages
- 722-735
- ISSN
- 0022-5193 (ISSN-L)
- OpenAlex
- W2161967671
- Cited by
- 241
- References
- 25
- Citations by year
- 2026: 15 · 2025: 15 · 2024: 11 · 2023: 8 · 2022: 16 · 2021: 12 · 2020: 19 · 2019: 15 · 2018: 9 · 2017: 13 · 2016: 14 · 2015: 14 · 2014: 20 · 2013: 8 · 2012: 10
- FWCI
- 8.50
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Theoretical Biology (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Health Sciences › Medicine › Surgery › Pancreatic function and diabetes
- Health Sciences › Medicine › Endocrinology, Diabetes and Metabolism › Diabetes Management and Research
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Differential Equations Analysis
- Keywords
- glucose-insulin regulatory system, time delay model, insulin secretion, mass conservation, enteral nutrition, glucose infusion
- MeSH terms
- Insulin Secretion, Activity Cycles, Computer Simulation, Diabetes Mellitus, Type 2, Enteral Nutrition, Glucose, Humans, Insulin, Islets of Langerhans, Liver, Models, Biological, Secretory Rate, Time Factors
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
