**Therapeutic Modelling of Type 1 Diabetes**

Nilam Nilam1, Seyed M. Moghadas2 and Pappur N. Shivakumar3

*1Department of Mathematics, Delhi Technological University, Delhi 2Centre for Disease Modelling, York University, Toronto, Ontario 3Department of Mathematics, University of Manitoba, Winnipeg, Manitoba 1India 2,3Canada* 

#### **1. Introduction**

460 Type 1 Diabetes – Complications, Pathogenesis, and Alternative Treatments

Yuan, JM., Ross, RK., Gao, YT. & Yu, MC. (2001). Fish and shellfish consumption in relation

Zhao, J., Del Bigio, MR. & Weiler, HA. (2009). Maternal arachidonic acid supplementation

December 2009), pp. 349-356, ISSN 0952-3278

1206

9262

*Allergy, Asthma, & Immunology*, Vol.100, No.1, (January 2008), pp. 66-73, ISSN 1081-

to death from myocardial infarction among men in Shanghai, China. *American Journal of Epidemiology*, Vol.154, No.9, (November 2001), pp. 809-816, ISSN 0002-

improves neurodevelopment of offspring from healthy and diabetic rats. *Prostaglandins, Leukotrienes, and Essential Fatty Acids*, Vol.81, No.5-6, (November-

> In this Chapter, we are mainly concerned with mathematical modelling (using differential equations) of controlled continuous subcutaneous infusion of insulin in Type 1 diabetes using pumps. It occurs mainly in children where controlling levels of sugar is entirely dependent on external infusion of insulin. Type I diabetes is a result of loss of beta-cell functions in the body due to an autoimmune reaction There is vast literature concerning continuous infusion of insulin where feedback is intermittent and the dosage is adhoc. Other ways of combating Type I diabetes include transplantation of insulin producing tissues or introducing artificial beta cells. We mathematically model the sugar concentration in the body and use it to dovetail a previously medically prescribed sugar concentration curve. The modelling, for the first time, aids the continuous infusion of insulin based upon individuals requirements in terms of the curve of decay of sugar concentration in a prescribed time. For each individual, depending on many personal factors like obesity, age, kidney functions, etc., a prescription is made of the desirable curve of sugar concentration from its highest level to the desired lowest level in a given period of time. This fine tunes the delivery of insulin as it takes away much guesswork of amounts of insulin given intermittently or continuously. Devices attached to continuous monitoring device will infuse insulin continuously and as per prescribed curve of reduction of sugar concentration. Thus, the pumps delivery takes into consideration the time profile of the insulin release, with the release stopping after the prescribed values are attained. The amount released in a dual wave shaped insulin bolus combining [8] both the usual normal and square wave methods. The therapy described will be the forerunner of intense clinical research work.Mathematical models with numerical simulations and analysis based on experimental data can be more effective in terms of costs and an extraordinary amount of time dealing with diverse physiological situations. This is particularly so in view of the complexities of the functions in the human body and incomplete existing knowledge.

> This chapter provides an overview of mathematical modelling of type 1 diabetes, with particular focus on pump therapy as a management strategy for continuous subcutaneous insulin infusion. Previous models describing the mechanism of glucose metabolism have mostly focused on type 2 diabetes, most notably the classical minimal model for explaining the profile of glucose concentration over time.[4,5] Here we summarize the conclusions of

Therapeutic Modelling of Type 1 Diabetes 463

Human body functions best at a certain level of sugar in the blood stream. Blood sugar levels are tightly controlled by insulin, the principal hormone that makes it possible for many cells (primarily muscle and fat cells) to use glucose from the blood. It is manufactured by the beta cells of the pancreatic islets of Langerhans, a small section of the pancreas. Secretion of insulin primarily occurs in response to increased concentration of glucose in the blood. Insulin helps the glucose from food get into the body cells. If body does not make enough insulin or if the insulin does not work the way it should, glucose can not get into the cells. It stays in the blood instead and blood glucose level gets too high causing to have Diabetes. Deficiency of insulin or its action plays a central role in all forms of diabetes. There

Type 1 diabetes is one of the most challenging medical disorder because of the demands it imposes on day-to-day life. It was formerly known as insulin dependent diabetes mellitus

In this type of diabetes, the pancreas undergoes an autoimmune attack by the body itself and is rendered incapable of making insulin. It is an autoimmune disorder, in which body's own immune system attacks the beta cells in the islets of Langerhans of the pancreas destroying them or damaging them sufficiently to reduce insulin production. The pancreas then produces little or no insulin. At present, scientists do not know exactly what causes the body's immune system to attack the beta cells, but it is believed that autoimmune, genetic, and environmental factors, possibly viruses, are involved. It develops most often in children and young adults, but can appear at any age.Type 1 diabetes, which predominately affects youth, is rising alarmingly worldwide, at a rate of 3% per year. Some 70,000 children worldwide are expected to develop type 1 diabetes annually. If not diagnosed and treated with insulin, a person with type 1 diabetes can lapse into a life-threatening diabetic coma,

Type 2 diabetes, formerly called adult-onset diabetes or non-insulin- dependent diabetes mellitus (NIDDM), is the most common form of diabetes. Type 2 diabetes is responsible for 90 -95% of diabetes cases and is increasing at alarming rates globally as a result of increased urbanization, high rates of obesity, sedentary lifestyles and stress. Type 2 diabetes is increasingly being diagnosed in children and adolescents though it can occur at any age. Millions of people don't even know they have it because it can arise with minimal outward signs or symptoms. It is diagnosed with insulin resistance in which the pancreas is producing enough insulin but for unknown reasons, the body can not use the insulin effectively. This leads to a situation similar to type 1 diabetes in which the pancreas can't secrete enough insulin because of which glucose builds up in the blood and the body cannot make efficient use of its main source of fuel. This form of diabetes is associated with obesity, older age, a family history of diabetes, a history of gestational diabetes, certain medications, impaired glucose metabolism, psychological factors, and physical inactivity. Type 2 diabetes can be controlled with exercise, diet and lifestyle modifications.[6] This type of diabetes may develop microvascular complications, which may lead to retinopathy, nephropathy and peripheral and autonomic nephropathies, and macrovascular complications include

are three major forms of diabetes:[18]

(IDDM) or juvenile onset diabetes mellitus.

also known as diabetic ketoacidosis.

atherosclerotic coronary and peripheral arterial disease.

**2.1.2 Type 2 diabetes** 

**2.1.1 Type 1 diabetes** 

these studies for management of diabetes, and attempt to lay out a framework for further development of these models to include pump therapy. These models are often formulated as a system of differential equations that describes the profile of insulin release and the dynamics of glucose concentration over specified period of time. In addition to providing background on existing modelling frameworks, the practical implications of their outputs are discussed.

The main goals are (a) formulation of the model using the pump mechanism (b) defining the parameters (c) profiling the insulin release (d) simulating using estimated parameter values and (e) modelling extensions to include obesity as it had been well established that obesity promotes insulin resistance through the inappropriate inactivation of a process called gluconeogenesis, where the liver creates glucose for fuel. The model consists of blood glucose concentration, remote insulin action and amount of insulin. The model predictions include insulin secreted, if any, in pancreas, role of other organs, tissue uptake etc. This chapter closes with future direction in mathematical modelling of type 1 diabetes for optimal usage of external insulin and measuring insulin dependency with an insight into the role of obesity in developing diabetes.
