Mathematical model of diabetes and lipid metabolism linked to diet, leptin sensitivity, insulin sensitivity and VLDLTG clearance predicts paths to health and type II diabetes

Modelling remission from overweight type 2 diabetes reveals how altering advice may counter relapse

The development or remission of diet-induced overweight type 2 diabetes involves many biological changes which occur over very different timescales. Remission, defined by HbA1c<6.5%, or fasting plasma glucose concentration G<126 mg/dl, may be achieved rapidly by following weight loss guidelines. However, remission is often short-term, followed by relapse. Mathematical modelling provides a way of investigating a typical situation, in which patients are advised to lose weight and then maintain fat mass, a slow variable. Remission followed by relapse, in a modelling sense, is equivalent to changing from a remission trajectory with steady state G<126 mg/dl, to a relapse trajectory with steady state G≥126 mg/dl. Modelling predicts that a trajectory which maintains weight will be a relapse trajectory, if the fat mass chosen is too high, the threshold being dependent on the lipid to carbohydrate ratio of the diet. Modelling takes into account the effects of hepatic and pancreatic lipid on hepatic insulin sensitivity and β-cell function, respectively. This study leads to the suggestion that type 2 diabetes remission guidelines be given in terms of model parameters, not variables; that is, the patient should adhere to a given nutrition and exercise plan, rather than achieve a certain subset of variable values. The model predicts that calorie restriction, not weight loss, initiates remission from type 2 diabetes; and that advice of the form 'adhere to the diet and exercise plan' rather than 'achieve a certain weight loss' may help counter relapse.

A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors

The concept of a Caputo fractal-fractional derivative is a new class of non-integer order derivative with a power-law kernel that has many applications in real-life scenarios. This new derivative is applied newly to model the dynamics of diabetes mellitus disease because the operator can be applied to formulate some models which describe the dynamics with memory effects. Diabetes mellitus as one of the leading diseases of our century is a type of disease that is widely observed worldwide and takes the first place in the evolution of many fatal diseases. Diabetes is tagged as a chronic, metabolic disease signalized by elevated levels of blood glucose (or blood sugar), which results over time in serious damage to the heart, blood vessels, eyes, kidneys, and nerves in the body. The present study is devoted to mathematical modeling and analysis of the diabetes mellitus model without genetic factors in the sense of fractional-fractal derivative. At first, the critical points of the diabetes mellitus model are investigated; then Picard's theorem idea is applied to investigate the existence and uniqueness of the solutions of the model under the fractional-fractal operator. The resulting discretized system of fractal-fractional differential equations is integrated in time with the MATLAB inbuilt Ode45 and Ode15s packages. A step-by-step and easy-to-adapt MATLAB algorithm is also provided for scholars to reproduce. Simulation experiments that revealed the dynamic behavior of the model for different instances of fractal-fractional parameters in the sense of the Caputo operator are displayed in the table and figures. It was observed in the numerical experiments that a decrease in both fractal dimensions ζ and ϵ leads to an increase in the number of people living with diabetes mellitus.

Virtual metabolic human dynamic model for pathological analysis and therapy design for diabetes

A virtual metabolic human model is a valuable complement to experimental biology and clinical studies, because in vivo research involves serious ethical and technical problems. I have proposed a multi-organ and multi-scale kinetic model that formulates the reactions of enzymes and transporters with the regulation of hormonal actions at postprandial and postabsorptive states. The computational model consists of 202 ordinary differential equations for metabolites with 217 reaction rates and 1,140 kinetic parameter constants. It is the most comprehensive, largest, and highly predictive model of the whole-body metabolism. Use of the model revealed the mechanisms by which individual disorders, such as steatosis, β cell dysfunction, and insulin resistance, were combined to cause diabetes. The model predicted a glycerol kinase inhibitor to be an effective medicine for type 2 diabetes, which not only decreased hepatic triglyceride but also reduced plasma glucose. The model also enabled us to rationally design combination therapy.

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A standard of virtual metabolic human dynamic models is proposed

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It integrates the three scales of molecules, organs, and whole body

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It gets insight into pathological mechanisms of type 1 and type 2 diabetes

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It enables the computer-aided design of medication treatment for diabetes

A multi-age mathematical modeling of the dynamics of population diabetics with effect of lifestyle using optimal control

Diabetes is a disease which caused by socio-environmental and / or genetic factors. The negative effect of socio-environmental or lifestyle leads a susceptible individual to become a diabetic. On the one hand, social interaction wields a great deal of influence over lifestyle. On the other hand, genetic factors are the main cause of the birth diabetes genetic disorder. Considering these above mentioned factors. In the present paper, we study a discrete age continuous mathematical model that describes the dynamics of diabetics. We highlight the negative impact of socio-environmental on diabetic patients according to age groups. We also suggest an optimal strategy to implement the best campaigns of rising awareness that aims at protecting diabetic patients from the negative impact of a lifestyle that leads them to complications. In addition to psychological treatment and follow-up of diabetic patients with complications, an awareness campaign will also be carried out for people with potential diabetes that aims at educating them about the dangerous of diabetes and its complications. Pontryagin's maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical simulation is carried out using MATLAB.

Type 2 diabetes progression: A regulatory network approach

In order to elucidate central elements underlying type 2 diabetes, we constructed a regulatory network model involving 37 components (molecules, receptors, processes, etc.) associated to signaling pathways of pancreatic beta-cells. In a first approximation, the network topology was described by Boolean rules whose interacting dynamics predicted stationary patterns broadly classified as health, metabolic syndrome, and diabetes stages. A subsequent approximation based on a continuous logic analysis allowed us to characterize the progression of the disease as transitions between these states associated to alterations of cell homeostasis due to exhaustion or exacerbation of specific regulatory signals. The method allowed the identification of key transcription factors involved in metabolic stress as essential for the progression of the disease. Integration of the present analysis with existent mathematical models designed to yield accurate account of experimental data in human or animal essays leads to reliable predictions for beta-cell mass, insulinemia, glycemia, and glycosylated hemoglobin in diabetic fatty rats.