Criticality control of insulin release: a novel alternative for detailed modelling of insulin secretion
Representation of the dynamic components of the glucose-insulin system has posed a major challenge in the field of physiological modelling for the past six decades. Early stages in development focused on a descriptive approach where mathematical complexity was usually compromised, causing misrepresentation of the system. The use of such models allowed the study of the system under extremely specific circumstances, and although it aided in the development of devices to manage type 1 Diabetes, it allowed little opportunity to study the system under normal circumstances. In the early 1990's, evidence of insulin oscillations in the system motivated a more detailed approach, with the analysis and representation of the molecular interactions involved. This work presents a novel modelling methodology which aligns with the aforementioned focus. The methodology focuses on representing a network of cells represented by systems which are inherently non-linear. In order to develop it, a review of reaction-diffusion systems was conducted, where four models were chosen as candidates to represent the building blocks for the resulting model. These were chosen due to their biological relevance and capability of generating a wide range of dynamics using a relatively simple formulation. The resulting model is comprised of a set of sixteen coupled oscillators organized into four clusters. It successfully incorporates characteristics that have been observed in the glucose-insulin system, such as nonlinear dynamics, coupling, and response to external influences. In order to tune the system and achieve multiple stable states, a biologically inspired control method (Rate Control of Chaos) was implemented. The overall structure will allow the study of the mechanisms that keep the system from reaching a chaotic state (diabetes), based on the property of self-organized criticality. The results show that the chosen candidate models are capable of representing the desired structure whilst maintaining the desired dynamics; achieved through the variation of system parameters and initial conditions. They are responsive to the controller and are tolerant to modifications in the system such as the increment of the control signal and coupling strength. The behaviour observed differs among the models and was instrumental in assessing biological relevance.
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