title: Mathematical investigation of diabetically impaired ultradian oscillations in the glucose-insulin regulation.
abstract: We study the effect of diabetic deficiencies on the production of an oscillatory ultradian regime using a deterministic nonlinear model which incorporates two physiological delays. It is shown that insulin resistance impairs the production of oscillations by dampening the ultradian cycles. Four strategies for restoring healthy regulation are explored. Through the introduction of an instantaneous glucose-dependent insulin response, explicit conditions for the existence of periodic solutions in the linearised model are formulated, significantly reducing the complexity of identifying an oscillatory regime. The model is thus shown to be suitable for representing the effect of diabetes on the oscillatory regulation and for investigating pathways to reinstating a physiological healthy regime.
authors.affiliation: Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, UK. Electronic address: benoit.huard@northumbria.ac.uk.
authors.forename: B
authors.initials: B
authors.lastname: Huard
authors.affiliation: Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, UK.
authors.forename: A
authors.initials: A
authors.lastname: Bridgewater
authors.affiliation: Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, UK; School of Information Technology, Deakin University, Burwood Vic 3125, Australia.
authors.forename: M
authors.initials: M
authors.lastname: Angelova
mesh_terms: D001683:Biological Clocks; D001786:Blood Glucose / Q000378:metabolism*; D003920:Diabetes Mellitus / Q000097:blood*; D006801:Humans; D007328:Insulin / Q000097:blood*; D008954:Models, Biological
chemical_list: D001786:Blood Glucose; D007328:Insulin
keywords: Delay differential equations; Diabetes; Four healthy regulation strategies; Impaired ultradian rhythms; Stability analysis