Dynamic Analysis Of Glucose Metabolism Model With Insulin Secretion Delay And Aerobic Exercise

In recent years,with the rapid rise of number of cases,diabetes mellitus has become one of the most serious chronic diseases worldwide.In order to improve the present situation of diabetic patients,it is necessary to build advanced mathematical models that can reliably describe the dynamic interrelationships among some key physiological variables,such as blood glucose and insulin etc.,under a range of metabolic and behavioral conditions(e.g.pre-or post-prandial,rest or exercise,relax or stress).Such models would not only provide help for the diagnosis of diabetes,but also can regulate their long-term blood glucose combining with an insulin pump.It is useful to postpone or even prevent the onset of the pathologies caused by long-time abnormal blood glucose in diabetic patients.In this paper,we established corresponding models based on the relationships between insulin and blood glucose.Furthermore,we analysed the effect of the insulin secretion delay and different intensities of aerobic exercise on blood glucose.In Chapter 1,it contained the biological background,significance and research status of diabetes firstly.Then,the research contents and methods of this paper were introduced.In Chapter 2,it established an intravenous glucose tolerance test(IVGTT)model according to blood glucose metabolism,which mainly took consideration of the insulin secretion delay and divided insulin into plasma insulin and interstitial compartments.In theory,we studied basic properties of the model and stability of the unique steady state.Furthermore,we analysed the Hopf bifurcation caused by delay.Finally,we did some numerical fitting with four true IVGTT experimental data,which verified the theoretical results.In Chapter 3,in view of the effect of exercise on blood glucose,it introduced a blood glucose metabolic model for diabetes patients under aerobic exercise.Furthermore,a silicon method was adopted to study the effects of different aerobic exercise intensities(light,moderate and vigorous)on blood glucose and optimal strategies of insulin infusion for type 1 diabetes mellitus(T1DM)and type2 diabetes mellitus(T2DM).The universality of proposed optimal strategies was verified to eliminate the influence of individual differences.These results were useful to the regulation and management of blood glucose for diabetes patients.In Chapter 4,summarized the main conclusions of this and some suggestions for future.